Growth and Yield Models for South

Australian Radiata Pine Plantations:

Incorporating Fertilising and Thinning.

James Francis O'Hehir

Submitted in total fulfilment of the requirements of the degree of

Doctor of Philosophy

September 2001

The School of Resource Management, Forestry,

and Amenity Horticulture

Institute of Land and Food Resources

The University of Melbourne

Statement of Originality

This is to certify that

i. The thesis comprises only my original work except where indicated

in the preface,

ii. Due acknowledgment has been made in the text to all other

material used,

iii. The thesis is less than 100,000 words in length, exclusive of tables,

maps, bibliographies and appendices.

James Francis O'Hehir

Septem ber 2001

ii

ABSTRACT

This thesis describes the development of models to predict the volume

growth response of South Australian radiata pine plantations to the

interaction of the silvicultural tools of thinning and fertiliser used in

combination. Some years ago this issue was identified as the component

of the ForestrySA yield regulation system most in need of addressing and

as a result a large thinning and fertiliser experiment was established. This

was designed to determine whether a thinning and fertiliser interaction

existed and to enable this interaction to be modelled. At the time it was

established it was believed to be the only experiment of its kind in the

world and this still appears to be the case.

The thinning and fertiliser interaction models described in this thesis were

designed to integrate with the models already implemented in the

ForestrySA yield regulation system so that more precise predictions of

future log availability can be provided, and improved management

decisions can be made. Three sets of component sub models are

described which operate at a stand level to:

• predict the total volume growth of the main crop between the time of

fertilising and the next thinning, approximately seven years hence;

• predict the total volume growth of the portion of the stand which will be

thinned (known as the thinnings elect) at the next thinning, between

the time of fertilising and the next thinning;

• predict the annual volume growth response of the stand between the

time of fertilising and the next thinning.

Further research is described to identify the data sets that are likely to be

required for future analysis and revision of the South Australian growth

and yield models. Adopting the future research recommendations will

ensure that the consideration of the financial and economic benefit of

iii

alternative silvicultural prescriptions is broadened to include a more

diverse range of sites and include log and wood quality considerations.

iv

ACKNOWLEDGMENTS

This research was undertaken under the supervision of Professor I.S.

Ferguson, The University of Melbourne and Dr J.W. Leech, of Forestry

Systems and the University of Melbourne. The helpful criticism and

support they have provided has been immensely valuable to me and is

greatly appreciated.

Permission to use ForestrySA data was given by the Chief Executive of

the South Australian Forestry Corporation (ForestrySA), Mr LB. Millard.

This research would not have been possible without the professional and

innovative work of the current and past staff of ForestrySA. The concept

for the establishment of Experimental Plot 190, the source from which

much of the data for this research was drawn, was a collaborative

development, of a number of senior staff of the former Woods and Forests

Department particularly Mr R. Boardman, Dr J.W. Leech and Mr A.

Keeves and Dr R.L. Correll of CSIRO Mathematical and Information

Sciences, Adelaide. The technical staff of the Forest Resources and

Forest Research Sections were responsible for the careful and consistent

measurement of the experimental plots, the maintenance of the

experiments, and the application of the treatments. Dr R.C. Woollons,

Senior Lecturer at the New Zealand School of Forestry, University of

Canterbury, Christchurch, was of considerable assistance in suggesting

alternate analysis and modelling approaches.

This thesis is dedicated to my wife, daughter and parents, without their

support it would not have been possible to undertake this research.

v

TABLE OF CONTENTS

ABSTRACT ...................................................................................................................... III

ACKNOWLEDGMENTS ................................................................................................... V

TABLE OF CONTENTS .................................................................................................. VII

LIST OF TABLES ............................................................................................................ IX

LIST OF FIGURES ........................................................................................................... Xl

PART I: GROWTH AND YIELD MODELS FOR FOREST MANAGEMENT ................... 1

1. INTRODUCTION ...................................................................................................... 2

2. THE REQUIREMENT FOR GROWTH & YIELD MODELS ..................................... 4

2.1 Organisational perspective ................................................................................... 4

3. MODELLING STRATEGIES AND METHODS ........................................................ 7

3.1 Model design ........................................................................................................ 9 3.2 Graphical techniques .......................................................................................... 10 3.3 Expert models ..................................................................................................... 11 3.4 Statistical modelling ............................................................................................ 12

4. FACTORS AFFECTING GROWTH AND YIELD ................................................... 34

5. STAND DENSITY EFFECTS ................................................................................. 39

5.1 Conceptual stand density models ....................................................................... 39 5.2 Stand density management models ................................................................... 47 5.3 Stand sub-population growth .............................................................................. 55

6. FERTILISER EFFECTS ......................................................................................... 57

6.1 Fertiliser response models ................................................................................. 59 6.2 Stand development. ............................................................................................ 64 6.3 Stem form ........................................................................................................... 67

7. STAND DENSITY AND FERTILISER INTERACTION ........................................... 69

PART II: GROWTH AND YIELD MODEL DEVELOPMENT ......................................... 71

8. INVESTIGATING STAND DENSITY AND FERTILISER INTERACTION ............. 72

8.1 Experimental design and mensuration ............................................................... 73 8.2 Basis of volume measurement ........................................................................... 82 8.3 Growth and yield data ......................................................................................... 83 8.4 Testing the design .............................................................................................. 99

vii

9. GROWTH RESPONSE COMPARISONS ............................................................ 106

9.1 General inspection of results ............................. , .............................................. 106 9.2 Detailed results and analysis ............................................................................ 111 9.3 Discussion ........................................................................................................ 118 9.4 Conclusions ...................................................................................................... 121

10. TOTAL STAND VOLUME GROWTH MODELS .................................................. 123

10.1 Model formulation strategy ........................................................................... 123 10.2 Total stand volume growth models .............................................................. 125

11. PERIODIC ANNUAL VOLUME GROWTH MODELS .......................................... 135

11.1 First stage .................................................................................................... 136 11.2 Second stage ............................................................................................... 137

12. STAND SUBPOPULATION VOLUME GROWTH MODELS ............................... 140

12.1 First stage .................................................................................................... 140 12.2 Second stage ............................................................................................... 141

13. MODEL PERFORMANCE AND SYNTHESIS ..................................................... 144

13.1 Total stand volume growth models .............................................................. 144 13.2 Periodic annual growth models .................................................................... 150 13.3 Combined total stand volume growth and periodic annual growth models .. 152 13.4 Stand sub population growth modeL ............................................................ 166

14. HYPOTHESISED TOTAL STAND RESPONSE MODEL .................................... 171

15. SUMMARY AND CONCLUSIONS ....................................................................... 174

16. FUTURE RESEARCH NEEDS ............................................................................. 176

16.1 Fertiliser re-treatment ................................................................................... 176 16.2 Geographic range ........................................................................................ 177 16.3 Alternative fertiliser forms ............................................................................. 178 16.4 Log quality and wood properties .................................................................. 178

17. IMPLEMENTING THE MODELS ......................................................................... 181

17.1 Model application ......................................................................................... 181 17 .2 Total stand growth model ............................................................................. 1 82 17.3 Periodic annual growth model ...................................................................... 182 17.4 Thinnings elect growth model ...................................................................... 184 17.5 Summary ...................................................................................................... 185

BIBLIOGRAPHy ........................................................................................................... 187

APPENDICES ............................................................................................................... 201

viii

LIST OF TABLES

Table 3.1 Common nonlinear growth models .................................................................. 27

Table 6.1 Alternative fertiliser response models ............................................................. 61

Table 8.1 EP190: thinning treatments applied to date ..................................................... 75

Table 8.2 EP190: fertiliser treatment summary ............................................................... 76

Table 8.3 Forest Mix 3: elemental analysis (%) ............................................................... 76

Table 8.4 EP190: fertiliser treatments applied to date ..................................................... 77

Table 8.5 EP190: summary of five sites established ....................................................... 80

Table 8.6 Hutchessons: summary of total stand growth results by treatment for

predominant height, basal area and volume ........................................................... 85

Table 8.7: Headquarters: summary of total stand growth results by treatment for

predominant height, basal area and volume ........................................................... 87

Table 8.8 Menzies: summary of total stand growth results by treatment for predominant

height, basal area and volume ................................................................................ 89

Table 8.9 Glencoe Hill: summary of total stand growth results by treatment for

predominant height, basal area and volume ........................................................... 91

Table 8.10 Headquarters: summary of thinnings elect growth results by treatment for

predominant height, basal area and volume ........................................................... 93

Table 8.11 Menzies: summary of thinnings elect growth results by treatment for

predominant height, basal area and volume ........................................................... 95

Table 8.12 Glencoe Hill: summary of thinnings elect growth results by treatment for

predominant height, basal area and volume ........................................................... 97

Table 8.13 Normality test of the initial stand parameters .............................................. 102

Table 8.14 Headquarters: ANOVA initial stand parameters and treatments ................. 103

Table 8.15 Menzies: ANOVA initial stand parameters and treatments ......................... 104

Table 8.16 Glencoe Hill: ANOVA initial stand parameters and treatments ................... 105

Table 9.1 Headquarters: ANOVA six year volume growth (016) by treatment. ........... 114

Table 9.2 Menzies: ANOVA six year volume growth (016) by treatment. .................... 114

Table 9.3 Glencoe Hill: ANOVA six year volume growth (Gt6) by treatment. ............. 114

Table 9.4 Headquarters: Tukey's HSD Test six year volume growth (Ot6) by treatment.

.............................................................................................................................. 115

Table 9.5 Menzies: Tukey's HSD Test six year volume growth (Gt6 ) by treatment. ... 116

Table 9.6 Glencoe Hill: Tukey's HSD Test six year volume growth (GI6) by treatment.117

Table 10.1 Total stand volume growth: first stage exponential models ......................... 131

Table 10.2 Total stand volume growth: second stage exponential models ................... 134

Table 11.1 Periodic annual growth model: second stage parameters .......................... 139

Table 12.1 Thinnings elect growth model: second stage parameters ........................... 143

ix

Table 13.1 Stand density and fertiliser growth response pattern by site ....................... 153

Table 16.1 Proposed experimental design for each geographic location by thinning by

fertiliser treatment. ................................................................................................ 178

x

LIST OF FIGURES

Figure 5.1 Stand density and growth model (Moller, 1954) ............................................. 43

Figure 5.2 Stand density and growth model (Langsaeter, 1941) ..................................... 43

Figure 5.3 First alternative to Langsaeter (1941) model of relationship between stand

density and growth (Smith, 1986) ........................................................................... 44

Figure 5.4 Second alternative to Langsaeter (1941) stand density and growth model

(Smith, 1986) .......................................................................................................... 44

Figure 5.5 Langsaeter model series relating stand age and biomass (West, 1985) ....... 45

Figure 5.6 Site capacity and Langsaeter (1941) model relationship (Lewis and Ferguson,

1993) ....................................................................................................................... 46

Figure 5.7 Optimum Thinning Range (Lewis et al., 1976) ............................................... 49

Figure 5.8 Optimum Thinning Guide (Lewis et al., 1976) ................................................ 50

Figure 5.9 Simplified Langsaeter model implemented in the ForestrySA yield regulation

system (Sutton and Leech, 1981) ........................................................................... 54

Figure 6.1 Alternative fertiliser response models ............................................................ 62

Figure 6.2 Stand nutritional requirements model (Miller, 1981 ) ....................................... 66

Figure 9.1 Headquarters: annual total volume growth by treatment .............................. 108

Figure 9.2 Menzies: annual total volume growth by treatment. ..................................... 109

Figure 9.3 Glencoe Hill: annual total volume growth by treatment. ............................... 110

Figure 10.1 Headquarters: actual volume growth as a proportion of the control relative to

stand density ......................................................................................................... 128

Figure 10.2 Menzies: actual volume growth as a proportion of the control relative to stand

density ................................................................................................................... 129

Figure 10.3 Glencoe Hill: actual volume growth as a proportion of the control relative to

stand density ......................................................................................................... 130

Figure 13.1 Headquarters: actual and predicted volume growth as a proportion of the

control relative to stand density ............................................................................ 147

Figure 13.2 Menzies: actual and predicted volume growth as a proportion of the control

relative to stand density ........................................................................................ 148

Figure 13.3 Glencoe Hill: actual and predicted volume growth as a proportion of the

control relative to stand density ............................................................................ 149

Figure 13.4 Headquarters: OTG- actual versus predicted annual volume growth ........ 154

Figure 13.5 Headquarters: OTG actual versus predicted annual volume growth ......... 155

Figure 13.6 Headquarters: OTG+ actual versus predicted annual volume growth ....... 156

Figure 13.7 Menzies: OTG- actual versus predicted annual volume growth ................. 157

Figure 13.8 Menzies: OTG actual versus predicted annual volume growth .................. 158

Figure 13.9 Menzies: OTG+ actual versus predicted annual volume growth ................ 159

Figure 13.10 Glencoe Hill: OTG- actual versus predicted annual volume growth ......... 160

xi

Figure 13.11 Glencoe Hill: OTG actual versus predicted annual volume growth .......... 161

Figure 13.12 Glencoe Hill: OTG+ actual versus predicted annual volume growth ........ 162

Figure 13.13 Headquarters: predicted annual volume growth ....................................... 163

Figure 13.14 Menzies: predicted annual volume growth ............................................... 164

Figure 13.15 Glencoe Hill: predicted annual volume growth ......................................... 165

Figure 13.16 Headquarters: predicted thinnings elect total volume growth relative to stand

density ................................................................................................................... 168

Figure 13.17 Menzies: predicted thinnings elect total volume growth relative to stand

density ................................................................................................................... 169

Figure 13.18 Glencoe Hill: predicted thinnings elect total volume growth relative to stand

density ................................................................................................................... 170

Figure 14.1 Simplified Langsaeter model showing three postulated thinning and fertiliser

interaction models ................................................................................................. 173

Figure 14.2 Alternatives to simplified Langsaeter modeL .............................................. 173

xii

PART I:

GROWTH AND YIELD MODELS

FOR FOREST MANAGEMENT

1. INTRODUCTION

Intensive forest management planning requires the integration of

appropriate inventory and predictive models to deliver unbiased and

precise estimates of growth and yield on which to base sound decisions.

Markets for timber and other forest products are becoming more exposed

to global competition and among timber industry stakeholders there is an

expectation that business performance will continually improve. These

economic and financial drivers require continuous improvement in the

precision of predictive models which are deployed in growth and yield

prediction systems.

The predictive models need to span the full range of silvicultural policies

and plantation management practices used by forest growers, including

establishment, rotation length, thinning and fertilising. The South

Australian yield regulation system, currently RADGAYM II, and its

replacement PL YRS, both contain examples of predictive models

appropriate for radiata pine (Pinus radiata D. Don). Some years ago an

economic benefiUcost analysis indicated that there was a high potential

benefit of developing a thinning and fertiliser interaction model if one could

be determined from experimental data. RADGAYM II lacked a thinning

and fertiliser interaction model, and sensitivity analysis indicated that this

was the component model most in need of development.

Consequently, a large and ongoing experiment, EP190, was established

to test if a thinning and fertiliser interaction existed and, if it did, to provide

the data to develop models to predict the interaction response. In the mid

1980's when the first experimental sites were established there was

believed to be no other study of this kind which was specifically testing for

thinning and fertiliser interaction and there is no evidence that one has

been established since.

2

The measurement of plots at all EP190 sites was intended to span two

thinning cycles of seven years each. The data from the first thinning cycle

at all EP190 sites are now available to allow an interim analysis of the

data, and the development of the predictive models, which form the pivotal

part of this thesis.

This thesis has the primary objective of analysing the available data to

determine if there is an interaction between thinning and fertiliser, but

practical considerations predicate that the development of models that can

be used in growth and yield prediction systems is a necessary secondary

objective.

3

2. THE REQUIREMENT FOR GROWTH & YIELD MODELS

Commercial forest growers use growth and yield models to predict future

log availability. These predictions provide a basis for strategic and

operational planning, and also for forest valuation.

Constraints on the availability and quality of growth and yield models

include the availability of appropriate data and techniques for developing

and implementing the models; and the extent to which the development of

predictors which deliver a specified level of precision can be financially

and economically justified. As a first step the evolutionary development

and use of growth and yield models should be explained in a South

Australian context.

2.1 Organ isational perspective

ForestrySA is the South Australian Government owned corporation

responsible for managing the State's commercial plantation forests. The

organisation- is long established and traces its beginnings back to the

creation of the Woods and Forests Department in 1882 (Lewis, 1975).

ForestrySA is a major grower of radiata pine plantations 1 and markets a

range of log products to Australian and international customers.

Forestry organisations rely on the successful integration of inventory data

with growth and yield models in a yield regulation system. Limiting

resources usually constrain the quantity of both relevant and accurate

inventory data and the data used to develop more precise growth2 and

yield models. The existing South Australian yield regulation system is

1 Approximately 65,000 ha of plantations at 1999 2 For consistency the terms growth and yield in this thesis will generally refer to stands of trees; increment and volume will refer to individual trees.

4

acknowledged as providing as precise predictions of plantation growth and

yield as any in the world (Ferguson, 1993).

Prior to 1930 in South Australia little effort was expended on the collection

of growth and yield data, although the need for this information as the

basis for planning was acknowledged as early as 1917 (Corbin, 1917).

Integral to the 1935 Royal Commission established to investigate the

possibility of the State's forest resources was the collection of growth and

yield information by E. H.F. Swain (Swain, 1935). Although some data

were collected prior to Swain (O'Hehir, et aI., 2000)3 his assessment and

growth projections represented the first attempt at predicting the future log

availability of the total radiata pine resource for the south east region of

South Australia.

The Royal Commission report (Swain, 1935) led to the realisation that

regional planning was required to sustain supply to a pulp mill and

resulted in a focusing of the State's plantation planning objectives. The

objectives had evolved from supplying small local sawmills (except for

Mount Burr Mill established in 1931) that could easily be supplied by

applying a simple silvicultural system (ie clear felling of unthinned stands -

or a single mechanical thinning) to a contemporary industrial pulpmill with

associated high levels of investment. The establishment of the pulpmill at

Tantanoola in 1942 provided the opportunity and need to develop a more

sophisticated silvicultural system. This system provided a greater supply

of log sizes favoured by the sawmilling industry because the pulpmill could

process large quantities of small log resulting from thinnings too small in

size or poor in quality for a sawmill to utilise economically.

Although discussed by N.W. Jolly as early as 1950 (Jolly, 1950), by the

middle to late 1950's it had become apparent than the productivity of

second rotation plantations was often significantly poorer that that of the

first rotation. This decline in productivity became known as second

5

a

rotation decline. Research initiatives eventually led to more intensive

management being applied in the re-establishment phase involving the

application of the so-called maximum growth sequence (Woods, 1976;

Boardman, 1988) on all re-established plantation sites. It was

subsequently realised that not all re-established sites required all of the

components of the regime. Therefore, site specific silviculture was

developed which used site and crop attributes to indicate which of the

components were required on each specific site to achieve the desired

productivity.

Thus initially planning at the forest estate level was based on a relatively

simple silvicultural regime with a predictable and fixed productivity, which

meant that a yield table was appropriate for forecasting log availability.

However, the recognition of the second rotation decline, use of the

maximum growth sequence and the introduction of site-specific silviculture

meant that further development of the system of yield prediction was

necessary. As forest management intensity increased so too did the need

for better predictions.

Recent commercial imperatives to maximise the return from the South

Australian Government plantations have exerted pressure to provide even

more precise predictions than previously of log quantity and quality,

including size. It is the relentless requirement for an improved basis for

decision making that is currently, and will continue, to drive the need to

improve the precision of predictors of growth and yield.

3 Appendix III

6

3. MODELLING STRATEGIES AND METHODS

The strategies used for growth modelling vary with the modeller's

objectives and the techniques and tools that are available for the model

development and application. In biologically based disciplines, both

process and empirical approaches to modelling are used. Process model

is the commonly used term for a physiologically based model and these

are usually developed in pursuit of a better understanding of an underlying

biological relationship. Empirical models are usually developed for use as

predictors and are less concerned with the underlying processes. Hybrid

models combine the attributes of the two approaches.

Process models are often developed for forest research applications to

predict total tree or stand biomass. Empirical models are usually

developed for forest management applications to predict the availability of

log products. Forest growth and yield models are usually empirical and are

constructed to predict the current or future value of a variable or group of

variables that describe the present or future state of a tree or stand.

These models can either be implemented at a single tree level and then

the results aggregated to a stand level, or used to predict growth and yield

directly. The intended use of models will determine the variable of interest

that is to be pred icted.

Growth and yield models for South Australian radiata pine plantations

have been developed to meet the requirements of commercial

management and so are essentially empirical using the accepted normal

definitions. The models are intended primarily for use as unbiased and

precise predictors of plantation (usually stand) growth and yield. The

models are pragmatic and relatively simple and are driven by data that are

readily available for most stands.

The high quality and consistency of the data available from Permanent

Sample Plot measurement in South Australia continue to be useful in

7

developing models for forest management application (O'Hehir, 1995).

The models that are used for yield prediction are as independent from

each other as possible, to avoid accumulating prediction errors, and

modular, to facilitate relatively easy revision. The development of the

models has been deliberately evolutionary so that consistency is

maintained between the models and the associated management data.

The models are typically stand based rather than tree based to minimise

the error propagation associated with agg regation.

Prior to the development of electronic computers, complex model fitting

calculations were laborious and their use was constrained by manual data

processing systems. This predicated the use of relatively simple yield

tables that were applied to forest productivity classes by areas to provide

aggregated growth and yield predictions. Once electronic computers

became available the statistical theory which had existed for some time

could be used for data analysis, model fitting and yield prediction systems.

The original yield and tarif tables used in South Australia were developed

using graphical and manual calculation methods (Keeves, 1961; O'Hehir,

et al., 2000). Permanent Sample Plot data were first computer processed -

as early as 1960 (Lewis, et al., 1976) and later a computerised area

statement system was developed and implemented. The availability of

computers and additional growth and yield data from the Permanent

Sample Plots allowed the development of computer-based growth and

yield models (Ferguson and Leech, 1976, 1978; Leech and Ferguson,

1981; Leech, 1984).

8

3.1 Model design

The process of designing a model requires a clear understanding of how

the model will be applied and knowledge of the influences operating on

the system being modelled. Clearly inappropriate models can be excluded

prior to applying formal numerical and/or statistical methods. The

development effort can then be concentrated on the form and structure of

those models most likely to satisfactorily fit the data, and more importantly

to meet the objective of the modelling process.

The principles of model design that are most emphasised in the general

literature are those of parsimony and keeping the design simple. The

principle of parsimony relates to not including unnecessary variables and

parameters in the model structure and is also referred to as Occam's4

razor (Ratkowsky, 1990; Vanclay, 1994).

The variables chosen for inclusion in growth models should be chosen to

'ensure biologically realistic predictions across the whole range of possible

conditions' (Vanclay, 1994). Vanclay's recommendation does not exclude

the possibility of applying growth models outside the range they were

designed for but it does emphasise the need to understand the risks of

using an inappropriate model.

The principle of keeping the model design as simple as possible is

especially advisable to ensure acceptance by practitioners, as the

predictions from unnecessarily complicated models may not be believed.

Using statistical methods to fit unnecessarily complicated models may

confound the model fitting procedure and potentially result in a less

appropriate model being chosen.

4 William of Occam was an English monk who espoused a minimalist approach to theology.

9

Once a series of candidate models have been designed there are various

modelling methods that can be used individually and sometimes in

combination to fit them. Conceptually simple approaches including

graphical techniques and expert models may be appropriate or more

complex methods based on the use of statistical methods for parameter

estimation and hypothesis testing may be necessary. The remainder of

this chapter discusses the various methods which can be applied and the

circumstances under which they may be appropriate.

3.2 Graphical techniques

The use of graphical methods for the development of yield tables arose in

Western Europe in response to an increasing need for intensive forest

management. A range of graphical methods were developed in which

growth and yield data were plotted and then lines were drawn to best fit

the trends (Jerram, 1949; Carron, 1968). The predicted yields are usually

read off the graphs for various site levels of productivity and age and

arranged in a tabular list as a yield table. Graphical methods are still used

for yield table construction and yield tables are still used in forest

management (West and Williams, 1993; Williams, 1995). Graphical

methods may still be appropriate where there are insufficient data

available to permit the application of rigorous statistical methods or due to

yield regulation system limitations (Williams, 1995).

The advent and application of both statistically based modelling

techniques and electronic computers extended the possibilities beyond

the graphical and manual calculation methods. More importantly, they also

enabled statistical hypothesis testing and the assessment of bias and

precision (O'Hehir, 1995).

10

3.3 Expert models

The process of developing all models requires some input from someone

who understands the system being modelled. However, the direct

influence of an expert on the form of the model may be so significant that

it is referred to as an expert model. An expert model may be required

when there are insufficient data available to develop a model by other

means.

It is important that the assumptions made in developing expert models are

explicit and, as with all models, that the users understand the limitations of

the model. A common problem with expert models is that they tend to be

retained unless overwhelming evidence is produced to indicate that they

are wrong.

Expert models may be appropriate for interim application, pending the

collection and analysis of the data appropriate for the construction of a

model with a sound statistical and/or numerical basis. Expert models are

often the only possible approach when major changes are made to

silviculture, genetics and/or the environment chosen for planting.

Modifiers or multipliers are often used to implement expert models where

there are limited data available and/or there is insufficient justification to

develop a more complex model. Alternately an existing reliable model may

be extended to a new situation by simply assuming that growth under the

new conditions is proportional to the growth under the conditions for which

the model was originally developed. Modifiers have the advantage of

generally being simple functions and may be adequate for the purpose

intended. More importantly they are seen to be simple models.

11

In South Australian forestry, the models that predict the productivity of the

next rotation are examples of expert models. These models partition the

site quality improvements between gains due to tree breeding, fertiliser

applied at a young plantation age and weed control (Boardman and

Simpson, 1981; Boardman, 1988). The models are modular and appear

simple but the underlying reasoning is extremely complex. Experimental

data exist to directly support some parts of what is a mUlti-dimensional

response surface. However, there was a significant reliance on the

expertise of R. Boardman, D. Boomsma and others to interpolate between

the surfaces with the partial support of experimental data.

3.4 Statistical modelling

The process of statistically modelling is one area of scientific learning

where 'known facts (data) suggest a tentative '" model ... which in turn

suggests a particular examination and analysis of data and/or the need to

acquire further data; analysis may suggest a modified model ... and so

on', (Box, 1980).

Regression is a general form of statistical modelling that aims to

investigate how one or more variables depend on one or more other

variables. If a relationship is found to exist then the objective is to define a

mathematical relationship between the variables called a model. Once the

model is developed it can be used to predict the value of a dependent

variable for specific values of the independent variables.

Linear regression is a relatively simple form of regression that is

concerned with the investigation of linear relationships between one

variable and other variables (Snedcor and Cochran, 1980). By convention

the data are described by a vector of the dependent variable (Y , where

there are n observations) depending on a matrix of m independent

variables (the X variables) and a vector of coefficients. The regression

12

line is fitted so as to minimise the sum of squares of the vertical (parallel

to the y axis) deviations from Y to the regression line and consequently

has the property of passing through the means, X and Y.

Ordinary Least Squares

The available empirical and theoretical knowledge is used in the initial

phase of any model development to synthesise a model with a logical

structure that includes the appropriate variables. Ordinary Least Squares

(OLS) then generally involves the following steps (Draper and Smith,

1998):

• calculation of the parameter estimates and associated statistical

information;

• evaluation of the model parameter estimates;

• testing of the statistical assumptions;

• evaluation of the model and estimator properties.

Parameter calculation

The parameter estimates are calculater.i after the model variables have

been chosen and the appropriate model structure has been defined. A

model being considered can be defined using matrix algebra to describe

the calculations associated with the estimation of the model parameters

(Draper and Smith, 1998):

Y=XB'+E .

Where the Y vector, the X matrix and the vectors Band E (the vector

of errors) can be defined as follows with n observations and m variables

of interest:

13

YI Xll PI &1

y= Yi , X= Xli , B'= P .J , E= &i .

Yn Xn1 Xnm Pm &n

Where the vector B' is the parameter vector, the vector of least squares

estimates is B' and is obtained by solving the following equations:

X'XB =X'Y.

If these m equations are independent then X'X is of full rank

(nonsingular), and there is a unique solution to the normal equations

(Freund and Littell, 1991) given by:

H' = (X'X)-l X'y .

:8' is an estimate of B' that minimises the error sum of squares

irrespective of the distribution properties of the errors (Draper and Smith,

1998).

If the errors are independent and &[ ~ N(O, 0-2 )5, then iJ', is also the

maximum likelihood estimate ofB', .

One implication of using OLS is that E(&) = 06 and V(&)= 10'2 7.

Irrespective of the distribution of the errors then the fitted values are

obtained from Y = xB' and the residuals vector is calculated as & = Y - Y .

The calculation V (if )= (x'xt l a 2 provides the variances and covariances

associated with fitting the model.

5 The errors are normally distributed. 6 The expected value of the errors is zero. 7 In simple linear regression the variance of the errors can be described by a constant multiplied by the identity matrix.

14

Parameter testing

Statistical hypothesis tests provide an objective method of evaluating the

significance of the individual parameters included in the model. One of the

most useful and commonly used tests is the Student's t test8 (Gossett,

1908; Sokal and Rohlf, 1981) which is calculated as:

t, = (ft, - fJ)/ ~2 [(x'Xt' L l~ Assuming that the null hypothesis is true and the errors are normally

distributed, the t, statistic has a Student's t distribution with v = (n - k)

degrees of freedom, where k is the number of parameters in the model. If

the calculated value exceeds the critical value of t at the chosen

probability level, the estimated parameter is said to be significantly

different from zero or to have a statistically significant effect on the

dependent variable.

Testing assumptions

To ensure the validity and usefulness of the linear models developed

using the least squares method there are a number of assumptions that

are made and may need to be tested (Sokal and Rohlf, 1981):

• homoscedastic variance of residuals;

• normally distributed residuals with mean zero;

• uncorrelated residuals;

• error free independent variable;

• linear relationship between dependent and independent variables.

Under certain conditions normally distributed and error free independent

variables are not necessary. The following sections detail these

8 W.S. Gosset 1876-1937 was a mathematician with the Guinness Brewery in Dublin, Ireland and undertook beer research often requiring inferences to be made based on small sample sizes.

15

assumptions and some corrective strategies which are commonly applied

when they are violated.

Homoscedastic variances

For hypothesis testing the variance around the regression line is assumed

to be homoscedastic. That is the residuals have a constant variance 0'2

which is assumed to be independent of the magnitude of X or Y. In

matrix notation V(&) = 10'2 , this notation also implies that the elements of

& are uncorrelated.

The homoscedasticity of variance can initially be indicated by inspection of

a plot of the residuals. For example, in tree measurement data sets there

is a tendency for the variance to increase with the increasing magnitude of

the data. Such patterns are often evident when the residuals are plotted

against the predictor variables or the fitted values.

Statistical tests to detect homoscedasticity exist but all have some

drawbacks (Draper and Smith, 1998). Bartlett's Test is commonly used by

subjectively partitioning the error data into cells, -calculating the variance of

each cell and then calculating a test statistic across all cells (Draper and

Smith, 1998). The statistic can be compared with critical X 2 values, but

can be sensitive to the size of cell selected. The test is also sensitive to

the normality of the error term and requires sufficient numbers of

observations to be present in each cell before variances can be precisely

calculated.

Weighted least squares can be employed to allow estimation of the

parameter estimates when the variances are heteroscedastic. In this

situation the observations are independent but have different variances so

that (Draper and Smith, 1998):

16

(J2 I 0 o

0 0"2 2

V0"2 = 0'2

J

0

where some but not all of the O"J may be equal.

Normally distributed residuals

If hypothesis testing is to be carried out then the test usually assumes that

the errors are normally distributed, ie 8, '-' N(O, 0"2 ). An appropriate statistic

for testing this assumption is the Kolmogorov-Smirnov (0) which is a

measure of the discrepancy between an empirical distribution and a

hypothesised distribution (Sakal and Rohlf, 1981):

D = maxI Fn{y ) - F(Y~

where F{y) is the hypothesised cumulative distribution function of the

function being tested Fn{y). The Kolmogorov-Smirnov statistic represents

the maximum vertical distance between the two distribution functions. As

is the case for most statistics for comparing distributions, the

discriminatory power of this test is not high (Sokal and Rohlf, 1981).

However, the Kolmogorov-Smirnov statistic is widely applied in the

literature and is generally accepted as a valid statistic for comparing

distributions.

The assumption that the errors 8 are normally distributed is not required

to obtain P' but is required to conduct hypothesis tests or to establish

confidence intervals. In hypothesis testing it is assumed that E(c~) = 0 and

that £{ is not related to any other £{ . Where the errors are found not to be

normally distributed then remedies such as restructuring the model or

applying an appropriate transformation to the data need to be considered.

17

Uncorrelated residuals

The residuals are usually assumed to be uncorrelated. The most common

way that this assumption is violated is when the residuals are said to

exhibit serial correlation. The existence of serial correlation is of particular

concern when modelling time series data derived from the repeated

measurement of the same sampling units. I n experimental forestry

individual trees and plots of trees are commonly repeatedly measured to

obtain a time series trend of observations and so the data need to be

examined for the existence of serial correlation within plots and within the

different treatments.

A common method of detecting the existence of serial correlation involves

inspecting scatter plots of the residuals against the time which the

observations were made or some other logical order to determine if any

patterns exist. A commonly applied statistical test used for detecting serial

correlation in an equally spaced sequence of observations is the Durbin­

Watson test (Durbin, 1950; Durbin, 1951; Durbin, 1970; Durbin, 1971)

which uses the statistic

n

"" (e - e )2 L....J { (-I

D=._I=_2 -n-- ~2(1-r)

Le{2 1=1

Where D is the test statistic, the e are estimates of the successive errors

and r is the correlation. The test measu res the correlation between each

residual with the one immediately preced ing the one of interest and so the

result obviously depends on the order of the data. A significant Durbin­

Watson test may also indicate a miss-specified model and so care must

be taken with the interpretation of the results.

18

The implication of the existence of serial correlation between the residuals

is that the efficiency of the ordinary least squares parameter estimates is

reduced because the standard error estimates are biased downwards

(Theil, 1971; Draper and Smith, 1998). In forestry experiments, individual

trees and plots of trees are commonly measured repeatedly to obtain a

time series of observations and therefore serial correlation commonly

needs to be considered and tested for.

Error free independent variable

The independent X variable is assumed to be measured without error.

This assumption is difficult to test and there is no agreed way to proceed

when X is known to be measured with error. In the case of forest

measurement data from Permanent Sample Plots the methods employed

and the high level of training of the measurement crews aims to ensure

that the possibility of errors is minimised (Lewis, et a/., 1976). However,

errors in X may and do occur; where they do it is not unreasonable to

assume that they are independent and random and can therefore be

considered to just inflate the error term E.

Linear relationship between dependent and independent variables

In applying simple linear regression it is assumed that the expected value

of the dependent variable Y for any given X is described by a linear

function of the values of YI' Where a curvilinear relationship is evident

between the dependent and independent variables it may be possible to

alter the structure of the model by transforming some or all of the

variables to obtain a linear relationship. Types of transformations

commonly applied include logarithmic and polynomial. Some relationships

cannot be made linear and in such situations the use of Ordinary Least

Squares for fitting the model may not be appropriate and alternative

iterative methods must be used.

19

Properties of estimators and predictors

There are statistical properties that estimators and predictors should

possess to maximise their usefulness.

Estimators and predictors should possess the property of increasing

precision with increasing sample sizes, defined as statistical consistency

such that if:

and as

E(" )2 X 2 2 Xi - Xi = x; + 0" x,

an estimator Xi' which is any parameter or variable, is consistent if

LimX. =0 x,

n~oo

Limer;, = 0

n~oo

Estimators and predictors should be sufficient, and are said to be so if

they contain all the information in the set of observaVons-regarding the

parameter to be estimated (Fisher, 1922).

Models intended for use as predictors should be unbiased, XI being an

unbiased estimator of x if I

where E is the expected value of the estimator. The bias X is defined x,

as:

20

Estimators and predictors should also be efficient; when comparing two

alternative estimates of Xi' Xi and x; then the more efficient estimator is

the one with the lower residual variance.

Conditioning

Model conditioning (sometimes referred to as constraining) is the process

of forcing a model to pass through a specified point or points. The

technique can be applied to ensure that a model predicts known, sensible

values under conditions when specific input values are applied. The

simple case where a linear relationship exists between two variables is

modelled as9

y = bo + b\x.

There may be prior reasons to assume that when X = 0, y = o. So the

fitted model can assume bo = 0 and be more appropriately fitted as the

even simpler model

y=btx.

Alternatively, the y -axis intercept bo can take on any specific value. It

should be recognised that the use of 'unconditioned' ordinary least

squares regression actually does condition the model which is deve10ped

through the mean of the observations. This will not always be an

appropriate assumption to make. Examples of the application of

conditioning in forest modelling include those used by Kozak (1973) and

Smith (1983), and in the South Australian situation by Leech (1978).

The following criteria are useful for justifying the use of conditioning

(Kozak, 1973). The user must have good reasons for imposing restrictions

on the coefficients; the basic assumptions of the regression analysis

should still be met after the restriction is imposed; and the conditioning

must be justified for the observations being considered.

9 In an attempt to minimise confusion the notation has been changed from the matrix notation used up until this point.

21

A difference equation was conditioned by Leech (1978) so that at age 10

the model predicted a yield consistent with a defined value based on site

quality. In this circumstance conditioning allowed one or more of the

parameters to be omitted from the original model, and provided a simpler

nonlinear model to fit. Conditioning also ensured that the difference

equation provided predictions that were consistent with the definitions of

site quality already used and provided better structured error bounds for

predictions.

Non linear least sq uares

A model is termed nonlinear if it is a nonlinear function of the parameters;

that is, if one or more of the partial derivatives is dependent on at least

one of the model parameters (Ratkowsky, 1 990). For example a model is

linear in hI if

but nonlinear in hI if

So the form of such a nonlinear model is

The requirement to fit a nonlinear model arises from prior evidence or

experience that such a model structure will fit the data more realistically

than a linear model.

The direct techniques used to fit the parameters in linear models result in

single correct estimates of the parameters in a finite and predictable

number of arithmetic operations. Least squares methods applied to fitting

linear models provide unbiased, minimum variance estimators but

nonlinear regression models tend to do so only with large sample sizes as

they can only be asymptotically efficient (Ratkowsky, 1983). In addition

there is no guarantee that nonlinear least squares solutions are unique.

22

Care must be taken when evaluating the results of fitting a nonlinear

model as it is possible for multiple minima of the least squares criterion to

exist with some model structures.

Nonlinear least squares parameter estimation requires the use of an

iterative algorithm that minimises the sum of squares of the error such that

the initial parameter estimates are successively improved until satisfactory

convergence is achieved (Draper and Smith, 1998). The converged

parameter estimates are not necessarily the optimum because they are

based on an iterative search, the outcome of which depends on the initial

values selected or the bounds chosen to apply to the iterative process.

The Gauss-Newton algorithm is the most commonly used for fitting

nonlinear models (Bard, 1967). The method requires starting values for

the parameters to be set to begin the iterative process and converges

rapidly for close to linear or intrinsically linear models (Ratkowsky, 1990).

Choosing good starting values will maximise the chances of the model

converging to a single solution faster than would otherwise be the case

(Draper and Smith, 1998). The choice of starting values is discussed in

detail by (Draper and Smith, 1998) and (Ratkowsky, 1990), the latter

describing appropriate methods for estimating them.

As with linear models, a major consideration relating to the structure of

nonlinear models are the statistical properties of the parameters which are

included. (Ratkowsky, 1983) warns against the problem of 'parameter­

effects' nonlinearity which can cause problems with the convergence of

nonlinear models. He recommends re-parameterisation as a solution for

reducing this effect so that the resulting model can behave in a similar

way to a linear model. Related to the issue of the parameters is that of

ensuring the independence of the parameters included in the structure of

a model (Leech, 1976). Failure to consider this issue can also result in

convergence problems using standard algorithms such as the Gauss-

23

Newton method. Other algorithms have been developed but their use is

generally restricted to particular model forms.

Non linear growth and yield models

Growth and yield models describe the change in a chosen size or weight

parameter of an organism, or group of organisms, with time (Zeide, 1993).

These models may describe a theoretical process for explaining an

observed behaviour, or alternatively may be empirical in that no such

inferences about the process are made (Vanclay, 1995). A carefully

formulated empirical model can be as precise a predictor in a forest

management application as a model explicitly based on a theoretical

process. It is important that the model selection process does not exclude

a potentially useful predictive model because a theoretical basis for its

application cannot be defined.

There are a number of published nonlinear growth model forms that are

often fitted as empirical models. A selection of the more common models

is shown in integral and differential forms in Table 3.1 10, The integral

forms are used as yield models whilst the differential forms explicitly

describe the growth rate.

(Vanclay, 1995) identified the production of graphically derived 'nonlinear'

yield tables in the late 1700's. Zeide (1993) ascribed the earliest nonlinear

growth model to the use of the Hossfeld IV model to describe tree growth

as early as 1822, Gompertz (1825) described the use of a nonlinear

equation for describing the age distribution for human populations,

subsequently used in modelling forest yield.

Zeide (1993) credited the logistic (also known as autocatalytic) equation to

Verhulst (1838). In a study of its usefulness as a predictor of tree diameter

10 Interestingly a number of the growth models listed in Table 3.1 including the Schnute model can be considered as special cases of the differential equation ascribed to the Swiss mathematician Jakob Bernoulli (Yongshun pers. comm. 2000).

24

growth Zeide found it to be the least accurate of the equations examined.

The monomolecular equation although attributed by Zeide (1993) to POtter

(1920) would appear to have been proposed earlier by Mitscherlich

(1910).

Von Bertalanffy (1957) reported a general theory of growth which included

a generalised growth model. The Gompertz, monomolecular, logistic and

Von Bertalanffy equations have all been shown to be empirical variants of

a common model (Vanclay, 1994). A cubic form r5 = 3 was found useful for

fitting volume growth relationships (Zeide, 1993).

The Von Bertalanffy equation was further simplified, independently by

Richards (1959) and Chapman (1961). The so-called Chapman-Richards'

model has been widely applied in forestry because of its flexibility. Zeide

(1993) questioned whether the property of flexibility is desirable in a

growth model and Ratkowsky (1983) expressed similar concerns. Both

question the value of the parameter estimates obtained from fitting the

Chapman-Richards equation. Ratkowsky (1990) stated that 'The Richards

model exhibits more undesirable nonlinear regression behaviour than

almost any nonlinear regression model in common use. The continued

use of this model is not recommended.' Attempts to develop an equation

to generalise the above models and other forms have been reported

(Zeide, 1993). The Chapman-Richards model equates to the three

parameter logistic model (when r5 = 1 ) and the three parameter Gompertz

model (as r5 ~ 0) and also the monomolecular model (Draper and Smith,

1998). Leech (1976) demonstrated that the parameter correlations in a

four parameter Chapman-Richards model made convergence much more

difficult than the equivalent Von Bertalanffy form with the same number of

parameters but apparently a more complex structure.

An alternative parameterisation of the Von Bertalanffy model Schnute

(1981) has been considered in forestry applications (Bredenkamp and

25

Gregoire, 1988; Huang, et al., 1992; Zhang and Leong, 1993; Yao, et a/.,

1995).

The Weibull model was originally intended to describe a probability

distribution but has been used as an empirical model of tree growth (Yang

et al., 1978; Clutter, et aI., 1983; Zeide, 1993).

The underlying growth theories described for the different models may not

be of value in determining which model is most appropriate for a specified

data set. Rather, a reasonable model selection strategy is to identify a

subset of potential models, fit each in turn to the data set, and then

compare each against a set of criteria with the objective of selecting the

model which best meets the requirements.

26

Table 3.1 Common nonlinear growth models.

y is tree or stand size; X is tree or stand age; Y' is tree or stand growth rate and a, f3 ,r and 17 are parameters of the

equations.

Equation Name Integral form Differential form References

Hossfeld IV Y = X r / (fJ + Xl /a ) y' = /JXxr-1/(f3+ XC /ar (Zeide, 1993; Woollons, 2000)

Gompertz Y = a exp[- fJ exp( - rX)] Y' = af3r exp( - rX )exp[ - f3( - Xx)] (Gompertz, 1825)

Log istic/ Autocatalytic Y = al[l + r exp( - fi\')] Y' = afirexp{- fiX)/[l + yexp{- px)y (Zeide, 1993)

Monomolecular Y = a[l- rexp{- fiX)] Y' = afir exp{ - px) (Zeide, 1993)

Von Bertalanffy Y = a[l- exp(- f3X)Y Y' = 3af3rexp{- PXXl- exp{- px)y (Bertalanffy, 1957)

Chapman-Richards y = a[l- exp(- f3X)Y yl = aj3rexp(- fJXXl- exp(- fJX)Y-1 (Richards, 1959)

Schnute Y = aX(I - f3yX}7~ Y' = afirexp(- PXXl- exp(- fiX)}-Yq-l (Schnute, 1981; Bredenkamp

and Gregoire, 1988)

Weibull Y = all- exp(- fJX 1 )J y' = aj3rX ,v-l exp(- fJXY) (Yang, et al., 1978)

Exponential Y = aX exp( - flX) yl = a[l- fJX]exp(-j3X) (Edwards and Hamson, 1989)

27

I

Growth model application

In many growth studies, the measurement data do not span the whole life

cycle of an organism, or group of organisms, which can make the

development of a yield model difficult. There are several strategies that

can be employed to develop a useful predictive model in such

circumstances.

A forest management example involved fitting a model to yield data from

unthinned radiata pine Permanent Sample Plots in South Australia. It

might be expected that a model with a point of inflection at a young

plantation age would be appropriate. However, Leech and Ferguson

(1981) found that a limiting form of the Chapman-Richards model

(Mitscherlich model) with no inflection point, fitted the data best. The yield

data spanned 'an intermediate portion of the whole yield curve, the first

observation mostly occurring after the likely point of inflection and the last

terminating before the asymptote is closely approached.' The intended

use of the model developed by Leech and Ferguson (1981) was as a

predictive tool for management and the existence or otherwise of an

inflection point at an age less than about 10 years was of little

consequence.

Obviously the purpose for which the model is intended is paramount. For

example, a study evaluating the early growth responses of radiata pine to

a range of site establishment practices is likely to require the use of a

model with a point of inflection to make sense.

Fitting a difference equation may be appropriate where the range of the

data is limited, but enough data and/or prior knowledge exist to indicate

that it is inappropriate to fit a linear model. Difference equations can be

developed based on nonlinear model forms (Ratkowsky, 1990). The

28

example below shows the general form of a difference equation which can

be used for modelling stand growth Leech and Ferguson (1981).

G = ~Y == (YA+T -YA) . M T

Where ~Y is the periodic annual growth (G), YA is the yield at age A, M

YA+7' is the yield at age A + T and T is the length of the interval between

A+T and A.

So for example, a nonlinear model can be substituted to develop a

difference equation:

G = bo {I - exp[- bl (A + T)]} - bo {I - exp[- bl (A )]} T '

where b , and b are parameters to be estimated. Modern computing o I

technology allows such apparently complicated structures to be fitted

relatively easily.

Generalised Least Squares

The use of Ordinary Least Squares for fitting regression models is not

always appropriate either because the assumptions are n-ot appropriate

and/or there is a requirement to combine seemingly unrelated regression

equations in the one consolidated model. If these circumstances are

evident then Generalised Least Squares is an extension of Ordinary Least

Squares which can be validly applied. The method has been developed in

the econometrics literature (inter alia) by Zellner and Theil (1962).

Generalised Least Squares may be useful where a relationship between

the seemingly unrelated regression equations exists because their

coefficients are in fact related or because their errors are correlated and

the respective sets of independent variables differ (Theil, 1971).

29

Generalised Least Sq uares methods operate by generalising the least

squares method with respect to the covariance matrix of the errors and

also in terms of the linear a priori constraints on the coefficients (Theil,

1971). A consequence of fitting serially correlated data using Ordinary

Least Squares may be that unnecessary explanatory variables are

included in the regression because hypothesis tests have indicated that

they are significant because of the bias in the estimation of the standard

errors.

One approach to Generalised Least Squares is based on two stage least

squares (2SLS), which is a method of extending regression to cover

models which violate ordinary least squares (OLS) regression's

assumption of uncorrelated residuals. The two stages in 2SLS refer to a

first stage in which new dependent variables, which do not violate the

assumption of uncorrelated residuals are created to substitute for the

original variables. The second stage involves the regression being

computed as for OLS, but using the newly created variables.

The statistical basis of 2SLS is shown using the simple linear regression

case (Ferguson and Leech, 1978):

k

p" = LPI;Z;I +8" +e", 1=1

where fill denotes the estimated value of the lth parameter for the ith

first stage regression; PI; is the I th parameter for the j th independent

variable; Z II denotes the .i th independent variable for the i th first stage

regression; 6'1 is the error term associated with the I th parameter for the

ith first stage regression; ell is the error term associated with the lth

parameter for the ith first stage regression.

30

The repeated measures problem in forestry

In South Australia, measurements from repeatedly measured Permanent

Sample Plots were used for the development of growth and yield models

in Ferguson and Leech (1978), Leech (1978) and Leech and Ferguson

(1981) described the application of Generalised Least Squares to address

the likely problem of serial correlation between observations and

heterogeneity of variance. I n an interchange that also clarified some of the

notation, West and Davis argued that Generalised Least Squares was

unlikely to be useful partly because of its effect on hypothesis testing

although the appropriateness of the method was not challenged (West,

1980; Davis and West, 1981). In fact, West explained why problems arose

with hypothesis testing of repeatedly measured data and summarised the

attempts reported in the forestry literature to deal with repeated measures

problems.

Generalised Least Squares has also been used for improving the

precision of forest inventory. VanDeusen (1989) identified a method

developed by (Ware and Cunia, 1962) for estimating volumes on a

second occasion from sampling with partial replacement as equivalent to

Generalised Least Squares. Generalised Least Squares has not been

commonly used for the development of generalised forestry growth and

yield models but examples do exist (Sullivan and Reynolds, 1976;

Ferguson and Leech, 1978; West, 1981; Magnussen and Park, 1991;

West, 1995).

Approaches based on Generalised Least Squares have been used to

provide summary statistics for analysing forestry experiments (Woollons,

1985; Woollons and Whyte, 1988; Woollons, et a/., 1994). In these

examples regression coefficients were used for hypothesis testing

between thinning treatments and sometimes fertiliser treatments, where

31

the direct comparison of observations would have been inappropriate and

may have led to incorrect conclusions being drawn.

A typical economics example of the application of Generalised Least

Squares is reported by Guldin (1984) where a generalised model was

used to predict the costs of hand planting southern pine in the southern

United States given a number of different data sets. Generalised Least

Squares was considered appropriate because it was found that the

variance of the error term was not constant between different land owner

groups. Serial correlation of residuals (as indicated by the Durbin-Watson

statistic) and correlation of independent variables were not found to be

problems in this situation.

Hypothesis testing

Errors associated with testing

Hypothesis testing involves the formal procedure of applying an

appropriate statistical test to a data set of observations so that objective

inferences can be drawn. In the context of empirical model building the

main value of hypothesis testing is in supporting the logical choice of the

model structure and parameters.

The errors that can arise during hypothesis testing are classified as Type I

and Type II. A Type I error is defined as the risk of rejecting a null

hypothesis when it is actually true. The probability of committing a Type I

error is defined as the level of significance chosen for a test procedure.

A Type " error arises when the null hypothesis is accepted when it is

actually false. The probability of committing a Type" error is dependent

on a combination of the alternative hypothesis, the level of significance

chosen and the data set being tested. Type II errors can be minimised by

increasing the replication or sample size. In practice the probability of

32

committing Type I and Type II errors has to be balanced as increasing one

decreases the other. After consideration a probability level of p = 0.05 was

considered appropriate for this study.

Analysis of variance

The Analysis of Variance (AN OVA) procedure is used to test whether two

or more samples are drawn from populations with the same mean (Fisher,

1934; Sokal and Rohlf, 1981). The procedure partitions the total variation

in the data into components, which measure the different sources of

variation. In the simplest application of ANOVA three components are

calculated; the total variation, which is considered to be a combination of

the variation due to the experimental error and to the treatments being

tested; the variation due to the treatments alone; and the variation due to

the measurement error. The ratio of the variation due to the treatment and

experimental error components is compared using an F distribution. If the

calculated F statistic is found to be significant then it is concluded that at

least two of the means are drawn from populations with different

parametric means.

Multiple comparisons among means

Multiple comparisons among three or more means are required when an

ANOVA has indicated that the means are being drawn from different

populations and there is a requirement to objectively test for differences

between pairs of means. There are a number of alternative tests available

for multiple comparisons and Sokal and Rohlf (1981) recommended

Tukey's honestly significant difference (HSD) test when sample sizes are

equal. Consultant statistical advice suggested that the test was still

appropriate when the sample size was only approximately equal as will be

seen pertains to this study.

33

4. FACTORS AFFECTING GROWTH AND YIELD

The scale at which forest growth and yield models are to be used will

largely determine which factors need to be included in a model or

alternatively which can be excluded. The intended use of a model can be

at a tree, stand or forest level. For example, for research purposes it may

be desirable to estimate the current volume and to predict the future

volume of individual trees. Alternatively for yield regulation purposes it will

be desirable to estimate the current and predict the future volume of

stands and then aggregate the predictions to a forest level. Errors

occasioned by using a tree-based model to predict forest resource

information may propagate to such a level as to make the results of limited

use as a predictor, especially where the models are biased.

Landsberg and McMurtrie (1984) criticised the use of empirically based

models for forest management because they are non-transportable and

'the analyses have to be repeated on data obtained in a new region before

the model can be applied in that region'. They advocated instead the use

of physiologically based models in which the emphasis is on modelling the

process involved. Using data from physiological experiments would enable

the models to be applied to conditions outside those of a particular region.

Goulding argues to the contrary that 'forest process models in New

Zealand have so far not been of much use to forest managers .... 1

(Goulding, 1994) He further states that 'the claim that a process model

would enable the results of regimes and growing conditions outside the

existing database to be predicted has not yet been proved.' In principle,

however, a better knowledge of the form of the underlying processes

should illuminate and improve empirical models. The major problem is that

they are currently being pursued at vastly different levels of detail or

aggregation, and the integration of the two has not been notably

successful. Also they do not generally account for the variables known to

be important in practice.

34

The fundamental processes of tree growth involve photosynthesis and

respiration. The mechanisms for photosynthesis are comparatively well

understood (Ludlow, 1997), but are not simple to model. Information is not

currently available to the detail required to model these fundamental

processes for intensively managed plantations. Recently Coops et al.

(1998) described the development of a physiologically-based model for

obtaining a region's productive capacity for growing forests. While minimal

information on soils and vegetation was required as input to the model,

the results reported were encouraging. However, the predictions were

designed at a regional level and not at a site level which is required for

applied forest management.

The effect of topography and aspect on radiata pine growth is minimal in

the south east region of South Australia as the landscape is mainly

comprised of low stranded dune systems (Harris, 1983). The dominant

features on the landscape are dormant and extinct volcanoes; the

maximum height above sea level of which does not exceed about 300

metres. Topography and aspect are more pronounced in the Mount Lofty

and Lower Flinders Ranges of South Australia (Twidale, 1976) but the

limited area of plantations in these regions constrains the effort which can

be economically justified in developing individual models for these regions.

Coulombe and Lowell (1995) attempted to use spatial information systems

to relate individual point stand resource data (basal area) to

cartographically derived ecophysiographic variables, to produce reliable

estimates over a whole forest. However, the correlation between the

ecophysiographic variables and stand data that could be obtained from

photointerpretation was limited. This and related studies have shown that

microsite characteristics (for example moisture and nutrient content) are

more important in determining growth, than more easily determined

characteristics such as topography (Beers, 1966).

35

Various physiographic site attributes have been defined in South

Australia. These include nutrient availability related to soil chemical and

physical characteristics, and the depth to the water retentive layer. South

Australian plantation studies in the establishment phase of silviculture

include those reported by Nambiar et al. (1984). These studies provided a

rigorous scientific basis for refining operational practices where necessary.

Research is currently being extended into the later age phase of

plantation silviculture to include fundamental thinning and fertiliser

research, which will complement the applied research already undertaken.

Leech (1978) was able to determine different growth trends for

qualitatively defined soil groups based on growth data from Permanent

Sample Plots. Dummy variables were used to determine the significance

of the volume-age differences between the soil groups and hypothesis

tests were used to test different aggregations of soil type. Leech

developed seven empirical models based on specific soil groups and an

eighth combined soil group (O'Hehir, et a/., 2000) At the time these

models were developed Geographic Information Systems were not readily

available and the application of predictive soil group models was not

possible. However, soil group data are now recorded spatially and these

predictive functions can now be applied. Nevertheless, the microsite

characteristics identified in the work cited earlier by Nambiar, Carlyle and

others are not currently measured or mapped to a sufficiently high

resolution to enable these potentially more refined and powerful

relationships to be exploited. Some recent work reported by Fox (Fox, et

aI., 2000) showed that it was possible to characterise and incorporate

structural stochastic components into individual tree modelling methods

and presumably this approach could be extended to stands. However, the

approach remains to be applied in practical management.

Temporal resolution is also important. Tree growth is undoubtedly

influenced by water availability particularly during the major growing

season. However, it is often impractical and usually unnecessary for yield

36

regulation purposes to modify the growth predictions for individual trees or

stands to account for variations in water availability. Over the 30 to 50

year time period involved in yield regulation predictions, such annual

variations form part of the annual error terms. On a small-scale

experimental basis functions have been developed that predict basal area

growth based on precipitation in the current growing season (LeGoff and

Ottorini, 1993). Elaboration of growth models for radiata pine plantations

to incorporate annual climatic data, such as Ferguson (1979), suggests

that this is not a critical component for long term predictions of yield.

Nevertheless, the influence of the climate change associated with

increasing 'greenhouse' gases in the atmosphere, together with the effect

of fluctuations in global weather such as those indicated by the southern

oscillation index, necessitate that greater attention be paid to these factors

in the future. But there is still doubt that process models will be able to

predict better than empirical models in this regard.

Models used for predicting growth and yield include the various yield

tables and growth functions developed specifically for South Australian

radiata pine plantations (Lewis. et aI., 1976; O'Hehir, et al., 2000).

Other tables and functions are also used to modify the estimates for

stands that are outside the 'normal' growing conditions which the tables

and functions assume. There are three main situations where stand

growth and yield is affected.

• When stands are located outside the geophysical range represented in

the Permanent Sample Plot data used to develop the tables and

functions.

• Where stand densities are outside of the Optimum Thinning Guide.

• When mid or late rotation fertiliser has been applied.

Increasingly stands have been and are being established in more remote

locations. Generally insufficient data exist to develop specific growth

37

functions for these locations and so growth is modelled by applying

multipliers to the above yield table. Modifiers often provide a simple way of

modelling when data are limited.

38

5. STAND DENSITY EFFECTS

Silviculture involves the deliberate application of various treatments to the

site and/or trees to achieve a particular forest management objective

(Smith, 1986). The application of a silvicultural treatment alters the pattern

of growth of either particular classes of trees, or of the whole stand and

these effects need to be accounted for when predicting the future growth

of a tree or stand.

Silvicultural treatments may be applied problematically or routinely to meet

a particular forest management objective. The approach in South Australia

has been to apply 'site specific' silvicultural treatments with the objective

of avoiding the high cost of applying remedial treatments at some later

date, probably at greater cost (Boardman, 1988).

5.1 Conceptual stand density models

The relationship of the growth of forest trees to the density of the stand is

a speCial -case of the density-size relationships described for other

organisms. According to Moller (1954) a theory arose in Danish forestry in

the 1750's that stated that volume growth was directly proportional to the

density of trees in a stand. Moller (1954) ascribed the idea to Reventlow

(1811) that heavier thinning of stands to provide a greater spacing

between trees would be of economic benefit.

Prussian thinning experiments on beech (Fagus sp.) showed

(Weidemann, 1932 cited by Moller, 1954) that stand density had no

influence on aggregate volume growth trends across a wide range of

densities. However, Moller (1954) also reported the results of Danish

experiments where slightly lower stand growth was associated with higher

thinning intensity. He also summarised the results of selected German

39

and Danish thinning experiments in a graph describing the relationship

between stand growth and density (Figure 5.1). This was a simple model

that did not adequately account for the transition in growth from an

understocked to a fully stocked stand, or for the possibility of reduced

growth from an overstocked stand.

A more general model to describe the relationship between stand growth

and stand density was proposed by Langsaeter (1941). Stand density was

expressed as stocking, basal area or volume, per unit area. The model

had five stages of response (Figure 5.2).

• Stage I represented the zone where the stand growth increased linearly

with increasing stand density. The stand had not fully occupied the site

and there was little if any competition between trees.

• Stage II represented a transition zone where the competition between

individual trees increased and caused the growth rate to decline.

• Stage III was reached when full site occupancy was achieved and the

growth per unit area was approximately constant. This was defined as

the 'plateau'.

• Stage IV represented a transition zone where stand competition

progressively increased causing reduced growth.

• Stage V occurred at extreme levels of stand competition causing

mortality and additional reduction in growth rate.

Two alternative models to those of Langsaeter have also been described

(Smith, 1986). The first assumes that volume increases up to the highest

level of stand density such that any vacancy in the growing space is

considered as reducing the total volume production (Figure 5.3).

Apparently this model is commonly used in North America to predict the

growth of stands that depart from 'normal' stocking. Although convenient

to apply, this model seems to have little merit as it implies that increasing

stand density beyond an extreme will not result in a reduction in the

merchantable volume growth (Smith, 1986) which would appear to be

counter intuitive.

40

The second alternative model appears similar to that proposed by

Langsaeter in recognising a zone of increasing stand growth with

increasing density which reaches a maximum point and then a zone of

reducing growth beyond an increasing density (Figure 5.4).

In a series of papers and reports a technique was described which

established separate stand density and growth relationships for the basal

area of unthinned and thinned stands (Horne and Robinson, 1985; Horne,

et al., 1986; Horne and Robinson, 1988a, 1988b). Adding unthinned and

thinned relationships together provided a density and total growth curve.

Horne reported that in New South Wales radiata pine thinning

experiments that total stand basal area growth was consistently

maintained at a maximum value over a wide range of stand stockings for

most ages and sites. Horne et al. were able to define the initial three

distinct segments of a stand density and growth model similar to that

defined by Langsaeter (1941).

West (1985) proposed a theoretical relationship between stand density

and growth incorporating a range of stand ages as a series of Langsaeter

model surfaces exhibiting progressively narrower plateaus with increasing

age and stand biomass (Figure 5.5). Lewis and Ferguson (1993)

postulated that the Langsaeter relationship for a particular stand could

also be dependent on seasonal climatic variation (Figure 5.6). These

conceptual models indicate the multi-dimensional nature of the

relationship between stand density and growth which has to be considered

when modelling time series data.

It is clear from the literature that the Langsaeter model is a useful starting

point for describing stand density and growth relationships and is also

supported by a significant body of empirical evidence. However, there is

the possibility that one or both of the variations proposed by Smith may be

appropriate in particular circumstances. The extensions proposed by West

41

and Lewis are significant in that they indicate that stand density and

growth relationships are not necessarily simple two-dimensional surfaces,

rather that the stand density and growth relationship even within a single

stand is dynamic, being affected by such factors as the stand age and the

availability of nutrients and water.

42

Figure 5.1 Stand density and growth model (Moller, 1954).

100

growth (%)

o 100 density (%) o

Figure 5.2 Stand density and growth model (Langsaeter, 1941).

critical

u III IV V

growth

density

43

Figure 5.3 First alternative to Langsaeter (1941) model of relationship

between stand density and growth (Smith, 1986).

growth

density

Figure 5.4 Second alternative to Langsaeter (1941) stand density and

growth model (Smith, 1986).

growth

density

44

Figure 5.5 Langsaeter model series relating stand age and biomass

(West, 1985).

Self-thinning

line

Stocking density (stans/unit area)

Figure 4 Basis of the density managerrent diagram. The bianass-stocking relationship is shown at various increasing ages (a.). Other notation on the figure is explained in the te.;-ct. ~

45

Figure 5.6 Site capacity and Langsaeter (1941) model relationship

(Lewis and Ferguson, 1993).

Site capacity

I

C;ood SC,'~SOr1S FE.'rtdr; bum~d profiles Acc(:sslbl(] GW L Su rWllf~ r r,Wi S

Site capacity at any given time

I COfllpactlon I I

PreCIpitation mtern'ptlofl I

T e m po r a ry soli d r 0 u 9 tl t I

I Temporary w3terlorJqlnq I

I Poor se('lsons

I I I .-~ ._-_._--------------------.... . -,--,-" Stocking as stems per unit area

46

5.2 Stand density management models

The stocking density of stands can be manipulated over time by thinning

(and also in plantations by the initial planting spacing) to produce the

range of log size assortments and log characteristics that are required by

industry. In practice stand density and growth relationships are often

expressed as a density management diagram. Examples include those for

Douglas fir (Pseudotsuga menziesii Mirb.) (Drew and Flewelling, 1979),

mountain ash (Eucalyptus regnans F Muell.) and swamp gum (Eucalyptus

ob/iqua L'Her.) (West, 1985), and for radiata pine (Lewis, 1963; Lewis, et

a/., 1976; Drew and Flewelling, 1977). Density management diagrams are

derived from conceptual stand density models and are used to implement

organisational thinning policy.

Density management diagrams are referred to as thinning guides in the

South Australian terminology. Two main versions of these guides have

been developed, the Optimum Thinning Range (Lewis, 1963) and the

Optimum Thinning Guide (Lewis, et al., 1976). Jolly (1950) is credited with

developing the first thinning regimes based on accumulated growth and

yield data for South Australian radiata pine stands (Lewis, 1963). These

regimes were initially presented as a table and were developed and

extended as more data became available, culminating in the development

of the Optimum Thinning Range (Figure 5.7).

The Optimum Thinning Range was expressed graphically to allow the

stand to be inspected, its condition assessed, and its future thinning

treatment determined (Lewis, 1963). The growth of the stand was

indicated by predominant height and the thinning intensity was prescribed

by stocking density.

47

The results from a number of South Australian experiments indicated that

radiata pine plantations could maintain maximum volume production for

specific ages over a wide span of thinning intensities and intervals (Lewis,

et al., 1976). However, South Australian thinning policy favoured the

growth of larger log sizes and therefore narrowed the range of stocking

densities that could be applied to achieve the thinning objectives.

The Optimum Thinning Range was later revised and extended and

renamed the Optimum Thinning Guide (Figure 5.8) (Lewis, et al., 1976).

The Guide differed from the original Range in that instead of one common

range for all site qualities, the Guide defines separate but bounded

maximum and minimum stocking curves for each site quality. The

bounded curves narrow with age reflecting the increasingly lower

stockings required to maintain the diameter increment necessary to meet

the desired log size assortments.

The guide has been applied as a stand density management tool in South

Australian radiata pine plantations for more than three decades with

minimal modification. However, as silviculture and management objectives

change in the future it is likely to need some adaptation to ensure it

continues to be appropriate.

48

Figure 5.7 Optimum Thinning Range (Lewis et ai., 1976).

Figure VI.2 THE ORIGINAL OPTIMUM THINNING RANGE

:;000

.:; 1500 ? -

"-J 1-

-'

f)

-" l' :D .-J ,"

r-Z - ~ ...., U"l '7

~ - 1000 f)

~oo

o o

900 7 x 7

800

700 9 7

8 . 8 1111 tldl ~.lldC Illtj

GOO -..,

.-. T'HI 111\1' V 1 .... 111

500 f·

" ... (f)

-100

300

700

100

f()1

t;()fl1 fnl~I\:1 ..II

11\11111111(\

20

Optlfl:I,un

StJII 111'1 SI.d l "

40

10

S tdbill t y St;.1I,.'

111 '1

, ~, .. , ) f i: I '( ) \, \1 I 1

I ), .," '1(11111), !III

tn

r i 1\'

Rl<;k CJ I) I I Illllni

()f

\ \ \

I) t ~v I.~ r 1.1 Tlllllllllllj

INI'I(I

RJI\(Jt'

60 Feet 80 100 120

20 Metres 30

PReDOMINANT HEIGHT

49

\ LY \ \

40

\ \111 \-

\ \­II

140 160

Figure 5.8 Optimum Thinning Guide (Lewis et al., 1976).

Figure V 1.3

OPTIMUM THINNING GUIDE for PINUS RADIATA in S.A.

1000

500

II

METRIC' VE RSION

For initial spacings of 2·0 m x 2·0 m to 2·5 m x 2·5 m

10

10

P.D.H. (metres)

AGE (years)

I

20

20

I 30

I

30 I I J

40

I 40

40 50 TIT ~I ____ ~ __ ~ __ ~ __ ~ __ ~J __ ~~~-J-JJ __ ~ __ L-U

- 10 20 30 N I I 1,1

20 30 40 50

I I J

40 5C I

50

'l. ' I I I "" 20 30 4050

VI ~ __ ~ __ ~~I~~L-~,~I __ ~I-LI~" 20 30 4050

y~ ~~~2~~~~~' ~1~3~b--~4~b~~0

PREDOMINANT

HEIGHT FOR AGE

AND SITE QUALITY

!-ty' .. '.

Thinning to below

the solid line

for each S.O. rlsks-·

Undue limb development

Loss of volume increment

Severe wind damage.

STOCKING FOR PREDOMINANT HEIGHT

AND SITE QUALITY

rhmnlng from outSide the broken line

101 each S.O rlsks-

Loss of crown

Instability 10 WIPd

Loss 01 olamPf!'r 'ncr~mli"f

II

PREDOMINANT HEIGHT (P.OHJ In METRES

50

low density

There are essentially two growth at low stand density modifier models

used in South Australian radiata pine plantation management, one applied

to stands up to age 10, the other to older stands.

An early age model is needed to predict the effects of pre-commercial

spacing operations carried out on previously unthinned stands at ages up

to and including ten years. The current model operates as a growth

multiplier which is only dependent on the ratio of the stocking before to the

stocking after thinning. The current model does not include an age or site

quality variable and as such is not likely to be a precise predictor.

However, the revision of this model is not urgent as pre-commercial

thinning has not been a standard practice for some years due to

favourable market conditions.

The later age, low stocking model used in South Australia is based on a

simplified Langsaeter model restricted to consist of Stages I to III (Figure

5.9). Assuming full yield table growth for all stands is untenable because

some stands are found to be at stocking densities significantly below the

Optimum Thinning Guide (ie at Stage I or II of the Langsaeter model). This

condition can be due to over-intensive thinning or to a reduction in

stocking due to wind, fire or some other agent. It can also be expected

that some stands will be either unthinned, or due to thinning operations

being delayed will be standing at stocking densities well above the

Optimum Thinning Guide; in Stages IV or V.

The model defines the stocking density point below which full yield table

growth is not applied and was constructed using an essentially graphical

method from Permanent Sample Plot data (Sutton and Leech, 1981). The

models are:

51

If A 217, then K = 0.95,

Else 10<A<17 I then K=0.S+(A-IO)xO.06.

Where A is current age and K is a constant. The models are

implemented using the Optimum Thinning Range and the current

stockings as:

If

Else

N ----21.0 (KxNotr)

N ----<1.0 (KxNotr)

then C = 1.0 I

then C=_N __ KxNatr

Where C is a volume growth multiplier, N is the current stocking and

Natr is the equivalent stocking based on the Optimum Thinning Range.

The adjusted growth is calculated by multiplying C by the predicted

periodic annual growth for a fully stocked stand.

There is no provision in these models for the change in stand growth

associated with mid and late age fertiliser applications or for any

interaction that might occur between the level of stand density and the

fertiliser dose. In 1981 the data were not available to develop a growth at

low stocking density model that incorporated fertiliser responses. It was

recognised at the time that such data would be required to develop

predictive models especially if middle and late rotation fertilising was

adopted as a common silvicultural practice. This need was identified as

the component of the ForestrySA yield regulation system most in need of

addressing.

High density

High density models are usually referred to as competition induced

mortality models and in effect represent model Stages IV and V of the

Langsaeter model. In the south east of South Australia mortality modelling

52

is applied to unthinned stands as both a stocking reduction and a volume

reduction. In practice most stands are thinned regularly and mortality

models are rarely applied. An analysis of mortality trends by Leech and

Dutkowski (1985) indicated that the Permanent Sample Plot data set

could not be used to refine the models developed earlier by Leech (1973)

or Ferguson and Leech (1976).

53

Figure 5.9 Simplified Langsaeter model implemented in the

ForestrySA yield regulation system (Sutton and Leech, 1981).

growth

critical stocking

I

stand density

54

5.3 Stand sub-population growth

There are situations where the variable of interest is the growth of a

subpopulation of the stand rather than, or in addition to, the growth of the

total stand. This is of particular relevance in South Australian radiata pine

plantations where the practice of thinning from below is the usual

silvicultural treatment applied on a cycle of between 5 and 9 year intervals

beginning at an approximate plantation age of 10 to 13 years. In these

situations the variable of interest is commonly the volume of the sub­

population which is to be thinned from the stand.

South Australian inventory practice

Current ForestrySA inventory practice requires that stands be inventoried

some years prior to being thinned. The requirement arises from the need

to establish log supply agreements and harvesting contracts well in

advance of the harvesting operations being due. To satisfy this

requirement the inventory procedure includes predicting the trees that will

be thinned, known as the 'thinnings elect'. The increm~nt o_n these trees is

predicted for the period between inventory and thinning, which may be up

to nine years. The effect of alternative silvicultural treatments (particularly

thinning intensity and fertiliser treatments) on the growth of the thinnings

elect must be predicted if model application bias is to be avoided.

The currently accepted thinnings elect models are (Leech, 1973):

Vmt = -3.2876 xl 0-2 -1.6480 x 10-3 X H + 3.2326 x 10-4

X D2 + 1.2550 x 10-5 X D2 X J-I

-1.3815 X 10-7 x D2 X f[ x B + 8.3909 X 10-9 x D2 X f[ X Sq

+ 1.6495 X 10-7 x D2 X H x A + 5.5223 X 10-4 x Ni

and

55

1= 1.9861 X 10-5 X T X R X SQ - 4.1920 xl 0-4

X T X R X A + 0.4653 x T x R B

- 2.2834 x 10-2 X T X Dtt + 2.2438 X 10-4

X T X Ni + 4.4680 X 10-2 X T X Vmt

Where Vmt is the estimate of tree volume (m3); I is the periodic

increment; T is increment period in years; D is overbark tree diameter at

breast height (1.3 metres above the ground); H is predominant height

(metres); B is stand basal area (m2 ha-1); Sq is site quality defined as the

total volume production to a 10 centimetre small end assortment to age 30

(m3 ha-1) obtained from the Lewis yield table; A is stand age in years

since planting; Ni is thinning intensity defined as the ratio of the stocking

removed to stocking standing before thinning expressed as a percentage;

R is relative tree size defined as the ratio of the tree diameter to the

quadratic mean tree diameter of the stand and Dtt is the thinning type

defined as the ratio of the quad ratic mean tree diameter of the thinnings

elect sub population to the quadratic mean tree diameter of the stand

before thinning.

For effective forest management it is essential that not only the predictions

of total stand growth are unbiased but also that the volume of sub

populations of interest, such as the thinnings elect, can be predicted with

similar confidence. Recent changes to plantation silviculture, including

routine post-thinning fertiliser application may affect the growth of the

thinnings elect differently from the growth of the whole stand.

The current models do not incorporate an adjustment for growth where

fertiliser has been applied, yet it is likely that the thinnings elect respond to

additional nutrition. A stand density parameter is incorporated, however,

the adequacy of this parameter to predict the growth of the thinnings sub

population where the stand density is significantly below the Optimum

Thinning Guide stocking needs to be tested.

56

6. FERTILISER EFFECTS

The fertilisation of forests is documented as commencing in Europe during

the 1800's in response to recognition that past land management

practices had depleted the nutritional status of soils (Tamm, 1967). Tamm

credits the work of E. Ebermayer in Germany in 1876 as recognising the

existence of forest nutrient cycles and of tree nutrient demands. Assman

(1970) suggests that although forest fertilisation experiments were

established as early as the start of the 1900's, only a small number of

experiments provided clear and positive results. This possibly reflects

some inadequacies in the design of these experiments by current

standards.

The understanding that when a nutrient, or water or light is at a critical

level it can be the major factor in determining the health and growth rate of

a crop led Mitscherlich (1910) to propose a 'law of minimum'. Savill, et a/.

(1997) credits Baker (1934) with the stating that increasing any factors

that are markedly deficient will increase the yield disproportionately.

J. Fielding in 1939 carried out the earliest documented work in the south

east of South Australia aimed at restoring radiata pine stands declining in

health and vigour (Boardman and Leech, 1995). Fertiliser experiments

were established in the Mount Lofty Ranges in 1943 to reverse the decline

in the growth of radiata and maritime pine (Pinus pinaster Ait.) on strongly

phosphate-fixing soils. Early success with superphosphate applied at a

range of dose rates and re-treatment frequencies led to a concerted

investigation of newly established plantations on these sites. Between

1948 and 1953 phosphate investigations were extended into the marginal

lands (potential radiata pine site quality classes V to VII) with low

phosphate fixation but extremely deficient in phosphorus. A systematic

study on marginal sites across a wide range of soil types and plantation

ages up to thirty years was made between 1959 and 1972 (Boardman,

57

1974). Foliar analysis was introduced in 1963 as a technique for the

interpretation of nutrient status (Raupach, et al., 1969). The studies

concentrated on the 'up-grading' of marginal fertility soils and established

that phosphorus was the principal limiting nutrient on a wide range of

sites, after the correction of zinc deficiency. Thereafter, the widespread

application of superphosphate was carried out according to schedules

derived from this research (Boardman, 1988). Only a few sites were

treated with nitrogen fertiliser as the price was prohibitive.

By the 1950's and early 1960's a more serious problem which affected all

classes of site quality, was demanding urgent attention recognised as

'second rotation decline' (Keeves, 1966). Consequently a series of diverse

studies spanning many sites and silvicultural practices was undertaken

(Bednall, 1968). There was an apparent lack of evidence for a decline in

productivity in mid-rotation and later ages in the first rotation. This together

with a clear reduction in growth rates in the earliest years of the second

rotation sustained for upwards of 20 years (the then limit of plantations

available for inspection) all indicated that remedial work should be

concentrated on the plantation establishment phase, considered to be the

first six years. These investigations were the major research activity

between 1966 and 1976 (Boardman, 1998, pers. comm.). Considerable

attention was given to nitrogen in conjunction with weed control and

organic matter retention.

These experiments had a major influence on understanding crop nutrition

and the vital importance of soil moisture management for increasing

productivity. The control of competing weedy vegetation and use of a

granulated, completely balanced mineral fertiliser were critical outcomes

of this research (Boardman, 1984).

Later, during the 1970's, a number of trials with nitrogen fertilisers were

undertaken in mid-rotation and extended over a range of site quality

classes, with promising but not sustained results (Boardman and

58

Simpson, 1981). In 1977, project EP176, was established in later age

stands spanning a range of non-marginal site qualities. It utilised the

history available in Permanent Sample Plots and was based on stem

analysis. This project indicated that fertiliser response patterns were

similar to those reported from overseas with a duration of response of

approximately seven years to a single adequate dose (Moller and

Rytterstedt, 1974; Miller, 1981; Puro, 1982). Studies also showed that

approximately one third of crop trees in multiple thinned plantations

responded strongly to nitrogen application but another one third barely

responded at all (Boardman, 1995). Would this result have significant

economic and financial implications if it were mainly the final crop trees

that benefit from the addition of fertiliser?

It is fair to say that in South Australia mid-rotation experiments with

nitrogen included with phosphorus and other essential nutrients

established up until the mid 1980's were inadequate in terms of the range

of treatments tested, the comprehensiveness of experimental design, and

the rigour of mensuration. The recognition of this situation led to the

establishment of a large thinning and fertiliser experiment specifically

designed to address these issues.

6.1 Fertiliser response models

Stand growth responses to nutrient application can be usefully described

by the empirical Type 1 and Type 2 model proposed by Waring (1981). In

essence, the model implies that a Type 1 response advances the phase

of plantation development but does not change the inherent productivity of

the site. A Type 2 response occurs when nutrient application causes a

long-term change in site properties, as has been observed with remedial

treatments such as zinc application (Boardman and McGuire, 1990a,

199Gb).

59

The experimental evidence suggests that fertilisation usually causes a

Type 1 response in that 'fertilizers are generally of benefit to the trees, not

the site' (Miller, 1981). The response can be considered as a reduction in

rotation length (Miller, 1981). It should be noted that a Type 1 response

may be economically advantageous even though the asymptotic

maximum volume the site may achieve is unchanged. It should also be

noted that there are some examples of Type 2 responses lasting many

years, predominantly on wetter sites.

Trends gleaned from a review of the international and national literature

together with the results of the then extant South Australian experiments

were used by, R. Boardman, A. Keeves, J.W. Leech and R.V. Woods to

construct three alternative fertiliser response models. These were termed

the low, most probable and high levels of response models (Table 6.1,

Figure 6.1).

The most probable model shows an increase in annual growth followed by

reversion to the expected rate of current annual growth of the stand;

effectively a Type 1 response. The 'high' level response model showed a

sustained increase in the volume growth signifying an effective permanent

increase in the site quality rating of the stand; corresponding to a Type 2

response. The 'low' level response showed an initial increase in volume

growth followed by a fall in growth below the level expected five to seven

years after the fertiliser application, that is, that the growth was less than

that predicted for an untreated stand. This last model is effectively a

reduced Type 1 response.

60

Table 6.1 Alternative fertiliser response models.

Stand Volume Growth multiplier

Years after Most High Low

application probable

1 1.10 1.25 1.05

2 1.50 1.70 1.30

3 1.60 1.70 1.45

4 1.55 1.60 1.40

5 1.30 1.40 1.20

6 1.05 1.20 1.00

7 1.00 1.10 0.90

8 1.00 1.10 0.80

9 1.00 1.10 0.90

10+ 1.00 1.10 1.00

61

-------------------

Figure 6.1 Alternative fertiliser response models.

z o

2

~1.75 o a.. o ~

e:.. ...J o ~ J-z

1.5

81.25 o J-W > ~ 1 w ~ J: J-

~O.75 ~ (!)

...J « ~ 0.5 z « ~

QO.25 ~ w a..

2

MOST PROBABLE HIGH LOW

4 6 8 TIME (YEARS SINCE FERTILISED)

62

10

Using all of the available evidence to choose between the three alternative

models, Leech implemented the most probable model in the Yield

Regulation System. This decision was made because the experimental

evidence showed the following:

• That where stands were treated with nitrogen fertiliser responses to

mid-rotation nitrogen fertiliser do not always occur (Shoulders and

Tiarks, 1990; Carlyle, 2001). Where they do, they are usually reported

as persisting for approximately seven years for a range of species

growing under different environmental conditions (Moller and

Rytterstedt, 1974; Miller, 1981; Puro, 1982; Turner, et aI., 1996).

• Responses tended to be transient, corresponding more to Type 1 than

Type 2 responses.

• Responses tended to peak during the second and third growing

seasons following treatment.

In South Australia the operational responses achieved were usually, but

not always, less than those achieved under experimental conditions. So

the fertiliser response model which was applied as a growth multiplier was

reduced by a further multiplier of 0.9 to account for the difference in

operational responses compared with the experimental responses.

Surprisingly the South Australian data initially did not show that responses

were proportionally greater in lower than higher productivity stands.

However, the model was only implemented for Site Quality IV or poorer

stands that had received a commercial thinning. This was because the

then available data were so limited. Later evidence has suggested that

this decision may not have been correct.

Some unpublished South Australian evidence suggested that responses

differed with soil type and stand age, however, there were insufficient data

to confirm this. More recent cooperative studies across 18 diverse sites in

Tasmania, Victoria and South Australia have sought to develop models

63

that predict the likelihood and extent of responses to nitrogen fertiliser

using the balance of nitrogen and phosphorus concentrations in foliage as

an indicator (Carlyle, 2001). The results from these experiments are still

preliminary.

The most probable fertiliser response model was the best that could be

developed with the information available at the time, with the limitation that

the model was developed for fully stocked stands as defined by the

Optimum Thinning Guide. Although in South Australia the majority of

stands are managed within the stocking ranges prescribed by the Guide

this limitation of the model was seen to be significant, as it was possible

that the application of fertiliser could change the economics of thinning to

the standard prescriptions. In other words a possibility existed to exploit an

interaction between stand density and fertiliser dose by modifying the

Optimum Thinning Guide prescriptions for stands where fertilisers have

been applied.

6.2 Stand development

Miller (1981) suggested that there is an association between the

development phase of a stand and the response to nitrogen fertiliser that

can be expected. Often the development phase can be represented by

stand age but is more directly a function of the extent to which nutrients

have accumulated within the stand, and on the site.

Miller postulated that there are three distinct nutritional phases in the

development of a forest stand (Figure 6.2). During Phase I the developing

tree crowns utilise large amounts of nutrients that are predominantly

available from the soil rather than from nutrient cycling from litter. During

this phase the availability of nutrients in the soil will determine the

productivity of the stand and additions of nutrients in the form of fertiliser

will cause a direct increase in productivity.

64

During Phase II most nutrients are recycled and so the demand from the

soil for nutrients is greatly reduced. Fertiliser application in this phase is

unlikely to result in a large increase in volume response, as sufficient

nutrients are available to support growth. Miller suggested that an event

such as thinning can temporarily revert a stand currently in Phase II back

to Phase I as an increased quantity of nutrients is required to support the

increased biomass that will accumulate to replace what has been

removed. This process is supported by evidence from mid and later aged

fertiliser experiments showing greater responses associated with recently

thinned stands than with stands at relatively higher stockings.

Phase III of this nutritional requirement occurs later when nutrient

immobilisation in the soil can lead to deficiencies at later ages. It is

unlikely that this phase is reached currently in radiata pine stands in South

Australia as rotation lengths are short relative to those applied in the

natural conifer forests of the northern hemisphere, which are the context

()f Miller's work. However, Phase III may be reached in future with multiple

rotations on the same site.

65

Figure 6.2 Stand nutritional requirements model (Miller, 1981).

current annual volume growth

Phase II

Phase I

crown fully ormed

Phase III

nitrogen mineralisation may fall to less than tree requires

66

6.3 Stem form

Although the results described in the literature are not consistent, there is

evidence to suggest that tree attributes can respond differently to different

fertiliser treatments. Miller and Cooper (1973) found in an experiment

where nitrogen fertiliser had been applied to Corsican pine (Pinus nigra

var. maritima, Ait.) that tree height, diameter and volume responded

differently to various rates of fertiliser. Maximum height growth coincided

wiith a relatively low rate of nitrogen application, but basal area growth was

maximised by the application of a relatively high dose of nitrogen. In New

Zealand, Whyte and Mead (1976) reported the estimated volume

response over a five period greatly exceeded that of the basal area

response to a combined application of nitrogen and phosphorus fertiliser.

In a comprehensive study, Snowdon (Snowdon, et a/., 1981) found that

fertilising radiata pine after first thinning may have had a significant effect

on stem form because the relative diameters in the central portion of the

stem are increased by fertilisation. This kind of response has also been

rE~ported by Barker (1 9aO) who indicated that this form factor change could

be transient. This study found that the widest rings were formed in the

section of the stem closest to the most actively growing section of the

green crown.

These results appear consistent with the results obtained from other

similar studies and conform to explanations of the pattern of wood growth

nnade in physiological studies such as those reported by Forward and

Nolan (1961). They proposed that the dominant effect on growth in the

upper stem portion of a tree is strongly controlled by total cambial growth.

This section of the tree is able to respond to favourable growing conditions

rnore quickly than the lower part of the stem, which is more controlled by

past apical growth.

67

These various results have implications for the mensuration methods

chosen for fertiliser experiments. Stem analysis was recommended as the

preferred method of volume estimation in fertiliser experiments (Whyte

and Mead, 1976). However, Whyte also suggested that it would be

possible to use volume equations relating volume measurements to

diameter at breast height and an upper stem diameter measurement to

adequately estimate tree volumes. Snowdon (Snowdon, et aI., 1995) went

further to state that 'stands top-dressed with fertilisers are likely to be

poorly assessed through the use of existing regional height, diameter

volume functions, which do not reflect induced changes in tree form.'

The conflicting literature suggests that different growth patterns would be

evident for different growth variables in different situations and signals that

appropriate mensuration methods need to be applied to fertiliser

experiments to account for possible differential form changes. It appears

that tree volume equations which incorporate an upper stem diameter

measurement are appropriate and it is advisable to also measure at least

some trees along the stem to ensure that if necessary a correction can be

made to the volume estimates obtained from any tree volume equation.

68

7. STAND DENSITY AND FERTILISER INTERACTION

There is little existing evidence on which to base the development of a

model that predicts fertiliser responses for various stand densities, and

fe\iv if any studies have been specifically designed to investigate the

possible interaction between stand density and fertiliser application on

stand growth and yield.

A number of experiments can provide incidental information on the

relationship between stand density and fertiliser including those in

Scandinavia (Moller, et al., 1991; Valinger, 1993), in South Africa (Donald,

19187), in New Zealand (Woollons and Will, 1975; West, 1998); North

Arnerica (Steinbrenner, 1967; Weetman, 1975; Schultz, 1997) and

Australia (Snowdon and Waring, 1981; Crane, 1982). The consistent

conclusion that can be drawn from these and other studies relevant to

intensive plantation management are that fertiliser application soon after

moderate to heavy thinning generally resulted in a greater overall growth

response than would be expected with no or light thinning. Exceptions

were found ~!Jch _ as where over stocked stands were found to respond

more than lower stocked stands (Pettersson, 1994).

In some instances stands had to have been thinned to obtain any

response from fertilising, such as Woollons and Will (1975). Where

experiments included more than one thinning level, it has been found that

the heavier the thinning the greater the response to fertiliser (Donald,

1 B87).

Although the instances described above provide indications of the

existence of a stand density and fertiliser interaction, they cannot provide

a basis for modelling it. It is reasonable to conclude that the interaction, if

any exists between stand density and fertiliser, especially in the context of

69

intensive radiata pine plantation management in South Australia, or

anywhere else, is little understood and warrants further research.

70

PART II:

GROWTH AND YIELD MODEL DEVELOPMENT

8. INVESTIGATING STAND DENSITY AND FERTILISER

INTERACTION

Once the considerable gains in productivity were achieved in South

Australian radiata pine plantations at the establishment phase through

more intensive practices, the next step was to consider the potential for

improving mid-rotation silviculture. Work based on South Australian

experiments had indicated that the critical stocking density was

approximately at a constant proportion of the Optimum Thinning Guide

stocking (Lewis, 1964; Lewis, et a/., 1976). This was a simple model, but

one that required further analysis and redefinition; especially to determine

whether a thinning and fertiliser interaction existed and to model it.

Analyses carried out by Leech for poorer site quality classes (V to VII)

reported by Boardman (1988) indicated that there was a large difference

in the estimated Net Present Value of the radiata pine plantations

depending on which fertiliser response model was assumed and on the

magnitude of any interaction effect.

These developments coincided with forest fires which In 1983 had

destroyed close to 30% of the stand ing plantations in the south east and

Mount Lofty Ranges forest region. Subsequent forecasts of future log

availability indicated a shortfall in the required quantity of medium to large

sized logs within several decades. This identified the need for more

flexibility in managing stand density than was available using the Optimum

Thinning Guide.

The conclusion drawn from these major considerations was that late age

fertilisation after thinning was essential and that the modelling of later age

fertiliser responses was the component of the growth and yield system

most in need of development. Existing experiments were inadequate to

provide a basis for this, and many experiments had been lost in the fires.

72

The establishment of a long term and expensive research experiment was

justified by the effect of the imprecision of the existing fertiliser response

model on the Net Present Value of the plantation estate and ignorance of

the interaction between stand density and fertiliser.

This led to the establishment of EP190, a large and comprehensive

research project incorporating multiple thinning and nitrogen fertiliser

treatments which was established on five separate plantation sites in the

south east of South Australia. When EP190 was established it was

believed to be the only experiment of its kind in the world and no evidence

has arisen since to suggest that this is not still the case. The analysis of

the thinning and fertiliser responses and the development of models to

predict the interaction form the pivotal part of this thesis.

8.1 Experimental design and mensuration

Experiment EP190 was designed primarily by R. Boardman and J.W.

Leech and established by the Forest Research, Forest Resources and

Forestry Systems functions of ForestrySA.

Thinning and fertiliser treatments

Three levels of thinning intensity, all defined relative to the prescribed

Optimum Thinning Guide stocking for site quality and plantation age, were

chosen as treatments in the experiment (Appendix I). Extremes of thinning

intensity were chosen to ensure a treatment expected to be well off the

Langsaeter plateau. The thinning prescriptions applied at each site were

defined relative to the Optimum Thinning Guide, being -45% less than the

optimum, at the optimum and 25% more than the prescribed stocking

(OTG- -45 %, OTG and OTG+ +250/0) for four of the five sites. These

stockings were defined for stands of specific age and site quality and it

was appropriate to use the same basis for achieving the experimental

objectives for EP190 (Table 8.1).

73

~ : 1

One of the sites (Glencoe Hill) was established at least five years later

than the other sites and with thinning treatments that were established

relative to a revised current practice stocking and density relationship.

Relative to the Optimum Thinning Guide prescription the three stocking

treatments at Glencoe Hill were the equivalent of -37.5% (OTG-), +7.5%

(OTG) and +32.5% (OTG+). The use of the Optimum Thinning Guide

meant that stand densities were not entirely consistent between sites. For

this reason it was thought that each site might need to be considered

individually for statistical data analysis and model development.

The fertiliser treatments included an untreated control and 75, 150 and

300 kg ha-1 applications of nitrogen (the timings and fertiliser doses are

shown in Table 8.2 and Appendix I), in a complete mineral fertiliser

mixture, called Forest Mix Number 311. The fertiliser applied is a specific

research formulation that contains a balanced range of macro and micro

nutrients in sufficient quantities to minimise the risk of inducing a nutrient

deficiency or imbalance in the crop and is detailed in Table 8.3. The

experiment was planned to span two thinning intervals of seven years to

investigate whether the response to fertiliser multiple treatments was

multiplicative or additive.

The data currently available from EP190 comprise measurements from

the first seven year thinning cycle at each site. As a consequence the data

from fertiliser treatments yet to be implemented can be used to increase

the sample size for some of the first thinning interval treatments.

Accordingly data from fertiliser treatment number 2 can be considered

with that from numbers 10, 3; with 11 and 4 with 12; effectively doubling

the number of measurements for these treatments (Table 8.4).

11 To minimise possible confusion, future references to nitrogen fertiliser relate to FM3 application with the nitrogen dose adjusted to give the three different rates ie and 75, 150 and 300 kg ha-1

.

74

Table 8.1 EP190: thinning treatments applied to date.

Site name Thinning Year of Plantation Assessed Experimental Stocking

event thinning age at Site Quality prescription (trees ha-1)

thinning

Hutchessons T1 1985/1986 11/12 II OTG 683

OTG -45% 375

OTG +25% 856

Headquarters T1 1985/1986 12/13 IV OTG 712

OTG -45% 392

OTG +25% 890

13/14 OTG 675

OTG -45% 371

OTG +25% 844

Menzies T3 1986 30 IV OTG 296

OTG -45% 163

OTG +25% 370

Glencoe Hill T2 1991 29 VI OTG +7.5% 316

OTG -37.5% 174

OTG +32.5% 395

75

Table 8.2 EP190: fertiliser treatment summary.

Nitrogen dose (kg ha-1) Allocated treatment Timing applied after first Total nitrogen applied

number thinning event (years) (kg ha-1) over two

thinning cycles

0 1 N/A 0

75 10 1 75

2 1,8 150

5 4,11 150

8 1,4,8,11 300

150 11 1 150

3 1,8 300

6 4,11 300

9 1,4,8,11 600

300 12 1 300

4 1,8 600

7 4,11 600

Table 8.3 Forest Mix 3: elemental analysis (%).

N P Pes K S Ca Mg Cu Zn Mn Mo Co B

total +ws

7.4 4.1 3.6 5.2 16.2 9.3 0.15 0.21 0.25 0.04 0.001 0.0001 0.002

76

Table 8.4 EP190: fertiliser treatments applied to date.

Nitrogen dose Allocated Timing applied Number of plots Total nitrogen

(kg ha-1) treatment after first thinning per treatment: applied (kg ha-1)

number event (years) Headquarters & over first thinning

Menzies cycle

(Glencoe Hill)

0 1 N/A 2 (4) 0

75 2,10 1 4 (8) 75

5 4 2 (4) 75

8 1,4 2 (4) 150

150 3,11 1 4 (8) 150

6 4 2 (4) 300

9 1,4 2 (4) 300

300 4,12 1 4 (8) 300

7 4 2 (4) 300

77

Sites and plots

The establishment of such a robust experiment necessitated finding large

(at least 70 hectares) relatively homogeneous sites in terms of age, site

quality, soil type and silvicultural attributes such as thinned state and

stand density. The choice of sites that met all these criteria was extremely

limited.

Beginning in 1985, five sites were established across a range of ages,

thinning states, soil types (Stephens, 1941) and stand productivity (Table

8.5). Each site was established with four replicates of plots representing

the three thinning and 12 fertiliser treatments in 31 x 44 factorial design

with 4 missing treatments, equivalent to 144 plots at each site. This was a

practical choice recognising that whilst more replicates would have been

desirable, sensitivity analysis had indicated that this level was justifiable

and appropriate. The objective was to maximise as far as possible the

ability to find any significant differences between the treatments where

they existed. Fertiliser treatments were assigned to plots by stratified

random sampling within the replicates. The experimental sites are large

and cost in the order of A$75,000 per year to maintain and measure and

much more to establish.

The difficulties in finding large and uniform areas of plantation required

two different years of planting to be included in the Headquarters site and

also four replicates to be reduced to three for some of the treatments at

Glencoe Hill.

A robust design is required for such a fertiliser interaction experiment

because any differences between growth responses were expected to be

generally small relative to the standard error of the treatment differences.

The analysis could also be confounded by agents which influence local

variation in growth including, lateral sub-surface movement of nutrients,

irregular rainfall and soil type. This requirement, the desire to apply

78

standard ForestrySA Permanent Sample Plot mensuration procedures,

and perceptions of the reliability of the results, influenced the choice of

multiple tree plots as against the alternative of single-tree plot designs.

The next consideration was that plots needed to include enough trees to

allow the sample to reflect closely the whole-population distribution of tree

sizes spanning two complete thinning cycles of seven years duration. The

design adopted used multiple-row plots of a variable size which depended

on the intensity of the thinning treatment retaining 25 trees per plot after

the first thinning event with 10 metre wide buffers. Plot locations were

selected with great care to ensure homogeneity.

Mensuration

The mensuration program implemented at all EP 190 sites included annual

basal area measurement, and predominant height and volume estimation,

consistent with South Australian Permanent Sample Plot measurement

practice (Appendix II). Basal area measurement was by steel diameter

tapes to obtain overbark diameter measurements at the Australian

standard of 1.3 metres above mineral earth on the high side of the tree

(Wood, et a/., 1999). Predominant height is defined as the arithmetic

mean of the height of the tallest trees in a plot (Wood, et a/., 1999). In

South Australia, predominant height is determined at the rate of the 75

tallest trees per hectare with the restriction to minimise clustering; trees

are selected by dividing the plot into four quarters with the necessary

number of trees being measured per quarter (Lewis, et a/., 1976). Tree

and plot volumes were measured and estimated to a small end diameter

underbark of 10 centimetres, which is the standard metric for South

Australian yield tables and growth models. Highly trained and specialised

technical staff undertook all plot measurements.

79

Table 8.5 EP190: summary of five sites established.

Site name Year of Previous land use & soil type Assessed Assigned Year

planting Site site experiment

Quality number established

Hutchessons 1974 First rotation plantation "

01 1985

established on ex pasture site -

Caroline Sand

Headquarters 1972 & Second rotation previously 1926 IV 02 1985

1973 and 1927 plantation - mainly

Mount Burr Sand

Menzies 1956 First rotation plantation IV 03 1986

established on ex pasture site -

Caroline Sand

Kilsbys 1962 First rotation plantation III 04 1986

established on ex pasture site -

Caroline Sand

Glencoe Hill 1962 First rotation plantation VI 05 1991

established on ex native forest -

mainly Mount Burr Sand with - -

some Hindmarsh Sandy Loam

80

Plot volume, basal area and predominant height were measured one year

after the first thinning event at all sites, except for Menzies (where for work

scheduling reasons the volume measurement was necessarily delayed for

two years). The three parameters were remeasured at the time of the next

thinning event.

Plot volumes were derived from tree volumes estimated using the

Regional Volume Table (a four-way tree volume equation that

incorporates an upper stem diameter measurement) to restrict the

measurement effort required (Lewis and Mcintyre, 1963; Lewis, et al.,

1973). A sample of ten trees was measured in each plot to allow a volume

basal area line to be constructed from which the plot standing volume to a

10 centimetre top diameter was estimated (Keeves, 1961). All thinned

trees were measured for volume using the three metre Sectional Method,

as was one standing tree in each plot, to be used as a check on the

Regional Volume Table. ForestrySA's computerised Plot Measurement

System was used for most recording of plot field data and subsequent

office calculations (Leech, et a/., 1989). This approach was considered to

be the most cost effective, integrated measurement protocol.

Sirex mortality

A Sirex noctilio (Fab.) infestation occurred in the south east radiata pine

plantations beginning in 1985 and peaking in severity from 1986 to 1988.

This occurrence seriously tested the viability of the experimental design.

Further measurement at Kilsbys was abandoned three years after the

establishment of the experiment due to a high incidence of Sirex induced

mortality in the more heavily stocked treatments.

Hutchessons was also heavily affected by Sirex activity such that

measurement of the OTG+ treatment was abandoned in 1990 reducing

the number of plots to 96 at that site. Also, the measurement effort was

81

reduced at Hutchessons such that only the OTG- treatments were

measured for plot predominant height and volume after 1990.

The design of the Hutchessons, Headquarters and Menzies sites included

additional plots beyond the required minimum of 144. The additional plots

were used to replace some of the more heavily Sirex affected plots. This

strategy was designed to ensure the viability of these sites in the event of

the loss of a small number of plots but not the extensive mortality

associated with such a severe Sirex infestation. It is suspected that Sirex

mortality influenced the growth of a large number of plots and the possible

effects need to be taken into account when using the growth and yield

data from EP190.

8.2 Basis of volume measurement

As previously indicated the plot volumes relied on the use of the Regional

Volume Table with the measurement of a sub sample of trees using the

three metre Sectional Method as a check on the possible effect of stand

density and fertiliser dose on tree shape. A separate study (Appendix IV)

- of tree shape indicated that errors introd uced by using the Regional

Volume Table to estimate tree volumes in thinning and fertiliser trials were

sometimes statistically significant. However, for the purpose intended,

where errors were identified they were found to be practically unimportant.

This was an important conclusion as no correction was necessary to the

volumes derived from the Regional Volume Table from EP190.

82

8.3 Growth and yield data

The first requirement was to analyse the growth and yield trends from

EP190 to determine the practical and statistical significance of the

alternative treatment levels of thinning and fertiliser on each site.

Several of the EP190 sites were severely affected by Sirex to the extent

that the stocking of some plots in the OTG+ treatments at H utchessons,

Headquarters and to a lesser extent Menzies was reduced to the OTG

stocking, and OTG plot stockings were reduced to stockings as low as

85% of the Optimum Thinning Guide. There was little reduction in stocking

due to Sirex induced mortality in the OTG- treatments at any site.

If Sirex induced mortality had occurred immediately after the first thinning

event after plot establishment then at least the resulting stocking and

growth relationship could have been analysed. However, in most

instances the Sirex induced reduction in stocking spanned a three of four

year period in each affected plot, a situation which was thought to

confound the stand density and growth relationship. Although the higher

incidence of mortality was associated with the higher stocked treatments

there was extreme variability. In some cases some plots within the same

thinning treatments lost up to the equivalent of 500 trees per hectare to

deaths whereas others were hardly affected losing less than 50 trees per

hectare.

Various approaches to the problem of correcting the growth data for the

effects of Sirex induced mortality were considered including covariance

analysis. It was concluded that the most simple and reliable approach was

to remove the data from the most affected plots from the data set. This

was possible because of the robustness of the original experimental

design, which despite the removal of some plot data still provided a viable

83

data set from which growth and yield trends could be analysed and

predictive models could be developed.

Plot data were removed from the Hutchessons, Headquarters and

Menzies data sets, the Glencoe Hill site was relatively unaffected by Sirex

and so all plot data were used. The procedure applied was to rank the

eight plots (four plots for treatment numbers 1 and 5 to 9) within each

thinning and fertiliser treatment according to the total number of deaths

recorded during the first thinning cycle. Half the plots were removed from

the data set from each of the thinning and fertiliser treatment

combinations, that is, the four worst affected plots for each of the

treatments 2 and 10, 3 and 11 and 4 and 12, and two plots each for

treatment numbers 1 and 5 to 9. This approach removed most of the plots

with significant Sirex induced deaths from the data sets for all sites except

Hutchessons. Consequently, removing Hutchessons from the analysis

was considered on the basis that the growth responses were likely to be

confounded; but deferred until the growth and yield trends were inspected.

The remaining data were then summarised as means by site, thinning and

fertiliser treatments at the start and the end of the six year fertiliser cycle

at each site (Tables 8.6 to 8.9) for predominant height, stand basal area

and stand volume. The volume growth and associated standard errors

were calculated for each treatment. Basal area and volume parameters

were also calculated for the thinnings elect (Tables 8.10 to 8.12).

84

Table 8.6 Hutchessons: summary of total stand growth results by treatment for predominant height, basal area and volume.

c:> 0:::: ("') 0

W l"-I __

I"- -- ("') -- I __ I"- __ ("') -- I __

0:::0::: 2 Cf) 00 -- en ..- .-Ir-(/) .-Ir-~ oo~ en~ .-Ir-~ Cf)w en ~ en ~ oo~ en~ «0 w ---1Cf) f- «s@ en co en co «sco en co en co «sco f- 2 0 ~ L- ~ L-~ ..c ~ ..c ~ ..c ~ ..c 00:::: -0 IID IID f-o+-J f-O..c f-O..c

Cf) 2 ~o .-I 0o:::~ «"'I «"'I 00:::1: 0("') 0("')

80:::1: 20:::

I 0.... o E o E r-c:>- roE- roE- r-c:>_ ~ E ~ E ~w f- W 0.... - 0.... - > - > - c:> -

LL Cf)

Hutchessons OTG- 1 (0) 2 21.3 30.2 8.9 18.08 36.42 18.34 136.8 384.9 248.1 8.8 i

2&10(75) 4 22.1 30.3 8.2 19.20 38.77 19.57 148.8 381.4 232.6 12.0

3 & 11 (150) 4 22.0 30.6 8.6 19.63 39.25 19.62 147.8 408.7 260.9 1.2

4 & 12 (300) 4 22.0 30.4 8.4 19.08 41.11 22.03 151.0 412.5 261.5 7.4

5 (75) 2 21.2 30.1 8.9 18.66 38.87 20.21 136.2 417.0 280.8 6.7

6 (150) 2 21.8 29.8 8.0 18.00 36.58 18.58 137.4 363.0 225.6 21.1

7 (300) 2 22.0 30.6 8.6 18.88 39.79 20.91 146.6 415.4 268.8 16.5

8 (75 + 75) 2 21.6 29.8 8.2 18.11 38.50 20.39 138.4 409.0 270.6 7.8

9 (150 + 150) 2 21.8 29.6 7.8 19.30 40.02 20.72 141.4 404.2 262.8 5.2

OTG 1 (0) 2 21.6 26.38 48.86 22.48 188.4 492.2 303.8 9.6

2&10(75) 4 22.1 26.57 46.40 19.83 196.7 383.1 196.7 4.2

3 & 11 (150) 4 22.1 28.26 49.82 21.56 215.9 415.9 200.0 5.8

4 & 12 (300) 4 22.1 26.64 46.77 20.13 205.3 375.4 170.1 30.1

5 (75) 2 22.0 27.40 50.00 22.6 201.2 472.3 271.1 35.2

6 (150) 2 22.1 25.78 46.22 20.44 196.6 420.3 223.7 22.4

7 (300) 2 22.5 27.44 50.20 22.76 217.6 510.8 293.2 26.0 - -

85

~

SITE

THINNING

c.o FERTILISER 00 ...... .--.. DOSE c..n --J 0 c..n + + ...... --J c..n c.n -9 -

PLOTS N N

PDH 1987 N N (metres) N ...... :.:.. to

- f:DH 1993 (metres)

TOTAL GROWTH (metres)

SA 1987 N N (m2 ha-1) 00 0)

N ~ ·0 ......

SA 1993 c.n ,.J::.. (m2 ha-1) !" 00 ...... ~ N 0

TOTAL N N GROWTH w ...... Co en (m2 ha-1) N c.o

V101987 N ...... (m3 ha-1) N <.0 N ...... Co en

V101993 ..j:::>. ,.J::.. (m3 ha-1) 0) ,.J::..

~ 00 ........ ~

TOTAL N N GROWTH ..j:::>. c.n 0) Q')

(m3 ha-1) N i::X>

STANDARD ..j:::>. N ERROR N 0)

m ~

Table 8.7: Headquarters: summary of total stand growth results by treatment for predominant height, basal area and volume.

c.9 0::: r-- (""') 0 W 00 ,- 0) ,- I,- r-- ,- (""') ,- I,- r-- ,- (""') ,- I,- 0:::0::: Z Cf)W Cf)

0) ~ 0) ~ --II-CJ) 00"";- 0)"";- --11-"";- 00"";- 0)"";- --11-"";-W 2 ---lC/) I- «S@ 0') CU 0) CU «SCU o)cu 0) CU «SCU «0 I- 0

...-- ..... ...-- ..... ...-- ...c ...-- ...c ...-- ...c ...-- ...c 00::: -0 Im :em 1-0

..... I-o...c I-o...c Cf) Z ~o --I °O::E «"" «"" 00::1: 0"" 0"" ~O::E 20::

I 0.... o E o E 1-<.9- roE, roE, 1-<.9-...-- E ...--E «w

I- w 0....- 0....- > ........... >- <.9 ........... l-LL Cf)

Headquarters OTG- 1 (0) 2 21.2 26.6 5.4 15.48 31.56 16.08 113.8 300.6 186.8 0.6

2&10(75) 4 21.2 29.0 7.8 14.74 31.40 16.66 110.9 313.0 202.1 4.1

3 & 11 (150) 4 21.9 29.2 7.3 14.92 33.18 18.26 118.2 340.8 222.6 7.6

4&12(300) 4 22.5 29.3 6.8 16.04 35.81 19.77 127.8 373.1 245.3 12.2

5 (75) 2 22.0 29.8 7.8 15.65 32.31 16.66 121.1 340.5 219.4 2.0

6 (150) 2 22.0 28.9 6.9 16.00 32.94 16.94 119.6 331.0 211.4 9.7

7 (300) 2 21.7 29.3 7.6 14.88 32.08 17.20 115.7 341.5 225.8 8.1

8 (75 + 75) 2 21.7 29.8 8.1 15.42 32.94 17.52 125.0 336.8 211.8 9.8

9 (150 + 150) 2 21.3 28.9 7.6 14.83 33.72 18.89 111.0 343.4 232.4 15.3

OTG 1 (0) 2 21.6 28.0 6.4 23.17 38.51 15.34 176.4 374.2 197.8 1.1

2&10(75) 4 21.2 27.6 6.4 22.40 39.86 17.46 166.7 400.8 234.1 4.5

3 & 11 (150) 4 21.2 27.5 6.3 21.78 38.92 17.14 160.5 392.9 232.4 12.2

4 & 12 (300) 4 21.0 27.0 6.0 22.72 41.77 19.05 169.8 415.3 245.5 9.7

5 (75) 2 20.3 26.7 6.4 21.73 37.48 15.75 153.2 347.0 193.8 9.4

6 (150) 2 20.1 26.7 6.6 21.82 36.76 14.94 165.5 349.6 184.1 31.2

I 7 (300) 2 20.7 26.8 6.1 22.48 40.50 18.02 165.6 411.2 245.6 8.3

- -

87

,-----

(9 0:::: 0 W I'- __ C"') I_ I'- .- C"')- -I~~

I'- _ C"')_ I_ 0::::0:::: Z Cf)W Cf) corn 0) --- -1l-rn CO '7 0)'7 CO'-;- 0)'7 -1 I- '7

W Z :::JCf) I- 0) ill 0) ~ «S~ O)CC O')CC «Scc 0) CC 0) CO «SCO «0

I- 0 ...- L- ...-- L- ...-- ..c ...-- ..c I-O..c ...-- ..c .....- ..c I-O..c 00::::

Cf) :z -0 IO) IO) I-

O-+-'

ti:o -1 °O::::E «'" «'" 00::::1: c:> CY") c:> CY") 00::::1: 20:::: I D- O E o E 1-(9- mS coS 1-(9--- .....-E .....-E

1-(9- ~w I- W D- --- D- - >- >-

LL Cf)

8 (75 + 75) 2 21.2 26.7 5.5 23.10 38.96 15.86 168.3 384.4 216.1 16.6

9 (150 + 150) 2 21.7 27.8 6.1 22.60 40.92 18.32 171.0 416.7 245.7 8.0

OTG+ 1 (0) 2 21.1 28.0 6.9 26.48 42.69 16.21 187.7 402.2 214.5 38.2

2 & 10 (75) 4 21.2 29.0 7.8 25.85 41.72 15.87 191.5 409.0 217.5 10.0

3&11(150) 4 21.9 29.2 7.3 25.32 40.39 15.07 182.3 409.1 226.8 14.3

4&12(300) 4 22.5 29.3 6.8 25.37 42.69 17.32 181.9 438.9 257.0 11.8

5 (75) 2 22.0 29.8 7.8 25.23 39.92 14.69 174.9 379.0 204.1 22.2

6 (150) 2 22.0 28.9 6.9 25.65 41.17 15.52 184.9 403.6 218.7 5.0

7 (300) 2 21.7 29.3 7.6 26.17 42.76 16.59 187.4 408.3 220.9 18.5

8 (75 + 75) 2 21.7 29.8 8.1 25.43 41.28 15.85 180.4 396.0 215.6 12.2

9 (150 + 150) 2 21.3 28.9 7.6 25.72 43.53 17.81 180.1 439.9 259.8 0.8 - -'---- -------'---

r

Table 8.8 Menzies: summary of total stand growth results by treatment for predominant height, basal area and volume.

,

(9 0::: 0 W co '8;cn I __ I __ co __

~ -- I .--.. co -- co .--.. ~ .--.. 0:::0::: Z (f)W (f) m ~ ~I-(J) co~ m~ ~ I- ~ co~ m~ ~ I- ~ W

~(f) I- mQ) «S~ m CO m co «SCO m co mco «SCO «0 I- 2 0

....- L- ....- '- ....- ..c ....- ..c ....- ..c ....- ..c 00::: (f) Z -0 IQ) IQ)

1-0

....... I-O..c I-O..c ~O ~ °O:::E «N «N 00:::'E OCT) OCT) 00:::'E 20:::

I 0.... o E o E 1-(9-- cog cog 1-(9-- ....- E ....-E 1-(9-- ~W I- W 0.... -- 0.... -- >- > --

LL (/)

Menzies OTG- 1 (0) 2 37.5 39.6 2.1 25.13 36.08 10.95 340.1 520.0 179.9 20.8

2 & 10 (75) 4 37.0 39.2 2.2 28.11 40.13 12.02 363.9 555.9 192.0 8.5

3&11(150) 4 36.5 39.1 2.6 26.86 38.95 12.09 340.3 529.8 189.5 4.4

4 & 12 (300) 4 37.6 39.8 2.2 28.48 41.06 12.58 371.0 580.3 209.3 1.7

5 (75) 2 36.5 39.4 2.9 27.70 39.12 11.42 354.2 546.5 192.3 2.9

6 (150) 2 38.3 41.1 2.8 27.79 40.39 12.60 369.6 589.3 219.7 24.5

7 (300) 2 36.9 40.2 3.3 26.12 37.53 11.41 330.0 525.8 195.8 0.1

8 (75 + 75) 2 36.9 39.8 2.9 25.58 37.23 11.65 330.2 532.2 202.0 13.0

9 (150 + 150) 2 37.3 40.5 3.2 26.01 38.28 12.27 351.1 561.3 210.2 29.7

OTG 1 (0) 2 38.1 41.2 3.1 39.27 50.04 10.77 512.5 704.1 191.6 6.8

2 & 10(75) 4 37.2 40.0 2.8 41.38 53.49 12.11 541.6 746.1 204.5 18.7

3 & 11 (150) 4 37.1 40.2 3.1 40.88 53.18 12.3 523.3 731.6 208.3 14.8

4&12(300) 4 38.4 39.9 1.5 41.09 52.18 11.09 531.6 724.2 192.6 3.6

5 (75) 2 37.6 40.3 2.7 40.97 53.04 12.07 534.7 748.1 213.4 37.4

6 (150) 2 36.9 I 39.7 2.8 40.30 53.87 13.57 508.1 741.8 233.7 49.9

7 (300) 2 38.2 I 40.7 2.5 41.76 53.10 11.34 531.8 743.2 211.4 2.6 -- -- -- - - - --- ,--

89

CJ oc 0 w co -.::r -,~Ci) -.::r ..--.. I_ co __ -.::r ..--.. I_ OCo::: Z U)w U) co -- 0) -- co -- -' I-- "'7 co "'7 0)"'7 -'1--"'7

W 0) ~ 0) ~ co "'7 0)"'7 <l:o .......JU) I-- <l:SID 0) CO en CO <l:SCO en CO 0) CO <l:SCU I-- Z 0 ...- L.... ...- L.... I--O~ ...-...c T"""...c I- ...c ...- ...c ...- ...c I-O...c 00:::

en :z: -0 :LCD :LCD OON Zo::: h:O ---' 0o:::~ ~'" ~N OM 0<':> 0o:::'E I D- OE o E mE. mE. I--O:::E T"""E ~E ~w I-- W 0....- (L -

1--(9- (9 --- >- > -- t-(9-

LL en

8 (75 + 75) 2 38.5 42.0 3.5 40.02 51.47 11.45 535.9 744.8 208.9 35.6

9 (150 + 150) 2 37.0 39.0 2.0 40.10 51.46 11.36 513.2 703.5 190.3 20.4

OTG+ 1 (0) 2 37.1 ' 39.4 2.3 45.26 56.51 11.25 567.2 752.7 185.5 30.0

2 & 10 (75) 4 37.2 I 39.6 2.4 47.07 59.49 12.42 605.7 828.2 222.5 17.7

3 & 11 (150) 4 37.9 40.2 2.3 50.61 63.52 12.91 631.1 868.6 237.5 25.8

4 & 12 (300) 4 37.8 40.4 2.6 46.75 58.03 11.28 591.0 805.1 214.1 9.7

5 (75) 2 37.2 39.7 2.5 48.19 58.88 10.69 600.8 802.3 201.5 24.4

6 (150) 2 36.8 38.7 1.9 45.19 56.06 10.87 545.1 717.4 172.3 3.4

7 (300) 2 36.7 37.8 1.1 49.34 61.16 11.82 608.3 801.2 192.9 32.6

8 (75 + 75) 2 37.2 39.7 2.5 44.82 57.16 12.34 559.4 757.2 197.8 2.8

9 (150 + 150) 2 I

38.2 40.2 2.0 48.10 60.25 12.15 624.2 842.9 218.7 21.8

If

Table 8.9 Glencoe Hill: summary of total stand growth results by treatment for predominant height, basal area and volume.

!

(9 ct:: co 0 W

N __

0) --I __

N -- co --I __ N __ co __ I __

ct::o::: Z (f)W (f) 0) CJ) 0) ~ --11-CJ) 0)"7 0)"7 --1 I- "7 0)"7 0)"7 --11-"7

W -.J(f) I- 0) Q) «S@ en CU en co ~S~ en CU 0) CU «SCU «0 I- Z 0 T""" L.... T""" L.... T""" ....c ...- ....c ...- ....c T""" ....c Oct:: (f) Z -0 Ia> Ia>

1- 0 ........ o ON I-O....c Zo::: ~O --1 °O:::E «N «N 0<":> 0<":> 00:::'E I 0.... o E o E coE. coE. I-O:::E T"""E T""" E ~w I- W a... - a... - 1-(9- (9 - >- >- 1-(9-

u.. (f)

Glencoe Hill OTG- 1 (0) 4 29.8 30.9 1.1 19.10 26.35 7.25 195.4 272.6 77.22 6.4

2 & 10 (75) 6 30.5 32.2 1.7 19.07 29.15 10.08 202.6 320.0 117.4 4.6

3 & 11 (150) 7 30.5 32.4 1.9 18.97 29.12 10.15 202.2 331.6 129.4 6.9

4 & 12 (300) 7 30.3 32.3 2.0 18.90 29.94 11.04 199.6 339.6 140.0 4.0

5 (75) 3 29.8 31.5 1.7 18.70 27.49 8.79 191.7 299.7 108.0 2.4

6 (150) 3 30.2 32.1 1.9 19.31 28.33 9.02 207.1 318.7 111.6 3.3

7 (300) 3 30.6 32.4 1.8 19.11 28.81 9.70 204.9 327.3 122.4 5.5

8 (75 + 75) 3 29.9 31.7 1.8 18.33 27.26 8.93 194.6 299.4 104.8 5.7

9 (150 + 150) 3 29.6 31.6 2.0 18.80 29.57 10.77 191.4 325.2 133.8 8.3

OTG 1 (0) 4 30.2 31.5 1.3 30.52 39.01 8.49 310.1 408.3 98.22 7.8

2&10(75) 8 30.2 31.8 1.6 30.65 39.83 9.18 313.8 424.2 110.4 2.9

3 & 11 (150) 8 30.6 32.8 2.2 31.01 40.79 9.78 325.7 455.5 129.8 6.5

4 & 12 (300) 8 30.6 32.9 2.3 31.15 42.57 11.42 323.2 479.7 156.5 6.5

5 (75) 4 30.7 32.5 1.8 31.22 40.63 9.41 313.5 433.4 119.9 11.0

6 (150) 4 30.7 32.6 1.9 30.67 40.05 9.38 313.9 431.7 117.8 2.8

7 (300) 4 30.4 32.4 2.0 30.73 40.26 9.53 328.4 444.3 115.9 12.2 -

91

JI",r' rl

ill I-if.)

(9 2 2 2 :::c I-

OTG+

0:::: ill Will -,W -0 ~O w LL

8 (75 + 75)

9 (150 + 150)

1 (0)

2&10(75)

3 & 11 (150)

4&12(300)

5 (75)

6(150)

7 (300)

8 (75 + 75)

9 (150 + 150)

N U) 0)-

~ ~ I-0 IQ) ......J a... o E

a... ---

4 30.9

4 30.1

4 30.0

7 29.9

7 30.1

7 30.0

3 30.2

3 30.0

3 30.0

3 29.9

3 29.9

00 -'~U) 0)- N- 00 --

0) ~ 0)'7 0)'7 «S~ 0":1 ctl O)m -r- L.

-r- ...c: -r- ...c: IQ) 1- 0 --0o:::~ «<"" «<"" o E mE- mE-a... --- 1-<.9---

32.7 1.8 30.87 40.11

32.5 2.4 30.99 41.2

31.8 1.8 35.45 44.11

32.2 2.3 36.34 45.54

32.8 2.7 36.36 45.92

32.8 2.8 35.47 46.55

32.0 1.8 35.76 43.90

31.7 1.7 35.64 44.30

32.5 2.5 36.20 45.85

32.2 2.3 35.31 44.32

32.3 2.4 35.70 45.62

0 :c _ -'~~ N_

00 _

0:::0::: -'1-'7 0)'7 0":1'7 «0 ~S~ 0":1 m 0":1 CO ~S~ -r- ...c: ...- ...c: 00:::: 00<"" c:> M c:> M o OM 20::: I-O:::E ...-E ...-E I-O::::E ~w <.9 --- > ---- > --- (9 --- (f)

9.24 322.1 437.0 114.9 3.9

10.21 318.5 449.6 131.1 3.2

8.66 351.8 455.0 103.2 5.7

9.20 366.3 477.3 111.0 6.6

9.56 368.6 501.4 132.8 9.7

11.08 358.0 509.2 151.2 5.5

8.14 353.3 457.2 103.9 2.2

8.66 338.7 474.1 135.4 13.5

9.65 369.4 494.5 125.1 7.6

9.01 356.1 471.4 115.3 11.7

9.92 357.7 495.8 138.1 7.2

Table 8.10 Headquarters: summary of thinnings elect growth results by treatment for predominant height, basal area and

volume.

(9 0:::: 1'-- C'0 0

W m-:r: _

I'- - C'0 ---:r: ___ r-- _ C'0 ___ :r: _

0::::0:::: Z (f)w (f) <X) en m ~ ---It-en 00'";" m'";" ---I t- '";" 00'";" m'";" ---It-'";"

W ---I(.f) t- m a.> «sa.> m ro m ro «sro m ro m ro «sro «0 I- z 0 ....- ~ ....- ~

I-o~ ....- ..c: ....-..c: ....- ..c: ....- ..c: 00:::: -0 :rID :rID I-o..c: I-o..c: (f) Z

~o ---I 0o:::~ «N «N 00:::'E oC") oC") 00:::1: Zo::: :r 0... o E o E 1-(9 .......... m..s m..s t-(9 .......... ....-E ....-E t-(9_ ~w I- W 0... .......... 0... .......... >- >-

l.L (.f)

Headquarters OTG- 1 (0) 2 4.72 8.82 4.10 33.4 80.6 47.2 3.1

2&10(75) 4 4.34 8.34 4.00 32.2 79.6 47.4 6.7

3 & 11 (150) 4 4.51 9.00 4.49 34.8 89.4 54.6 6.3

4&12(300) 4 4.79 9.56 4.77 37.6 92.6 55.0 4.3

5 (75) 2

6 (150) 2

7 (300) 2 .

8 (75 + 75) 2

9 (150 + 150) 2 :

OTG 1 (0) 2 4.54 6.67 2.13 32.4 57.9 25.5 6.1

2&10(75) 4 2.93 4.54 1.61 20.5 39.3 18.8 5.0

3&11(150) 4 4.33 6.91 2.58 31.0 63.1 32.1 7.8

4&12(300) 4 4.01 6.58 2.57 29.4 59.0 29.6 4.2

5 (75) 2

6 (150) 2 - -- ._- --

93

0 0::: 0 W r--. C'0 :r: .....-..

C'0 -- -1~~ r--. .....-.. C'0 .....-.. :r: __

0:::0:::: Z co -- ol""'-" r-- ---W U)w U)

ol ~ ol ~ -I.-CIl co '"7 ol'"7 co '"7 ol'"7 -I.- '";" <Co ---1U) .- «s~ Ol CO Ol CO «SCO ol co ol co <CS CO .- z 0 ..- ~ ..- s.... ~ ...c ~ ...c ~ ...c ~ ...c 00::: Z -0 :em :r:1D .-0 ........ '-o...c '-o.c (f)

ti::o -l 0a:~ «N «N 00:::1: o ~ 0<"'> 00::::1: 20::: :e 0... o E o E coS coS ...-E ...-E ~w .- W 0... -- 0... --

l-(9---- l-O __ > ---- > -- l-(9--

l.L. Cf)

7 (300) 2

8 (75 + 75) 2

9 (150 + 150) 2

OTG+ 1 (O) 2 5.02 6.78 1.76 33.7 56.2 22.5 4.5

2&10(75) 4 4.05 5.88 1.83 28.0 49.6 21.6 5.5

3&11(150) 4 l 2.29 3.08 0.79 15.4 28.7 13.3 8.2

4&12(300) 4 t 1.28 1.82 0.54 9.1 14.0 4.9 3.3

5 (75) 2

6 (150) 2

7 (300) 2

8 (75 + 75) 2

9(150+150) I 2 - -

,.".,e' t

Table 8.11 Menzies: summary of thinnings elect growth results by treatment for predominant height, basal area and volume.

I

I <..9 0::: eo C1;(j) 0 ill eo ..--.. :L..--.. eo ..--.. ~..--.. :L..--..

eo ___ ~..--.. :L..--.. 0:::0::: Z <J)ill <J)

0) ~ --.JI-cn co'":- 0)'":- --.JI-'":- CO'":- 0),":- --.J I- '":-W Z ::i<J) I- crt a.> «sa.> 0) co 0) co «sco 0) co 0) co « S co «0 I- 0

,.-- ~ ,.-- ~ ,.--..c ,.--..c I- ..c ,.-- ..c ...- ..c 00::: ....... 1-0

';:' I-o..c Z -0 IQ) I CD o°C'J ZO::: <J) Ero --.J °O:::E «C'J «C'J C)= C)= 00:::1:

I 0... o E o E cog cog I-O:::E ...-E ...- E ~w I- ill 0....- 0....- 1-(9-- (9- >- >- 1- 0 -LL <J)

Menzies OTG- 1 (0) 2 7.38 10.40 3.02 97.8 144.4 46.6 4.9

2 & 10 (75) 4 8.51 11.81 3.30 109.2 156.6 47.4 2.5

3 & 11 (150) 4 7.24 10.14 2.90 90.9 137.7 46.8 4.3

4 & 12 (300) 4 8.71 12.34 3.63 112.7 174.6 61.9 2.1

5 (75) 2

6 (150) 2

7 (300) 2

8 (75 + 75) 2

9 (150 + 150) 2

OTG 1 (0) 2 8.84 11.08 2.24 110.4 148.0 37.6 12.5

2 & 10 (75) 4 9.56 11.78 2.22 123.7 151.4 27.7 7.8

3 & 11 (150) 4 9.90 11.98 2.08 123.4 151.2 27.8 5.7

4 & 12 (300) 4 9.37 11.30 1.93 116.1 150.8 34.7 3.7

5 (75) 2

6(150) 2

7 (300) 2 - -

95

(9 c:r 0 W ro ~cn

:r: ___ co - """" --- :r: ___ ex:> ___

""""- ::c ,.-... 0::::0:::: Z ex:> --W U)w U) mg5 .....JI-cn co"";" m"7 .....J I- "7 ex:> "7 m"7 .....J I- "7 «0 I- Z =:iU) I- m Q) <CS(J.) m co m co ~SJg m co m co <C S co

0 ....- L- ....- I.... ...- .I::. .,..-.I::. .,..- .I::. ...- .I::. 00::: (j) :z: -0 IQ) IQ) I-O~ I-O...c

~o ---1 0o:::~ «"'" «"'" 00"", 0<"> 0= 00:::1: 20::: :r: 0.... o E o E aJ5 aJ5 I-O:::E ....- E ...-E ~w I- W 0.... ............ 0....- 1-(9- (9 - >- >- 1-(9---

lL. U)

8 (75 + 75) 2

9 (150 + 150) 2

OTG+ 1 (0) 2 7.13 8.38 1.25 81.0 104.4 23.4 4.5 i i

2 & 10 (75) 4 9.60 11.28 1.68 120.6 143.6 23.0 9.4

3&11(150) 4 10.35 12.06 1.71 124.4 152.9 28.5 5.6

4 & 12 (300) 4 10.46 11.90 1.44 126.5 146.4 19.9 2.2

5 (75) 2

6 (150) 2

7 (300) 2

8 (75 + 75) 2

9 (150 + 150) 2 --~---- .... - .. -- -

I'

Table 8.12 Glencoe Hill: summary of thinnings elect growth results by treatment for predominant height, basal area and

volume.

~ 0:::

N 0 W ex:> I .--.. I .--.. N .--.. ex:> .--.. I .--.. en .--.. en .--.. N .--.. ex:> .--.. O:::c.:r:: z U)w U)

~~ en ~ .....JI-cn en '7 en '7 .....J1-'7 en '7 en '7 .....J I- '7 W z :::::iU) I- «SQ.) en co en CO «SCO enro enro «Sro «0 I- 0 ~ L... 1-0.0 ~ ...c ~ ...c ~ ...c ~ ...c 00::: U) Z -0 IQ) IQ) I-O...c 1-0-'= Zc.:r:: trO .....J 0c.:r::~ «N «N 0c.:r::'E 0("'") 0("'")

0c.:r::'E I 0.... o E o E cog cog ~E ~E ~w I- ill 0.... -- 0.... -- I-~-- I-~-- > -- > --- 1-(9---LL (J)

Glencoe Hill OTG- 1 (0) 4 5.83 7.88 2.05 60.0 80.0 20.0 2.5

2 & 10 (75) 6 5.83 8.61 2.78 62.1 92.3 30.2 1.3

3 & 11 (150) 7 5.79 8.69 2.90 60.7 94.6 33.9 1.5

4 & 12 (300) 7 5.75 8.87 3.12 60.8 98.6 37.8 1.1

5 (75) 3

6 (150) 3

7 (300) 3 ,

8 (75 + 75) 3

9 (150 + 150) 3

OTG 1 (0) 4 9.09 11.31 2.22 94.0 112.6 18.6 3.3

2 & 10 (75) 8 9.10 11.51 2.41 91.4 119.5 28.1 1.2

3 & 11 (150) 8 9.09 11.64 2.55 96.3 127.4 31.1 0.8

4 & 12 (300) 8 8.90 11.70 2.80 89.8 126.0 36.2 3.4

5 (75) 4

6(150) 4 - -_.- --~ --- --

97

-

(9 n::: 0 w ~V) co :r: ___

C"J ...---. co .--... -I~~ C"J ___ C() ___ I __

0:::0::: z: 0) --CJ)w CJ) O)~ -11-00 O)~ O)~ 0) '7 0) '7 -I I-- '7

ill Z ---ICJ) I-- 0) CD «S~ 0) etS 0) etS «SetS 0) etS 0) etS «SetS «0

I-- r- ~ r- ~ r- ..c ~ ...c 00:::: 0 :r:W +-' 1--0+-' ~...c ~...c 1--0

...c 1--0

...c CJ) z: -0 :r: Q) Zo::: b:: O ---1 2a:~ «'"" «"" 00::1: <=:l C";) <=:l C";) 00:::1: :r: D- O E o E eng eng ~E ...-E ~ill

I- ill CL -- 0.. -- (9 -- 1--(9-- > -- > -- 1-(9--LL CJ)

7 (300) 4

8 (75 + 75) 4

9 (150 + 150) 4

OTG+ 1 (0) 4 9.40 11.29 1.89 91.4 111.2 19.8 4.9

2&10(75) 7 10.21 12.39 2.18 99.4 127.2 27.8 2.0

3 & 11 (150) 7 10.12 12.31 2.19 102.5 130.3 27.8 3.1

4 & 12 (300) 7 9.17 11.53 2.36 91.7 120.3 28.6 1.6

5 (75) 3

6 (150) 3 ;

7 (300) 3 I

8 (75 + 75) 3

9 (150 + 150) ! 3

r

8.4 Testing the design

The validity of the analysis and predictive model of growth and yield

responses from EP190 rely on the plots at each site, and within each

thinning treatment, being relatively homogeneous at the beginning of the

experiment. Conversely, the experimental design specifies differences in

the initial stand parameters between thinning treatments. Both these

aspects of the experimental design need to be tested. The key growth and

yield variable predicted in the South Australian yield regulation system is

stand volume and therefore the most important variable for evaluation.

However, basal area and predominant height also need to be considered

in testing initial comparability as differences in these parameters could

complicate the interpretation of later results.

The objectives of this part of the study were to test that within each site

that the productivity of the plots assigned to each treatment was not

significantly different. Also it was necessary to test that within each site

and thinning treatment, the plots randomly assigned to the different

fertiliser treatments ·vl/ere not different in terms of the initial predominant

height, basal area and volume; and conversely that within each site the

initial basal area and volume were significantly different across the

thinning treatments.

Normality of initial stand data

Prior to comparing the initial predominant height, basal area and volume

data the distribution of the data was tested for Normality using the

Kolmogorov-Smirnov test. The results of the Normality test for the site and

treatment combinations indicate that there is no reason to conclude that

the initial stand variables, predominant height (Hs), basal area (Bs) and

volume (Ys) are drawn from populations that are other than Normally

99

distributed (Table 8.13). Of some 21 tests 20 were not significant implying

that the remaining one significant difference could be considered a Type

I/Type II error condition and due to chance rather than detecting an

underlying statistical difference.

Comparison of treatment means

Having validated the assumption of Normality for the three stand

variables, initial predominant height (Hs), basal area (Bs) and volume

(Ys), an Analysis of Variance (ANOVA) was used to compare the stand

data by thinning (NI) and fertiliser (F ) treatment.

The initial predominant heights were compared across treatments within

each site as the best available indicator of stand productivity. The results

of this comparison (Tables 8.14 to 8.16) indicated that the predominant

heights were not significantly different between treatments within each

site. This implied that the productivity of the plots assigned to each

treatment were not significantly different 12.

The comparisons of the initial basal area and volume data (Tables 8.14 to

8.16) indicate that within each site and thinning treatment that the plots

randomly assigned to the different fertiliser treatments were not

significantly different.

As part of the experimental design the initial basal area and volume were

deliberately varied within sites to achieve the prescribed three levels of

stand density as defined by stocking. Within each site the comparison

indicated that the initial basal area and volume were significantly different

between the thinning treatments (Tables 8.14 to 8.16).

12 This conclusion was confirmed by inspecting the plot layout for each of the EP190 sites superimposed on a site quality map.

100

Overall, the comparison of the initial stand variables, predominant height,

basal area and volume indicated that there was no practical basis to

assume (where it was sensible to do so) that the various treatment

combinations were not homogeneous. Where the stocking was

deliberately varied between thinning treatments the statistical differences

were significant. Therefore, there was no need to adjust the raw data for

differences using covariance analysis, prior to statistically analysing the

growth responses from the EP190 sites. This outcome has the advantage

of making any conclusions drawn more credible because they are

relatively simple to understand and no additional error is introduced for

subsequent analysis and model development.

101

Table 8.13 Normality test of the initial stand parameters.

Site Parameter Nt Levels Calculated 0 Sig nificance

HQ Hs All 27 0.9620 NS

Bs OTG- 9 0.8918 NS

OTG 9 0.9091 NS

OTG+ 9 0.9195 NS

Ys OTG- 9 0.9541 NS

OTG 9 0.9497 NS

OTG+ 9 0.9772 NS

Menzies fIs All 27 0.9311 *

Bs OTG- 9 0.9348 NS

OTG 9 0.9707 NS

OTG+ 9 0.9452 NS

Ys OTG- 9 0.9169 NS

OTG 9 0.9100 NS

OTG+ 9 0.9475 NS

Glencoe Hill Hs All 27 0.9545 NS

Bs OTG- 9 0.9378 ~. - NS

OTG 9 0.9567 NS

OTG+ 9 0.8903 NS

Ys' OTG- 9 0.9328 NS

OTG 9 0.9372 NS -~

OTG+ 9 0.9239 NS ..

Note: * significant at 900/0 probability level

102

Table 8.14 Headquarters: ANOVA initial stand parameters and

treatments.

Model: Hs = NZ + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

NZ 2 2.552 1.276 1.565 0.2180

NZxF 8 5.466 0.83 0.8,38 0.5735

F 4 1.201 0.300 0.368 0.8304

Model: Bs = NZ + F + NZ x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

NI 2 1054 526.9 352.6 0.0000

F 4 5.446 1.362 0.911 0.4637

NZxF 8 4.109 0.514 0.344 0.9449

Model: Ys = NI + F + NZ x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

Nl 2 44986 22493 107.4 0.0000 - -NlxF 8 1034 129.2 0.617 0.7600

F 4 342.7 85.68 0.409 0.8014

103

Table 8.15 Menzies: ANOVA initial stand parameters and treatments.

Model: Hs = Nt + F + Nt x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

Nt 2 2.792 1.396 1.332 0.2720

F 4 5.379 1.345 1.283 0.2874

NtxF 8 4.927 0.616 0.588 0.7839

Model: Bs = Nt + F + NI x F

Source Degrees of Sum of Mean square F statistic P r> F statistic

freedom squares errors

NI 2 3970 1985 312.3 0.0000

F 4 39.89 9.972 1.569 0.1950

NlxF 8 41.68 5.210 0.820 0.5885

Model: Ys = Nt + F + Nt x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

Nt 2 585243 292621 142.3 0.0000

F 4 5573 1393 0.677 0.6105

NlxF 8 6742 842.8 0.410 0.9104

104

Table 8.16 Glencoe Hill: ANOVA initial stand parameters and

treatments.

Model: Hs = NI + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr> F statistic

freedom squares errors

Nt 2 3.113 1.556 1.957 0.1461

F 4 1.489 0.372 0.468 0.7591

NlxF 8 2.496 0.312 0.392 0.9227

Model: Bs = NI + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

Nl 2 4966 2483 569.3 0.0000

F 4 2.217 0.554 0.127 0.9724

NlxF 8 5.307 0.663 0.152 0.9962

Model: Ys = Nt + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr>F statistic

freedom squares errors

Nt 2 457908 228954 272.8 0.0000

F 4 1655 413.8 0.493 0.7408

NlxF 8 1084 135.5 0.161 0.9953

105

9. GROWTH RESPONSE COMPARISONS

Having confirmed that the implementation of the experimental design for

EP190 was statistically acceptable the next requirement was to compare

the six year growth responses to thinning and fertiliser treatments at each

site.

9.1 General inspection of results

The analysis of the growth responses over a six year period was initiated

by inspecting the total growth responses for each site and treatment in

Tables 8.6 to 8.9. This provided a basis to identify trends that would

warrant further investigation.

Inspection of the volume growth responses for Hutchessons indicated that

the results were highly variable with the OTG and a kg ha-1 fertiliser

treatment out-performing all other treatments. These results confirmed the

earlier concern regarding the viability of the Hutchessons data set, even

with the worst Sirex affected plots removed. On this basis it was

concluded that the additional Sirex induced mortality had serioosly

confounded the treatment responses to the extent that the results from the

Hutchessons site should not be considered further in this study.

It was self evident from inspecting the results (Tables 8.6 to 8.9) that the

treatments where fertiliser was applied at other than one or two years after

thinning provided no increase in the level of the growth response. In

addition there is currently no operational advantage in deviating from

applying fertiliser immediately after thinning. As a result of these

conclusions the repeated and delayed treatments (Treatments 5 to 9)

were excluded from further analysis and model development as part of

this investigation.

106

The irrelevant and confounded data were removed leaving the remaining

data to be drawn from three sites; Headquarters, Menzies and Glencoe

Hill, and included all three thinning treatments and 0, 75, 150 and 300 kg

ha-1 nitrogen fertiliser treatments applied one or two years after thinning

(Figures 9.1 to 9.3). Culling the available data in this way was consistent

with the need to ensure the simplicity of further analyses. In doing so the

confidence of testing observed responses and predicting responses was

also increased. In effect a balance was sought between insuring all

relevant data were available for further analysis, whilst ensuring the

maximum precision and utility of the system of models which could then

be developed.

107

Figure 9.1 Headquarters: annual total volume growth by treatment.

~60 « w

~ 50 ::I: ........ M :E "'-" ::I: 40 I-~ o c.t: 30 (!) ..J « ~ 20 Z « o C 10 o -~ w a. 0

OTG- OTG

108

.. 0 KG/HAN - 75 KG/HAN -150 KG/HAN II1II300 KG/HAN

OTG+

Figure 9.2 Menzies: annual total volume growth by treatment.

~60 « w

~ 50 J: --M ~ "'-"

J: 40 t-~ o ~ 30 (!) ...I <:(

~ 20 Z <:( ()

C 10 o -0:: w a. 0

OTG- OTG

109

_ 0 KG/HAN - 75 KG/HAN -150 KG/HAN - 300 KG/HAN

OTG+

J

Figure 9.3 Glencoe Hill: annual total volume growth by treatment.

~60 « w >-« 50 ::I: ........ M :E ~

::I: 40 I-~ o c::: 30 (!) ...I « ~ 20 Z « ()

C 10 o -C!:: W Q. 0

OTG· OTG

110

.. 0 KG/HAN - 75 KG/HAN -150 KG/HAN .. 300 KG/HAN

OTG+

9.2 Detailed results and analysis

Following the initial analysis the results were analysed on an individual site

basis.

Headquarters

The annual volume growth of the untreated control treatment (OTG and 0

kg ha-1 nitrogen) was higher at Headquarters than at any other site.

However, the absolute growth response to fertiliser was slightly less than

that observed at Glencoe Hill. Inspection of the thinning treatment

responses indicated that the lowest growth was associated with the OTG­

stocking and 0 kg ha-1 nitrogen treatment. All 300 kg ha-1 nitrogen

treatments responded strongly with the highest response associated with

the OTG+ thinning.

An ANOVA was applied to the six year volume growth (Gt6) for the

thinning (NI) and fertiliser (F) combinations that indicated that there were

strongly statistically different growth responses associat~d wJth the various

fertiliser treatments (Table 9.1). However, no significant differences were

evident between the thinning treatment responses or the thinning and

fertiliser interaction terms.

Where no fertiliser was applied, there was a trend for increasing growth

with increasing stand density. Where 75 kg ha-1 nitrogen or more was

applied the relative growth was higher than the unfertilised plots and was

relatively constant between stand densities. Using Tukey's HSD to test

between treatments indicated that there were two distinct sets of

responses; 0, 75, 150 kg ha-1 nitrogen and 300 kg ha-1 nitrogen

( FO, F75, F150, F300 respectively) with higher responses being associated

with higher fertiliser doses (Table 9.4). Consideration of the combined

thinning and fertiliser responses showed that the OTG+ and 300 kg ha-1

111

nitrogen combination was statistically different from all the OTG-, 0 and 75

kg ha-1 of nitrogen combinations.

Menzies

The annual volume growth of the untreated control treatment (OTG and 0

kg ha-1 nitrogen) at Menzies was slightly lower than at Headquarters.

However, at Menzies the absolute growth response to all fertiliser

treatments was substantially less than that observed at the other sites.

Although the growth of the three thinning treatments where no fertiliser

had been applied was relatively constant the lowest growth was

associated with the OTG- treatment. The responses to the 75 and 150 kg

ha-1 nitrogen treatments increased with increasing stand densities.

However, the 300 kg ha-1 nitrogen responses were inconsistent.

An ANOVA applied to the six year volume growth (GI6) for the thinning

(HI) and fertiliser (F) combinations from Menzies indicated that none of

the thinning or fertiliser treatments or the interaction term were statistically

significantly different from each other (Table 9.2). Comparison of the

thinning, fertiliser and combined thinning and fertiliser treatment means

using Tukey's HSD test showed no significant statistical differences (Table

9.5).

Glencoe Hill

The annual volume growth at Glencoe Hill was approximately half that of

the untreated control treatments (OTG and 0 kg ha-1 nitrogen treatment) at

the other sites. However, the relative and absolute growth responses to

fertiliser were generally much higher than those measured at the other

sites.

112

Increasing growth was evident with increasing stand density for the

unfertilised treatments. However, once any fertiliser was applied the

increased responses caused similar growth across the three thinning

treatments relative to each fertiliser dose.

The ANOVA applied to the six year volume growth (Gt6) for the thinning

and fertiliser combinations at Glencoe Hill indicated a statistically

significant difference between the fertiliser treatments (F), but not

between the thinning treatments (Nt) or the combined thinning and

fertiliser treatments (NI x F) (Table 9.3).

Further analysis of the thinning responses with Tukey's HSD test indicated

no statistically significant differences (Table 9.6). The Tukey's HSD test

applied to the fertiliser treatment indicated that there were two distinct

groups of responses; the unfertilised and the fertilised. As with

Headquarters there was a clear trend for higher responses to be

associated with higher fertiliser doses. The Tukey's HSD test results from

the combined thinning and fertiliser treatments supported some of the

indicated trends with treatments involving 300 kg ha-1 nitrogen showing as

statistically significantly different from the 0 kg ha-1 and often the 75 kg ha-

1 nitrogen treatments across the thinning treatments.

113

Table 9.1 Headquarters: ANOVA six year volume growth (Gt6) by

treatment.

Model: Gt6 = NI + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr> F statistic

freedom squares errors

F 3 11419 3806 8.125 0.0004

NI 2 1688 843.9 1.801 0.1825

NlxF 6 1751 291.8 0.623 0.7104

Table 9.2 Menzies: ANOVA six year volume growth (Gt6) by

treatment.

Model: Gt6 = NI + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr> F statistic

freedom squares errors

NI 2 3337 1669 2.108 0.1391

F 3 2803 934.3 1.180 0.3337

NlxF 6 3094 515.7 0.652 0.6885

Table 9.3 Glencoe Hill: ANOVA six year volume growth (Gt6) by

treatment.

Model: GI6 = NI + F + NI x F

Source Degrees of Sum of Mean square F statistic Pr> F statistic

freedom squares errors

F 3 28969 9656 36.64 0.0000

NI 2 1029 514.7 1.953 0.1501

NlxF 6 2087 347.8 1.320 0.2611

114

I

Table 9.4 Headquarters: Tukey's HSD Test six year volume growth

( Gt6) by treatment.

Tukey's HSD Comparisons (95% confidence interval)

Nt Response mean Compares equal to Standard error Confidence interval

(Gt6)

OTG- 214.2 All 6.05 199-230

OTG 227.5 All 6.05 212-243

OTG+ 228.9 All 6.05 214-244

F Response mean Compares equal to Standard error Confidence interval

(Gt6 )

0 199.7 75 8.84 176-223

75 217.9 0,150 6.25 201-235

150 227.3 75 6.25 211-244

300 249.3 None 6.25 233-266

NI F Response Compares equal to Standard Confidence

mean error interval

(Gt6 )

OTG- 0 186.7 All but OTG+ 300 15.3 139-234

75 202.1 All but OTG+ 300 10.8 169:236

150 222.6 All 6.25 189-256

300 249.3 All 6.25 212-279

OTG 0 197.8 All 8.84 150-245

75 234.2 All 6.25 201-268

150 232.4 All 6.25 199-266

300 245.5 All 6.25 212-279

OTG+ 0 214.6 All 8.84 167 -262

75 217.5 All 6.25 184-251

150 226.8 All 6.25 193-260

300 257.0 All but OTG- 0,75 6.25 223-291

115

Table 9.5 Menzies: Tukey's HSD Test six year volume growth (Gt6)

by treatment.

Tukey's HSD Comparisons (95% confidence interval)

Nt Response mean Compares equal to Standard error Confidence interval

(Gt6)

OTG- 192.7 All 7.86 173-213

OTG 199.3 All 7.86 179-219

OTG+ 214.9 All 7.86 195-235

F Response mean Compares equal to Standard error Confidence interval

(Gt6 )

0 185.7 All 11.49 155-216

75 206.3 All 8.12 185-228

150 211.8 All 8.12 190-233

300 205.3 All 8.12 184:227

Nt F Response Compares equal to Standard Confidence

mean error interval

(Gt6)

OTG- 0 180.0 All 19.9 118-242 .. -75 192.1 All 14.1 148-236

150 189.5 All 14.1 146-233 c----"

300 209.3 All 14.1 166-253

OTG 0 191.7 All 19.9 130-253 .-~

c-_

75 204.5 All 14.1 161-248 .. _-

150 208.3 All 14.1 165-252

300 192.6 All 14.1 149-236 "-----.

OTG+ 0 185.5 All 19.9 124-247 _._---

75 222.5 All 14.1 179-266

150 237.5 All 14.1 194-281

300 214.1 All 14.1 170-258

116

I

I

-

Table 9.S Glencoe Hill: Tukey's HSD Test six year volume growth

( Gt6) by treatment.

Tukey's HSD Comparisons (95% confidence interval)

Nt Response mean Compares equal to Standard error Confidence interval

(Gt6 )

OTG- 116.0 All 3.40 108-124

OTG 123.7 All 3.21 116-132

OTG+ 124.6 All 3.34 116-133

F Response mean Compares equal to Standard error Confidence interval

(Gt6 )

0 92.9 None 4.69 81-105

75 112.9 150 3.57 104-122

150 130.7 75,300 3.47 122-140

300 149.2 150 3.47 140-158

NI F Response Compares equal to Standard Confidence

mean error interval

(Gt6 )

OTG- 0 77.2 OTG 0,75; OTG+ 0}5 8.12 53-101

75 117.4 OTG-150,300; OTG 0-150; OTG+ 0-150 6.63 98-137

150 129.4 All but OTG- 0 6.14 111-148

300 140.0 OTG- 75,150; OTG 150-300; OTG+ 75-300 6.14 122-158

OTG 0 98.2 OTG- 0-150; OTG 75,150; OTG+ 0,75 8.12 74-122

75 110.4 OTG- 0-150; OTG 0,150; OTG+ 0-150 5.74 93-127

150 129.5 All but OTG- 0 5.74 113-147

300 156.5 OTG- 150,300; OTG 150; OTG+ 150,300 5.74 140-174

OTG+ 0 103.2 OTG- 0-150; OTG 0-150; OTG+ 75,150 8.12 79-127

75 111.0 All but OTG 300; OTG+ 300 6.14 93-129

150 132.8 All but OTG- 0; OTG 0 6.14 114-151

300 151.2 OTG- 150,300; OTG 150;300; OTG+ 150 6.14 133-169

117

9.3 Discussion

It is appropriate to consider a theoretical basis for understanding stand

nutrition to assist in synthesising the results across the three EP190 sites.

Stand development considerations

Miller's postulate (described in Chapter 6 of this thesis) regarding stand

development Phases I and " represent a useful conceptual model for

understanding the responses which can be expected from the various

treatment combinations at the EP190 sites. Headquarters is best

represented by Phase I of Millers conceptual model. This relatively young

stand is growing vigorously, and correspondingly the nutritional demands

are likely to be high and nitrogen application following thinning caused a

strong growth response. Increasing the dose level is likely to increase the

response to a maximum, however, this situation is unlikely to be reached

by the nitrogen dose levels trialed at this site.

The Menzies and Glencoe Hill plantations are of a. sim_ilar age and similar

growth responses could be expected if it were not for the difference in the

inherent fertility of each of the sites. The site quality assessment of the

Menzies site indicated a plantation of intermediate productivity (Sa IV)

and presumably not overly constrained by nutrient availability at that time.

A limited response could be expected at Menzies which at a later rotation

age is likely to be in Miller's nutrient Phase II. The application of additional

nitrogen will not necessarily cause a corresponding increase in the level of

the response as other nutrients, and perhaps water, are likely to become

limiting to growth.

Glencoe Hill is a site inherently poor in nutrients, particularly in nitrogen,

and the plantation has probably been deficient in nitrogen throughout its

life. Although at this age nutrient cycling should be well established I it is

118

likely that the total pool of nitrogen in the soil, litter and stand itself is

deficient. It could be expected that increasing the total pool of available

nitrogen would result in a significant growth response. Increasing the dose

level is likely to cause a corresponding increase in the response.

These differences in stand development characteristics makes between

site comparisons difficult to interpret. However, the characteristics of the

three sites do represent a considerable span of the site types relevant to

South Australian radiata pine plantations.

Stand growth at low stocking density without fertiliser

The relative growth trends associated with the unfertilised treatments at

Headquarters and Glencoe Hill strongly indicate that thinning below the

prescribed Optimum Thinning Guide stocking caused a loss of volume

growth. Such a trend is not clearly evident in the Menzies results. The loss

of growth was proportionally greater at the lower productivity site (Glencoe

Hill) than at the higher productivity site (Headquarters). Generally this

result supports the assertions made by Langsaeter (1941), Lewis et al.

(1976) and others which suggest that maintaining a stand at a lower than

'full' stocking density for a particular age and productivity will cause a loss

in relative volume and basal area growth.

The growth of the OTG- thinning on the higher productivity sites

(Headquarters and Menzies) was approximately 95% of the OTG

treatment, indicating that although a loss of growth was associated with

the lower stocking densities, that for these sites the plateau does not 'fall

off' rapidly. This would indicate that the growth of higher productivity

stands rapidly increases to take advantage of the additional growing

space under less dense regimes. However, the trees in the OTG­

treatment at the lower productivity site (Glencoe Hill) were clearly less able

to respond to the additional growing space than the OTG- treatment at the

other sites.

119

The practical implication of these results is that the Optimum Thinning

Guide needs to be reviewed using the full South Australian Permanent

Sample Plot database to determine if the stocking prescriptions,

particularly for higher productivity stands could be changed, probably

reduced. However, it should be stressed that this analysis is based on

three sites even though replicated.

Stand growth at low stocking density effected by fertiliser

The responses at all sites indicated that the 75 kg ha-1 nitrogen treatment

generally compensated for the loss of relative growth associated with the

OTG- density. This trend was strongest at the lowest productivity site

where the unfertilised OTG- treatment response was approximately 75%

of the control, whereas the OTG- and 75 kg ha-1 nitrogen treatment

responded at a level approximately 15% above the control and an

additional 5% above the OTG and 75 kg ha-1 nitrogen treatment. These

results indicate that in general the major limiting factor to growth at

Glencoe Hill is nutrition rather than water availability.

Increasing the fertiliser dose did not always increase the growth response.

Irrespective of the dose, Menzies exhibited a maximum response above

the control of approximately 100/0. Presumably this result indicates that the

inherent nutrient availability at Menzies was close to the maximum that the

stand could use. In this situation the water availability to the stand appears

to be the limiting growth factor when fertiliser was applied.

The relative fertiliser responses at Headquarters were somewhat

intermediate to those at the other sites. The OTG and 75 kg ha-1 nitrogen

treatment responded to a similar level as for the other sites, at about 10%

above the control. However, the relative responses of the 150 and 300 kg

ha-1

nitrogen treatments were relatively lower than those for Glencoe Hill

but higher than for Menzies.

120

The results indicate that the application of even moderate doses of

fertiliser to stands maintained at low stocking densities will not only

increase the stand growth above that expected from an unfertilised OTG

treatment but will affect the zone of minimum stocking density required to

achieve maximum site occupancy. However, these results alone do not

provide a basis for defining exactly where the revised zone of minimum

stocking density lies. What is evident is that when fertiliser is applied, the

revised zone of minimum stocking density does not lie within the span of

stocking density represented in EP190 but rather is at stockings

significantly lower than prescribed by the Optimum Thinning Guide.

9.4 Conclusions

Tentative conclusions can be drawn from this analysis which have

significant implications for applied forest management in South Australian

radiata pine stands and also for the development of predictive models

using this data set including:

• Stands of the site types represented in EP190 have the potential to

respuild to some extent to the addition of nitrogen fertiliser.

• Where stands are reduced either deliberately or inadvertently to

stocking densities significantly below the Optimum Thinning Guide, the

stand growth can be quickly restored to the equivalent of full site

occupancy at an unfertilised level by the application of even moderate

doses of nitrogen fertiliser.

• Nitrogen deficient stands of inherently low productivity will respond at a

proportionally greater level to higher doses of additional nitrogen than

stands of higher productivity, where growth appears to be limited more

by water than nitrogen availability.

• Stands of inherently higher productivity and whose growth is limited

primarily by water availability are unable to respond to additional

applied nitrogen beyond a maximum level. There is a tendency for the

121

highest dose rates to be associated with a lower response than

intermediate rates especially where higher stocking densities are

maintained. This may be due to an 'induced' competition effect caused

by a deficiency of water and/or of a nutrient other than nitrogen,

although there is no evidence from elsewhere to confirm this.

• Younger stands of intermediate productivity are able to respond to

increasing levels of nitrogen to the same absolute level but not to the

same relative level as lower productivity stands. Stands of intermediate

productivity appear to be able to utilise a significant quantity of the

additional nitrogen during a dynamic growth phase. However, as

nitrogen becomes less limiting it is the availability of water that

becomes the major limiting factor to tree growth.

122

10. TOTAL STAND VOLUME GROWTH MODELS

A major strength of the growth and yield tables and functions used in

South Australia for forest management is that they predict stand volume

growth directly. This approach is both simpler and has the potential to

minimise error propagation compared with the more common application

of separate (although potentially compatible) basal area and height

predictive models. Therefore, an objective of this current research was to

develop thinning and fertiliser response models that are compatible with

the existing models which predict stand periodic annual volume growth to

a 10 centimetre top diameter underbark.

10.1 Model formulation strategy

A system of models is required which modifies the existing stand model

for predicting periodic annual growth to allow for the combined responses

to thinning and fertiliser. It was decided to include interaction terms in the

models tested because of the potential economic benefit13 stemming from

the adoption of revised silvicultural practices that recognise such an

interaction. This strategy was not statistically defensible, as the ANOVA in

Section 9.2 showed no statistically significant interaction effects.

Nevetheless, field experience and the summarised results indicated

otherwise.

Several approaches were tried. The first adapted the Posterior

Generalised Least Squares growth model developed by Leech (1978). An

additional parameter was included in the model to represent the response

to thinning and fertiliser. It was anticipated that a relationship could be

defined between this response parameter and the relative levels and

13 An early preliminary analysis conducted by ForestrySA indicated that taking advantage of the interaction by adopting a postulated model would increase the Net Present Value of the forest estate of the order of 5 to 8%.

123

combinations of thinning and fertiliser applied in EP190. Such an

approach could then be used to model other responses including those

due to genetic improvement. A model was developed which directly

predicted annual volume growth, however, it was found to be an

unacceptably poor predictor.

The second approach was to estimate a proportional modifier of the

predictions from the growth models currently implemented in the

ForestrySA yield regulation system. The modifier used was the simple

ratio between the growth response expected from a stand thinned to the

Optimum Thinning Guide relative to a stand thinned to a different stocking

density, with or without a fertiliser treatment. Such a multiplier could be

applied together with any alternative predictor of the base volume growth.

Given the complex form of the response surfaces apparent in earlier

chapters the proposed model was fitted in two stages as a single model

form could not be readily identified and postulated in all instances. The

first stage aimed to develop a satisfactory total volume growth response

model across the six year interval and three thinning treatments, from the

time of fertilising to the next thinning at each site for each level of fertiliser. -

In the second stage, a two stage estimation process was used to

interpolate the response surface between the individual fertiliser level

models.

The need for unbiased and precise predictions of the total response

relative to the fertiliser dose and the thinning interval was paramount. The

usual thinning interval for radiata pine plantations usually ranges from five

to nine years so the response surface needed to be as accurately defined

across the six year response interval as was possible. The predictions

could then be easily adjusted to allow for growth one or two years beyond

six years or estimated for intervals less than six years.

124

I ~

An additional requirement was to develop models that adequately

predicted the response surface between the origin and the OTG+ thinning

intensity rather than just the thinning intensity spanned by the EP190 data

(from OTG-45% to OTG+25%); the origin was a known point.

10.2 Total stand volume growth models

The first phase of the model development required calculating the

dependent variable, which was the proportion of the volume growth for

each plot relative to the mean volume growth of the control plots

(Optimum Thinning Guide defined thinning and unfertilised). To help

determine any trends the proportional growth responses for each thinning

and fertiliser treatment combination were calculated and graphed to show

the volume growth as a proportion of the control, versus stand density for

each site for the three thinning treatments and 0, 75, 150, 300 kg ha-1

fertiliser treatments (Figures 10.1 to 10.3). The graphs showed differences

in the response patterns both between site and fertiliser doses but further

suggested that a staged model development would be required to ensure

that the complex response trends would be successfully accounted for.

First stage

Various modelling approaches were considered at the first stage with the

intention of modelling the whole response surface from zero stocking to

beyond the Optimum Thinning Guide stocking. Desirably, the appropriate

models should meet all of these criteria to be of practical use:

• When the relative stocking density is 0.0 the predicted relative growth

should also be 0.0 for all treatment combinations.

• When the relative stocking density is 1.0 the predicted relative growth

should also be 1.0 for the Optimum Thinning Guide and 0 kg ha-1

nitrogen treatment.

• The transition of the predicted response surface from zero relative

stocking density to the Optimum Thinning Guide defined stocking

125

should be consistent with the understanding of the relationship

inherent in the Langsaeter model.

• The parameters estimated for each fertiliser treatment should be

sufficiently consistent to allow successful modelling of the response

surface between fertiliser treatments as a two stage process.

Inspection of Figures 10.1 to 10.3 indicates that across the span of the

available data (ie -45% to +250/0 of the prescribed Optimum Thinning

Guide stocking) there is no indication for fertilised treatments of a critical

stocking value below which growth declines rapidly. This suggests that the

addition of even moderate quantities of nitrogen fertiliser moves the critical

stocking zone to less than the OTG -45% represented in the EP190 data.

However, because it is known that all the thinning and fertiliser treatment

responses can be conditioned through the point where both relative

stocking density and relative growth are 0.0 then it is reasonable to extend

the model from the OTG -450/0 stocking point to that point. This strategy

could result in prediction bias but the potential for negative bias is

preferable to restricting the model to use predictions across the span of

the data represented by EP190. The associated prediction errors are likely

to be small and for an applied forestry application it was considered

preferable to provide predictions of a stated reliability than not to provide

predictions when they were required.

The application of this approach for modelling responses from EP 190 can

be considered as a special case of density dependence in the general

field of population dynamics. There is a precedent for fitting nonlinear

functions as density dependent models for radiata pine plantations (Horne

and Robinson, 1988b). The equations tested included many of the more

common functional forms (Table 3.1) which were evaluated firstly against

the criteria established above and then if they were found to be

appropriate they were then fitted to the data.

126

Considerable effort was spent on fitting various forms of the Von

Bertalanffy model as a simplified form (Mitscherlich, 1910) had previously

been used for growth and yield modelling in South Australia (Leech,

1978). However, problems encountered with fitting various forms of both

unconditioned and conditioned versions of the Von Bertalanffy model to

the Glencoe Hill data ultimately led to the consideration of an alternative

two parameter exponential model:

Gc% = bo Notg% exp( -bl Notg%) ,

where band b are parameters to be estimated, Gc% is the proportion of o I

the volume growth relative to the control (Optimum Thinning Guide and 0

kg ha-1 nitrogen treatment) and No tg % is the stocking as a proportion of

the Optimum Thinning Guide. This model has a structure that allows a

maximum of Gc% to be reached and to then decline for increasing values

of Notg%.

The exponential model was fitted to the relative responses to each group

of plots that represented each site and fertiliser treatment. The model

fitted all fertiliser treatments at all three sites adequately. Inspection of the

parameters estimated for each site indicated trends in the values that

could be fitted in the second stage analysis. The results of fitting this

exponential model are shown in Table 10.1.

127

Figure 10.1 Headquarters: actual volume growth as a proportion of

the control relative to stand density.

0 FO Z 0 F75 0 0 F150 ~1.75 0 F300 0 Q.

0

" e:. 1.5 ..J 0 0:: I-

~ z

81.25 ~ I~ 'U 0 I-

~ W >

~ 1 ill

w 0:: J: I-~0.75 0 0:: (!) ..J < 0.5 :::l z z « ~

80.25 ~ w Q.

00 0.2 0.4 0.6 0.8 1 1.2 1.4 STOCKING PROPORTION OF OTG

128

Figure 10.2 Menzies: actual volume growth as a proportion of the

control relative to stand density.

2 0 FO -z 0 F75

0 0 F150 ~1.75 0 F300 0 a. 0 0::: ~ 1.5 ..J 0 0::: ... z 81.25 0 ... w @ >

~ 1 , w 0::: J: ... ~0.75 0::: <!) ..J < ~ 0.5 z < ()

§0.25 C2 w a.

00 0.2 0.4 0.6 0.8 1 1.2 1.4 STOCKING PROPORTION OF OTG

129

Figure 10.3 Glencoe Hill: actual volume growth as a proportion of the

control relative to stand density.

0 FO - 0 F75 z 0 0 F150 ~1.75 0 F300 0 0.

~ 0 IX: I e:. ...I 0 I ! IX: ....

~ z

81.25 0 ~ J .... ID w >

If I ~ 1 ..J W IX: :x: I-

~0.75 0:':: (!) ...I «

0.5 ::> z z « u 0 00.25 C2 w 0..

0.6 0.8 1 1 .2 1.4 STOCKING PROPORTION OF OTG

130

rF"""I'

Table 10.1 Total stand volume growth: first stage exponential

models.

Headquarters FO F75 F150 F300

b 2.850 3.309 3.724 4.003 0

(SE) (0.6294) (0.2041 ) (0.3715) (0.4028)

b 0.984 1.050 1.136 1.112 I

(SE) (0.2198) (0.0619) (0.1014) (0.1019)

Menzies FO F75 F150 F300

b 3.178 3.039 2.772 3.682 0

(SE) (0.6278) (0.4837) (0.5086) (0.3749)

b 1.138 0.982 0.861 1.192 1

(SE) (0.2009) (0.1584) (0.1797) (0.1044)

Glencoe Hill FO F75 F150 F300

b 2.137 4.220 4.371 4.577 0

(SE) (0.3291 ) (0.4010) (0.5381 ) (0.3497) b 0.750 1.270 1.151 1.051

I

(SE) (0.1488) (0.0968) (0.1253) (0.0767)

131

Second stage

Keeping the model development separate for each site allowed the most

appropriate model to be fitted to the values of each parameter for each

site 14. The polynomial model forms considered for the second stage were:

p==a+bxP

p==a+bxP+cxP2

p == a + b x P + C X p2 + d X p 3

Where p == b or p == b , a, b, c, d are parameters to be estimated and F is o I

the fertiliser dose.

Results

For all sites, quadratic models adequately fitted both first stage

parameters. On the basis of the adjusted coefficient of determination the

fit achieved for the hi parameter at Glencoe Hill was poorer than achieved

at the other sites. However, the fit was adequate and alternative simple

model forms were no better, so the model was adop ~d. -

Both unweighted and weighted versions of linear regression were applied

in the second stage, the unweighted models providing better predictions.

14 A unified second stage model was also developed using the variables: stand age at time of fertiliser application, and stand volume at age 9.5, to differentiate between the three sites. However, compared with the individual site models, this model was a poor predictor of total stand volume and was discounted. Perhaps this reflects true site differences or perhaps error differences in the Optimum Thinning Guide stocking between sites.

132

The results of fitting the preferred unweighted models to the parameter

estimates for each site are shown in Table 10.2.

133

--

Table 10.2 Total stand volume growth: second stage exponential models.

Headquarters a b c R2 MSE

b 2.8386 0.0076 -1.238.10-5 0.9937 0.0016 l)

(SE) (0.0383) (0.00001) (0.200.10.5)

b 0.9770 0.0015 -0.339. 10-5 0.8716 0.0006 I

(SE) (0.0234) (0.0004) (0.122.10.5)

-

I Menzies b R2 MSE

I

a c I

b 3.2279 -0.0062 2.555.10-5 0.9360 0.0304 i

0

(SE) (0.1670) (0.0028) (0.874.10.5)

b 1.1508 -0.0036 1.257.10.5 0.9122 0.0020 I

(SE) (0.0428) (0.0007) (0.224.10.5)

Glencoe Hill a b

\ C JI2 MSE

b 2.2925 I 0.0244 I -5.658.10.5 0.7710 0.2954 0

I .(SEl (0.5208)

i (0.0088) (2.725.10.5)

I

b 0.8060 0.0053

!

-1.528. 10.5 0.2243 0.0384 I

j S.SL---,----~ 1877) (0.0032) (0.982.10.5)

11. PERIODIC ANNUAL VOLUME GROWTH MODELS

The total volume growth response models developed were of limited

practical use as they were based on a fixed six-year period between

fertiliser application and the next thinning. In practice operational thinning

intervals can vary from five to nine years after fertilisation with a few

operations outside this range. So there was a requirement to develop a

system of models to predict the periodic annual volume growth of the

thinning and fertiliser treatment combinations for each of the three sites.

Essentially the models developed would need to predict the fertiliser

response pattern.

To maintain consistency with the predictions from the existing South

Australian growth and yield models it was necessary to estimate the

annual volume growth. However, the data for each plot consisted of six

annual basal area measurements but only two volume measurements six

years apart. Could the proportional increases in basal area be used to

represent the proportional increase in plot volume?

An understanding of the way tree stems respond to nitrogen fertilisation

provided a useful basis from which to consider the relationship between

stand basal area and volume growth. In a separate study O'Hehir (2000) 15

showed that for fertilised trees, the annual change in basal area at a tree

level was not exactly in phase with the annual change in tree volume.

Immediately following fertilising there appeared to be concentration of

initial growth around the base of the green crown meaning that volume

growth was initially greater than that lower on the stem, as would be

indicated by basal area measurements alone. However, it was concluded

that a correction was unnecessary because the Regional Volume Table

was sensitive enough to take account of the response and the magnitude

15 Appendix IV

135

of the stem shape change was so slight as to be practically insignificant.

Consequently the proportion of basal area periodic annual growth could

be used to estimate the volume area periodic annual growth.

Previous experience suggested that it was easier to model responses as a

proportion of the control treatment as this provided some dampening of

the effect of climatic variation (particularly rainfall) on growth when

compared with modelling absolute responses. A two stage estimation

process was applied to modelling the responses because the time series

nature of the growth data was expected to cause serial correlation

between measurements.

11.1 First stage

The first stage periodic annual growth models should meet the following

criteria to be of practical use:

• In the first year of fertiliser application the predicted proportional

periodic annual growth should be 0.0.

• At the conclusion of the sixth year after the fertiliser application the

predicted proportional periodic annual growth should be 1.0 ...

• Beyond the sixth year after the fertiliser application the model should

behave in an asymptotic manner to allow reasonable predictions of

proportional periodic annual growth up to at least ten years after

fertiliser application.

The cumulative response per year was modelled for each year between

the application of fertiliser and the next thinning. Inspection of graphs of

the cumulative responses for each treatment combination for each site

were sigmoid in shape so a conditioned form of the Von Bertalanffy model

was chosen as the most appropriate model form 16. This model form had

16 The use of logit and lor probit models was contemplated but these would only be useful for modelling growth up to six years after fertiliSing and not beyond as was required for potential use. Polynomial models were fitted as part of the investigation but being

136

the advantage of being able to be conditioned both through the points

T/ = 0 and Gc% = 0 and Tf = 6 and Gc% = 1. The model fitted for each

plot on all sites was:

Where Gc% is the proportion of the periodic annual volume growth

relative to the control (Optimum Thinning Guide, a kg ha-1 nitrogen

treatment), TI is the elapsed time since fertilisation (in years), bo and

bl are parameters to be estimated.

11.2 Second stage

The first stage parameters were graphed against the stocking as a

proportion of the Optimum Thinning Guide stocking for each plot by each

site and fertiliser treatment and it was evident that a linear relationship

could be fitted in the second stage.

The model forms considered for the second stage were: -

p = a+bx Notg%

p = a+bx Notg%+Cx Notg%2

p=a+dxF

p=a+dxF+exF2

p = a+bx Notg%+cx Notg%2 +dx F +ex F2

p = a +bx Notg% +cx Notg%2 +dx F +ex F2 + Ix Notg%x F

Where p = bo or p = bl are the first stage parameters, Q, b, c, d, e, I are

parameters to be estimated, Notg% is the stocking as a proportion of the

Optimum Thinning Guide stocking and F is the nitrogen fertiliser dose. All

parameters were subjected to a Student's t test of significance and were

unconditioned exhibited the undesirable characteristic of not necessarily returning a value

137

excluded from the model if found to be not significantly different from zero.

The fitted second stage equations are shown in Table 11.1. Although

consistent models between sites would have been desirable, applying the

same model form to the Menzies data as to the other two sites gave a

noticeably poorer fit and so the separate model form was retained.

of 1.0 six years after fertiliser was applied.

138

1 Table 11.1 Periodic annual growth model: second stage parameters.

Headquarters a b c d e R2 MSE

b 0.3278 -0.2851 0.0020 -4.883.10-6) 0.6481 0.0042 0

(SE) (0.0451 ) (0.0445) (0.0004) (1.066.10-6) i

b 0.1515 -0.1043 0.0017 -3.759.10-6) 0.5218 0.0035 !

I

(SE) (0.0414) (0.04081 (0.0003) (0.977.10-6)

Menzies a b c d e R2 MSE

b 0.3238 -0.1520 0.0009 -2.700.10-6 0.9284 0.0032 0

(SE) (0.0660) (0.0521 ) (0.0003) (0.919.10-6)

b 0.3402 -0.1309 0.0009 -2.374.10-6 0.9683 0.0019 I

(SE) (0.0514) (0.0405) (0.0002) ( 0 .715.1 O-B)

Glencoe Hill I

a b c d R2 MSE ! e !

b 0.5762 -0.3874 0.0016 -4.046.10-6 0.6558 0.0083 !

0

(SE) (0.0421 ) (0.0341 ) 0.0004} (1.087.10-6)

b 0.4579 -0.2642 0.0012 -2.831.10-6 0.7467 0.0027 I

(SE) (0.0239) (0.0194) 10.0002) (0.617.10-6)

139

III

12. STAND SUBPOPULATION VOLUME GROWTH MODELS

The models developed in the previous sections for predicting the

interaction between thinning and fertiliser responses can only be applied

at a total stand level. However, there is a requirement to be able to predict

the growth of the trees that are to be removed at the next thinning (the

thinnings elect) separately from the growth prediction for the total stand.

For yield scheduling reasons models need to be developed which predict

the growth of the thinnings elect between the year of inventory and the

year when they are thinned.

For consistency with the stand volume response models already

developed, the variable of interest used was the total six year volume

response for each plot relative to the response of the OTG, unfertilised

control plots. The aim was to provide a basis for adjusting the growth

calculated for the thinnings elect for situations where either the intended

thinning intensity departed from the Optimum Thinning Guide and/or

fertiliser has been applied to the stand. This model would make available

more precise estimates of the volume of the thinnings elect for short term

yield regulation planning in South Australian plantations.

A two-stage model development was considered appropriate for the same

reasons identified in the description of the total stand model development.

12.1 First stage

The first stage thinnings elect growth models should meet the following

criteria to be of practical use:

• When no thinnings are removed the predicted relative growth should

be 0.0.

140

i

j

-

• When all trees are removed the predicted relative growth should be

1.0.

• The parameters estimated for each fertiliser treatment shou Id be

sufficiently consistent to allow successful modelling of the response

surface between fertiliser treatments as a two-stage process.

Scatter plots of the variable of interest against the relative average

stocking indicated that a relatively simple model would fit the data for most

fertiliser doses. It was found that a satisfactory predictive model could be

fitted to the plot data at the first stage using nonlinear least squares:

Ge6 = (YesJh1

Gt6 Yts

Where Ge6 is the six year growth of the thinning elect; Gt6 is the six year

growth of the total stand; Yes is the volume yield of the thinnings elect at

the start of the growth period; Yts is the volume yield of the total stand at

the start of the growth period and b is a parameter to be estimated using 1

non linear least squares. This model structure and form was found to be

adequate for each of the three sites.

12.2 Second stage

I nspection of scatter plots of the first stage model coefficients showed that

a relationship appeared to exist between the variable of interest and the

relative stocking variable. Simple linear regressions were fitted to the b I

coefficient, initially as a combined model for all sites, and then for

individual sites. The intercept term was removed from the models as it

was not Significantly different from zero. The alternatives models fitted and

evaluated were:

141

p=bxNotg%

p = bxNotg% +ex Notg%2

p=dxF

p = dxF+ex F2

p = bx Notg% +ex Notg%2 +dx F +ex F2

p = bx Notg% + ex Notg%2 + d x F + ex F2 + f x Notg% x F

Where p = log(b1

) which is the transformed first stage parameter,

b,c,d,e,f are parameters to be estimated, Notg% is stocking as a

proportion of the Optimum Thinning Guide and F is the nitrogen fertiliser

dose (nitrogen kg ha-1) applied one year after thinning.

There was also an attempt made to develop a unified model which

allowed predictions of the growth of the thinnings elect across all three

sites using the variable YIO, defined as the total production volume yield

at age 10, to separate the sites. The models fitted were:

p = b x Notg% + g x Yl 0

P = b x NotgO/o + h x Notg% x YI 0

Where g and h are parameters to be estimated.

All variables were evaluated for significance against the standard error of

the coefficient using Student's t test. The objective was to obtain the most

powerful predictive model for each parameter at each site, and

accordingly the alternative models were compared on the basis of the

mean square error and the adjusted coefficient of determination. The most

appropriate second stage equations are shown in Table 12.1 including the

unified model which was found to be a satisfactory predictor. Although

consistency would have been desirable the poorer fits suggested that it

was more appropriate to use inconsistent model forms.

142

I

Table 12.1 Thinnings elect growth model: second stage parameters.

Headquarters a b c d e f R2 MSE

log(b, ) 0.1705 -0.0738 0.7731 0.0022

(SE) (0.0438) (0.0456)

Menzies a b c d e f R2 MSE

log\b, ) 0.0644 -2.072.10-6 0.0088 0.7937 0.0029

JSE) (0.0177) iO.515.10-~ JO.0002)

Glencoe Hill J

a b c d e f R2 MSE :

log(b, ) 0.1616 -0.0662 -0.0004 1.177.10-6 0.5470 0.0036 i

(SE) (0.0471) (0.0331 ) (0.0002) (0.718.10-6)

Unified model b h R2 MSE

log(b] ) 0.0459 0.0004 0.6603 0.0034

(SE) (0.0094) (0.0001)

143

I

13. MODEL PERFORMANCE AND SYNTHESIS

The EP190 data set does not provide sufficient data to support the

development of a unified response surface across multiple sites. However,

the data that were available, together with a theoretical and applied

understanding of the likely mechanisms that are operating, provided a

useful and sound basis for the development of reliable predictive models.

13.1 Total stand volume growth models

The total stand growth models are shown for each of the three sites as

two-dimensional surfaces (Figures 13.1 to 13.3). The fertiliser responses

with increasing dose appear to be additive for the Headquarters and

Glencoe Hill sites, whereas Menzies was modelled as an increasing

response to 200 kg ha-1 and then decreasing with the 300 kg ha-1 dose.

These attributes of the models concur with the trends evident in the data.

The two-dimensional models also provide some insight into the position of

the critical stocking point.

The modelled response surface for Headquarters shows that the addition

of even moderate quantities of nitrogen causes the critical stocking point

to coincide with a lower stand density which indicates that there was a

thinning and fertiliser interaction at this site. The implication for applied

forest management is that the stands such as those at Headquarters can

be thinned to a stocking density below that prescribed by the Optimum

Thinning Guide, and with the application of nitrogen fertiliser the

productivity can still be maintained at a maximum level.

The modelled surface for Menzies does not clearly indicate that the critical

stocking point is changed by the addition of nitrogen fertiliser so an

interaction between thinning and fertiliser is not evident. However, the

responses to fertiliser at this site are relatively much smaller than the

144

>

responses at the other two sites, and any interaction would be more

difficult to detect.

The response surface for the control treatment at Glencoe Hill shows the

relationship between stocking density and stand growth more extreme

than evident at the other sites. The growth rate at densities less than the

Optimum Thinning Guide is progressively reduced, clearly indicative of a

Langsaeter surface. It appears that stands on less fertile sites are less

able to maintain growth with lower stockings than are those on higher

fertility sites. This situation is relieved by the addition of even a small

quantity of nitrogen fertiliser and the resulting response indicates that the

point of critical stocking moves to a lower level of stand density.

The form of the modelled stand density and total stand growth surfaces

suggests that for stands with a capacity to respond to the addition of

nitrogen fertiliser (represented by the Headquarters and Glencoe Hill sites)

that a stocking lower than the Optimum Thinning Guide is optimum when

fertiliser is applied. It appears that for stands with less capacity to respond

to additional nitrogen that the Optimum Thinning Guide stocking may still

be appropriate when fertiliser is applied (represented by Menzies).

Given the differences between the sites and resulting models, the

application of the models developed for each of the three EP190 sites has

to be generalised so they can be implemented in the South Australian

yield regulation system.

The models developed for Headquarters can be applied to young age

plantations (say 10 to 30 years old), that are established on second or

subsequent rotation sites, of Site Quality ranging from IV to V. The

Menzies models can be used with older plantations (say 31 years or older)

of Site Quality III or better. The Glencoe Hill models can be used for older

plantations (say 31 years or older), of Site Quality poorer than V.

145

These recommendations exclude substantial areas of the ForestrySA

resource, part because the Hutchessons data could not be used, and the

three remaining EP190 sites are not representative of all South Australian

radiata pine stands. However, practical forest management requires that

the best estimates are to be available and so the implementation of the

models must cover all plantations. Accordingly, the application of the

models can be extrapolated to cover the whole plantation resource; by

using the Menzies models to represent plantations of ages 10 to 30, of

Site Quality better than III; the Headquarters models can include first

rotation plantations, plantations aged 31 and older and Site Qualities

poorer than IV; and, the Glencoe Hill models for Site Qualities poorer than

V.

146

p

Figure 13.1 Headquarters: actual and predicted volume growth as a

proportion of the control relative to stand density.

2

Z Q

~1.75 o 0.. o Q! 0..

::;- 1.5 o Q! ..... z 81.25 o ..... w >

3 w Q!

1

J: ..... ~0.75 Q! (!) ...I <t ~ 0.5 z <t u

80.25 Q! w 0..

0.2 0.4 0.6 0.8

o o o o

1

ACTUAL FO ACTUAL F75 ACTUAL F150 ACTUAL F300 MODELLED FO MODELLED F75 MODELLED F150 MODELLED F300

1.2 1.4 STOCKING PROPORTION OF OTG

147

Figure 13.2 Menzies: actual and predicted volume growth as a

proportion of the control relative to stand density.

-z o ~1.75 o a.. o et:: a.. ::T 1.5 o et:: ~ z 81.25 o ~

w > 5 1 w et:: J: ~

~0.75 et:: C!) ..J « ~ 0.5 z « ~

gO.25 a::: w a..

l] o o

ACTUAL FO ACTUAL F75 ACTUAL F150 ACTUAL F300 MODELLED FO MODELLED F75 MODELLED F150 MODELLED F300

0.2 0.4 0.6 0.8 1 1.2 1.4 STOCKING PROPORTION OF OTG

148

..

Figure 13.3 Glencoe Hill: actual and predicted volume growth as a

proportion of the control relative to stand density.

2

-z o ~1.75 o a.. o c:: e:.. ..J o c:: I­z

1.5

81.25 o I-W >

~ w c:: :r:

1

I-

~0.75 c:: C) ..J <{

~ 0.5 z <{ ()

gO.25 c:: w a..

0.2 0.4 0.6 0.8

o o o o

1

ACTUAL FO ACTUAL F75 ACTUAL F150 ACTUAL F300 MODELLED FO MODELLED F75 MODELLED F150 MODELLED F300

1.2 1.4 STOCKING PROPORTION OF OTG

149

13.2 Periodic annual growth models

The periodic annual growth models developed represent four-dimensional

surfaces and are difficult to depict graphically. The four variables included

are stand stocking, fertiliser dose, time since the application of fertiliser (in

years), and the variable of interest which is the annual volume growth to

10 centimetres underbark diameter as a proportion of the control (OTG, 0

kg ha-1 nitrogen treatment). Two-dimensional surfaces that compare the

actual annual responses with those modelled based on the six-year

growth provide a useful visualisation (Figures 13.4 to 13.12).

The modelled response surfaces to some extent smooth the annual

growth responses, particularly at Glencoe Hill where all the responses

peaked strongly in the third year after the application of fertiliser. At this

site the third year coincided with a period of above average rainfall, which

appeared to provide exceptional growing conditions.

The response patterns for the various stand density treatments were not

completely consistent across the three sites and even within sites. All

three postulated response patterns which are described in Chapter 6 are

evident across the site, stand density and fertiliser dose combinations and

no firm conclusion can be made as to the existence of a single response

pattern which is independent of these factors. Table 13.1 shows the site,

stand density and fertiliser dose combinations together with the apparent

response pattern. Where no one pattern could be discerned the possible

patterns have been indicated. Beyond six years what initially appeared to

be a high response pattern may revert to a most probable or even a low

response.

One conclusion that can be drawn is that the response pattern appears to

be subject to a stand density and fertiliser interaction. The high response

150

p

pattern was only associated with relatively high stocking densities

indicating that stands need to be sufficiently stocked to maintain a fertiliser

response beyond six years. This result implies that water availability at

Menzies and Glencoe Hill was adequate to support the ongoing fertiliser

response in the OTG+ and OTG treatments. The low response pattern

was only evident in some treatments at Headquarters, perhaps indicating

the relatively high nutrient and water requirements of a young stand, which

constrains ongoing response to fertiliser as competition between trees

increases more quickly.

The trends indicated by the models show that young, dynamically growing

stands (represented by Headquarters) will tend towards the low response

pattern. I n such stands there may be some potential for shortening

thinning intervals, instead of, or more likely in addition to reducing the

stand density to a level below the Optimum Thinning Guide by thinning.

Older stands that have been fertilised and maintained at stocking

densities between the OTG- and OTG treatments (Menzies and Glencoe

Hill) appear more likely to follow the most probable response pattern. In

these situations it is considered more appropriate to maintain the current

thinning interval and to thin the stand to a density below the Optimum

Thinning Guide.

Where the objective is to maximise the volume growth of stem wood,

irrespective of the resulting piece size a growth response can be

maintained beyond six years by the application of a relatively large dose of

nitrogen to a stand overstocked relative to the Optimum Thinning Guide

(represented by the OTG+ treatments at Menzies and Glencoe Hill).

The implementation of the periodic annual growth model should conform

to a generalisation of the models. Where it is appropriate to use the

Headquarters-based total stand model, the low response model should be

used for stands below the Optimum Thinning Guide stocking. There is

151

..

justification to use the most probable model for stands at or above the

Optimum Thinning Guide stocking represented by Headquarters and all

other stands represented by Menzies and Glencoe Hill. There are

insufficient time series data available to this interim study to confirm the

existence of a genuine Type 2 response at either Menzies or Glencoe Hill.

The use of the most probable model will provide predictions of a high

precision over short time periods without risking over estimation and over

commitment of the resource in strategic plans.

13.3 Combined total stand volume growth and periodic annual growth models

Combining the total stand volume growth and periodic annual growth

models represents the usual way in which the models will be implemented

for predicting growth and yield. Firstly the total stand growth model is used

to predict the total proportional six year response relative to the

appropriate stand density and fertiliser combination. Secondly, the

periodic annual growth model is used to partition the response across a

six year period (and for additional years beyond when necessary). Figures

13.13 to 13.15 show the resulting predicted cumulative growth (m3 ha-1)

response surface for each EP190 site, stacked by year, for each year of a

six year growth period.

152

ax

Table 13.1 Stand density and fertiliser growth response pattern by

site.

Site Thinning Nitrogen dose lkg ha-1) Response pattern Headquarters OTG- 0 low

75 150 300 low/probable

OTG 0 nil 75 low/probable 150 300 probable

OTG+ 0 low 75 150 300 low/probable

Menzies OTG- 0 no response 75 150 300 no response/probable

OTG 0 nil 75 probable 150 300 no response

OTG+ 0 no response 75 high 150 300

Glencoe Hill OTG- 0 no response 75 probable 150 300

OTG 0 nil 75 high 150 300

OTG+ 0 no response 75 high 150 300

153

Figure 13.4 Headquarters: OTG .. actual versus predicted annual

volume growth.

-z o ~1.75 o D. o ~ D. :; 1.5 o ~ I­z

81.25 o ..... w > ~ 1 w ~

::t: ..... 3:0.75 a ~ C.!) -I « ~ 0.5 z « ()

80.25 ~ W D.

1 2 3 4

[ I D D [-I

5

ACTUAL OTG-,FO ACTUAL OTG-,F75 ACTUAL OTG-,F150 ACTUAL OTG-,F300 MODELLED OTG-,FO MODELLED OTG-,F75 MODELLED OTG-,F150 MODELLED OTG-,F300

6 7 ELAPSED TIME SINCE FERTILISED (YEARS)

154

»

Figure 13.5 Headquarters: OTG actual versus predicted annual

volume growth.

2 -z o ~1.75 o Q. o 0:: ~ -I o 0:: I­z

1.5

81.25 o J-W > ~ 1 w 0:: ::J: I-

~O.75 0:: C> -I « ~ 0.5 z « ~

gO.25 ~ w a..

o ACTUAL OTG,F75 o ACTUAL OTG,F150 o ACTUAL OTG,F300

MODELLED OTG,F75 MODELLED OTG,F150

---- MODELLED OTG,F300

1 2 3 4 5 6 7 ELAPSED TIM E SINCE FERTILISED (YEAR)

155

..

Figure 13.6 Headquarters: OTG+ actual versus predicted annual

volume growth.

-z 0

~1.75 0 0-0 0::: 0-- 1.5 ..J 0 0::: t-z 81.25 0 t-W > i= 1 ~ W 0::: J: t-~0.75 0::: (!)

..J « 0.5 :J

z z « u

gO.25 0::: w 0-

00 1

[I ACTUAL OTG+,FO D ACTUAL OTG+,F75 D ACTUAL OTG+,F150 [) ACTUAL OTG+,F300

MODELLED OTG+,FO MODELLED OTG+,F75 MODELLED OTG+,F150 MODELLED OTG+,F300

23456 7 ELAPSED TIME SINCE FERTILISED (YEARS)

156

...

Figure 13.7 Menzies: OTG- actual versus predicted annual volume

growth.

2

-z o ~1.75 o 0.. o ~ 0..

::J" 1.5 o ~ t­z

81.25 o t-UJ > i= :3 UJ ~

1

:::r:: t-~0.75 o

" C) -I <C ~ 0.5 z <C ()

80.25 " W 0..

o ACTUAL OTG",FO o ACTUAL OTG .. ,F75 o ACTUAL OTG .. ,F150 o ACTUAL OTG-,F300

------ MODELLED OTG",FO MODELLED OTG .. ,F75

--- MODELLED OTG .. ,F150 MODELLED OTG .. ,F300

00 1 2 3 4 5 ELAPSED TIME SINCE FERTILISED (YEARS)

157

Figure 13.8 Menzies: OTG actual versus predicted annual volume

growth.

-z 0

~1.75 0 a.. 0 ~ a.. - 1.5 ..J 0 ~ I-z 81.25 0 I-W > i= 1 ~ w ~

J: I-

~0.75 ~ (!)

..J « 0.5 ::>

z z « u

80.25 ~ w a..

00 1

o ACTUAL OTG,F75 o ACTUAL OTG,F150 [I ACTUAL OTG,F300

MODELLED OTG,F75 MODELLED OTG,F150 MODELLED OTG,F300

23456 7 ELAPSED TIME SINCE FERTILISED (YEARS)

158

>

Figure 13.9 Menzies: OTG+ actual versus predicted annual volume

growth.

2 -z o ~1.75 o Q..

o 0:: Q..

::; 1.5 o 0:: ..... z

81.25 o ..... w > i= :) W 0::

1

:c ..... ~O.75 0:: (!) ..J « i 0.5 z « u

gO.25 0:: w 0..

o o o o

ACTUAL OTG+,FO ACTUAL OTG+,F75 ACTUAL OTG+,F150 ACTUAL OTG+,F300 MODELLED OTG+,FO MODELLED OTG+,F75 MODELLED OTG+,F150 MODELLED OTG+,F300

1 2 3 456 7 ELAPSED TIME SINCE FERTILISED (YEARS)

159

..

Figure 13.10 Glencoe Hill: OTG- actual versus predicted annual

volume growth.

2

-z 0

~1.75 0 0-0 0::: 0-- 1.5 ..J 0 0::: .... z 81.25 0 .... w > i= 1 ~ W 0::: ::I: .... ~0.75 0::: (!)

..J <

0.5 :::> z z < u

80.25 0::: w 0-

00 1 2 3 4

[ I o o [ I

5

[II

ACTUAL OTG-,FO ACTUAL OTG-,F75 ACTUAL OTG-,F150 ACTUAL OTG-,F300 MODELLED OTG-,FO MODELLED OTG-,F75 MODELLED OTG-,F150 MODELLED OTG-,F300

6 7 ELAPSED TIME SINCE FERTILISED (YEARS)

160

-

Figure 13.11 Glencoe Hill: OTG actual versus predicted annual

volume growth.

2 -z o ~1.75 o a. o 0::: a. ::; 1.5 o 0::: ..... z

81.25 o ..... w ~ ..... S w 0::: :r:

1

I-

~O.75 0::: (!) ..J « ~ 0.5 z « u

QO.25 0::: w a..

o o o

ACTUAL OTG,75N ACTUAL OTG, 150N ACTUAL OTG,F300 MODELLED OTG,F75 MODELLED OTG,F150 MODELLED OTG,F300

1 2 3 4 5 6 7 ELAPSED TIME SINCE FERTILISED (YEARS)

161

....

Figure 13.12 Glencoe Hill: OTG+ actual versus predicted annual

volume growth.

2

-z o ~1.75 o a. o 0:: a. :; 1.5 o 0:: .... z

81.25 o .... w > 5 1 w 0:: :r: .... ~0.75 0:: (!)

...J « i 0.5 z « (.)

80.25 ii: w a.

-----------

1 2 3 4

II o o LI

5

ACTUAL OTG+,FO ACTUAL OTG+,F75 ACTUAL OTG+,F150 ACTUAL OTG+,F300 MODELLED OTG+,FO MODELLED OTG+,F75 MODELLED OTG+,F150 MODELLED OTG+,F300

6 7 ELAPSED TIME SINCE FERTILISED (YEARS)

162

.... ....

Figure 13.13 Headquarters: predicted annual volume growth.

163

Figure 13.14 Menzies: predicted annual volume growth.

164

~ « w

~ :::t -(II') :e -:::t ~ ;: o 0:: <.!) ..J « ::J z z « ()

c o i:'2 w a.

....

Figure 13.15 Glencoe Hill: predicted annual volume growth.

165

~ « w

~ :I: -C")

~ :I: I-~ o ~ C) ..J « :::> z z « ~ c o ~ w a.

--

13.4 Stand sub population growth model

The stand sub population growth models predict the response of the

thinnings elect to the various combination of thinning and fertiliser. Few, if

any, models of this kind have been reported in the forestry literature.

Figures 13.16 to 13.18 compare the actual growth responses (with

associated standard errors) with the predicted growth responses. The

predicted responses are based on predicted rather than actual total stand

volume growth and so reflect the level of precision which could be

expected in the application of these two models in combination.

Inspection of Figure 13.16 shows that the predictions for Headquarters fall

within the standard error ranges for all the treatment combinations except

for the OTG- and nil fertiliser treatment. The prediction for that particular

treatment is approximately 100/0 less than the actual. However, overall the

model is an acceptable predictor with no indication of any bias.

Figure 13.17 compares the actual and the predicted treatment responses

for Menzies. There is less differentiation between the OTG and OTG+

treatment responses at Menzies than at the other two sites. The actual

responses are clustered and the model generally predicts the responses

with a high level of precision. The OTG- treatment exhibits some variation

between the growth response to the 300 kg ha-1 nitrogen and the other

fertiliser doses. This model predicts the response to a high level of

precision. The OTG- and 150 kg ha-1 nitrogen treatment response is

predicted only just outside of the standard error range with a negative

bias, of the order of 10%•

The model for Glencoe Hill predicts the growth response of the thinnings

elect with a relatively high level of precision (Figure 13.18). The model

166

appears to be an unbiased predictor with the predictions for all except one

treatment combination falling within the span of the standard errors. The

model over estimates the growth response of the OTG and nil fertiliser

treatment by approximately 150/0. However, the predicted response pattern

is similar for all treatment combinations indicating that the model is

appropriate overall.

Overall there is a reasonable level of agreement between the actual and

predicted growth for each site, thinning and fertiliser combination

indicating that the predictions are acceptably precise. The models for the

thinnings elect can be implemented on the same basis as those for the

total stand volume, both in terms of the plantations of which they are

representative and the use of the periodic annual growth model. The

thinnings elect model will be useful in predicting short term log availability

as currently no allowance is made for the addition of fertiliser.

167

Figure 13.16 Headquarters: predicted thinnings elect total volume

growth relative to stand density.

100

90

<-~ 80 (II')

:E -:I: 70 ~

3: 0 60 ~ (!)

:I: 50 ~

3: 0 40 ~ (!)

~ 30 « w >- 20 ~ en

10

0

ACTUAL FO <> ACTUAL F75 <> ACTUAL F150 <> ACTUAL F300 • MODELLED FO • MODELLED F75 • MODELLED F150

---~-~ MODELLED F300

0.6 0.8 1 1.2 1.4 STOCKING PROPORTION OF OTG

168

;:::

Figure 13.17 Menzies: predicted thinnings elect total volume growth

relative to stand density.

100 (; ACTUALFO <> ACTUALF75

90 <> ACTUAL F150 <> ACTUALF300

~ .~~~ ......• ~ .. ~ .. --. MODELLED FO

• MODELLED F75 80 • MODELLED F150 « . - • MODELLED F300

:I: 70 -('I) :E -:I: 60 I-3: 0 50 0:: (!)

0:: 40 « w >- 30 ~ en

20

10

0 0.6 0.8 1 1.2

STOCKING PROPORTION OF OTG

169

--

c

,"

Figure 13.18 Glencoe Hill: predicted thinnings elect total volume

growth relative to stand density.

80 -« ~ 70 ('I')

~ -J: 60 I-~ 0 50 0::: C)

0::: 40 « w >- 30 ~ UJ

20

10

0

.~, ACTUAL FO <> ACTUAL F75 <> ACTUAL F150 <> ACTUAL F300 .. MODELLED FO • MODELLED F75 ~~ MODELLED F150 -~-~.- MODELLED F300

0.6 0.8 1 1.2 1.4 STOCKING PROPORTION OF OTG

170

po

14. HYPOTHESISED TOTAL STAND RESPONSE MODEL

Having developed a series of predictive models it is appropriate to

consider the implications of the trends indicated by these models for

understanding the form of the Langsaeter model. Although the application

of nitrogen and phosphorus based fertiliser is expected to raise the

periodic annual volume growth of the Langsaeter Plateau (Langsaeter,

1941) up until now it has been unclear whether the shape or position of

the plateau would change with thinning.

A simplified representation of the Langsaeter model is useful for

illustrating the possible effect on stand growth (volume and/or basal area)

of the alternative interactions between stand density and fertiliser dose.

The position of the Optimum Thinning Guide prescribed stocking with no

fertiliser applied post thinning can be represented as point A on Figure

14.1. Points B, C and 0 depict the alternative stand growth responses to

thinning and fertiliser application in combination and the resulting change

in the level of the critical stocking.

The data point B represents an additive response when there is no

fertiliser and thinning interaction and the application of fertiliser shifts the

critical stocking pOint vertically. Points C and 0 illustrate a multiplicative

interaction between thinning and fertiliser; point C where the interaction

reduces the critical stocking and 0 where the critical stocking is increased.

The combination of the results and the predictive models from the three

EP 190 sites indicate that the interaction model indicated by point C

appears to be operating at Headquarters and Glencoe Hill. It is unclear

whether the interaction model is operating at Menzies; either it is not

operating or the fertiliser response is so weak that its effect cannot be

discriminated. Given the comparisons between sites the latter is the more

171

.....

likely. There is no evidence of the model represented by point 0 operating

at any site.

An alternative to the model proposed by Langsaeter is shown in Figure

14.2. The shape of the response surface is consistent with the exponential

model that was fitted to the total stand response data. This surface is

similar to that proposed by Smith (1986) and appears to fit the data from

EP190 better than the model proposed by Langsaeter. However, the

previous comments relating to the position of the critical stocking point on

the Langsaeter model remain unchanged as it would appear that a stand

density below the Optimum Thinning Guide may be appropriate when

stands are fertilised with nitrogen and have the capacity to respond.

EP190 has provided data used to fit a series of models that predict stand

growth under various combinations of stand density and fertiliser dose.

These are extremely useful and in some part a unique series of models.

However, from these models alone it is not possible to define an absolute

combination of stand density and fertiliser dose which can be defined as

the most appropriate.

-Further evaluation of the implications at a stand and forest level of the

predictions needs to be undertaken once the models have been

implemented in the ForestrySA yield regulation system. This will allow

financial data to be incorporated into the analysis and a series of

silvicultural prescriptions can be formulated to meet the forest

management objectives.

172

--

Figure 14.1 Simplified Langsaeter model showing three postulated

thinning and fertiliser interaction models.

c B o

growth

stocking

Figure 14.2 Alternatives to simplified Langsaeter model.

c B

growth

stocking

173

-

15. SUMMARY AND CONCLUSIONS

The objective of this thesis was to determine if a thinning and fertiliser

interaction existed in radiata pine stands in the south east of South

Australia using the information from EP190 and, if an interaction was

found to exist, to develop models to predict the interaction. The results

indicated that an interaction existed at the Headquarters and Glencoe Hill

sites. However, at Menzies the data were inconclusive: there is either no

interaction or the interaction is too small to be able to discriminate it.

The analysis of the results indicated that the interaction response surfaces

were complex and operated in greater than four dimensions. This

necessitated the development of a series of integrated sub models to

predict the interaction responses at each of the experimental sites.

The first submodel predicts the total volume response due to thinning and

fertiliser including the interaction. This submodel incorporates a series of

Langsaeter type responses to stand density and predicts the response

surfaces for the 0, 75, 150 and 300 kg ha-1 nitrogen dose levels.

The second submodel partitions the total volume response surface on an

annual basis for up to six years after the fertiliser application and beyond if

needed.

The third submodel predicts the response of the trees that are to be

thinned in the next commercial thinning operation (thinnings elect) due to

the interaction between the thinning and fertiliser treatments. This

submodel also implies a series of Langsaeter type responses specific to

the thinnings elect.

When combined, the predictions from the three submodels provide

predictions with improved precision relative to the South Australian yield

174

sa

regulation system. They can therefore provide the basis for better forest

management planning and so increase economic profitability through

more efficient use of fertiliser.

The results of this large and complex experiment, possibly one of the

largest in the world, are less conclusive than might have been expected

when the experiment was established. This indicates how difficult it is to

establish and measure a replicated experimental design to detect

relatively minor growth differences. The differences may be small but they

are economically important. Nevertheless, this study does provide a basis

for improved planning and more efficient management.

175

--

rl

16. FUTURE RESEARCH NEEDS

The combination of the three sets of submodels described in this thesis

are appropriate for predicting the interaction between thinning and

fertiliser responses in radiata pine plantations in South Australia. However,

these need to be assessed when longer run of time series data become

available from EP190. More limited experiments are also needed to

improve the overall precision of the yield regulation system predictions. A

number of areas merit future investigation based on the results and

analyses to date.

16.1 Fertiliser re-treatment

The effect of re-treatment with fertiliser needs to be assessed, as does the

timing of the application. Evidence from limited South Australian

experiments established prior to EP190 indicated that the response after

re-treatment did not diminish relative to the first treatment. However, this

finding differs from experience elsewhere.

Following the second thinning cycle, the data available from EP190 will

enable the response due to the repeated fertiliser applications to be

evaluated. Firstly an approach similar to the comparative study described

in this thesis can be used to determine if the re-treatment responses are

significantly different from the responses from the first thinning cycle. If the

responses are similar then the first and second thinning data sets can be

combined and a revised set of predictive models developed. Alternatively,

if the responses are found to be different, a Bayesian approach could be

used to model the re-treatment responses using the first thinning cycle

models as a prior and using the second thinning cycle data to develop a

posterior model.

176

Repeated treatment associated with thinning has become standard

operational practice for ForestrySA and therefore future fertiliser

experiments should incorporate at least an option for re-treatment in the

experimental design. Future designs need to include enough trees in each

plot to allow at least one additional thinning, just as in EP190.

16.2 Geographic range

More importantly, the study of the magnitude of the absolute growth

response to fertiliser needs to be extended to more sites. Radiata pine

plantations are established across a wide geographic range with a diverse

range in rainfall and soil properties in particular. Although a series of

experiments established prior to EP190 tested fertiliser responses across

part of the range, there are significant site types for which there are no

data.

The initial stage of an extended geographic range study would involve

stratifying site types on which radiata pine plantations are now established

and estimating the plantation area established to each site type. The

priority foro-assessing each site type can then be established and a plan for

establishing appropriate simple experiments could then be developed.

Unlike the experimental design of EP190, the appropriate strategy would

propose the establishment of experiments across a large number of sites

with few treatments and replications on each site; an OTG- 60 % treatment

instead of the OTG+ treatments and fewer fertiliser dose options.

Otherwise the experimental design would be similar to that of EP190.

Table 16.1 shows a proposed experimental design for a series of plots

that could be replicated in each of say seven major site types, in each of

two age classes (say 11-13 years and 24-26 years) of plantations. The

experiment would include two thinning cycles of about seven years each.

This design represents a total of 378 plots, the measurement of which

177

-

maw

would be feasible at the conclusion of EP190. This compares with the 511

plots currently included in EP 190.

Table 16.1 Proposed experimental design for each geographic location by thinning by fertiliser treatment.

Thinning treatment Fertiliser dose

FO F150 F300

OTG -60% 3 3 3

OTG -45% 3 3 3

OTG 3 3 3

16.3 Alternative fertiliser forms

There is a need to compare the growth responses obtained with other

fertiliser forms with those obtained from EP190 from one specific forest

mix. There is some indication that there is a high potential for the loss of

nitrogen response from fertilisers with high nitrogen content, such as urea,

which are more chemically volatile than the forest mix used in EP190. This

need has been partially addressed as part of cooperative experiments.

However, comparative studies of fertiliser forms need to be incorporated

as a sub study to the geographic range series. A proposed sub study

would add the urea equivalent of a 150 kg ha-1 treatment of nitrogen to

each of the site types and age classes proposed in the geographic range

series, requiring an additional 42 plots.

16.4 Log quality and wood properties

In evaluating the results of forest growth and yield experiments, log quality

and wood properties are often assumed to be invariant under the various

treatments. This assumption needs to be tested across the range of the

treatments applied in EP 190 to ensure that any possible effects on log

178

....

quality and wood properties which are of economic importance can be

quantified.

Attributes which need to be evaluated include the range of log size

assortments which can be derived from stands treated under the various

regimes. In South Australia log size is frequently used as a proxy for log

quality and is the major attribute which determines the log sale price. Data

for such a study could be derived from further analysis of the Sectional

tree measurement data already available for EP190.

The characteristics of tree branches are known to be influenced by

silviculture and need to be considered in relation to the effect on log

quality. Wider growing space regimes tend to promote the development of

larger, live knots in logs. Regimes which maintain closer stockings can

cause branches which are held lower on the stem to die earlier in the life

of the stand. The result of premature branch death is a higher incidence of

the logs which exhibit encased knots, a defect which is detrimental to the

value of the stand. The depth of the green crown can be calculated for

trees measured by Sectional and Regional Volume Table methods.

Therefore, the data already available from EP190 could be used to

estimate the likely incidence of encased knots under the various regimes.

Wood properties which need to be evaluated include wood density and

ring width as both these have a particular effect on the strength properties

and value of structural timber products. The data are not available from

the existing EP190 data set to support such a study. However, destructive

sampling of wood from the various regimes at the conclusion of EP190

would provide such data.

The evaluation of the economic implications of the effects on log quality

and wood properties would ensure that the benefits and costs of

alternative silvicultural systems are understood at a system level. This is

179

better than simply assuming that a one to one direct relationship exists

between volume and value.

180

---

17. IMPLEMENTING THE MODELS

This thesis describes the development of three sets of component sub

models which when integrated predict thinning and fertiliser interaction

responses in radiata pine stands.

The three EP190 sites are not representative of all South Australian

radiata pine stands but practical forest management requires that the best

estimates of yield are available and so the implementation of the models

must cover all plantations. To implement the three sets of submodels in

the South Australian yield regulation system requires their application as

predictors to be generalised.

17.1 Model application

The models developed for Headquarters can be applied from young to

mid-rotation age plantations (say 10 to 30 years old) of poorer than Site

Quality III; and older plantations (say 31 plus years) with Site Quality in the

range of IV to V. Site" quality in terms of the application of these models

should be based on the current equivalent growth rate not the assessed

site quality. The Menzies models can be used with plantations (say 10

plus years old) of Site Quality III or higher. The Glencoe Hill models can

be used for older plantations (say 31 plus years old), of poorer than Site

Quality V.

Implementing these models provides a more precise estimate of yield than

if no models were implemented. If anything the predictions are likely to be

slightly conservative and it is improbable that decisions based on the

predictions will result in the resource being overcommitted.

181

-

17.2 Total stand growth model

The first set of models predict the total stand growth response to the

interaction of thinning and fertiliser levels for a six year response period.

The initial basis of each sub model is a nonlinear two parameter model

which estimates the total response for four specific fertiliser doses (F ):

Gc% = boNotg%exp(-blNotg%),

where b , and b are parameters to be estimated, Gc% is the proportion o 1

of the periodic annual volume growth relative to the control (Optimum

Thinning Guide, 0 kg ha-1 nitrogen treatment) and Notg% is the stocking

as a proportion of the Optimum Thinning Guide stocking.

The responses across the fertiliser dose levels were estimated for a

nonlinear two parameter model using a second stage quadratic in fertiliser

level:

p=a+bxF+cxF2,

where p = b or p = b , a,h,c are parameters to be estimated and F is the o 1

fertiliser dose (kg ha-1). The estimated parameters were as follows:

Headq uarters Menzies Glencoe Hill

parameter h h h h h h 0 I 0 I () I

--.--"~"

a 2.8386 0.9770 3.2279 1.1508 2.2925 0.8060 -_.--_ .. _------

b 0.0076 0.0015 -0.0062 -0.0036 0.0244 0.0053

c -1.238.10.5 -0.339.10.5 2.555.10 .. 5 1.257.10-b -5.658.10 5 -1.528.10.5

-.-~--------~

17.3 Periodic annual growth model

The second set of sub models partition the total growth by predicting the

annual response for one to six years after the application of fertiliser and

182

beyond when needed. Again a two stage procedure was employed using

a first stage nonlinear model fitted for each plot at each site as follows:

where Gc% is the proportion of the periodic annual volume growth relative

to the control (Optimum Thinning Guide, 0 kg ha-1 nitrogen treatment), Tf

is the elapsed time since fertilisation (in years), in this case six years, bo

and bl are parameters to be estimated.

The second stage model fitted was a quadratic of the general form:

p = a+bx F +cx F2 +dx Notg%+ex Notg%2,

where p = bo and p = b, are the first stage parameters, a, b, c, d, e are

parameters to be estimated, Notg% is the proportional average stocking

and F is the nitrogen fertiliser dose.

Headquarters Menzies Glencoe Hill

parameter h b b b b b 0 I () 1 () 1

a 0.3278 0.1515 0.0000 0.0000 0.5762 0.0239

b -0.2851 -0.1043 0.3238 0.3402 -0.3874 0.0194

c 0.0000 0.0000 -0.1520 -0.1309 0.0000 0.0000

d 0.0020 0.0017 0.0009 0.0009 0.0016 0.0002

e -4.883.10-6 -3.759.10-6 -2.700.10-6 -2.374.10-6 -4.046.10-6 0.616.10-6

The additional functionality provided by the combination of these first two

sets of models addresses the strategic planning need to evaluate

alternative management strategies for the manipulation of stand density

using thinning intensity and thinning interval in combination and/or

together with the fertiliser application at different dose levels. Once

implemented in the yield regulation system more, flexible silvicultural

183

-

management options can be evaluated relative to ForestrySA's strategic

business objectives and customer needs.

17.4 Thinnings elect growth model

The third set of sub models predict the response of the thinnings elect to

the combination of stand density and fertiliser for a six year response

period. These models are intended to be implemented in the short term

yield regulation system to predict the future growth of stands from the time

of inventory to the time of the next thinning operation. Currently no

adjustments are made to the data derived from inventory for the addition

of fertiliser. The inclusion of fertiliser response models for the thinnings

elect will remove a known source of bias from yield estimates that are

used for forest estate valuation and harvest planning purposes. In this

case it was found that a reasonable predictive model could be constructed

for the first stage using a simple nonlinear model. The first stage model

fitted for all sites was:

Ge6 = (Yes]h' Gt6 Yts !

where Ge6 is the six year growth of the thinning elect; (1/6 is the six year

growth of the total stand; Yes is the volume yield of the thinnings elect at

the start of the growth period; Yls is the volume yield of the total stand at

the start of the growth period and hi is a parameter to be estimated using

non linear least squares.

Simple linear regressions were fitted to the h coefficient for each site' I .

184

p = b x Notg%

p = b x Notg% + ex Notg%2

p=dxF

p = dx F+ex p2

p = b x Notg% + ex Notg%2 +dxF +exF2

p = bx Notg%+ex Notg%2 +dxF+exF2 + fxNotg%xF

where p = log(b1

) wh ich is the transformed first stage parameter,

b,e,d,e,f are parameters to be estimated, Notg% is stocking as a

proportion of the Optimum Thinning Guide and F is the nitrogen fertiliser

dose (nitrogen kg ha-1) applied one year after thinning.

Headquarters Menzies Glencoe Hill

parameter log(b1

) log(b1

) log(b1

)

b 0.1705 0.0644 0.1616

c -0.0738 -0.0662

d -0.0004

e -2.072. 10-6 1.177.10-6

f 0.0088

17.5 Summary

The thinning and fertiliser interaction models described were designed to

be integrated with other component models already included in the

ForestrySA yield regulation system, currently RADGAYM II but soon to be

superseded by PL YRS being developed by the Information for Forest

Technology Program of the University of Melbourne. The implementation

of more precise predictors in what is currently considered the weakest

area of the yield regulation system will increase the overall precision of

predictions from the system.

185

r

BIBLIOGRAPHY

Assman, E. (1970) The Principles of Forest Yield Study. Translated by

S.H. Gardiner. Pergamon Press, Oxford, UK, 506 pp.

Baker, F.S. (1934). Theory and practice of silviculture. Ed. 1, McGraw-Hili,

New York, USA, 518 pp.

Bard, Y. (1967) Nonlinear parameter estimation and programming. IBM,

New York, USA, 154 pp.

Barker, J.E. (1980) Bole growth patterns of Pinus radiata D.Don in relation

to fertilisation, bending stress, and crown growth. New Zealand

Journal of Forest Science, 10(2):445-459.

Bednall, B.H. (1968) The problem of lower volumes associated with

second rotations in Pinus radiata plantations in South Australia.

Bulletin No.17, Woods and Forests Department, 17 pp.

Beers, T. W., P. E. Dress, et al. (1966). Aspect transformation in site

productivity research. Journal of Forestry, 64(10): 691-692.

Bertalanffy, L. Von. (1957) Quantitative laws in metabolism and growth.

Quarterly Review of Biology, 32:217-231.

Boardman, R. (1974) Pine stand improvement in the South-Eastern

Region of South Australia. Bulletin No.21. Woods and Forests

Department, 141 pp.

Boardman, R. (1984) Fast-growing species - pattern, process and ageing.

Proc. Symposium on Site and Productivity of Fast Growing

Plantations, 30 April - 11 May 1984, Pretoria and Pie term a ritzb urg,

South Africa, IUFRO, pp. 1-49.

Boardman, R. (1988) Living on the edge - the development of silviculture

in South Australian pine plantations. Australian Forestry, 51 (3):135-

156.

Boardman, R., and Leech, J.W. (1994) Monitoring procedures to assess

sustainability in successive rotations of Pinus radiata D.Don

187

plantations in South Australia. Proc. IUFRO Study Group S4.02.03,

7 -9 November 1994, Stellenbosch, South Africa, 22 pp.

Boardman, R. (1995) Perspectives gained from the South Australian

experience of mid rotation studies with radiata pine. Proc.

Management of Stand Nutrition to Increase the Productivity of Later

Age Softwood Plantations, 23-25 May 1995, Mount Gambier,

Australia, 15 pp.

Boardman, R., and McGuire, D.O. (1990a) The role of zinc in forestry. I.

Zinc in forest environments, ecosystems and tree nutrition. Forest

Ecology and Management, 37: 167-205.

Boardman, R., and McGuire, D.O. (1990b) The role of zinc in forestry. II.

Zinc deficiency and forest mangement: effect on yield and

silviculture of Pinus radiata plantations in South Australia. Forest

Ecology and Management, 37:207-218.

Boardman, R., and Simpson, J.A. (1981) Fertilization to optimize

productivity. Proc. Australian Forest Nutrition Workshop:

Productivity in Perpetuity, 10-14 August 1981, Canberra, Australia,

CSIRO, pp. 303-317.

Box, G.E.P. (1980) Sampling and Bayes' inference in scientific modelling

and robustness. Journal of the Royal Statististical Society B,

143(4):383-430.

Bredenkamp, B.V., and Gregoire, T.G. (1988) A forestry application of

Schnute's generalized growth function. Forest Science, 34(3):790-

797.

Carlyle, C. (2001) Fertilising pines - aids to decision-making. Onwood

No.32, CSIRO, 1 pp.

Carron, L. (1968) An outline of forest mensuration with special reference

to Australia. Australian National University Press, Canberra,

Australia, 224 pp.

Chapman. (1961) Statistical problems in dynamics of exploited fish

populations. Proc. Fourth Berke/ey Symposium of Mathematics,

Statistics and Probability, Los Angeles, USA, pp. 153-168.

188

Clutter, J.L., Fortson, J.e., Pienaar, L.V., Brister, G.H., and Bailey, R.L.

(1983) Timber Management: A Quantitative Approach. John Wiley

& Sons, New York, USA, 333 pp.

Coops, N.C., Waring, R.H., and Landsberg, J.J. (1998) Assessing forest

productivity in Australia and New Zealand using a physiologically­

based model driven with averaged monthly weather data and

satellite-derived estimates of canopy photosynthetic capacity.

Forest Ecology and Management, 104:113-127.

Corbin, H.H. (1917) Working plan of the forest of Kuitpo, South Australia

1916. Proc. Interstate Forestry Conference, 15-23 November 1917,

Perth, Australia, pp. 74-91.

Coulombe, S., and Lowell, K.E. (1995) Ground-truth verification of

relations between forest basal area and certain ecophysiographic

factors using a geographic information system. Landscape and

Urban Planning, 32:127-136.

Crane, W.J.B. (1982) Fertiliser treatment of Pinus radiata at establishment

and at thinning - an evaluation of its potential in Australia. New

Zealand Journal of Forest Science, 12:293-307.

Davis, A.W., and West, P.W. (1981) Remarks on "Generalized least

squares estimation of yield functions" by I.S. Ferguson and J.W.

Leech. Forest Science, 27(2):233-239.

Donald, D.G.M. (1987) The application of fertiliser to pines following

second thinning. South African Forestry Journal, 142:13-16.

Draper, N.R., and Smith, H. (1998) Applied Regression Analysis. Ed. 3,

John Wiley & Sons Inc., New York, 706 pp.

Drew, T.J., and Flewelling, J.W. (1977) Some recent Japanese theories of

yield-density relationships and their application to Monterey Pine

plantations. Forest Science, 23:517-534.

Drew, T.J., and Flewelling, J.W. (1979) Stand density management: an

alternative approach and its application to Douglas-fir plantations.

Forest Science, 25:518-532.

189

Durbin, J. (1970) An alternative to the bounds test for testing for serial

correlation in least-squares regression. Econometrica, 38(3):422-

428.

Durbin, J., and Watson, G.S. (1950) Testing for serial correlation in least­

squares regressions. I. Biometrika, 37:409-428.

Durbin, J., and Watson, G.S. (1951) Testing for serial correlation in least­

squares regressions. II. Biometrika, 38: 159-178.

Durbin, J., and Watson, G.S. (1971) Testing for serial correlation in least­

squares regressions. III. Biometrika, 58:1-19.

Edwards, D., and Hamson, M. (1989) Mathematical Modelling. Macmillan

Press Ltd, London, UK, 277 pp.

Ferguson, 1.8. (1979) Computer based growth model for ACT Forests.

Unpublished Report. ANU, 139 pp.

Ferguson, I. 8. (1993). Review of Woods and Forests inventory and

growth models incorporated in the yield regulation system.

Unpublished Report. The University of Melbourne, 34 pp.

Ferguson, 1.8., and Leech, J.W. (1976) Stand dynamics and density in

radiata pine plantations. New Zealand Journal of Forest Science,

6(3):443-454.

Ferguson, I.S., and Leech, J.W. (1978) Generalized least squares

estimation of yield functions. Forest Science, 24(1 ):27 -42.

Fisher, R.A. (1922) On the mathematical foundations of theoretical

statistics. Royal Society of London Philosophical Transactions

Series A, 222:309-368.

Fisher, R.A. (1934) Statistical Methods for Research Workers. Ed. 5,

Oliver and Boyd, London, UK, 319 pp.

Forward, D.F., and Nolan, N.J. (1961) Growth and morphogenesis in the

Canadian forest species. V. Further studies of wood growth in

branches and main axis of Pinus resinosa Ait. under conditions of

open growth, suppression and release. Canadian Journal of

Botany, 39:411-436.

190

Fox, J.C., Ades, P.K., and Bi, H. (2000) Stochastic structure and

individual-tree growth models. Forest Ecology and Management, In

Press.

Freund, R.J., and Littell, R.C. (1991) SAS System for Regression. Ed. 2,

SAS Institute Inc., Cary, USA, 210 pp.

Gompertz, B. (1825) On the nature of the function expressive of law of

human mortality, and on a new mode of determining the value of

life contingencies. Philosophical Transactions of the Royal Society,

115:513-585.

Gossett, W.S. (1908) The probable error of a mean. Biometrika, VI(1):1-

25.

Goulding, C.J. (1994) Development of growth models for Pinus radiata in

New Zealand - experience with management and process models.

Forest Ecology and Management, 69:331-343.

Guldin, R.W. (1984) Site characteristics and preparation practices

influence costs of hand-planting southern pine. Journal of Forestry,

82(2):97 -100.

Harris, W. K. (1983). Geology. In: Natural History of the South East. M. J.

Tyler, C. R. Twidale, J. K. Ling and J. W. Holmes. Adelaide, Royal

Society of South Australia Inc., pp. 1-6.

Horne, R., and Robinson, G. (1985) Response increment: The basis of a

stand growth model. Proc. Modelling Trees, Stands and Forests,

26-28 August 1985, Melbourne, Australia, R.E. McMurtrie, J.W.

Leech, P.W. West, R.D. Spencer and B.M. Spencer, University of

Melbourne, pp. 277-288.

Horne, R., and Robinson, G. (1988a) Development of basal area thinning

prescriptions and predictive yield models for Pinus radiata

plantations in New South Wales 1962-1988. Research Paper No.6,

Forestry Commission of N.S.W., 36 pp.

Horne, R., and Robinson, G. (1988b) Response increment: the basis for a

Pinus radiata stand growth model. Research Paper No.5, Forestry

Commission of N.S.W., 16 pp.

191

....

Horne, R., Robinson, G., and Gwalter, J. (1986) Response increment: a

method to analyze thinning response in even-aged forests. Forest

Science, 32(1 ):243-253.

Huang, S., Titus, S.J., and Wiens, D.P. (1992) Comparison of nonlinear

height-diameter functions for major Alberta tree species. Canadian

Journal of Forest Research, 22:1297-1304.

Jerram, M.R.K. (1949) Elementary Forest Mensuration. Thomas Murby

and Co., London, UK, 124 pp.

Jolly, N.W. (1950) The thinning of Pinus radiata plantations in the South­

East of South Australia. Bulletin No.4, Woods and Forests

Department, 27 pp.

Keeves, A. (1961) A consideration of certain mensurational methods for

intensive forest management of coniferous plantations. Diploma of

Forestry, Oxford, 134 pp.

Keeves, A. (1966) Some evidence of loss of productivity with successive

rotations of Pinus radiata in the South-East of South Australia.

Australian Forestry, 30:51-63.

Kozak, A. (1973) Notes on the uses of conditioned regressions in forestry.

Proc. Statistics in Forestry Research, 20-24 August 1973,

Vancouver, Canada, IUFRO, pp. 113-126.

Landsberg, J.J., and McMurtrie, R. (1984) Models based on physiology as

tools for research and forest management. Proc. Research for

Forest Management, 21-25 May 1984, Canberra, Australia, J. J.

Landsberg, and W. Parsons, CSIRO, pp. 214-228.

Langsaeter, A. (1941) Om tynning i enaldret gran- og furuskog. Norske

skogforsokresen Meddeldser, 8: 131-216.

Leech, J.W. (1973) Tree volume and increment models for radiata pine

thinnings. M.Sc. Thesis, Australian National University, 190 pp.

Leech, J.W. (1976) Structural implications in a growth model. Proc.

Research Working Group No.2: Mensuration and Management,

December 1976, Melbourne, Australia, Research Working Group 2,

12 pp.

192

Leech, J.W. (1978) Radiata Pine Yield Models. PhD Thesis, Australian

National University, 262 pp.

Leech, J. W. (1984) Modelling for forest management. Prac. Research far

Forest Management, 21-25 May 1984, Canberra, Australia, J.J.

Landsberg, and W. Parsons, CSIRO, pp. 229-233.

Leech, J.W., and Dutkowski, G.W. (1985) Mortality and growth of

unthinned stands of radiata pine. Unpublished Internal Memo,

Woods and Forests Department, 31 pp.

Leech, J.W., and Ferguson, I.S. (1981) Comparison of yield models for

unthinned stands of radiata pine. Australian Forest Research,

11 :231-245.

Leech, J.W., Sutton, M.W., and Archer, G.R. (1989) Recording field

measurements on Husky Hunter microcomputers. Australian

Forestry, 52(2):68-73.

LeGoff, N., and Ottorini, J.M. (1993) Thinning and climate effects on

growth of beech (Fagus sy/vatica L.) in experimental stands. Forest

Ecology and Management, 62:1-14.

Lewis, N.B. (1963) Optimum thinning range of Pinus radiata in South

Australia. Australian Forestry, 27(2):113-120.

Lewis, N.B. (1964) Yield regulation in South Australian State Forests.

Australian Timber Journal, 30(6):59-65.

Lewis, N.B. (1975) A hundred years of State forestry; South Australia

1875-1975. Bulletin No.22, Woods and Forests Department, 122

pp.

Lewis, N.B., and Ferguson, I.S. (1993) Management of Radiata Pine.

I nkata Press, Melbourne, Australia, 404 pp.

Lewis, N.B., Keeves, A., and Leech, J.W. (1976) Yield regulation in South

Australian Pinus radiata plantations. Bulletin No.23, Woods and

Forests Department, 174 pp.

Lewis, N.B., and Mcintyre, G.A. (1963) Regional Volume Table for Pinus

radiata in South Australia (Imperial Edition). Bulletin No.14, Woods

and Forests Department, 59 pp.

193

Lewis, N.B., Mcintyre, G.A., and Leech, J.W. (1973) Regional Volume

Table for Pinus radiata in South Australia (Metric Edition). Bulletin

No.20, Woods and Forests Department, 64 pp.

Ludlow, A.R. (1997) Some factors influencing the increment of forests.

Forestry, 70(4):381-388.

Magnussen, S., and Park, Y.S. (1991) Growth-curve differentiation among

Japanese larch provenances. Canadian Journal of Forest

Research, 21(4):504-513.

Miller, H.G. (1981) Forest fertilization: Some guiding concepts. Forestry,

54(2):157-167.

Miller, H.G., and Cooper, J.M. (1973) Changes in amount and distribution

of stem growth in pole-stage corsican pine following application of

nitrogen fertilizer. Forestry, 46(2): 157-190.

Mitscherlich, E.A. (1910) Das gesetz des minimums und das gesetz des

abnehmenden bodenertrages. Landwirfschaftliche jahrbucher,

38:537 -552.

Moller, C.M. (1954) The influence of thinning on volume increment. World

Forestry Series Publication No.1, State University of New York, pp.

5-49.

Moller, G., and Rytterstedt, P. (1974) God 0slingseffektens varaktighet och

f0rlopp hos tall och gran. Skogsforbattring, 75-97 pp.

Moller, G., Tveite, B., Gustavsen, H.G., and Pettersson, F. (1991)

Godslingens tidsmassiga anpassning till gallring. Delresultat fran en

9-arig samnordisk studie. Report No.23, Skogsforbattring, 42 pp.

Nambiar, E.K.S., Squire, R.O., R.Sands, and Will, G.M. (1984)

Manipulation of water and nutrients in plantations of fast growing

species. Proc. Symposium on Site and Productivity of Fast Growing

Plantations, 30 April - 11 May 1984, Pretoria and Pietermaritzburg,

South Africa, IUFRO, pp. 489-506.

O'Hehir, J.F. (1995) Yield Regulation in South Australia, Tools or Toys:

The certainty of the past, the challenge for the future. Proc.

Applications of New Technologies in Forestry, 16th Biennial

194

Conference, 18-21 April 1995, Ballarat, Australia, Institute of

Foresters of Australia, pp. 275-280.

O'Hehir, J. F. (2000) Use of the regional volume table to determine stem

volume in thinning and fertiliser trials in radiata pine stands. Proc.

Research Working Group 2, Forest Measurement and Information,

27 November -1 December 2000, Perth, Australia, Research

Working Group 2, 17 pp.

O'Hehir, J.F., J.W.Leech, and Lewis, N.B. (2000) The evolution of growth

and yield models for South Australian radiata pine plantations.

Australian Forestry, 63(4): 159-165.

Pettersson, F. (1994) Predictive functions for impact of nitrogen

fertilization on growth over five years. Report No.3, The Forestry

Research Institute of Sweden, 56 pp.

Puro, T. (1982) Lannoitusajankohdan merkitys eri puulajien

kasvureaktiossa. Folia Forestalia NO.507. Metsantutkimuslaitos

Institutum Forestale Fenniae, 14 pp.

Ratkowsky, D.A. (1983) Nonlinear Regression Modeling. Marcel Dekker

Inc. New York, USA, 276 pp.

Ratkowsky, D.A. (1990) Handbook of Nonlinear Regression Models.

Marcel Dekker Inc., New York, USA, 241 pp.

Raupach, M., Boardman, R., and Clarke, A.R.P. (1969) Growth rates of

Pinus radiata D.Don in relation to foliar levels of nitrogen and

phosphorus for plantations in the south-east of South Australia.

Australian Soils. Publication No.26, CSIRO, 28 pp.

Richards, F.J. (1959) A flexible growth function for empirical use. Journal

of Experimental Biology, 10:290-300.

Savill, P., Evans, J., Auclair, D., and Falck, J. (1997) Plantation Silviculture

in Europe. Oxford University Press, Oxford, UK, 297 pp.

Schnute, J. (1981) A versatile growth model with statistically stable

parameters. Canadian Journal of Fish and Aquatic Science,

38:1128-1140.

195

------'

Schultz, R.P. (1997) Loblolly Pine: The ecology and culture of Loblolly

Pine (Pinus taeda L.). Agricultural Handbook No.713, USDA Forest

Service, 514 pp.

Shoulders, E., and Tiarks, A.E. (1990) Nine-year response of thinned

slash pine to nitrogen, phosphorus, and potassium. Soil Science of

America Journal, 54:234-237.

Smith, D.M. (1986) The practice of silviculture. John Wiley & Sons, New

York, USA, 527 pp.

Smith, V.G. (1983) Compatable basal area growth and yield models

consistent with forest growth theory. Forest Science, 29(2) :279-

288.

Snedcor, G.W., and Cochran, W.G. (1980) Statistical Methods. Ed. 7, The

Iowa State University Press, Ames, USA, 507 pp.

Snowdon, P., Crane, W.J.B., and Woollons, R.C. (1995) Response to

applications of nitrogen, phosphorus and sulphur fertilizers to three

Pinus radiata stands in the Tumut region, New South Wales. User

Series NO.20, CSIRO, 22 pp.

Snowdon, P., and Waring, H.D. (1981) Forest fertilisation and thinning

practice. Proc. Economics and techniques of thinning plantations in

Australia and New Zealand) 28 September - 2 October 1981,

Canberra) Australia, pp. 159-162.

Snowdon, P., Waring, H.D., and Woollons, R.C. (1981) Effect of fertilizer

and weed control on stem form and average taper in plantation­

grown pines. Australian Forest Research, 11 :209-221.

Sokal, R.R., and Rohlf, F.J. (1981) Biometry. Ed. 2, W.H. Freeman and

Company, New York, 859 pp.

Steinbrenner, E.C. (1967) Research in forest fertilization at Weyerhaeuser

Company in the Pacific Northwest. Proc. Symposium on Forest

Fertilization) April 1967, Gainesville, Florida, USA, Tennessee

Valley Authority National Fertilizer Development Center, pp. 209-

215.

196

Stephens, C.G. (1941) A soil and land use survey of the Hundreds of

Riddoch, Hindmarsh, Grey, Young and Nangwarry, County Grey,

South Australia. Bulletin No.142, C.S.I.R., 60 pp.

Sullivan, A.D., and Reynolds, M.R. (1976) Regression problems from

repeated measurements. Forest Science, 22(4):382-385.

Sutton, M.W., and Leech, J.W. (1981) Estimation of increment at low

densities. Unpublished Internal Memo, Woods and Forests

Department, 3 pp.

Swain, E.H.F. (1935) Forest and economic survey in the South East of

South Australia. Volume No.2, 206 pp.

Tamm, C.O. (1967) The evolution of forest fertilization in European

silviculture. PrOG. Symposium on Forest Fertilization, April 1967,

Gainesville, Florida, Tennessee Valley Authority National Fertilizer

Development Center, pp. 242-247.

Theil, H. (1971) Principles of Econometrics. North-Holland Publishing

Company, Amsterdam, Holland, 736 pp.

Turner, J., Knott, J.H., and Lambert, M.J. (1996) Fertilization of Pinus

radiata plantations after thinning. I Productivity gains. Australian

Forestry, 59(1):7-21.

Twidale, C. R. (1976). Geomorphological evolution. In Natural History of

the Adelaide Region. C. R. Twidale, M. J. Tyler and B. P. Webb.

Adelaide, Royal Society of South Australia Inc., pp. 43-59.

Valinger, E. (1993) Effects of thinning and nitrogen fertilization on growth

of scots pine trees: total annual biomass increment, needle

efficiency and aboveground allocation of biomass increment.

Canadian Journal of Forest Research, 23:1639-1644.

Vanclay, J.K. (1994) Modelling Forest Growth and Yield: Applications to

Mixed Tropical Forests. CAB International, Wallingford, UK, 312 pp.

Vanclay, J.K. (1995) Growth models for tropical forests: a synthesis of

models and methods. Forest Science, 41 (1 ):7 -42.

Van Deusen, P.C. (1989) Multiple-occasion partial replacement sampling

for growth components. Forest Science, 35(2):388-400.

197

Ware, K.D., and Cunia, T. (1962) Continuous forest inventory with partial

replacement of samples. Forest Science - Monograph No.3,

Society of American Foresters, 40 pp.

Waring, H.D. (1981) Forest fertilization in Australia: Early and late. Proc.

Australian Forest Nutrition Workshop: Productivity in Perpetuity, 10-

14 August 1981, Canberra, Australia, CSIRO, pp. 201-218.

Weetman, G.F. (1975) Ten-year growth response of black spruce to

thinning and fertilizer treatments. Canadian Journal of Forest

Research, 5:302-309.

West, G., and Williams, N. (1993) Managing stands of radiata pine using

PC-STANDPAK. What's New in Forest Research No.229, NZFRI, 4

pp.

West, G.G. (1998) Pinus radiata growth responses to pruning, thinning,

and nitrogen fertiliser in Kaingaroa Forest. New Zealand Journal of

Forest Science, 28(2):165-181.

West, P.W. (1980) Difficulties with generalized least squares regression in

forest modelling. Occasional Paper No.5, CSIRO, 16 pp.

West, P.W. (1981) Simulation of diameter growth and mortality in

regrowth eucalypt forest of Southern Tasmania. Forest Science,

27(3):603-616.

West, P.W. (1985) Density management diagrams and thinning practice in

monoculture. Proc. ANZIF Conference, 20-24 May 1985, Hobart,

Australia, IFA, pp. 163-168.

West, P.W. (1995) Application of regression analysis to inventory data

with measurements on successive occasions. Forest Ecology and

Management, 71 :227-234.

Whyte, A.G.D., and Mead, D.J. (1976) Quantifying responses to fertiliser

in the growth of radiata pine. New Zealand Journal of Forest

Science, 6(3):432-444.

Williams, N. (1995) Computer software for plantation foresters - a

perspective from New Zealand. Proc. Applications of New

Technologies in Forestry, 18-21 April 1995, Ballarat, Australia, IFA,

10 pp.

198

Wood, G.B., Turner, B.J., and Brack, C.L. (eds). (1999) Code of Forest

Mensuration Practice: A guide to good tree measurement practice

in Australia and New Zealand. Research Working Group 2,62 pp.

Woods, R.V. (1976) Early silviculture for upgrading productivity on

marginal Pinus radiata sites in the South-Eastern Region of South

Australia. Bulletin NO.24. Woods and Forests Department, 90 pp.

Woollons, R. (1985) Problems associated with analyses of long-term

Pinus fertiliser X thinning experiments. Australian Forest Research,

15:495-507.

Woollons, R.C. (2000) Comparison of growth of Pinus radiata over two

rotations in the central North Island of New Zealand. International

Forestry Review, 2(2):84-89.

Woollons, R.C., Smale, P.J., and Burgess, F.F.D. (1994) Analytical

methods to aid interpretation of thinning experiments. New Zealand

Journal of Forest Science, 24: 18-26.

Woollons, R.C., and Whyte, A.G.D. (1988) Analysis of forest fertilizer

experiments: obtaining better precision and extracting more

information. Forest Science, 34(3):769-780.

Woollons, R.C., and Will, G.M. (1975) Increasing growth in high

production radiata pine stands by nitrogen fertilisers. New Zealand

Journal of Forestry, 20:243-253.

Yang, R.C., Kozak, A., and Smith, J.H.G. (1978) The potential of Weibull­

type functions as flexible growth curves. Canadian Journal of

Forest Research, 8:424-431.

Yao, N.Y.N., and Leong, R.C.M. (1995) Deriving growth function for

formosan ash (Fraxinus formosan a) plantations in Taiwan. Proc.

IUFRO XX World Congress, 6-12 August 1995, Tampere, Finland,

IUFRO, 8 pp.

Zeide, B. (1993) Analysis of growth equations. Forest Science, 39(3):594-

616.

Zellner, A., and Theil, H. (1962) Three-stage least squares: simultaneous

estimation of simultaneous equations. Econometrica, 30(1):54-78.

199

Zhang, L., Moore, J.A., and Newberry, J.D. (1993) A whole-stand growth

and yield model for interior Douglas-fir. Western Journal of Applied

Forestry, 8(4):120-125.

200

APPENDICES

Appendix I EP190: treatment schedule.

Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Thinning/Fertiliser T1fT3 FM3 I FM3 T2fT4 FM3 FM3 T3fT5

1 X 0 0 X 0 0 X I

2 X 75 0 X 75 0 X ..

3 X 150 0 X 150 0 X

4 X 300 0 X 300 : 0 X 5 X a 75 x a 75 x 6 X 0 150 X 0 150 X

r-7 X 0 300 X 0 300 X

8 X 75 75 X 75 75 X 9 X 150 150 X 150 150 X

10 X 75 0 X 0 0 X

11 X 150 0 X 0 0 X

12 X 300 0 X 0 0 X

Note: FM3 denotes complete mineral fertiliser application in kg nitrogen ha- '. I I I I

Measurements SA SA SA SA SA SA SA SA SA SA SA SA SA SA SA BA Stem VOL VOL VOL Analysis

Experiments

01 HUTCHESSONS 1974 - (T1) 1985/86 1987 88 89 1990 91 92 1993 1994 95 96 1997 98 99 2000 01 02

02 HEADQUARTERS 1972/73 - (T1 ) 1985/86 1987 88 89 1990 91 92 1993 1994 95 96 1997 98 99 2000 01 02

03 MENZIES 1956 - (T3) 1986 1988 89 90 1991 92 93 1994 1995 96 97 1998 99 00 2001 02 03 05 GLENCOE HILL 1962 - (T2fT3) 1991 1992 93 94 1995 96 97 1998 1999 00 01 2002 03 04 2005 06 07 --------------_ .. _-

202

L._.,.~ _".'_. ______ ''' ........ '' •..•• _. _______ ' ______ ----'-~~ __ ~ __ ~"'"""-'-___ ~ _______ ~ _______ ~ ___ ~ ____________ ~~_~~~ __ ~~_._, __ .. _ .. _, ... ".

Appendix II EP190: measurement schedule.

I 85/86 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

I I I

01 T1 T2 T3

HUTCHESSONS DBH DBH DSH DBH DBH DBH DBH DBH DBH DBH DBH OBH DBH DBH DBH STEM

VOL VOL VOL ANAL

FM3 FM3 FM3 FM3

I i !

\

! \ I ! I I I I I I I I , i I ! I

02 T1 T2 T3

HEADQUARTERS DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH STEM

VOL VOL VOL ANAL

FM3 FM3 FM3 FM3 I I I I I 1 !

I I I

I I I I I I I I I I I I 1

03 T3 T4 T5

MENZIES DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH STEM VOL VOL VOL ANAL

FM3 FM3 FM3 FM3

I I I I \ I I I I I I I I I I I I I

05 T2ff3 T4 T5

GLENCOE HILL DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH DBH STEM

VOL VOL VOL ANAL

FM3 FM3 FM3 FM3 --

203

Appendix III The evolution of growth and yield models for South

Australian radiata pine plantations.

Australian Forestry ~ 63, No.3 1'1'.159-165 JS9

The Evolution of Growth and Yield Models for South Australian radiata pine plantations

J.P. O'Hehirl, J.W. Leech2,4 and N.B. Lewis3,4

'ForcstrySA, PO Box J 62, Mount Gambier, South Australia 5290 lJ'orestry Systems,' PO BOll 1632, Moont Gambier, South Australia 5290 312 McLlchlan Avenue, Glenelg North. Adelaide, South Australia 5045

4FormerJy of the Woods and Fousts Department of South Australia

Revised manuscript ~ived 6 April 2000

Summary The evolution of growth and yield models for South Austral­ian radiata pine plantations is traced from the fteSt yield table developed by H.R. Gray in 1931 to the most recently devel­oped growth functions. The adoption of Dew technologies is discussed both in terms of the techniques available for devel­oping growth and yield predictors and the implementation of them in computerised systems. Growth and yield models in South Australia were initially developed to meet the market­ing needs of a plantation resource reaching critical mass. The continuing improvement of the models remains a market driven process due to the increasing intensity with which the forests are being,managed to meet the demands for a wide range of log products. Intensive silviculture coupled with genetic improvement of the planting stock requirc:s cQntinu­ing improvement to growth and yield models.

Introduction The requirement for growth and yield models in forest man­agement stemmed from a Deed to predict the yield and pro- ' ductive capacity of the growing stock. Increasingly intensive' forest management created demands for predictive rnOOels well beyond those required for the estimation of stand vol­ume for the purposes of log sale.

Description and Application The increasing financial investment required to establish and maintain larger and more tecnnically complex processing plants meant that the forest growers needed to predict the sustainable supply of logs of relevant assortments from the . forest resource. In South Australia, sustainability was a pre­requisite given the need to support the investment in process­ing technologies and the social imperati ve for secure employ­ment.

Before high-speed electronic computers were available, pre­dictive calculations had to be completed manually, usually by graphical methods. As computing technology developed, the calculations were automated through computer program­ming. The increasing availability of computers and rugh level programming languages allowed the application of improved statistical methods to fit mathematical functions to the data. These functions were incorporated in computer models such asRADGAYMIin 1972 (Lewisetal. 1976) and RAOOAYM n in 1983 (Leech 1985) and were used for simulating stand growth and yield and the results were then aggregated to a whole forest level.

More recently, research has indicated (Boardman 1988) that new silvicultural practices result in growth trends that no longer consistently match unused and current growth and yield tables and functions. The changes identified by R. Boardman and olbers are simulated in the ForestrySA yield regulation system (RAOOAYM II).

In this paper we trace the evolution from the early manually prepared yield tables to computer based techniques and then identify an emerging need for the further development and application of more rigorous methods of adapting past growth and yield models to current circumstances.

In its simplest fonn a yield table consists of a tabular statA::­ment that predicts the development of a stand (usually even­aged) up to a certain afJe (usually the maximum rotation age) at periodic time intervals. Such tables are generally based .on data from the measurement of trees within tA::mporary or per­manent sample plots selected from different geographic lo­calities. Usually the sample plots are remeasured at intervals. or periodic increment is determined by stem analysis.

Yield tables were constructed in pre-electronic computer days to facilitate the mahual prediction of yields (Schwappach 1912). In South Australia, C.E. Lane Poole was one of the first to conduct an inventory and prepare yield curves, oow­ever, Gray (1931) was credited (Lewis et aJ. 1976) as devel­oping the first yield table specifically for South Australian pluntations. Subsequently, E.H.F. Swain, N.W. Jolly and then N.B. Lewis developed yield tables for use in South Austral­ian rndiata pille plantations. In aU the published South Aus­tralian tables, the variable of greaiest interest, volume, has been estimated directly at a stand level. Alternatively, the iden­tification of site qUality 'has been based for over 50 years on visually recognisable stand types, and not solely on volume productivity which constitutes the basis of these yield lables (Lewis et Ill. (976).

Early yield tables Lane Poole. Depanmental inventories of standing log vol­ume were carried out in 1923-4, 1926, 1930 and 1932. An inventory of part of Mount Burr Forest conducted by Lane Poole and students from the Australian Forestry School as­sessed the 'volume of timber on an area of 1936.85 acres of pine plantation offered for sale by the South Australian Gov­ernment to a private paper pulping interest' (Lane Poole 1927). Lane Poole used stem analysis data to construct total volume yield curves for each compartment (ranging in area from less than one hectare up to approximately J 50 hectares). These curves and tables are similar to the local yield tables described by Assman ( 1970).

Gray. Lewis et ai. (1976) described the yield table constructed by Gray (1931) as being developed from data from tempo­rary plots (actually established as strips) and by Baur's or the 'limiting curve' method (Schlich 1911; Spurr 1952).1bislo­cal yield table. developed for Mount Burr Forest, used only three Site Qualities (Table I and Appendix I) and was claimed by Gray (1931) to be the fIrst yield table developed for' Aus­tralian grown forests.' The reason for developing this yield table is not clear, although utilisation by a sawmill and a pulpmill is mentioned (Gray 1931). Unpublished merrulS in-

204

160 . Growth and yield models for radiata pine

Table 1. A comparison of the predicted volumes (m3 per ha) for yield tables and functions developed for South Australian radiata pine stands.

Age Yield Tablel

I Gray's Site Qualities do not directly match other Site Qualities and volumes are standing (probably merchantable volume only) 1 Volumes are standing to a four inch top diameter underbark J Volumes are probably standing to a four inch top diamecer underbark' 4 Volumes are total production to a 10 em top diameter underbark , UT = Unthinned; TH::: Thinned

dieare that part of the data used to develop this yield table was based on the work of Lane Poole (1927).

Inspection of Gray's Mount Burr curves (based on the stand­ing volume to a four inch diameter underbark) indicates a point of inflection for aU Site Qualities between the ages of 10 and 15 (see Appendix I). whereas the curves ascribed to Swain, Jolly. Lewis and l.W. Leech indicates points of in­flection prior to age 10. This suggests that the curves devel­oped by Gray significantly under estimate stand growth at least between the ages of to and 20. Lane Poole (1927) also indicated inflection points for total standing volume produc-

tion to a four inch underbark diameter prior to age 10. It may be that Gray was concerned with merchantable rather than total yield.

As part of the investigation into a possible sawmill at Nangwarry to utilise that resource (internal Woods and For­ests Department memos) Gmy (1936 to 1940) constructed a variable density yield table for Penola Forest (Table 1 and Appendix I). The yield table spanned four Site Qualities de­fined by the height of the mean tree as defined by basal area.

In various unpublished Departmental memos around 1940, Jolly argued that the use of the height of the mean trees as an

205

AU3tralian Forestry Vol 6:3, No.:3 pp. 159-165_ 161

index of productivity was unreliable compared with the use of the mean height of the dominants, especially in thinned stands. This observation led to the use of mean predominant height as the height based index of productivity in South Australia (defined as the mean height of the equivalent of the 75 tallest trees per hectare). A more reliable index of produc~ tivity than height is the volume based site qu8Iity which bas been used for at least the last 50 years in South Australia. Site quality is defined as the total production volume of a stand to a 10 em underbark diameter at age 10 years and is defined as flO' Swain. Swain (1935) developed both unthlnned (Table 1 and Appendix I) and thinned stand yield tables for volume to a four inch small end diameter assortment underbark, and'in­cluded tables of mean annual increment and periodic annual increment by seven Site Quality classes spanning ages five to forty years (Swain 1935),

The yield tables were developed as part of an investigation into the feasibility of establishing a pulp and paper industry in South Australia, and were based on data derived from a number of measun::ments in temporary study plots ill stands of different ages. Although overseen by Swain. the data were collected by officers of the Woods and Forests Department in 1934 over a ,period of approxiJ:nately one year (Carron 1985). The yield tables spanned seven Site Qualities and were based Oft data collected from the existing plantation areas of Mount Burr, Mount Gambier and Penola (Lewis et Ill. 1976). Some data from rerneasured plots were available but it is not clear if this infonnation was used.

JoDy. The development of the first yield table (Table 1 and Appendix I) in South Australia to use data from the Perma­nent Sample Plot series is ascribed to Jolly (Lewis et al. 1976). r The series was begun by M.A. Rankin in 1934-5, However, unpublished Departmental records indicate that frequent measurement of 'sample plots' was undertaken from at least 1921 at Mount Burr Forest by A.L. Pinches and F.C. Kay; since 1924 at Penola Forest by R.H. Davey and J.C,H. Russen. and at Bundaleer Forest by F.R. field. The Pennanent Sam­ple Plot data provided growth trends from the re-measure­ment of the plots, rather than from singl.e sets of measure­ments made in multiple stands of various ages, as had been used by Swain and Gray. The 1941 Jolly Yield Table recog" nised seven Site Qualities and spanned P3es 10 10 30 years,

The modem yield tables Lewis. Beginning in 19531011y's yield table was revised and extended as more measurement data became available from the Pennanent Sample Plots (Lewis et al. 1976). Later revi­sions extended the yield table to thinned stands based on stand­ing volume plus thinning and mortality volumes to a 10 em top diameter underbark (Table 1 and Appendix I). Until the early 1970s the tables were constrocted by the directing curve method attributed to Heyer in 1846 (Schlich 1911; Spurr 1952) using data obtained from the repeated measurement of the Permanent Sample Plots. The yield tables provide total vol­ume (initially to a four inch, but later metricated to a 10 cm top diameter underbark). basal area, and predominant height, for seven Site Qualities of thinned stands.

The final revision attributed to Lewis was made in 1972 (fa­ble 1 and Appendix I), In the same year the total volume pro­duction table was supplemented by a table of the equi valent periodic annual increments by age and site quality and was integrated into the Woods and Forests Department compu­terised Yield Regulation System (Lewis et al. 1976).

The tables are specific to the radiata pine plantations of the south east of South Australia for stands 'whose stocking-stand height history lies within the bouods of the South Australian Optimum Thinning Guide' (Lewis 1963). The tables are for thinned stands, but can be used for unthinned stands up to age 25 to 30 'without significant error: (Lewis et a/. 1976). Beyond these ages, the application of the tables to unthinned stands progressively over estimates the total volume produc­tion. A number of additional refinements were added to the Lewis Yield Tables in the period from 1958,

A. Keeves developed unpublished tables or extensions thereof for total production volume and basal area from ages 50 to 60; predominant height from ages 4 to 10, and basal area from ages 6 to 10. The age 50 to 60 extensions to the yield table are incorporated in RADGAYM II, C . .K. Pawsey (1964) used monthly remeasurements of tree height and diameter to derive estimates of mean monthly growth of radiata pine in South Australia. This information was used to extrapolate the Site Quality Table ~s et al. 1976) backwards from age 10 years to age 9.5 years, to coin­cide with the usual time of the allocation of site quality to a stand,

R. Boardman and G.R. Archer developed young-age total stem volume growth and yield functions for use with research tri­als. In addition. commencing in 1966, young age trends in basal area and predominant height were measured directly in first and second rotation stands at ages from one to eight years. In due course, yield curves were developed that were melded with the 1972 Lewis Yield Tables.

Growth and Yield functions Attempts to fit mathematical functions to describe stand yield are reported in the forestry literature as early as 1903 (Assman 1970). MacKinney (1937) is credited (Husch and Miller 1982) with the first appUcation of least squares regression to fit log transfonned yield functions in 1937, using mechanical cal­culators. Later the advent of electronic computers increased the power of the analytical methods that could be applied to the measurement data and resulting functions were incorpo­rated in software applications to simulate the growth of stands, The adoption of new technology has also been evident in South Australia (O'Hehir (995).

The growth models developed for South Australian radiata pine plantations by l.W. Leech used the Permanent Sample Plot database extending from the original measurements in 1935 up until the 1974 measurement year (Leech 1978; Ferguson and Leech 1978; Leech and Ferguson 1981). The development used advanced statistical modelling techniques including non linear and Generalised Least Squares regres­sion (Theil 1971). These methods allowed the use of the greater proportion of the available stand growth data in the Pennanent Sample Plot database and the development of models that are both statistically valid and pragmatic. The models give predictions that are consistent with the Lewis tables used previously.

Unthlnned and thinned stand models

Leech working with I.S. Ferguson, developed three further sets of models. They (Leech 1978, Leech and Ferguson 1981) described the construction of a series of model fonns to pre­dict the pericx1ic annual increment and yield of unthinned and thinned stands. These studies compared the perionnance of

206

-.62 . Growth and yield models for radiala pine

various non-linear models fitted by Ordinary Least Squares and Generalise~ Least Squares (Ferguson and Leech 1978) together with the 1972 Lewis Yield Table.

The Ordinary Least Squares investigation was extended to include other factors expected to influence stand growth and yield. The factors identified were thinning ap.d soil type. At­tributes of thinning were taken into account with respect to thinning type and thinning shock (the depression in expected growth immediately after a thinning). Seven groups of soil types were included by using dummy variables. Regional models were also identified.

The knowledge obtained from the use of Ordinary Least Squares was then used to develop a Generalised Least Squares model to fit an unthinned stand model as this enabled a two­stage formulation; the models being first fitted to the data from each plot; then in the second stage, extended to include site qUality. The Generalised Least Squares approach was introduced to 'overcome the statistical defects in the Ordi­nary Least Squares analysis' (Leech 1978). Ordinary Least Squares applied to data derived from the repeated measure­ment of the same units is likely to result in the underestima­tion of the parameter standard errors; the implication being that parameters that are in fact not significant may be included as explanatory yariabJes in the rn~el (Theil 1971).

The model fitted in the first stage was as follows: I

_ ll-eXP(-p(l-m)(A-a))jt:; Y - YIO ) 1 - exp(-p(l - m)10 - a)

. Where:

f is total production volume yield.

f,o is the total production volume yield to a 10 cm underbark diameter. the index of site quality. is the total production vol­ume yield.

The second stage model was:

p=po-Pl ln Y1

a = 10 exp(- a1Y.O)

m=O The above growth function was cal~ulated using Ylo values from the 1972 Lewis Yield Table as the site quality variable and integrated to provide a yield table (Table L and Appendix 1). Note that there is no point of inflect jon represented in this function because there was no indication of this to 10 em small end diameter underbark.

Thinned stand model- Posterior Generalised Least Squares

The development of the Posterior Generalised Least Squares model made use of a Bayesian approach (Leech 1978), build­ing on analyses by Ferguson, and the collaboration between Ferguson and Leech. The use of such methods with a fully infonnative prior obviates the major argument against arbi­trariness of the use of Bayesian statistics. The un thinned stand Generalised Least Squares function was used as an infonna­ti ve prior on a plot by plot basis to develop a model for thinned stands. The first stage model was of the fonn:

{l-eXP(-p(A-a)) }

y= Y10 l-exp(-p(IO-a))

and all first stage parameters were significantly different from zero.

Thinning and soil variables were omitted from the Bayesian Generalised Least Squares model because the parameter es­timates were not significantly different from zero. Neverthe­less, the approach used in the incorporation of the seven soil groups into the Ordinary Least Squares stand model does in­dicate the potential for developing different fonns of the same growth model for predicting the growth of stands influenced by different factors.

This approach to ensuring compatibility across growth mod­els could be applied to other factors such as the influence of post thinning fertilising on stand growth.

The above model bas been calculated using yield at age 10 values from the 1972 lewis Yield Table as the index of site quality (Table 1) and incorporated into a yield table (A~pen­dixI).

Comparison of Yield Models The South Australian yield tables have been converted ~here necessary from imperial units (cubic feet per acre) to metric (cubic metres per hectare), and the yield functions presented in tabular fonn to pennit comparisons to be made (Table 1 and Appendix I). Past comparisons have been made between the Lewis (Lewis.et al. 1976) yield table and various ~ield functions developed by Leech (1978) and also between the Lewis (Lewis tt al. 1976) and the Swain (1935) Yield Table (Boardman and McGuire 1990). .

leech. and Ferguson (1981) subjected the Lewis Tabl~ and other models to tests of predictive accuracy. They concluded that the Lewis Table was not significantly different from two of the best yield functions. However, .one of the yield func­tions (Mitscherlich) was preferre8, mainly because it llas an explicit mathematical fonn and approaches a limiting value of yield as age increases. Others, for example Boardman and McGuire (1990) in their examination of the role of zinc deficiency on forest manage­ment compared the 1972 Lewis Yield Table with the Swain (1935) yield table.

Inspection of Table 1 indicates a number of issues relating to the evolution of growth and yield tables and models for South Australia. It is clear that the site quality definitions used by Gray (1931 and 1938) bear little similarity to those applied by all other modellers. In addition, Gray identified fewer stand types. '):'he yield table prepared by Swain (1935) appears to share some common definitions of stand type with that of later ta­bles and functions. However, it was not until the yieldlable of Lewis (Lewis et al. 1976) and the functions of Leech (1978) that sufficient long tenn Permanent Sample Plot data· were available to allow confident modelling of total production volume (i.e. standing plus thinning plus mortality volume. to a 10 cm top diameter). Swain would only have had access to limJted mortality data compared with that available to '-ewis (Lewis et al. 1976) and Leech (1978). Nevertheless. com· parison with the later tables indicates a reasonable agreement. It is only Site Qualities I and II that noticeably diverge:from the general trends, and then only at later ages.

Comparison of the predictions of the yield tables of Swain (1935), Lewis (Lewis et al. 1976) and Leech (1978) indi­cates a reasonable agreement which is perhaps not surprising given that all were essentially based on data collected from

207

Australian Forestry Vol 63, No.3 pp. 159-165

the same plantations, even though the latter had double the age range availa~le. The mensurational data used for the de­velopment and testing of all tables and models was derived from plantations planted between 1910 and approximately 1962. The attributes of the stands in which growth plots were established were similar in regard to silvicultuf$:, genetics and environment including climate and soils.

Discussion The need to provide progressively better information to fa­cilitate more informed decision making has been the impera­tive for the origin and development of yield tables and growth functions in South Australia. This was especially true before 1941 when the development of yield tables was driven by the need to estimate the availability of log for industry expan­sion (Lewis 1975). Since the early 1970s significant improvements have been made to the genetic composition of plantations and the silvi­culture applied to them (Boardman 1988; Boardman and Leech 1995). These improvements are designed to, and known to change plantation yield. Predicting the growth and yield of plantations established since the 1970s by applying un­modified yield tables and models developed prior to 1980 incurs significant bias. In RADGAYM II, modifiers to site quality have been used to predict the appropriate increment in the respective yield table or growth function. This pro­vided a pragmatic, short tenn solution. However, it would be preferable to introduce explicit parameters into the growth functions to predict the effects of these other factors. Statistically rigorous techniques need to be developed to im­prove the predictive accuracy of growth models when ap-, plied to the new plantations. The ability to address these is­sues is the future challenge for South Australian growth and yield models, and the process of managing a resource required to meet the evolving demand for a wide range of products.

Acknowledgments Acknowledgment is given to the past and present professional and technical staff of ForestrySA, and its predecessor the Woods and Forests Department, involved in the establish­ment, implementation and maintenance of the rigorouS' mensurational standards that form the basis of the Permanent Sample Plot data from which growth and yield predictors are developed.

This paper is part of research towards a Doctor of Philoso­phy degree at the University of Melbourne by the senior au­thor who acknowledges the contribution of Professor I.S. Ferguson (as supervisor), for helpful comments on the draft. Permission to publish this paper has been granted by LB. Millard, General Manager ForestrySA. However, the views expressed are those of the authors and do not necessarily re­flect ForestrySA's position.

References Assman, E. (1970). The Principles oj Forest Yield Study. Ox­

ford. Pergamon Press. 506pp. Boardman, R. (1988). Living on the edge - the development

oj silviculture in South Australian pine plantations. Aus­tralian Forestry 51(3): 135-156.

Boardman. R. and J.w. Leech (1995). Monitoring procedures to assess sustainability in successive rotations of Pinus radiata D.Don plantations in South Australia. IUFRO S4.02.03, Stellenbosch. South Africa.

Boardman. R. and D.O. McGuire (1990). The role oJzinc in forestry. II. Zinc deficiency and forest mangement: effect on yield and silviculture of Pinus radiala plantations in South Australia. Forest Ecology and Management. 210: 207-218.

Carron, L.T. (1985). A History of Forestry in Australia. Syd­ney, Pennagon Press. 355pp.

Ferguson, I.S. and J.W. Leech (1978). Generalized least squares estimation ofyieldfunclions. Forest Science 24( 1): 27-42.

Gray, H.R. (1931). A yield table for Pinus radiala in South Australia. Canberra, Commonwealth Forestry Bureau. 41pp.

Husch, B. and C.I. Miller (1982). Forest Mensuration. New York. 402pp.

Jerram, M.R.K. (1949). Elementary Forest Mensuration. Lon­don, Thomas Murby and Co. 124pp.

Lane Poole, C.E. (1927). Assessment 1936.85 acres of Monterey pine Mount Burr Forest Reserve. Australian For­estry School. 27pp.

Leech, J.W. (1978). Radiata Pine Yield Models. Canberra, Australian National University. 262pp.

Leech, J.W. (1985). Analyses using the South Australian long term planning model. Modelling Trees, Stands and For­

. ests; Melbourne, Australia, University of Melbourne.

Leech, J.W. and I.S. Ferguson (1981). Comparison o/yield models for unthinned stands of rcu!iata pine. Australian Fores[ Research 11: 231-245. •

Lewis, N .B. (1963). Optimum thinning range of Pinus rat!iata in South Australia. Australian Forestry 27(2): 113-120.

Lewis, N.B. (1975). A hundred years oJStateforestry; South Australia 1875-1975. Woods and Forests Department. Bul­letin No.22. 122pp.

Lewis, N.B., A. Keeves and J.W. Leech (1976). Yield regula­tion in South Australian Pinus radiata plantations. Woods and Forests Department. Bulletin No.23. 174pp.

O'Hehir. J.F. (1995). Yield Regulation in South Australia. Tools or Toys: The certainty of the past, the challenge for the future. 16th !FA Biennial Conference, Ballarat, 275-280pp.

Fawsey, C. K. (1964). Height and diameter growth cycles in Pinus radiata. Australian Forest Research 1( 1): 3-8.

Schlich, W. (1911). SchUch's Manual of Forestry. Volume III. Forest Management. London, Bradbury, Agnew & Co. 403pp.

Schwappach, D. (1912). ErtragstaJeln der wicllligeren Holzarten. Neudamm. 82pp.

Spurr, S. H. (1952). Forest inventory. New York, Ronald Press. 476pp.

Swain, E.H.F. (1935). Pinus radiara pIantations in the S.E. of South Australia. Woods and Forests Department. Vol­ume 2, 206pp.

Theil, H. (1971). Principles Of Econometrics. North-Holland Publishing Company. 736pp.

208

164 Growth and yield models for radiata pine

Appendix Graphs showing the predicted volumes for yield tables and functions developed for South Australian pine stands.

MOUNT BURR UNTHINNEO STAND YIELD TABLE· GRAY 1931 -11100-.----------------------....

1~~------------------------------------~

"1400 1--------------------------4

1~r_--------------------------~

I 1000-----------------------------------4 I ~ 800 - ___________ - __ ~~_~ __ _

I'!

10 20 30 40 50 00 70

AGE (YEARS)

SE REGION UNTHINNED STAND YIELD TABLE· SWAIN 1935 1800

1\100

1-400

0:- 12110 15

~ " ~

~ ~

~ 600

g ~ V b 600 l-

V!

400

VII

200

10 20 30 40 50 110 70

AGE(YEARSI

PENOLA UNTHINNED STAND YIELD TABLE· GRAY 1938

11OOr-----------------------------------,

~~-------------------------------~

1~~------------------------------~

1300~-----------------------------~

·11000 1-----------:...-----------1

~ ~ 100

200~-----~---------------------~

1() 20 Ie) ... JIG .a ra f'DE (YfAAII1

SE REGION UNTHINNED STANO YIELD TABLE - JOLLY 1941 1&00

1800

1400

i 1200

~ 1000

~

~ i!.

~ &00

g 111

~ tIOO

V 400

V!

~ HI 20 30 40 so 00

...oE (yEARS)

209

-----------__________ wr-

. Australian Fort:slry Vo163. No.3 pp. J 59-165 165

MOUNT BURR THINNED STANO YIELD TABLE - LEWIS 1953 SE REGION UNTHINNED STAND YIELD TABLE· LEECH GlS 1978

1~r-------------------------------------1 1~.-__ ----__ ------------__ ------------~

1600 .. ------------.-------- 1600

1~00 1400

~ ~ g 1200 "

~

~

400

200

O~ __ ~ ____________________ --______ ~

o 10 20 30 50 70 10 20 30 40 110 70

AGE (YEARS) IIGE(YEAAS)

SE REGION THINNED STAND YIELD TABLE· LEWIS 1972 SE REGION THINNED STAND YIELD TABLE - LEECH GlS 1978

I~.-------------------------------------, 1600.-------__________________________ ~--~

1600

1400 --.-----~ l~OO

IN

~ 1200 •

IV

~ - v 12 ~ 1~ -. -

VI

~ => 600 ~ il

VM ~

~ 000

r:: ffi ::Ji III

~ 1200

~ IV

f:? 1000

~ ~ V

~ cl 800 >

~ VI

g I~ f2 ~

0 BOO 0 0: 0..

~ e VM

4OC) 200

200

10 ~o 60 70

Io.GE{yEARS)

O~--_4~--~----~----~--~----~--~ o 10 20 30 40 70

AGE (yEARS)

210

Appendix IV Use of the Regional Volume Table to determine stem volume

in thinning and fertiliser trials in radiata pine stands.

USE OF THE REGIONAL VOLUME TABLE TO DETERMINE STEM

VOLUME IN THINNING AND FERTILISER TRIALS IN RADIATA

PINE STANDS.

J.F.O'Hehir

ForestrySA, PO Box 162, Mount Gambier, South Australia 5290

For Research Working Group 2, Forest Measurement and Information,

27 November- 1 December 2000, Perth, Western Australia.

Summary

An interim study has indicated that errors introduced by using the Regional

Volume Table to estimate tree volumes in thinning and fertiliser trials were

sometimes statistically significant. However, for the purpose intended, where

errors were identified they were found to be practically unimportant. This was

an important conclusion as it simplifies the analysis and development of -

predictive models from a large and important experiment.

Introduction

In South Australia, mid-rotation nitrogen based fertiliser experiments

established beginning in the early 1940's had indicated the possibilities for

increasing the growth and yield of radiata pine stands and the data supported

some limited development of fertiliser response models. The need to

investigate any interaction on growth between the level of thinning and fertiliser

in radiata pine plantations led to the establishment in the south east of South

Australia of a large research experiment, Experimental Plot 190 (EP190). The

application of nitrogen and phosphorus-based fertiliser was expected to raise

the periodic annual increment of the Langsaeter Plateau (Langsaeter 1941),

211

however, it was unclear whether the shape or position of the plateau would

change.

There are a number of fertiliser experiments reported where only tree diameter

and height were used to estimate tree volume using a two-way volume table

without regard for tree form (Gessel et al. 1969; Mitchell and Kellogg 1972;

Lowell 1986). Meng (1981) states that 'measurements of growth responses

could be ... misleading if treatment effects on stem form were not considered'

and (Mitchell and Kellogg 1972) others have suggested that 'the estimation of

volume response to fertilisation in dominant trees from breast-height

measurements should be approached with caution.' Flewelling and Yang (1976)

suggest that 'the accuracy of tree volume equations, when used to compute

growth, may be biased by fertilization.' Woollons and Will (1975) and Whyte

and Mead (1976) both found that basal area measurements alone

underestimate the magnitude of fertiliser responses because the greatest

responses occur up the stem.

There are other examples where although stem form changes were found to be

associated with fertiliser application the effects were found to be either not

statistically or practically significant (Shoulders et al. 1988, McKee 1988).

These concerns needed to be evaluated in the South Australian situation to

determine the most appropriate analytical strategy and also if possible to see if

significant form differences could be discerned and to see whether any such

changes were ongoing or transitory.

Summary of Experimental Design and Mensuration of EP190

The levels of thinning intensity included in EP190 are defined by stocking

relative to the Optimum Thinning Guide (OTG) (Lewis et al. 1976) as the OTG,

OTG +25% and OTG -45% (OTG -45% to ensure a treatment well off the

Langsaeter plateau). Fertiliser dosages of 75, 150 and 300 kg/ha of nitrogen

were applied in a complete mineral fertiliser mixture. Untreated controls were

also established. The timing of the fertiliser applications were either one, or four

212

years after thinning, or both (except for the 300 kg treatment). Treatments were

included to investigate whether the response of multiple treatments was

multiplicative or additive.

A robust design is essential with fertiliser interaction experiments because the

responses are expected to be generally small relative to the standard error of

the measurement and it is difficult to find large, homogeneous plantation areas.

F our experimental sites were established in existing plantations, each with four

replicates of plots which were initially thinned to contain 25 trees each. Three

thinning and 12 fertiliser treatments were established in each replicate in a 31 x

44 factorial design with 4 missing treatments, equivalent to 144 plots at each

site. Subsequently, one of the sites (Hutchessons) was heavily affected by

Sirex noctilio induced mortality to the extent that the OTG+ treatment was

abandoned reducing the number of plots on that site to 96. The measurement

effort was also reduced to the extent that data from that site was excluded from

this study. There are currently four sites that comprise EP190 (Table 1).

Table 1 Four sites which comprise EP190.

Site name Site Assessed Site Past land use Year of

number Quality1 planting

Hutchessons 01 II first rotation plantation established on 1974

ex pasture site

Headquarters 02 IV second rotation plantation 1973 & 1972

Menzies 03 IV first rotation plantation established on 1956

ex pasture site

Glencoe Hill 05 VI fi rst rotation plantation established on 1962

ex native forest

1 Site Quality is a volume based index of productivity at a standard plantation age of 9.5 years (Lewis et al.

1976).

Basal area was measured annually beginning with the first thinning event after

the establishment of each site. Plot volume and predominant height (Lewis et

al. 1976) were measured one year after the first thinning event at all sites,

213

------------------------__ ~rt

except for Menzies (where for work scheduling reasons the volume

measurement was delayed for two years) and then again to coincide with the

next thinning. Plot volumes were calculated from volume lines derived from tree

volumes estimated using the Regional Volume Table (RVT - a four-way tree

volume equation, Lewis, and Mcintyre 1963 and Lewis, Mcintyre and Leech

1973).

The input parameters to the Regional Volume Table requires measurement of

tree height to the tip, with underbark diameters of the stem being estimated by

taking overbark measurements and estimating bark thickness with a 'Swedish'

bark gauge at 1.5 and 7.5 meters above the ground. The diameter estimates at

the two points on the stem provide a measure of taper. It was expected that the

this measure of taper would adequately detect any changes in tree shape.

However, it was necessary to test that this assumption was valid and if it was

found to be then the analysis of the volume data would be considerably simpler.

A smaller number of trees per plot were also measured using the three metre

Sectional method (Lewis et al. 1976) so that a comparison could be made with

the quicker but less precise Regional Volume Table estimates. This comparison

was intended to provide a correction to the Regional Volume Table volume

estimates if this was found to be necessary.

This study was intended to be interim as on completion of the experiment at

each site a large number of trees are to be felled and subjected to stem

analysis to conclusively determine the stem shape changes which may have

occurred throughout the experiment.

214

Data

There were two data sets available to study the stem shape changes

associated with thinning and fertiliser in combination. These data sets CQuid be

used for Stem Analysis and the Direct RVT -Sectional comparisons.

Stem Analysis Based RVT-Sectional Comparison

At Glencoe Hill 24 sample trees were selected at the time of the second

thinning event from plot surrounds for stem analysis, this was six years after the

fertiliser was applied. For work program reasons the thinning treatments

sampled were restricted to the OTG and OTG-, and the fertiliser treatments 0,

75, 150 and 300 kg nitrogen dosages which were applied one year after

thinning. These trees were subjectively sampled from each treatment to

represent the dominant, co-dominant and suppressed crown class categories

within each plot.

The trees were felled and disks were cut from the stem avoiding stem

irregularities that would complicate th<? measurement of radial increments

(Wood et al. 1999). Typically, ten disks were taken from each tree at

approximately three metre intervals. A disk from the butt was cut at

approximately 0.3 metres, at breast height (1.3 metres), and at the lower and

upper measurement points for the Regional Volume Table (1.5 and 7.5 metres).

The annual increment of each growth ring was measured in four directions and

averaged beginning at the start of the application of fertiliser in 1993 and

concluding in 1998. Tree heights for each year between 1993 and 1998 were

also estimated but the accuracy of these was believed to be poor, as it can be

difficult to determine the annual increment points of radiata pine trees growing

under South Australian conditions. However, accurate estimation of the annual

height increment is not critical where it is of the order of 0.5 metres per year or

less as with this experiment.

215

Direct RVT -Sectional Comparison

The Direct Sectional-RVT data were available for Headquarters, Menzies and

Glencoe Hill from measurements made at the time of the first and second

thinning events at each site. The first measurements were initiated at the time

of the first thinning event and so no thinning effects should be evident in

measurements taken at that time; however, by the second thinning event

treatment effects could be established.

When each site was thinned 10 trees from each plot were selected using a

stratified random sampling approach and then their volumes were estimated

using the Regional Volume Table. These trees were used to fit a volume line to

each plot (Lewis et al. 1976) and the standing plot volume estimated at the

commencement of the experiment and at the time of the next thinning. A

proportion of the sample trees were also measured by the three metre

Sectional method to test that form changes were being adequately detected by

allowing direct comparisons to be made of the stem volumes estimated by the

two methods.

Methods and Results

The objective of this study was to test the extent to which the mensuration is

sensitive to the changes in form that are likely to be caused by thinning and

fertiliser effects.

216

Stem Analysis Based RVT-Sectional Comparison

The first stage of the Sectional-RVT comparison from the stem analysis data

set involved plotting individual stem profiles (Appendix 1 contains two

examples). These plots indicated a stem form change associated in particular

with dominant trees that were subjected to the more extreme thinning and

fertiliser treatments in combination, relative to dominant trees in the control

plots. The growth appeared to be concentrated around the upper part of the

stem near the base of the green crown.

To confirm the effects indicated by the stem profile plots a quantitative analysis

was required. Measurements were made of a series of past diameters so a two­

stage approach was used to avoid any effects of serial correlation would not be

a concern when conducting hypothesis tests.

In the first stage Ordinary Least Squares (OlS) was used to develop a model

for each of the 6 sets of observations of the 24 trees for estimating the

Sectional volume using the Regional Volume Table volume as a predictor. In

the second stage the resulting parameters were analysed as summary

statistics. Plotting the Sectional against the Regional Volume Table estimates

indicated a simple linear relationship and so the first model fitted was:

5'EC = a + {JRVT,

where SEC is the tree volume estimated by the three metre Sectional method,

R VT is the tree volume estimated by the Regional Volume Table and fJ is the

parameter to be estimated using OlS. For most trees the intercept term was

not significantly different from zero, so the form of the first stage model was

simplified to:

SEC = fJRVT.

No clear trend was evident in the fJ values in the first stage models sorted by

fJ (Appendix 2), however, this needed to be confirmed with an Analysis of

Variance. Prior to the application of the Analysis of Variance a test of the

217

- -----~.~

Normality of the data was considered essential. For all tests of Normality in this

analysis the Kolmogorov-Smirnov 0 was calculated and its significance was

evaluated at a 95% confidence level. For n=24 trees the 0 was calculated as

0.9600 which is not significant.

The factors included in the Analysis of Variance were the two thinning

treatments (OTG and OTG-) , and four of the fertiliser dosages (0, 75, 150 and

300 kg nitrogen). The fertiliser dosage was clearly not significant, however, the

status of the thinning treatment was less clear so the Analysis of Variance was

refitted with the thinning variable only (Table 2). The thinning variable in the

refitted model was still not significant indicating that within the stem analysis

data set that the Regional Volume Table is a reasonable proxy for the three

metre Sectional method.

Table 2 Analysis of Variance for Stem Analysis Derived RVT -Sectional

Comparison.

Dependent Variable VOLRVT = THINNING

Source df S5 ms F Pr>F

THINNING 1 0.0025 0.0025 3.53 0.0738

Direct RVT - Sectional Comparison

Again there was a requirement to make multiple comparisons between

treatments which suggested the appropriateness of an Analysis of Variance.

However as always, irrespective of the results of the statistical analysis it was

necessary to consider the practical implications. The Direct RVT-Sectional

comparison consisted of two discrete sets of measurements, one taken at the

start and the other at the end of the first thinning cycle. It was appropriate to

test the two sets of measurements separately and establish if any differences

were caused by stem shape differences between treatments. The variable of

interest chosen was the difference between the tree volume estimated by the

Sectional and the Regional Volume Table methods standardised by dividing by

the Sectional volume (variable SSECMRVT).

218

RVT -Sectional Comparison at the start of the thinning cycle

The dependent variable was Normally distributed (0 for n=274 trees was

calculated as 0.9881 which is not significant) and it was valid to apply an

Analysis of Variance.

The factors included in the Analysis of Variance were site, thinning treatment

and the four fertiliser dosages (0, 75, 150 and 300 kg/ha nitrogen). As

expected, the thinning and fertiliser effects were not significant, however, the

site variable was strongly significant so the model was refitted with this variable

only (Table 3).

Table 3 RVT -Sectional Comparison at the start of the thinning cycle.

Dependent Variable SSECMRVT = SITE

Source df ss ms F Pr>F

SITE 2 0.0384 0.0192 23.94 0.0000

Further analysis with Tukey's Honestly Significant Difference (HSD; Sokal and

Rohlf 1981) test indicated that there were two distinct groups of the site

variable; Menzies being significantly different from the other sites (Table 4). The

Regional Volume Table was unbiased at Headquarters, exhibiting a small

negative bias at the other sites. The Regional Volume Table was the poorest

predictor at Menzies indicating in the worst case a bias of 2.90/0 in standing

volume.

219

Table 4 Direct Sectional- RVT - Analysis of Variance, at the start of the

thinning cycle: results of Tukey's HSD test.

SITE Observed Mean Equal To

( SeC-RVT) Sec

02 0.000 Site 05

03 "0.029 No other site

05 "0.007 Site 02

RVT -Sectional Comparison at the end of the thinning cycle

The variable of interest was Normally distributed (0 for n=482 trees was

calculated as 0.9852 which is not significant and was similar to the calculated 0

at the start of the experiment of 0.9881). It was concluded that it was

reasonable to apply an Analysis of Variance. The factors included in the

Analysis of Variance were site, thinning and fertiliser treatments. The fertiliser

treatments were not significant (to at least a 950/0 confidence level), however,

both site and thinning factors were significant so the model was refitted (Table

5) including only site and thinning.

Table 5 RVT -Sectional Comparison at the end of the thinning cycle.

Dependent Variable SSECMRVT = SITE + THINNING

Source df ss ms F Pr>F - - -

SITE 2 0.0236 0.0118 13.33 0.0000 --

THINNING 2 0.0124 0.0062 7.000 0.0010 --

Further analysis of the data with Tukey's HSO test on site and thinning factors

indicated that some were of the errors were significantly different from others.

The site results (Table 6) indicated that the errors at Headquarters and Menzies

were significantly different from each other but neither were significantly

different from Glencoe Hill. The OTG- and OTG thinning treatments were

220

significantly different from each other but the OTG+ results were not

significantly different from either of the other thinning treatments (Table 7).

Table 6 Direct Sectional-RVT - Analysis of Variance, at the end of the

thinning cycle: results of Tukey's HSD test.

SITE Observed Mean Equal To

(sec- RVT) Sec

02 0.016 Site 05

03 -0.002 Site 05

05 0.005 All other sites

Table 7 Direct Sectional-RVT - Analysis of Variance, at the end of the

thinning cycle: results of Tukey's HSD test.

THINNING Observed Mean Equal To

(sec -RVT) Sec

OTG- 0.014 Site 05

OTG -0.001 Site 05

OTG+ 0.002 All other sites

The maximum observed mean error for any site and thinning treatment

combination was only 1.6%, a difference considered small enough to be

insignificant in this situation where the standing volume for the plots were a

minimum of 300 m 3/ha and periodic annual increment for all treatments

exceeded 30 m3/ha/year. Testing thinning treatments separately indicated an

error of 1.4% which was also considered insignificant.

221

--

Discussion and Conclusions

The conclusions of this study indicate that a change in tree form takes place

particularly with the heavy thinning and fertiliser treatments in combination.

Limited evidence from the stem analysis of 24 trees at Glencoe ind icates that

the change may be transitory. Despite these form changes there is no

indication that the Regional Volume Table should not be used to estimate the

volume of trees in even heavily thinned and fertilised plots in EP190. The close

agreement between tree volumes estimated by the two methods confirms that

no correction factor is required.

Author's Acknowledgments

Acknowledgment is given to past and present professional and technical staff of

ForestrySA, in the establishment, implementation and maintenance of the

rigorous mensuration standards that form the basis of the EP190 data on which

this study relies.

The need for this paper evolved from research towards a Doctor of Phil.osophy

Degree at the University of Melbourne. I acknowledge the contribution of my

supervisors, Professor I.S. Ferguson and Dr J.W. Leech in the helpful

comments provided on the draft.

Permission to publish this paper has been granted by Mr I.B. Millard, General

Manager ForestrySA. However, the views expressed are those of the author

and do not necessarily reflect ForestrySA's position.

222

References

Flewelling, J.W., and Yang, Y.C. (1976). Tree volume table growth relationships

possibly affected by fertilization. For. Sci. 22(1): 58-60.

Gessel, S.P., Stoate, T.N., and Turnbull, K.J. (1969). The growth behavior of

Douglas-fir with nitrogenous fertilizer in western Washington. Institute of

Forest Products Report NO.2.

Langsaeter, A. (1941). Om tynning i enaldret gran - og furuskog. Norske

skogforsokresen Meddeldser 8: 131-216.

Lewis, N. B. and G. A. Mcintyre (1963). Regional Volume Table for Pinus

radiata in South Australia (Imperial Edition). Adelaide, Woods and

Forests Department: 59.

Lewis, N. B., G. A. Mcintyre, et al. (1973). Regional Volume Table for Pinus

radiata in South Australia (Metric Edition). Adelaide, Woods and Forests

Department: 64.

Lewis, N.B., Keeves, A., and Leech, J.W. (1976). Yield regulation in South

Australian Pinus radiata plantations. Woods and Forests Dept. Bulletin

No.23.

Lowell, K. (1986). A flexible polynomial taper equation and its suitability for

estimating stem profiles and volumes of fertilized and unf~rtili~ed radiata

pine trees. Aust. For. Res. 16: 165-174.

Meng, C.H. (1981). Detection of stem form change after stand treatment. Can.

J. For. Res. 11: 105-111.

McKee, W. H. (1988). Changes in pattern of stem growth in pole-sized loblolly

pine after sewage sludge application. In Fifth Biennial Southern

Silvicultural Research Conference, 1-3 Nov. 1988, Memphis, Tennessee,

U.S.A. USDA. pp. 461-463.

Mitchell, K.J. and R. M. Kellogg (1972). Distribution of area increment over the

bole of fertilized Douglas fir. Can. J. For. Res. 2: 95-97.

Shoulders, E., Baldwin, V.C., and Tiarks, A.E. (1988). Mid-rotation fertilization

affects stem form in planted slash pine. In Fifth Biennial Southern

Silvicultural Research Conference, 1-3 Nov. 1988, Memphis, Tennessee,

U.S.A. USDA. pp. 455-459.

223

Sokal, R. R. and F. J. Rohlf (1981). Biometry. New York, W.H. Freeman and

Company.

Whyte, A.G.D., and Mead D.J. (1976). Quantifying responses to fertiliser in the

growth of radiata pine. N. Z. J. For. Res. 6(3): 432-444.

Wood, G.B., Turner, B.J., and Brack C.L. (1999). Code of Forest Mensuration

Practice: A guide to good tree measurement practice in Australia and

New Zealand, Research Working Group #2.

Woollons, R.C., and Will G.M. (1975). Increasing growth in high production

radiata pine stands by nitrogen fertilisers. N. Z. J. For. 20: 243-253.

224

Appendix 1 Examples of stem form plots from stem analysis

35

30

25

-~ 20 I-::J: (!) w 15 ::J:

10

5

GLENCOE HILL: OTG-, OKG N, DOMINANT TREE

-.:::'-.~ "~~

'-'-.~ .. ,,'-.~ -,\~

''\\\\ .. ~ '\'\~

.. ~~

\\\ \\\\ '~~~ "Z'\~ \~ \\~ \~ \\~ \~ \\~

1994 1995 1996 1997 1998

00 5 10 15 20 25 30 35 40 45 50 DIAMETER UNDER BARK (eM)

225

GLENCOE HILL: OTG·, 300KG N, DOMINANT TREE 35

30 "''':.''.~ ----w-~·- 1994 '-.':..

":" ~ ---.. --- 1995 ',<" ~ - -.- - 1996

25 '~'-....~ 1997 . '" '" ",,:

- --..--

.,\.'\. ~ 1998 - \\. \'\ ~ 20 \ \ \'\ I- "\ -\-\'\ J: '\ \ \\ (!) \, \,-\\ W 15

\ \ \ \ J: ~\\"\\

10 "\ "\ \\ -\ "'\- \\

1 '\\ ~\ ,'"

\. \ \ \ 'H 5 '~.'~ ~~

\ \ \\ ':.. .~ ).\.

00 5 10 15 20 25 30 35 40 45 50 55 60 DIAMETER UNDER BARK (eM)

226

Minerva Access is the Institutional Repository of The University of Melbourne

Author/s:

O'Hehir, James Francis

Title:

Growth and yield models for South Australian radiata pine plantations: incorporating fertilising

and thinning

Date:

2001

Citation:

O'Hehir, J. F. (2001). Growth and yield models for South Australian radiata pine plantations:

incorporating fertilising and thinning. PhD thesis, School of Resource Management, Forestry,

and Amenity Horticulture, The University of Melbourne.

Publication Status:

Unpublished

Persistent Link:

http://hdl.handle.net/11343/36548

File Description:

Growth and yield models for South Australian radiata pine plantations: incorporating fertilising

and thinning

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