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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
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IUFRO, 8 pp.
Zeide, B. (1993) Analysis of growth equations. Forest Science, 39(3):594-
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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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