Allometric equations for biomass and yield predictions of ...
Transcript of Allometric equations for biomass and yield predictions of ...
Allometric equations for biomass and yield predictions of coffee,
enset and khat in Southern Ethiopia
BSc Thesis
M.J. (Matheo) Mourik
Student registration number 930107585030
Supervisors
Dr.ir. K.K.E. (Katrien) Descheemaeker, Plant Production Systems
Dr.ir. G.W.J. (Gerrie) van de Ven, Plant Production Systems
March 2, 2016
BSc Thesis Plant Sciences (YPS-82318)
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Abstract Traditional homegardens in Sidama, Ethiopia are being replaced by cash crop monocultures as a
result of food shortage and commercialization. Little attention has been paid to develop allometric
models for perennials to relate geometric variables to biomass components. The objective of this
research was to derive linear allometric equations for twig yield of khat (Catha edulis), bean yield of
coffee (Coffea arabica) and biomass and food products of enset (Ensete ventricosum). Data gathered
from 100 khat plants, 50 coffee plants and 20 enset plants were used for analysis. For khat and
coffee crown area was the best performing predictor of yield with maximum adj. R2 of 0.77 for khat
and 0.80 for coffee. When combined with environmental data influencing yearly yields of khat and
coffee these structural characteristics of the perennials can form the basis for a yield prediction
model. Diameter at 50 cm height was the most important variable for enset biomass. Model
performance was best for the pseudostem (adj. R2 0.92) followed by corm (adj. R2 0.88) and leaves
(adj. R2 0.62). Also for the kocho food product model performance was good with adj. R2 of 0.89.
These results show that simple linear equations based on easily measured geometric characteristics
can provide reliable predictions of enset products.
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Contents Abstract .................................................................................................................................................... i
1. Introduction ......................................................................................................................................... 1
1.1 The shift from homegardens to mono-cropping ........................................................................... 1
1.2 Using allometry in plants to estimate biomass ............................................................................. 2
1.3 Description of the perennial homegarden crops .......................................................................... 3
1.3.1 Coffee ..................................................................................................................................... 3
1.3.2 Enset ....................................................................................................................................... 3
1.3.3 Khat......................................................................................................................................... 3
1.4 Existing allometric relationships for coffee and enset .................................................................. 3
1.4.1 Coffee ..................................................................................................................................... 4
1.4.2 Enset ....................................................................................................................................... 4
2. Materials and methods ....................................................................................................................... 5
2.1 Study site and data collection ....................................................................................................... 5
2.1.1 Khat......................................................................................................................................... 5
2.1.2 Coffee ..................................................................................................................................... 5
2.1.3 Enset ....................................................................................................................................... 6
2.2 Data transformations .............................................................................................................. 6
2.3 Goodness-of-fit statistics ............................................................................................................... 7
2.4 Data analysis and modelling .......................................................................................................... 8
2.4.1 Data analysis ........................................................................................................................... 8
2.4.2 Model selection using adjusted R2 ......................................................................................... 8
2.4.3 Detailed model analysis .......................................................................................................... 9
2.4.4 Specific approach per crop ..................................................................................................... 9
3. Results ............................................................................................................................................... 10
3.1 Khat.............................................................................................................................................. 10
3.2 Coffee .......................................................................................................................................... 12
3.3 Enset ............................................................................................................................................ 14
3.3.1 Total dry weight .................................................................................................................... 14
3.3.2 Corm dry weight ................................................................................................................... 14
3.3.3 Edible pseudostem dry weight ............................................................................................. 14
3.3.4 Leave dry weight .................................................................................................................. 15
3.3.5 Kocho dry weight .................................................................................................................. 15
3.3.6 Bula dry weight ..................................................................................................................... 15
4. Discussion .......................................................................................................................................... 17
4.1 Khat.............................................................................................................................................. 17
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4.2 Coffee .......................................................................................................................................... 17
4.3 Enset ............................................................................................................................................ 18
4.4 Allometric equations on farm level ......................................................................................... 19
5. Acknowledgements ........................................................................................................................... 19
6. References ......................................................................................................................................... 20
7. Appendices ........................................................................................................................................ 22
7.1 Appendix I – Allometric equations for khat twig dry weight....................................................... 22
7.2 Appendix II – Allometric equations for coffee bean dry weight ................................................. 23
7.3 Appendix III – Allometric equations for dry weight of biomass and food products of enset ..... 24
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1. Introduction
1.1 The shift from homegardens to mono-cropping A substantial part of agriculture in southern Ethiopia is dominated by small homegardens, which
provide a sustainable production of human food, cattle fodder and resources for buildings in the
past. Often these homegardens are part of an agroforestry system, where crops are grown along
with local forest species (Negash, 2013). A great diversity of crops is cultivated in these
homegardens, such as vegetables, trees, enset (Ensete ventricosum (Welw.) Cheesman) and coffee
(Coffea arabica L.) (Figure 1). Enset is of major importance as staple food source while coffee
generates the cash income for the farmer. This diversification of different crop species with their
different harvest times and end products has traditionally provided stable food and cash resources
for the families depending on them (Abebe, 2005).
Nevertheless, this type of system has undergone a change towards mono-cropping systems (Figure
2), dominated by cash crops as maize (Zea mays L.), pineapple (Ananas comosus (L.) Merr.) or khat
(Catha edulis Forskal) (Tsegaye, 2002, Abebe et al., 2010). It is assumed that this change is connected
to the growing population in Ethiopia and commercialization, stimulating the intensive exploration of
the cultivated land (Dessie and Kinlund, 2008). On the one hand, this shift to mono-cropping
obviously generates a flow of cash
to the farming households. On the
other hand the crop diversity on
such farms is lower, making them
more vulnerable to extreme
environmental conditions, pests and
diseases, resulting in higher risks of
crop failure. Price fluctuations are
another concern for farmers
dependent on a cash crop.
The current food production system
with many small homegardens is no
longer sufficient to maintain food
security. The rapid increase of
monoculture systems is a concern in
terms of sustainability and farmers
dependence on cash flows and
changing market conditions. For
example, the expanding khat
production is associated with
reduced availability of fodder from
crop residues and enset leaves,
resulting in a change in livestock
composition from oxen towards
animals like goats which are less
dependent on crop residues (Feyisa
and Aune, 2003). Another concern
is the increasing consumption of
khat by farmers, their families and
local young adults (Feyisa and Aune,
2003). Due to the high profitability
Figure 1 A traditional homegarden with a diversity of crops like enset, coffee, maize and vegetables grown together Source: Van de Ven, 2011
Figure 2 A field with khat grown in monoculture, guarded in the yield season to protect the valuable twigs. Traditional crop species like enset are displaced to the margins of the field. Source: Van de Ven, 2013
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of the crop, khat producers are able to hire labor, becoming employers themselves (Feyisa and Aune,
2003). Another important issue is the relation between khat expansion and the rate of forest decline,
studied for the Wondo Genet area of southcentral Ethiopia (Dessie and Kinlund, 2008). All these
examples show the impact of expanding monocultures on the economic, environmental and social
dimensions of sustainability.
There has been done a lot of research on aspects of homegardens, including farm type
characterisation, nutrition balance and sustainability of the system. Little research has been done on
estimation and prediction of biomass production and yield of edible products from the perennial
crops khat, coffee, enset. Accurately estimated yields for both the homegarden and monocropping
system can provide valuable information about the differences between the systems in terms of
nutrient flows, direct food production and cash incomes. Therefore more research is necessary to
gain insight in the actual productivity of the main crops of both the traditional and upcoming way of
farming. The development of allometric equations using simple measurable plant variables and dry
weight of yield as input could be a powerful tool for farmers and researchers to predict the yield on
plant and farm level.
The aim of this research is to develop linear allometric equations to predict khat twig yield, coffee
bean yield and enset yield on homegardens in Sidama, Ethiopia. The objectives linked to the research
subject are:
(1) to provide an overview of existing allometric relationships for these crops from literature
(2) to analyse data from Sidama,Ethiopia if relations exist between measured crop structure variables
and yield and to compose a set of allometric equations with linear regression analysis
(3) to test model performance by calculating the goodness-of-fit statistics and evaluating the plots of
the regression analysis.
(4) to construct a ranking of the models for each crop based on goodness-of-fit statistics and to
compare these with the existing allometric equations from literature.
1.2 Using allometry in plants to estimate biomass In trees growing under natural conditions it is observed that the proportions between e.g. height and diameter or biomass and diameter are roughly the same for all trees of a species when growth conditions are the same (Picard et al., 2012). This principle is called allometry, often used for prediction of variables like total biomass from another variable of that tree. For instance, total height, diameter at breast height (dbh), crown area and basal area are used in allometric equations to estimate total biomass (Parresol, 1999, Segura et al., 2006). Most allometric equations have been developed for forest systems predicting total biomass of trees growing under natural conditions. Using allometric equations for crops or trees in agroforestry systems is more difficult, because of differences in architecture as a result of management of plants or trees by farmers (Segura et al., 2006). Despite this limitation, models for reliable estimates of biomass production would be very useful in productivity and sustainability assessments. For several crops including coffee and enset allometric relationships have been derived (Segura et al., 2006, Negash et al., 2013, Negash et al., 2012, Hairiah et al., 2001). The allometric equations for coffee are used to predict total biomass of the plants. At this moment there is no information found in literature about allometric equations for khat. To construct a set of allometric relations for a crop data is gathered by non-destructive and destructive measurements, including all variables of interest, hereafter referred to as crop structure variables. Graphs plotting the variable of interest (yield, biomass) against an easily measured crop structure variables give an indication about which measured characteristics might be good predictors for yield or total biomass. Once the general form of the equation is obtained the exact values of the equation parameters are determined by regression analysis (Picard et al., 2012). It is often observed that the derived equations are specific for a certain species and location. Therefore in most cases
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individual parameterization is required for location and species (Negash et al., 2013, Youkhana and Idol, 2011).
1.3 Description of the perennial homegarden crops
1.3.1 Coffee Coffee (Coffea arabica L.) is an evergreen shrub, grown for the production of coffee berries and
beans. The plant is shade tolerant: moderate shading promotes a slower ripening of the fruits
ensuring good quality, production and bean size (Vaast et al., 2006). Multi-stemmed plants are
desired for higher production and often the plants are pruned to increase bean production (Negash
et al., 2013). Although there is much heterogeneity in cultivation of coffee, four dominant
management systems can be distinguished: forest coffee, semi-forest coffee, garden coffee and
plantation coffee (Labouisse et al 2008). The garden coffee management system is associated with
the small homegardens, where coffee is grown together with other crops (Negash et al., 2013,
Labouisse et al., 2008). In southern Ethiopia coffee fulfils an important role as cash crop for the
homegarden households (Melisse, 2012).
1.3.2 Enset Enset (Ensete ventricosum (Welw.) Cheesman) is a large single-stemmed perennial plant also known
as ‘false banana’ and is related to banana (Musa spp.). In Ethiopia the plant has been domesticated
from the wild (Bizuayehu, 2008) and functions as an important food source for the population
(Kanshie, 2002, Tsegaye, 2002). Almost all plant parts are used: the corm and edible pseudostem are
processed for food, leaves are used as roofing material or together with other plant parts as livestock
feed (Melisse, 2012).
For enset four main types of cropping systems are mentioned with enset as major staple food, co-
staple food, secondary crop or where enset is of minor importance (Negash et al., 2012). The
cultivation of enset is concentrated in the central and southern parts of the Ethiopia, with best
cultivation conditions between 2,000 and 2,700 meter above sea level (Negash et al., 2012).
The two most important food products for human consumption derived from enset plant parts are
kocho and bula. Kocho is a flour from which bread-like products are made. To produce kocho a
mixture of corm and pseudostem biomass is first fermented and then squeezed to remove the
moisture. Bula is the food of the highest quality, derived from an unfermented biomass mixture of
corm and pseudostem which is squeezed to remove moisture (Kanshie, 2002).
1.3.3 Khat Khat (Catha edulis, Forskal) is an evergreen tree cultivated for the production of fresh young leaves
and twigs that are chewed as a stimulant. The maximum height is around 25 meters, but as
cultivated crop it is kept at a maximum height of 3-4 meters for easy managing and yielding (Feyisa
and Aune, 2003). Khat is a cash-crop of increasing importance in Ethiopia, more and more grown in
monoculture (Dessie and Kinlund, 2008). Khat grows well at the altitude range between 1,500 and
2,100 meters (Feyisa and Aune, 2003). During the last years much attention is paid to the large
expansion of khat cultivation in Ethiopia (Dessie and Kinlund, 2008, Feyisa and Aune, 2003, Melisse,
2012) displacing coffee, enset and other crops traditionally grown on the Ethiopian homegardens. At
this moment there is a lack of information about productivity and yield of khat in Ethiopia.
1.4 Existing allometric relationships for coffee and enset Allometric equations for estimation of biomass or edible products of crops are scarce. Some of the
models constructed for coffee and enset are listed below. Allometric relationships for khat are not
found yet.
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1.4.1 Coffee Segura (2006) developed allometric equations for estimation of aboveground biomass of coffee in
Nicaragua. Both linear and non-linear regression analyses were used to predict biomass. The models
were selected using the adjusted coefficient of determination (adjusted R2), mean square error
(MSE), root mean square error (RMSE), Furnival index (FI), the predicted residuals sum of squares
(PRESS) and the biologic logic of the model. The best performing model predicting total biomass (BT)
is an equation with log10 – log10 transformation using diameter at 15 cm height (d15) and total height
(h) as crop structure variables (Table 1).
Negash (2013) developed allometric equations for estimation of aboveground biomass of coffee (BT)
in the Rift Valley, Ethiopia. Power equations were fitted and parameterized using non-linear
regression analysis. The best model was selected by the coefficient of determination (R2), root mean
square error (RMSE), average bias (B), average absolute bias (AB), prediction residuals sum of
squares (PRESS) and index of agreement (D). The best performing model for total and plant
component biomass of stem, branches and leaves is a square power equation using diameter at 40
cm height (d40) as crop structure variable (Table 1).
1.4.2 Enset Negash, 2012 developed allometric equations for estimation of biomass of enset in the Rift Valley, Ethiopia. Linear allometric models with untransformed and log-transformed data and nonlinear allometric models were determined for total biomass and biomass components separately. Goodness-of-fit statistics for model performance used in this research are the coefficient of determination (R2), root mean square error (RMSE), average bias (B), average absolute bias (AB), prediction residuals sum of squares (PRESS) and index of agreement (D). The best performing model for estimation of total biomass includes diameter at 10 cm height as crop structure variable in a power equation (Table 1). For estimation of biomass of the different plant components corm, pseudostem and leaves a power equation including d10 and height (H) was giving the best results (Table 1).
Table 1 Existing allometric equations in literature for total biomass of coffee and enset in Ethiopia
Allometric equation b1 b2 b3 R2 R2 adj. RMSE PRESS D
Coffee
log10(BT) = b1 + b2 * log10(d15) + b3 *log10(h) 1.113 1.578 0.581 - 0.94 0.15 2.21 - BT = b1 * d40
2 0.147 0.80 - 2.67 1723.46 0.94
Enset
BT = b1 * d10 b2 4*10-4 2.770 0.90 - 1.30 125.62 0.97
BT = b1 * d10b2 * hb3 7*10-4 2.571 0.102 0.91 - 1.29 122.67 0.98
With BT total biomass, d10, d15 and d40 diameter at 10, 15 and 40 cm height respectively and h total height. b1, b2 and b3 are model coefficients. R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares and D index of agreement.
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2. Materials and methods
2.1 Study site and data collection For this research data was used from field measurements on khat, coffee and enset. Field
measurements were performed in the Sidama region, southern Ethiopia by B.T. Melisse as a part of
his PhD project. Sidama zone is located at 5°45’ - 6°45’ N and 38° - 39° E. In this zone 19 districts,
locally named Woredas, can be distinguished. Sidama zone is one of the most densely populated
zones with over 450 people per km2 (CSA, 2007). Based on calculations of the CSA, at this moment
the population in Sidama zone exceeds 500 people per km2 (CSA, 2014). The average landholding is
estimated at 0.25 – 1.2 ha (Tadele, 2008). In Sidama zone four districts were selected covering the
midland and highland agro-ecological zones (AEZ) (Melisse, 2012). In most of the districts in Sidama
zone a homegarden system with both enset and coffee as main crops is most common (Melisse,
2012). Several crop structure variables were determined on 10 farms in the context of determining
the productivity of the different homegarden systems (Melisse, 2012). From these farms, 6 were
located in the midland zone and 4 farms were located in the highland zone. A detailed description for
the data of each crop is given below.
2.1.1 Khat For khat, data was collected for two different cultivation systems: farms with tall khat plants with
maximum height up to 3 meters and farms with pruned khat plants with maximum height up to 1
meter, further mentioned as dwarf plants. For both cultivation types measurements were done on
10 farms, 5 plants per farm, so 50 plants per cultivation type in total. The following crop structure
variables and biomass components were used in the analysis:
- Total height
- Crown area
- Diameter of the stems per plant at ground
- Fresh and dry weight of leaves and stems of the twigs
Most of the plants were multi-stemmed and therefore the diameter equivalent was calculated for d40
and d130 by taking the square root of the summed squared diameters of the stems (Eq. 1).
diameter equivalent = √∑ di2n
i=1 (Eq. 1)
where n = number of stems, i = 1,2,…,n and di is the diameter of the ith stem.
2.1.2 Coffee On 10 farms in the Sidama region the following crop structure variables and biomass components
were measured on 5 randomly selected coffee plants per farm, 50 coffee plants in total. The
measurements were non-destructive, except for the coffee berries, of which the dry weights were
determined.
- Total height
- Crown height
- Crown area
- Diameter of stems at heights of 40 cm (d40) and 130 cm (d130)
- Total fresh weight of coffee berries
- Subsample fresh and dry weight of coffee berries
- Subsample dry weight of coffee beans
- Subsample dry weight of coffee berry flesh
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From this data the total dry weight of coffee berries, beans and flesh was calculated. Because all
plants were multi-stemmed the same calculation was done as for khat to obtain the diameter
equivalent (Eq. 1).
2.1.3 Enset From both the midland zone and highland zone 10 plants
were selected, 20 enset plants in total. The age of the
plants varied from 3-7 years. Per region two plants of the
same age were chosen.
Both non-destructive and destructive measurements have
been done yielding the following crop structure variables
and biomass components. For the definitions of the
different plant parts see Figure 3.
- Total height: distance from ground to the petiole
of the last emerging leaf
- Crown height: difference between total height
and pseudostem height
- Pseudostem height, see Figure 3
- Edible pseudostem height: the part of the
pseudostem used for production of food, always
shorter than pseudostem height. The upper part
of the pseudostem consists mostly of leaf sheaths
and is therefore not used in food production.
- Diameter of the pseudostem at heights of 20 cm
(d20), 50 cm (d50), 130 cm (d130) and at the edible
pseudostem height
- Fresh weight of corm, edible pseudostem and
leaves
- Subsample fresh and dry weight of corm, edible pseudostem and leaves
Besides these variables the amounts of kocho and bula harvested per plant were measured:
- Fresh weight of fermented kocho before squeezing
- Subsample fresh and dry weight of kocho before and after squeezing
- Fresh weight of bula
- Subsample fresh and dry weight of bula
From this data the total dry weight of the different plant parts and food products was calculated.
2.2 Data transformations In linear regression analysis the following four assumptions should be justified: the relationship
between the dependent and independent variable is linear (1), the errors are statistical independent
from each other (2), there is constant variance of the errors (homoscedasticity) (3) and normality of
the error distribution (4) (Ott and Longnecker, 2008). The linearity assumption can be checked with a
scatterplot and residuals plot. A violation of the constant variance assumption can also be revealed
with the residuals plot of the regression model. When there is an unequal spread of the points
around zero and a bowed or funnel shaped pattern is visible, the assumptions of linearity and
constant variance are possibly violated. Assumption (2) about the independence of the errors is often
only violated when time series data is used: more measurements on one measurement unit over
Figure 3 Schematic drawing of a flowering enset plant with the names of the different plant parts. Source: Tsegaye, 2002
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time. Independence of the errors do not give a problem when the sampling of the measurement
units is done random and with no interaction between measurement units. With a normal probability
plot like the quantile-quantile plot (Q-Q plot) the assumption of normality of the errors can be
tested. When the errors follow a normal distribution, the points in the Q-Q plot will overlap with the
straight diagonal reference line.
For biological data it is a general trend that the greater the volume or biomass of organisms, the
greater the variability of the volume or biomass. This principle of non-constant variance, called
heteroscedasticity, applies also to plants (Picard et al., 2012). In most cases the relationship between
crop structure variable and response variable is best approached by a power function or exponential
function (Picard et al., 2012). When possible these contradictions of the linear regression
assumptions should be eliminated by transformation of the data. Using the natural logarithm of both
the response variable and the crop structure variable renders the power relation linear (Eq. 2). For an
exponential function, taking the natural logarithm of the response variable results in a linear function
(Eq. 3). Also the amount of heteroscedasticity is decreased by using log transformation, a crucial
factor as homoscedasticity is one of the assumptions for linear regression.
Y = aXb {X′ = ln XY′ = ln Y
ln Y = ln a + b ln X Eq. (2)
Y = a𝑒bX {X′ = X Y′ = ln Y
ln Y = ln a + bX Eq. (3)
With Y the response variable, X the crop structure variable and a and b the coefficients of the
equation.
2.3 Goodness-of-fit statistics To test the performance of allometric equations, several goodness-of-fit statistics were
recommended in earlier studies on allometric equations (Negash, 2013, Kozak and Kozak, 2003). The
list of goodness-of-fit statistics stated below could be expanded further, because much more test
statistics and procedures are available. In this research most of the goodness-of-fit statistics are the
same as the ones used by Negash (2013) to be able to compare the results for the analysis of enset.
The test statistics used are root mean square error (RMSE), absolute bias (AB), prediction residuals
sum of squares (PRESS) and index of agreement (D), see equations below.
Instead of the coefficient of determination (R2) used by Negash, 2013, the adjusted coefficient of
determination is used (adj. R2), see Eq. 4. This because R2 is always increased when an extra predictor
is added to a linear model. The adjusted R2 does not automatically increase with addition of an extra
variable, but only increases when the new predictor enhances model performance above what would
be obtained by chance. RMSE is the square root of the squared differences between observed and
predicted values divided by the number of observations (Eq. 5). PRESS can be used as cross-validation
to test model performance, when no other dataset is available from a particular region to test the
model directly. The procedure for the PRESS statistic makes for each observed data point a
prediction of that data point while the observation itself is excluded in the calculation. The sum of
the squared differences between observations and predictions gives the value for PRESS (Eq. 6). The
index of agreement is a standardized measure of the degree of model prediction error (Eq. 7). The
value of AB is defined as the sum of absolute differences between observed and predicted values
divided by the number of observations (Eq. 8). An equation with good performance should have
values up to 1 for R2 and D and low values for RMSE, AB and PRESS.
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adj. R2 = 1 − (1 − R2)n−1
n−p−1 , with R2 = 1 −
∑ (Yi−Yi)2 ni=1
∑ (Yi−Yi)2ni=1
(Eq. 4)
RMSE = √∑ (Yi−Yi)2n
i=1
n (Eq. 5)
PRESS = ∑ (Yi − Yi,−i)2n
i=1 (Eq.6)
D = 1 − ∑ (Yi−Yi)
2ni=1
∑ (|Yi−Y|+|Yi−Yi|)2n
i=1
(Eq. 7)
AB = ∑ |Yi−Yi|n
i=1
n (Eq. 8)
where n = number of observations, i = 1, 2,…,n; p = number of predictors, Yi are the observations of the response variable, Ŷi is the predicted value of Yi, Ȳ is the average of Yi, Ŷi,-i is the prediction of the ith data point by an equation that did not make use of the ith point in the estimation of the parameters.
2.4 Data analysis and modelling
2.4.1 Data analysis In this section the general approach as used for each of the three crops is described. The first step of
the data analysis consists of the plotting of the response variable against crop structure variables in
order to see if any linear patterns or relationships become visible. A linear pattern between a crop
structure variable and response variable was interpreted as an indication of potential predictive
value of this crop’s structure variable. When the original data did not show a linear pattern, log
transformations of the data were used. Two different transformations were used: taking the natural
logarithm from the response variable, further mentioned as single log transformation, or from both
the response and crop structure variable, further mentioned as double log transformation.
2.4.2 Model selection using adjusted R2 Because of the numerous combinations which could be made between the crop structure variables
and a response variable an approach for first-cut model selection was necessary. The result was a
selection of linear models consisting of one or more crop structure variables as predictors of the
response variable. This selection was obtained with the leaps package in RStudio (RStudio, 2015)
based on two algorithms, one based on the highest adjusted R2 and one based on the lowest BIC
(Bayesian Information Criterion). The leaps package searched for the best subsets of the independent
variables for prediction of the dependent variable. The output was a table with subsets of
independent variables with highest adjusted R2 or lowest BIC. As a control, model selection was
carried out with the procedures of forward selection and backward selection in the leaps package.
Forward selection starts with one independent variable as predictor. In each step an extra
independent variable is added to the model and model performance is evaluated. Addition of
independent variables stops when no further gain in model performance is performed. The backward
selection procedure starts with a model with all independent values incorporated and in each
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calculation step the variable with lowest performance is removed until best model performance is
reached. The choice for addition or removal of independent variables in the forward and backward
selection method respectively was based on the value of AIC (Aikake Information Criterion).
Dependent on the height of adjusted R2 the 10 best performing models were listed for more detailed
analysis. This was done for both the single and double log transformation, yielding around 20 models
per response variable for further examination.
2.4.3 Detailed model analysis From each of the selected models the model coefficients were listed and the model performance was
tested with RStudio. Statistical significance of the model coefficients was determined, only models
with coefficients of crop structure variables significantly different from zero were selected. The
prerequisite of significance was not applied to the intercept of the equations, because the removal of
the intercept would force the regression equation through the origin. After calculation of the
goodness-of-fit statistics the linearity of Q-Q plots and the equal spread of points in residual plots
was evaluated. The goodness-of-fit statistics of these models were ranked and the ranks summed.
Based on lowest sum of ranks the top-five best performing models were listed.
2.4.4 Specific approach per crop In the analysis of khat the crop structure variables total height, crown area and diameter of the stem
at ground level were included as predictors for total dry weight of the twigs. The selection procedure
was executed for untransformed data and for data with both single and double log transformation.
For the analysis of coffee total height, crown height, crown area, d40 and d130 were included. As
response variable total dry weight of coffee beans was used. Data from the midland region and
highland region were studied both separately and combined. Model selection was based on the
single and double log transformed data. In the case of enset, the crop structure variables d130 and dep
were left out because of missing data for young enset plants. The remaining variables for analysis
were total height, pseudostem height, edible pseudostem height, crown height, d20, and d50. Crown
height was calculated by subtracting pseudostem height from the total height, which resulted in a
linear dependency between total height, crown height and pseudostem height. The procedure of
data analysis and model selection was therefore done three times, including only two of the height
components at one time. The response variables of interest were dry weights of plant parts (corm,
edible pseudostem, leaves and total dry weight) and food products (kocho and bula) of the enset
plants.
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3. Results
3.1 Khat In the analysis of tall khat plants crown area proved to be the best predictor of twig dry weight. The
relation between crown area and twig dry weight has a linear character for both untransformed and
transformed data (Figure 4 A, 4B). The plots with transformed data show a more linear relationship
between crown area and twig dry weight compared to the plot with untransformed data. The
coefficients of the two equations listed in Table 2 were statistically significant (α = 0.05). These were
the equations with single and double transformed data and crown area as crop structure variable.
Despite the low adjusted R2 the other goodness-of-fit statistics show good model performance
compared to other tested equations. The residual plots in Figure 4 C and D show the benefit of data
transformation in terms of constant variance: for the untransformed equation there is a less equal
spread of the points according to the loess smoother than for the single transformed equation.
Allometric equations with total height and crown area gave the best results for dwarf khat plants
explaining 57-77 % of the variation in twig dry weight. This percentage explanation was higher for
dwarf khat plants than for tall khat plants with adjusted R2 between 0.41-0.43. Values of RMSE,
PRESS, D and AB also indicate a higher degree of agreement between measured and predicted values
(Table 2) for dwarf than for tall khat plants. Tested equations with crown height and dg and d130 were
not significant and therefore not listed. Appendix I provides an overview of the other equations with
significant model coefficients but lower performance than the equations in Table 2.
Table 2 Model coefficients and goodness-of-fit statistics of the best performing allometric equations for estimation of twig dry weight of khat plants with tall and dwarf growth habit in Sidama, Ethiopia Allometric equation b1 b2 b3 R2 adj. RMSE PRESS D AB
Tall (n = 50)
ln(dwt) = b1 + b2ca 3.359 1.102 0.43 0.33 5.55 0.79 0.25 ln(dwt) = b1 + b2ln(ca) 4.444 0.724 0.41 0.33 5.79 0.77 0.26
Dwarf (n = 50)
ln(dwt) = b1 + b2ln(ht) + b3ln(ca) 1.983 0.495 0.522 0.77 0.15 1.25 0.93 0.12 ln(dwt) = b1 + b2ht + b3 ca 2.165 0.008 2.505 0.73 0.17 1.44 0.92 0.13 ln(dwt) = b1 + b2ln(ca) 4.453 0.727 0.71 0.17 1.55 0.91 0.14 ln(dwt) = b1 + b2ca 2.498 3.684 0.66 0.19 1.81 0.89 0.15 ln(dwt) = b1 + b2ln(ht) -1.471 1.093 0.57 0.21 2.28 0.85 0.16 With dwt twig dry weight, ca crown area and ht total height. b1, b2 and b3 are model coefficients (α = 0.05). R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares, D index of agreement and AB absolute bias.
11
adj. R2 = 0.45
A B
adj. R2 = 0.43
C D
Figure 4 A. The relation (untransformed data) between crown area (ca) and dry weight of twigs (dwt) for
tall khat plants (n = 50) in Sidama, Ethiopia with the allometric equation derived (black line). B. The
corresponding residuals plot with loess smoother (red line). C. The relation (single log transformation)
between crown area and dry weight of twigs for tall khat plants (n = 50) in Sidama, Ethiopia with the
allometric equation derived (black line). D. The corresponding residuals plot with loess smoother (red
line).
12
3.2 Coffee The best performing models for coffee bean yield with a single variable used crown area or diameter
at 40 cm height. The linear equation with single log transformation and crown area as predictor gives
the best result for coffee plants from the midland region (Figure 5A). According to the adjusted R2, 74
percent of the variation in the measured coffee bean yield was explained by this equation. Plotting
the residuals with the fitted values shows no violations of the assumptions for linear regression
(Figure 5B). After ranking, two more equations were selected with significant model coefficients, one
with crown area and the other one with both crown area and diameter at 130 cm. For coffee plants
from the highland region the equations with diameter at 40 and 130 cm as single variables had a
good fit with adjusted R2 of 0.63 and 0.61 respectively. In the ranking they came up after the
equation including total height, crown height, crown area and d40, which showed best values of the
goodness-of-fit statistics. When the plants from the midland and highland region were analysed
together, the allometric equation with crown area and d40 had the highest ranking followed by the
equation with only crown area (Figure 5C, 5D). The differences in terms of goodness-of-fit statistics
were small. At most 81 percent of the measured data points were explained by the model. The other
equations selected were all expanded forms of these models with total height and crown height as
predictors. In general all the allometric equations derived showed good model performance with low
values for RMSE, PRESS and AB and values for D ranging from 0.86 to 0.95. Values for the model
coefficients and goodness-of-fit statistics are summarized in Table 3 and Appendix II
R2 = 0.80
R2 = 0.74
C
B A
D
Figure 5 A. The relation between crown area (ca) and dry weight of coffee beans (dwb) for coffee plants (n
= 30) from the midland zone in Sidama, Ethiopia with the allometric equation derived (black line). B. The
corresponding residuals plot with loess smoother (red line). C. The relation between crown area and dry
weight of coffee beans for coffee plants from the midland and highland zone combined (n = 50) with the
allometric equation derived (black line). D. The corresponding residuals plot with loess smoother (red line).
13
Table 3 Model coefficients and goodness-of-fit statistics of the best performing allometric equations for estimation of coffee bean dry weight of coffee plants in the midland and highland zones of Sidama, Ethiopia
Model equation b1 b2 b3 b4 b5 R2 adj. RMSE PRESS D AB
Midland (n = 30)
ln(dwb) = b1 + b2ca -0.871 0.101 0.74 0.37 4.21 0.92 0.27 ln(dwb) = b1 + b2ln(ca) -1.716 0.877 0.61 0.45 6.62 0.87 0.34
Highland (n = 20)
ln(dwb) = b1 + b2ht + b3hc + b4ca + b5d40 -1.548 0.003 -0.005 0.095 0.010 0.77 0.24 1.54 0.95 0.15 ln(dwb) = b1 + b2ca + b3d40 -1.304 0.055 0.008 0.69 0.28 1.73 0.91 0.15 ln(dwb) = b1 + b2d40 -1.458 0.014 0.63 0.31 2.16 0.88 0.22 ln(dwb) = b1 + b2ln(d130) -3.443 0.755 0.61 0.31 2.41 0.87 0.25
All (n = 50)
ln(dwb) = b1 + b2ca + b3d40 -1.203 0.079 0.006 0.81 0.33 5.86 0.95 0.23 ln(dwb) = b1 + b2ca -0.981 0.107 0.80 0.35 6.10 0.94 0.24 ln(dwb) = b1 + b2ln(ht) + b3ln(hc) + b4ln(ca) + b5ln(d40) -5.059 0.931 -0.604 0.393 0.497 0.73 0.40 8.72 0.93 0.30 ln(dwb) = b1 + b2ln(ht) + b3ln(hc) + b4ln(ca) -5.159 1.326 -0.674 0.558 0.70 0.42 9.69 0.91 0.30 ln(dwb) = b1 + b2ln(ca) + b3ln( d40) -3.466 0.342 0.653 0.71 0.42 9.38 0.91 0.33 With dwb coffee bean dry weight, ca crown area, ht total height, hc crown height, d40 diameter at 40 cm and d130 diameter at breast height (130 cm). b1, b2, b3, b4 and b5 are model coefficients (α = 0.05). R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares, D index of agreement and AB absolute bias
14
3.3 Enset Diameter at 50 cm height was one of the main predictors in the allometric equations for enset plants.
The top five rank list of best performing models (Table 4) includes d50 in one or more of the selected
equations for the dry weight of the different plant parts and food products. For an overview of all
allometric equations with significant coefficients see Appendix III.
3.3.1 Total dry weight For total dry weight of enset plants two allometric equations were selected with d50 as single crop
structure variable and single (Figure 6) or double log transformation. The residuals plot shows no
evident pattern and an equal spread
around zero. The model performance of
these equations was high with adjusted R2
of 0.93 and 0.91. No other equations with
significant model coefficients showed up
during analysis.
3.3.2 Corm dry weight Dry weight of the corm was best modelled
with the single log transformed equation
using diameter at 20 cm height and total
height, also with good model performance
(adj. R2 = 0.88). Next to this equation the
equations with crop structure variables d50
and ht and d20 and hc (crown height) were
selected both with single log
transformation. Model selection based on
double log transformed data resulted in
the same combinations as mentioned
above with slightly lower model
performance explaining 85 % of the
measured data points.
3.3.3 Edible pseudostem dry weight The data analysis of dry weight of the
edible pseudostem results in 21 allometric
equations with significant model
coefficients (Appendix III). Single log
transformation was used for 13 of the
equations, double log transformation for
the remaining equations. In general the
models with single log transformation
show slightly better model performance
with adjusted R2 between 0.92 and 0.71.
As an example, the model with d20, hep
and ht as predictors shows no large violations of linear regression assumptions, according to the Q-Q
plot (Figure 7A) and the residuals plot (Figure 7B). The adjusted R2 for the models with double log
transformation was between 0.88 and 0.62. The best performing models with single log
transformation include 3 or 4 of the crop structure variables in different combinations. In contrast 2
crop structure variables were used in the best performing equation with double log transformation.
Figure 6 Top: The relationship between total dry weight (dwt) and diameter at 50 cm height (d50) of enset plants (n=20) with log transformation of the response variable. Bottom: The residuals of this relationship plotted against the fitted values from the allometric equation with loess smoother (red line)
R2 = 0.93
15
This equation with d20 and hc had higher position in the ranking than several of the equations with
single log transformation and 3 variables included.
3.3.4 Leave dry weight The trend observed between dry weight of the leaves and crop structure variables was weak.
Equations with more than one crop structure variable result in insignificance of one or more of the
model coefficients. Finally two models were selected both with d50 as predictor. The equation with
double log transformation showed the best performance (adj. R2 = 0.62) and only 52 % of the
measured data points was explained by the equation with single log transformation.
3.3.5 Kocho dry weight Diameter at 50 cm height was not only the best predictor for total dry weight and leaf dry weight,
but also for the dry weight of kocho. Up to 89 % of the measured data was explained by the model
with untransformed data of d50. The equation with ln(d50) included had a lower value of adjusted R2:
0.84. Values of the other goodness-of-fit statistics were comparable in range with the values for total
dry weight and edible pseudostem dry weight. Other possible combinations for modelling of kocho
dry weight using two or more crop structure variables included height of pseudostem or total height
combined with d50. However the addition of this extra parameter resulted in insignificant model
coefficients and these equations were therefore not included in the summary of results listed in
Table 4.
3.3.6 Bula dry weight The combination of d50 with a height variable yielded the best performing models for dry weight of
bula. In this part of the analysis the sample size was reduced to 14 instead of 20 plants, because the
bula food product could be derived only from the older enset plants (>5 years). Data analysis and
model selection based on the reduced dataset resulted in 9 equations with significant model
coefficients for the crop structure variables. The double log transformed allometric equation with d50,
height of pseudostem and height of edible pseudostem as crop structure variables showed best
performance (adj. R2 = 0.85). The same model with single log transformation and the double log
transformed model with d50 and hc were both able to declare 81 % of the measured data. For the
equation with d50 and ht as predictors the adjusted R2 was 0.79.
adj. R2 = 0.90
A B
Figure 7 A Q-Q plot for the allometric equation of edible pseudostem dry weight (dwep) of enset plants (n=20) with diameter at 20 cm height (d20), height of the edible pseudostem (hep) and total height (hp) as independent variables. B The residuals plot of this allometric equation with loess smoother (red line).
16
Table 4 Model coefficients and goodness-of-fit statistics of the best performing allometric equations for estimation of dry weight of enset plants and food products in Sidama, Ethiopia Model equation b1 b2 b3 b4 b5 R2 adj. RMSE PRESS D AB
Total dry weight
ln(dwt) = b1 + b2d50 0.452 0.067 0.93 0.25 1.42 0.98 0.18 ln(dwt) = b1 + b2ln(d50) -5.214 2.298 0.91 0.27 1.69 0.98 0.22
Dry weight corm
ln(dwc) = b1 + b2d20 + b3ht -3.877 0.082 0.003 0.88 0.47 4.96 0.97 0.36 ln(dwc) = b1 + b2d50 + b3ht -2.494 0.065 0.003 0.87 0.49 5.07 0.97 0.33 ln(dwc) = b1 + b2d50 + b3hc -2.370 0.081 0.003 0.87 0.48 5.31 0.97 0.35 ln(dwc) = b1 + b2ln(d50) + b3ln(ht) -16.842 2.203 1.716 0.85 0.51 6.24 0.96 0.40 ln(dwc) = b1 + b2ln(d20) + b3ln(ht) -22.166 3.237 1.859 0.85 0.53 6.38 0.96 0.39
Dry weight edible pseudostem
ln(dwep) = b1 + b2d20 + b3d50 + b4hp + b5ht -0.220* 0.036 0.031 0.004 -0.003 0.92 0.26 1.70 0.98 0.17 ln(dwep) = b1 + b2d20 + b3d50 + b4hc -0.136* 0.036 0.038 -0.003 0.92 0.26 1.69 0.98 0.19 ln(dwep) = b1 + b2d50 + b3hep + b4ht 0.371* 0.054 0.005 -0.002 0.91 0.28 2.08 0.98 0.19 ln(dwep) = b1 + b2d20 + b3hep + b4hc -0.675 0.061 0.004 -0.002 0.91 0.28 2.06 0.98 0.21 ln(dwep) = b1 + b2d20 + b3hep + b4ht -0.677 0.061 0.006 -0.002 0.90 0.29 2.16 0.98 0.21
Dry weight leaves
ln(dwl) = b1 + b2ln(d50) -3.476 1.356 0.62 0.41 3.77 0.88 0.29 ln(dwl) = b1 + b2d50 -0.009* 0.036 0.52 0.45 4.73 0.84 0.32
Dry weight kocho
ln(dwk) = b1 + b2d50 -0.594 0.064 0.89 0.30 2.13 0.97 0.22 ln(dwk) = b1 + b2ln(d50) -5.896 2.171 0.84 0.36 3.42 0.96 0.28
Dry weight bula
ln(dwb) = b1 + b2ln(d50) + b3ln(hep) + b4ln(hp) -7.844 1.890 4.223 -3.872 0.85 0.38 2.86 0.97 0.17 ln(dwb) = b1 + b2d50 + b3hep + b4hp -2.458 0.054 0.020 -0.015 0.81 0.43 3.57 0.96 0.30 ln(dwb) = b1 + b2d50 + b3hc -1.873 0.063 -0.003 0.81 0.43 3.01 0.95 0.32 ln(dwb) = b1 + b2ln(d50) + b3hc -3.415 2.121 -0.785 0.78 0.46 3.53 0.95 0.32 ln(dwb) = b1 + b2d50 + b3ht -1.679 0.075 -0.003 0.79 0.44 3.72 0.95 0.33 With dwt total dry weight, dwc dry weight crom, dwep dry weight edible pseudostem, dwl dry weight leaves, dwk dry weight kocho, dwb dry weight bula, ht total height, hc crown height, hp pseudostem height, hep edible pseudostem height, d20 diamter at 20 cm, d50 diameter at 50 cm. b1, b2, b3, b4 and b5 are model coefficients (α = 0.05, except * = not significant). R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares, D index of agreement and AB absolute bias
17
4. Discussion
4.1 Khat The current research on khat in Ethiopia is mainly focused on the impact of the plant on public health
(Al-Hebshi and Skaug, 2005), agricultural, policy and trade conditions (Gessesse, 2013, Kandari et al.,
2014) and forest decline (Dessie and Kinlund, 2008). The quantitative determination of khat yield is
an unexploited field of research yet. In literature khat yield is mostly referred to in terms of financial
returns (Feyisa and Aune, 2003), but this gives no information on e.g. dry matter flows or nutrient
fluxes at farm level. To understand the influence of increased khat cultivation in monoculture
compared with the traditional homegarden system research on actual yields in terms of dry weight is
essential. The aim of this research was to obtain knowledge about the yield of harvestable stems of
khat in relation to measured crop structure variables to easily predict khat yield in the future. Crown
area turned out to be the best predictor for twig dry weight which seems logical because the twigs
are part of the crown of khat plants. The second crop structure variable included in the allometric
equations is total height. The spread in height measurements for tall khat plants was larger
compared to the dwarf khat plants pruned at a more equal height. This results in lower model
performance of the allometric equations for tall khat plants. It is also possible that the simple
approach of linear log transformed equations was not sufficient to describe the relation between dry
weight of the twigs and crown area for tall khat plants. Therefore it is recommended to look for other
methods, e.g. non-linear regression or weighted regression to end up with more reliable equations to
determine the twig yield of the plants. The connection between crown area, total height and khat
yield is a first indicator of which plant characteristics can help to establish and predict khat yield in
the future. It should be taken in consideration whether it is actually possible to model the yearly
harvest of twigs from the perennial khat plant based on the principle of allometry alone over more
years. Probably yearly fluctuations in for instance precipitation and diseases will affect khat yield
from year to year. In that case the derived equations are only applicable to the conditions of a
particular season. There is uncertainty about drought and disease resistance of khat, different studies
reporting opposite (Dessie and Kinlund, 2008, Lemessa, 2001). To improve the findings of this
research more datasets of quantitative khat yield are needed on other locations and agro-ecological
zones in Ethiopia. Khat becomes more and more a crop with substantial influence on a large
proportion of the population of Sidama region in Ethiopia. More knowledge would be beneficial in
the understanding of the constraints of this crop to ensure sustainable production in the future.
4.2 Coffee Crown area is the most important predictor for coffee bean yield in the midland region. For the
highland region d40, d130, hc and ht are also listed in the best performing equations. With this
difference between crop structure variables used for the allometric equations of the two different
regions it should be taken in consideration what is responsible for this. A reason could be the
relatively low number of plants used (n=30 for midland region and n=20 for highland region). Then
one should conclude that the variation between the different regions is rooted in an inadequate
representation of the variation present in the plants of each region, giving rise to different crop
structure variables listed as best performing. Combination of all data shows that despite the
differences between the regions when analysed separately, it is possible to derive adequate
equations for both regions together. Despite these findings it is important to be aware of the limited
applicability of the allometric equations in terms of yield prediction in the future. While yearly
fluctuations of environmental conditions for khat yield are assumed to affect production mildly, for
coffee bean yield this is a more important concern. In particular during flowering and fruit set water
availability and temperature are important factors determining final yields (Lin, 2008). Pests and
18
diseases are also responsible for yield reductions. These factors complicate the estimation and
prediction of coffee bean yield. The focus of models to estimate coffee bean yield present yet is
mainly on agrometeorological factors combined in complicated process-based models (Van Oijen et
al., 2010, Maro et al., 2014). Taking this into account allometric equations for coffee bean yield could
give at best only an estimate of production for a certain season on plant level. To predict actual yield
the allometric equation should be combined with data of weather and soil conditions for some of the
crucial stages in coffee bean development (e.g. flowering and fruit set).
4.3 Enset The importance of d20 and d50 in the allometric equations for enset composed in this research
approve the major role of stem diameter in allometric equations for enset as reported by Negash et
al., 2012. The same could be said for total height as crop structure variable in the allometric
equations and the order in which model performance is decreased, with total dry weight equations
having the highest performance and leave dry weight equations having the lowest performance. An
important difference is the use of non-linear regression models by Negash et al. 2012 in contrast to
the linear regression models used in this research. The model performance of the linear allometric
equations derived in this research are comparable and sometimes better than the non-linear models
developed by Negash et al., 2012.
It should be noticed that the minimum and maximum values of the data for dry weight of the plant
parts often show a slight deviation in the Q-Q plot and residual plot. Partly these deviations are
explained by the natural variability of biological data but it could also be an indication of some
heteroscedasticity.
The analysis during this research was limited to simple linear regression. Extension of the analysis
should probably not be at first on non-linear allometric equations but rather on weighted linear
regression or other more refined linear regression methods. For simplicity in use and interpretation
of the equation a linear model is preferred above a non-linear model as long as good model
performance is assured.
Another difference with the research of Negash et al., 2012 is the continuous range in age of the
selected enset plants instead of only 3 and 5-year-old plants selected by these authors. Because of
the increasing population pressure on food resources farmers are often forced to use the young
plants as food source. Therefore the 3 and 4-year-old plants were not removed from analysis,
although this implies that d130 and dep could not be used because of absence of data for these crop
structure variables for the young plants. A part of the deviations for minimum values of dry weight
mentioned in the previous paragraph can also be explained by the fact that the 3-year-old plants
show more variability due to effects of transplanting from the propagation site to the field.
Next to the different plant part dry weights it turns out to be possible to derive allometric equations
for the food products of enset. Predictions of kocho yield are made by Duriaux Chavarría, 2014
correlating kocho yield to the total biomass yield. For estimation of total biomass yield in that
research the allometric equation with diameter and total height from Negash et al., 2012 was used.
In this research the crop structure variables associated with pseudostem and corm dimension seems
to be of most importance for determination of the amount of kocho and bula produced. This is a
reasonable outcome because the food products of enset are produced from the pseudostem and the
corm of the enset plants. The results for bula are less reliable because of the lower number of
measurements: only from the 14 oldest enset plants bula was produced. With a relatively low sample
size (n=20) the reliability of the data analysis is strongly affected when values are missing. Therefore
a lager sample size is recommended for future research.
To determine and predict enset yield on homegardens in Sidama region the allometric equations of
this research could be a first helpful tool. The successful use of one of the allometric equations from
19
Negash et al., 2012 in a research on energy flows in farming systems of Southern Ethiopia (Duriaux
Chavarría, 2014) is a first indication of the wider applicability of allometric equations of enset.
Parameterization based on local data improved the predictive strength of the allometric equation.
Further research and more datasets are necessary to check the performance of the equations for
other farms and agroecological zones in Ethiopia.
4.4 Allometric equations on farm level The use of allometric equations to estimate and predict yearly coffee bean yield is limited. Modelling
of coffee bean yield on farm level in agroforestry systems is assumed to be complex process which
requires multi-year data on wheater conditions, soil conditions and coffee tree management (Van
Oijen et al., 2010). Allometric equations could be a part of these models. Future research on
allometric relationships for coffee is recommended, together with the ongoing search for simple
process based models for coffee bean yield in agroforestry systems.
Prediction of khat yield could benefit from the models being developed for coffee bean yield after
modification for the characteristics of this crop. At this moment there is no information available on
models or allometric equations for actual khat yields in terms of dry weight. The findings of this
research are a first indication for the relation between crown area and twig dry weight. Same as for
coffee it is not reliable that allometric equations can accurately predict yields over the years. It is
quite possible that the negative attention on khat as stimulant is responsible for the limited research
done yet. However, the current situation of khat expansion in Sidama, Ethiopia needs more attention
to prevent further replacement of homegardens by mono-cropping systems with reduced
sustainability.
Scaling up to farm level is possible for allometric equations of enset although measurements on
individual plants are necessary when applying the allometric equations of this research. The
approach followed by Duriaux Chavarría, 2014, measuring all enset plants in three random selected
subsamples of 50 m2 on an enset field is an option. Extrapolation of the biomass yield to the whole
field should be done carefully, because for instance the plants on the margins of the field could have
an aberrant biomass yield because different light interception and exposure to wind can effect
growth. To gain insight to which extent such factors play a role, testing of the allometric equations
for enset is highly recommended.
The search for a new sustainable homegarden system combining the best aspects of the traditional
homegarden and khat monocropping system in Sidama, Ethiopia by Beyene Melisse is still going on.
Hopefully, the derivation of allometric equations for khat, coffee and enset in this research is one of
the fragments contributing to the whole picture of a sustainable farming system able to produce
sufficient food for the growing population in Southern Ethiopia.
5. Acknowledgements I wish to thank my supervisors, dr. ir. Katrien Descheemaeker and dr. ir. Gerrie van de Ven, for their
advice and support during this research and their detailed review and constructive comments on this
thesis report. I am thankful to Beyene Melisse who shared his extensive measurements and datasets
which are the basis of this research. I am very grateful to Arinda, my parents and all others which
supported me during the work at home. Above all I thank God, my Creator.
20
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7. Appendices
7.1 Appendix I – Allometric equations for khat twig dry weight
Appendix I Model coefficients and goodness-of-fit statistics of the best performing allometric equations for estimation of twig dry weight of khat plants with tall and dwarf growth habit in Sidama, Ethiopia Allometric equation b1 b2 b3 b4 R2 adj. RMSE PRESS D AB
Tall (n = 50)
ln(dwt) = b1 + b2ca 3.359 1.102 0.43 0.33 5.55 0.79 0.25 ln(dwt) = b1 + b2ln(ca) 4.444 0.724 0.41 0.33 5.79 0.77 0.26 dwt = b1 + b2ca 10.030 82.580 0.46 23.87 30273.74 0.79 17.45 dwt = b1 + b2hc + b3ca -0.865 0.246 57.756 0.53 22.42 27535.20 0.83 17.59 dwt = b1 + b2ht + b3hc + b4ca 24.627 -0.116 0.282 55.897 0.57 21.71 25788.71 0.85 16.91
Dwarf (n = 50)
ln(dwt) = b1 + b2ln(ht) + b3ln(ca) 1.983 0.495 0.522 0.77 0.15 1.25 0.93 0.12 ln(dwt) = b1 + b2ht + b3 ca 2.165 0.008 2.505 0.73 0.17 1.44 0.92 0.13 ln(dwt) = b1 + b2ln(ca) 4.453 0.727 0.71 0.17 1.55 0.91 0.14 ln(dwt) = b1 + b2ca 2.498 3.684 0.66 0.19 1.81 0.89 0.15 ln(dwt) = b1 + b2ln(ht) -1.471 1.093 0.57 0.21 2.28 0.85 0.16 ln(dwt) = b1 + b2ht 2.079 0.015 0.57 0.21 2.28 0.85 0.16 dwt = b1 + b2ca 7.961 93.254 0.73 4.03 836.55 0.92 3.48 dwt = b1 + b2ht -2.151* 0.379 0.61 4.84 1210.00 0.87 3.77 dwt = b1 + b2ht + b3ca 0.113* 0.178 65.423 0.80 3.48 632.09 0.94 2.70 With dwt twig dry weight, ca crown area and ht total height. b1, b2 and b3 are model coefficients (α = 0.05, except * = not significant). R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares, D index of agreement and AB absolute bias.
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7.2 Appendix II – Allometric equations for coffee bean dry weight
Appendix II Model coefficients and goodness-of-fit statistics of the best performing allometric equations for estimation of coffee bean dry weight of coffee plants in the midland and highland zones of Sidama, Ethiopia
Model equation b1 b2 b3 b4 b5 R2 adj. RMSE PRESS D AB
Midland (n = 30)
ln(dwb) = b1 + b2ca -0.871 0.101 0.74 0.37 4.21 0.92 0.27 ln(dwb) = b1 + b2ln(ca) -1.716 0.877 0.61 0.45 6.62 0.87 0.34
Highland (n = 20)
ln(dwb) = b1 + b2ht + b3hc + b4ca + b5d40 -1.548 0.003 -0.005 0.095 0.010 0.77 0.24 1.54 0.95 0.15 ln(dwb) = b1 + b2ca + b3d40 -1.304 0.055 0.008 0.69 0.28 1.73 0.91 0.15 ln(dwb) = b1 + b2d40 -1.458 0.014 0.63 0.31 2.16 0.88 0.22 ln(dwb) = b1 + b2ln(d130) -3.443 0.755 0.61 0.31 2.41 0.87 0.25
All (n = 50)
ln(dwb) = b1 + b2ca + b3d40 -1.203 0.079 0.006 0.81 0.33 5.86 0.95 0.23 ln(dwb) = b1 + b2ca -0.981 0.107 0.80 0.35 6.10 0.94 0.24 ln(dwb) = b1 + b2ln(ht) + b3ln(hc) + b4ln(ca) + b5ln(d40) -5.059 0.931 -0.604 0.393 0.497 0.73 0.40 8.72 0.93 0.30 ln(dwb) = b1 + b2ln(ht) + b3ln(hc) + b4ln(ca) -5.159 1.326 -0.674 0.558 0.70 0.42 9.69 0.91 0.30 ln(dwb) = b1 + b2ln(ca) + b3ln( d40) -3.466 0.342 0.653 0.71 0.42 9.38 0.91 0.33 ln(dwb) = b1 + b2ln(ca) + b3ln( d130) -2.759 0.387 0.499 0.69 0.43 9.99 0.91 0.32 ln(dwb) = b1 + b2ln(ht) + b3ln(ca) -5.596 0.787 0.513 0.68 0.44 10.40 0.90 0.34 With dwb coffee bean dry weight, ca crown area, ht total height, hc crown height, d40 diameter at 40 cm and d130 diameter at breast height (130 cm). b1, b2, b3, b4 and b5 are model coefficients (α = 0.05). R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares, D index of agreement and AB absolute bias
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7.3 Appendix III – Allometric equations for dry weight of biomass and food products of enset Appendix III Model coefficients and goodness-of-fit statistics of the allometric equations with significant coefficients for estimation of dry weight of enset plants and food products in Sidama, Ethiopia Model equation b1 b2 b3 b4 b5 R2 adj. RMSE PRESS D AB
Total dry weight
ln(dwt) = b1 + b2d50 0.452 0.067 0.93 0.25 1.42 0.98 0.18 ln(dwt) = b1 + b2ln(d50) -5.214 2.298 0.91 0.27 1.69 0.98 0.22
Dry weight corm
ln(dwc) = b1 + b2d20 + b3ht -3.877 0.082 0.003 0.88 0.47 4.96 0.97 0.36 ln(dwc) = b1 + b2d50 + b3ht -2.494 0.065 0.003 0.87 0.49 5.07 0.97 0.33 ln(dwc) = b1 + b2d50 + b3hc -2.370 0.081 0.003 0.87 0.48 5.31 0.97 0.35 ln(dwc) = b1 + b2ln(d50) + b3ln(ht) -16.842 2.203 1.716 0.85 0.51 6.24 0.96 0.40 ln(dwc) = b1 + b2ln(d20) + b3ln(ht) -22.166 3.237 1.859 0.85 0.53 6.38 0.96 0.39 ln(dwc) = b1 + b2ln(d50) + b3ln(hc) -13.365 2.926 0.818 0.85 0.53 6.89 0.96 0.43
Dry weight edible pseudostem
ln(dwep) = b1 + b2d20 + b3d50 + b4hp + b5ht -0.220* 0.036 0.031 0.004 -0.003 0.92 0.26 1.70 0.98 0.17 ln(dwep) = b1 + b2d20 + b3d50 + b4hc -0.136* 0.036 0.038 -0.003 0.92 0.26 1.69 0.98 0.19 ln(dwep) = b1 + b2d50 + b3hep + b4ht 0.371* 0.054 0.005 -0.002 0.91 0.28 2.08 0.98 0.19 ln(dwep) = b1 + b2d20 + b3hep + b4hc -0.675 0.061 0.004 -0.002 0.91 0.28 2.06 0.98 0.21 ln(dwep) = b1 + b2d20 + b3hep + b4ht -0.677 0.061 0.006 -0.002 0.90 0.29 2.16 0.98 0.21 ln(dwep) = b1 + b2ln(d20) + b3ln(hc) -7.725 4.015 -0.989 0.88 0.29 1.99 0.97 0.18 ln(dwep) = b1 + b2d20 + b3hp + b4ht -0.686 0.064 0.006 -0.003 0.90 0.29 2.12 0.98 0.22 ln(dwep) = b1 + b2d50 + b3hp + b4ht 0.427 0.057 0.004 -0.003 0.90 0.29 2.26 0.98 0.21 ln(dwep) = b1 + b2d50 + b3hc 0.509 0.065 -0.003 0.90 0.29 2.24 0.98 0.22 ln(dwep) = b1 + b2d20 + b3hc -0.764 0.081 -0.003 0.88 0.32 2.50 0.97 0.24 ln(dwep) = b1 + b2ln(d20) + b3ln(hep) + b4ln(ht) -5.427 2.537 1.171 -1.290 0.86 0.35 3.29 0.97 0.26 ln(dwep) = b1 + b2d50 + b3ht 0.557 0.077 -0.003 0.85 0.35 3.29 0.96 0.25 ln(dwep) = b1 + b2ln(d50) + b3ln(hep) + b4ln(ht) -0.604* 1.908 0.883 -1.378 0.84 0.36 3.94 0.96 0.25 ln(dwep) = b1 + b2ln(d20) + b3ln(hp) + b4ln(ht) -4.967 2.698 1.233 -1.567 0.84 0.36 3.53 0.96 0.28 ln(dwep) = b1 + b2d50 + b3hep + b4ht -0.059* 0.040 0.016 -0.010 0.83 0.38 3.94 0.96 0.25 ln(dwep) = b1 + b2d20 + b3hep -0.895 0.039 0.007 0.80 0.41 4.17 0.95 0.30 ln(dwep) = b1 + b2ln(d50) + b3ln(ht) 1.630* 2.685 -1.471 0.80 0.42 4.52 0.95 0.28 ln(dwep) = b1 + b2ln(d20) + b3ln(ht) -4.773 3.849 -1.252 0.73 0.48 5.35 0.93 0.35
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ln(dwep) = b1 + b2ln(d20) + b3ln(hep) -9.797 1.624 1.135 0.72 0.48 6.33 0.92 0.36 ln(dwep) = b1 + b2hep 0.180* 0.012 0.71 0.49 5.35 0.92 0.37 ln(dwep) = b1 + b2ln(d20) -9.039 2.924 0.62 0.57 7.16 0.88 0.44
Dry weight leaves
ln(dwl) = b1 + b2ln(d50) -3.476 1.356 0.62 0.41 3.77 0.88 0.29 ln(dwl) = b1 + b2d50 -0.009* 0.036 0.52 0.45 4.73 0.84 0.32
Dry weight kocho
ln(dwk) = b1 + b2d50 -0.594 0.064 0.89 0.30 2.13 0.97 0.22 ln(dwk) = b1 + b2ln(d50) -5.896 2.171 0.84 0.36 3.42 0.96 0.28
Dry weight bula
ln(dwb) = b1 + b2ln(d50) + b3ln(hep) + b4ln(hp) -7.844 1.890 4.223 -3.872 0.85 0.38 2.86 0.97 0.17 ln(dwb) = b1 + b2d50 + b3hep + b4hp -2.458 0.054 0.020 -0.015 0.81 0.43 3.57 0.96 0.30 ln(dwb) = b1 + b2d50 + b3hc -1.873 0.063 -0.003 0.81 0.43 3.01 0.95 0.32 ln(dwb) = b1 + b2ln(d50) + b3hc -3.415 2.121 -0.785 0.78 0.46 3.53 0.95 0.32 ln(dwb) = b1 + b2d50 + b3ht -1.679 0.075 -0.003 0.79 0.44 3.72 0.95 0.33 ln(dwb) = b1 + b2ln(d20) + b3ln(hep) + b4ln(hp) -11.429 2.096 4.147 -3.341 0.77 0.47 4.19 0.95 0.31 ln(dwb) = b1 + b2ln(d50) + b3ln(ht) 1.310* 2.745 -1.823 0.78 0.46 3.86 0.95 0.34 ln(dwb) = b1 + b2d20 + b3hc -2.732 0.072 -0.003 0.71 0.53 4.89 0.92 0.38 ln(dwb) = b1 + b2d20 -3.402 0.068 0.56 0.65 7.25 0.85 0.47 With dwt total dry weight, dwc dry weight crom, dwep dry weight edible pseudostem, dwl dry weight leaves, dwk dry weight kocho, dwb dry weight bula, ht total height, hc crown height, hp pseudostem height, hep edible pseudostem height, d20 diamter at 20 cm, d50 diameter at 50 cm. b1, b2, b3, b4 and b5 are model coefficients (α = 0.05, except * = not significant). R2 adj. adjusted coefficient of determination, RMSE root mean square error, PRESS predicted residual sum of squares, D index of agreement and AB absolute bias