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

6. References ABEBE, T. 2005. Diversity in homegarden agroforestry systems of southern Ethiopia. Wageningen

University. ABEBE, T., WIERSUM, K. F. & BONGERS, F. 2010. Spatial and temporal variation in crop diversity in

agroforestry homegardens of southern Ethiopia. Agroforestry Systems, 78, 309-322. AL-HEBSHI, N. N. & SKAUG, N. 2005. Khat (Catha edulis)-an updated review. Addict Biol, 10, 299-307. BIZUAYEHU, T. 2008. On Sidama folk identification, naming, and classification of cultivated enset

(Ensete ventricosum) varieties. Genetic Resources and Crop Evolution, 55, 1359-1370. CSA 2007. The 2007 Population and Housing Census: Results of Southern Nations Nationalities

Peoples Region. Central Statistical Agency. CSA 2014. Population projection figures based on the May 2007 National Population and Housing

Census of Ethiopia. Central Statistical Agency. DESSIE, G. & KINLUND, P. 2008. Khat expansion and forest decline in Wono Genet, Ethiopia.

Geografiska Annaler: Series B, Human Geography, 90, 187-203. DURIAUX CHAVARRÍA, J.-Y. 2014. Energy flows in the farming systems of Southern Ethiopia:

implications for sustainable intensification. Master of Science thesis, Wageningen University. FEYISA, T. H. & AUNE, J. B. 2003. Khat Expansion in the Ethiopian Highlands. Mountain Research and

Development, 23, 185-189. GESSESSE, D. 2013. Favouring a Demonised Plant: Khat and Ethiopian smallholder enterprises. HAIRIAH, K., SITOMPUL, S., VAN NOORDWIJK, M. & PALM, C. 2001. Methods for sampling carbon

stocks above and below ground, ICRAF Bogor, Indonesia. KANDARI, L. S., YADAV, H. R., THAKUR, A. K. & KANDARI, T. 2014. Chat (Catha edulis): a socio

economic crop in Harar Region, Eastern Ethiopia. SpringerPlus, 3, 579. KANSHIE, T. K. 2002. Five Thousand Years of Sustainablity? A Case study on Gedeo Land Use

(Southern Ethiopia). Wageningen University. KOZAK, A. & KOZAK, R. 2003. Does cross validation provide additional information in the evaluation

of regression models? Canadian Journal of Forest Research, 33, 976-987. LABOUISSE, J.-P., BELLACHEW, B., KOTECHA, S. & BERTRAND, B. 2008. Current status of coffee

(Coffea arabica L.) genetic resources in Ethiopia: implications for conservation. Genetic Resources and Crop Evolution, 55, 1079-1093.

LEMESSA, D. 2001. Khat (Catha edulis): botany, distribution, cultivation, usage and economics in Ethiopia. Addis Ababa: UN-Emergencies Unit for Ethiopia.

LIN, B. B. 2008. Microclimate effects on flowering success in coffee agroforestry systems. American-Eurasian J. Agric. Environ. Sci, 3, 148-152.

MARO, G. P., MREMA, J. P., MSANYA, B. M., JANSSEN, B. H. & TERI, J. M. 2014. Developing a coffee yield prediction and integrated soil fertility management recommendation model for Northern Tanzania. International Journal of Plant & Soil Science, 3, 380-396.

MELISSE, B. T. 2012. Trends and prospects for the Productivity and Sustainability of Homegarden Agroforestry Systems in Southern Ethiopia, PhD Project Proposal. Wageningen University and Research Centre.

NEGASH, M. 2013. The indigenous agroforestry systems of the south-eastern Rift Valley escarpment, Ethiopia: Their biodiversity, carbon stocks, and litterfall. Tropical Forestry Reports.

NEGASH, M., STARR, M. & KANNINEN, M. 2012. Allometric equations for biomass estimation of Enset (Ensete ventricosum) grown in indigenous agroforestry systems in the Rift Valley escarpment of southern-eastern Ethiopia. Agroforestry Systems, 87, 571-581.

NEGASH, M., STARR, M., KANNINEN, M. & BERHE, L. 2013. Allometric equations for estimating aboveground biomass of Coffea arabica L. grown in the Rift Valley escarpment of Ethiopia. Agroforestry Systems, 87, 953-966.

OTT, R. & LONGNECKER, M. 2008. An Introduction to Statistical Methods and Data Analysis, Cengage Learning.

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PARRESOL, B. R. 1999. Assessing Tree and Stand Biomass: A Review with Examples and Critical Comparisons. Forest Science, 45, 573-593.

PICARD, N., SAINT-ANDRÉ, L. & HENRY, M. 2012. Manual for building tree volume and biomass allometric equations: from field measurement to prediction., 215 pp.

RSTUDIO 2015. RStudio: Integrated Development for R. Boston: RStudio, Inc. SEGURA, M., KANNINEN, M. & SUÁREZ, D. 2006. Allometric models for estimating aboveground

biomass of shade trees and coffee bushes grown together. Agroforestry Systems, 68, 143-150.

TADELE, R. 2008. Farmer’s Perception of Environmental Degradation and Their Response to Environmental Management A Case of Dale Woreda, Sidama Zone, SNNPR.

TSEGAYE, A. 2002. On indigenous production, genetic diversity and crop ecology of enset (Ensete ventricosum (Welw.) Cheesman). Wageningen University.

VAAST, P., BERTRAND, B., PERRIOT, J.-J., GUYOT, B. & GÉNARD, M. 2006. Fruit thinning and shade improve bean characteristics and beverage quality of coffee (Coffea arabica L.) under optimal conditions. Journal of the Science of Food and Agriculture, 86, 197-204.

VAN OIJEN, M., DAUZAT, J., HARMAND, J.-M., LAWSON, G. & VAAST, P. 2010. Coffee agroforestry systems in Central America: II. Development of a simple process-based model and preliminary results. Agroforestry systems, 80, 361-378.

YOUKHANA, A. & IDOL, T. 2011. Allometric models for predicting above- and belowground biomass of Leucaena-KX2 in a shaded coffee agroecosystem in Hawaii. Agroforestry Systems, 83, 331-345.

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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