The Foraging Behaviour of the Arid Zone Herbivores the Red Kangaroo (Macropus Rufus) and the Sheep (Ovis Aries) and Its Role In

The Foraging Behaviour of the Arid Zone Herbivores the Red Kangaroo (Macropus rufus) and the Sheep (Ovis aries) and its Role in Their Competitive Interaction, Population Dynamics and Life-History Strategies

Steven McLeod

A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy

University of New South Wales

February, 1996 Summary

(1) The foraging behaviours of the arid zone herbivores the red kangaroo (Macropus rufus) and the sheep ( Ovis aries) were studied over a four year period in arid western New South Wales. These herbivores are subject to wide temporal variation in food abundance and quality. I examined their foraging behaviour to test the hypothesis that their population dynamics could be explained from the basis of their food and energy intake.

(2) Previous studies of these herbivores have hypothesised that they compete exploitatively for food. The results of these studies have been suggestive but not conclusive. I conducted a controlled removal experiment to examine the hypothesis that these herbivores interspecifically compete. There were three treatments (x2 replicates); i) sheep only, ii) red kangaroos only and iii) sheep and red kangaroos. The productivity of each herbivore in the presence and absence of its putative competitor were compared to determine any competitive effect. The results indicated that exploitative competition between sheep and red kangaroos occurs rarely. Interference competition is more common. Red kangaroos were found to consistently avoid areas used by sheep. The effect of interference competition sheep productivity was less clear and appeared to be associated with unusual circumstances such as the combination of low food availability and high red kangaroo density. Interspecific competition was asymmetric with sheep dominating.

(3) Coincident with the removal experiment I solved a mechanistic model of exploitative competition between sheep and red kangaroos. The model indicated that these herbivores share most of their food resources, but were always had exclusive food resources that were not eaten by the other species. The results of the mechanistic model of exploitative competition support the conclusions of the controlled removal experiment.

(4) The ability ofred kangaroos and sheep to choose an optimal diet was examined. I used a linear programming model of optimal diet choice to predict the percentage in the diet of three categories of food plants; forbs, grasses and shrubs. The herbivores were hypothesised to follow a feeding goal of either energy maximisation, time minimisation ii or being completely unselective. The model indicated that the dominant feeding goal of sheep and red kangaroos was energy maximisation. Even under extremes of environmental variation the herbivores were able to select, or closely approach, an optimal diet. However, when food availability declined the predicted diets of the alternative goals converged to the point when there was no longer a detectable difference between any predicted diet and the observed diet.

( 5) I used the linear programming model of optimal diet choice to examine the hypothesis that red kangaroo body size is dependent upon the rate of energy intake. Comparing the predictions of an individual's energy intake with its requirements I predicted the upper and lower limits of each sex' s body size, as well as the optimum body size (defined as the body size at which the ratio of net energy intake to requirement is maximised). Furthermore, I used the model to examine a proposed mechanism for the evolution of sexual dimorphism in a fluctuating environment. Specifically, I hypothesised that male red kangaroos will exceed their optimum body size, foregoing long-term survivorship for short-term dominance over other males. In contrast, females will approach optimal body size in order to maximise survivorship. The results indicated partial agreement with the hypotheses. At times when food was abundant the body size model failed to explain the upper limit to body size of either sex. As food availability declined there was closer agreement between the predictions of the body size model and observed body sizes. These results indicate that the upper limit to the body size of both sexes may be set by infrequent and unpredictable times of food limitation, whereas the lower limit seems to be independent of food availability. As predicted, the largest males exceeded the optimum body size of 50 kg and probably would not survive a period of prolonged food limitation. Females did not approach the 50 kg optimum but reached a maximum size of about 35 kg. Possible reasons for the failure of the model to predict female optimum body size are discussed.

(6) I simulated the population dynamics of a typical arid zone herbivore (the red kangaroo) to examine the usefulness of the concept of herbivore carrying capacity in a variable environment. The results of the simulations indicated that the concept of carrying capacity is only valid in slightly variable plant-herbivore systems that closely iii approach equilibrium. In highly variable systems, such as the arid zone of Australia, the concept is not useful and cannot be used to predict sustainable herbivore density.

(7) The results of this study indicate that simple measurements of food or energy intake can be used to examine hypotheses about exploitative competition, optimal diet choice, the coevolution of herbivores and plant communities, the evolution of body size and sexual dimorphism and the long-term population dynamics of herbivores in variable environments. iv

Acknowledgments

I would like acknowledge the assistance of Glenn Edwards, Adam McLean, Graeme Moss, Shane Maloney, Nicky Marlow, Gary Belovsky, Os Schmitz, Mark Ritchie, Glen Saunders, Greg Curran, David Choquenot, the staff of Fowlers Gap Station, Trevor Warburton, and Rick Taylor who helped with various aspects of the field work, reviewing earlier drafts or advice. I would also like to thank my supervisors, Terry Dawson and David Croft for their guidance through all aspects of this project. I would particularly like to acknowledge the assistance ofmy wife Lynette, who unselfishly gave me love, support and encouragement when I needed it the most.

During this study I was financially supported by an Australian Postgraduate Scholarship, the RSPCA Alan White Scholarship (1992) and the Fowlers Gap Scholarship. Support for the running of the study was provided by a grant to Terry Dawson from the Australian Research Council. The rainfall data for Tibooburra was provided by the Bureau of Meteorology. V

Table of Contents

Summary i

Acknowledgments iv

Table of Contents V

List of Figures X

List of Tables xv

CHAPTER 1: LITERATURE REVIEW

The Feeding Strategies and Diet Choice of Generalist Mammalian Herbivores 1.1 Introduction 1 1.2 Diet Choice Descriptions 2 1.3 Feeding Strategy and Diet Choice 4 1.3.1 Optimal Foraging Theory 4 1.3.1.1 Contingency Models 4 1.3.1.2 Central-place Foraging 6 1.3.1.3 Risk-sensitive Foraging 8 1.3.1.4 LinearProgramming 11 1.3.1.5 Other Optimisation Models 13 1.3.2 Complementary Nutrients 14 1.3 .3 Plant Defence 15 1.3.3.1 Spines and Thorns 15 1.3.3.2 Secondary Compounds 16 1.4 Field Studies of Mammalian Herbivore Diet Choice 19 1.5 Synthesis 22 1.5.1 Why Linear Programming? 22

CHAPTER2

Thesis Introduction 2.1 Introduction 24 2.2 European settlement and the land laws 24 2.3 Increasing sheep numbers 26 2.4 The extent of land degradation 29 2.5 Changes in native herbivore communities 30 2.6 Outline of the thesis 31 2.6.1 The Study Site 33 2.6.2 Competition between sheep and kangaroos 33 2.6.3 Optimal diet selection and the evolution of arid zone herbivores 37 2.6.4 Carrying capacity 37 2.6.5 Conclusion 38 vi

CHAPTER3

General Description of Study Site 3 .1 Location 39 3.2 Land Systems 40 3.3 Climate 40 3 .3 .1 Rainfall 40 3.3.1.1 Annual and Seasonal Rainfall 41 3.3.1.2 Wet Spells 41 3.3.1.3 Droughts 42 3.3.2 Temperature 42 3.3.2.1 Summer Temperatures 42 3.3.2.2 Winter Temperatures 42 3.3.3 Humidity and Evaporation 43 3.4 Soils 44 3.5 Vegetation 44 3.5.1 Low Shrubland 44 3.5.2 Perennial Grasslands 45 3.5.3 No Perennial Vegetation 45 3.5.4 Tall Open-Shrubland 46 3.6 Fauna 46 3.6.1 Monotreme Mammals 46 3.6.2 Marsupial Mammals 47 3.6.3 Eutherian Mammals 47 3.6.4 The Biology of Red Kangaroos 48 3.6.4.1 Distribution and Abundance 48 3.6.4.2 Reproduction 49 3.6.4.3 Body Size and Growth Rate 49 3.6.4.4 Movement, Social Organisation and Home Range 49 3.6.4.5 Management 50 3.6.5 The Biology of Sheep 50 3.6.5.1 Distribution and Abundance 50 3.6.5.2 Reproduction 51 3.6.5.3 Body Size and Growth Rate 52 3.6.5.4 Movement, Social Organisation and Home Range 52 3.6.5.5 Management 52

CHAPTER4

Experimentally Examining Competition Between Sheep and Red Kangaroos. 4.1 Introduction 53 4.2 Materials and Methods 54 4.2.1 Sheep 56 4.2.1.1 Statistical analyses 58 4.2.2 Red Kangaroos 58 4.2.2.1 Statistical Analyses 60 4.3 Results 62 4.3.1 Sheep 62 4.3.2 Red Kangaroos 69 vii

4.4 Discussion 73

CHAPTERS

Mechanistically Modelling Competition Between Sheep and Red Kangaroos. 5 .1 Introduction 80 5.2 Materials and Methods 82 5 .2.1 Modelling 82 5.2.2 Parameterising the Model 84 5.3 Results 90 5.3.1 Parameterising the Model 90 5.4 Discussion 102 5.5 Appendixes 106

CHAPTER6

Optimal diet choice by sheep and red kangaroos. 6.1 Introduction 108 6.2 Materials and Methods 109 6.2.1 The Foraging Model 109 6.2.1.1 Feeding Time Constraint 110 6.2.1.1.1 Cropping Efficiency 110 6.2.1.2 Energy Requirement Constraint 111 6.2.1.3 Digestive Capacity Constraint 112 6.2.1.3.1 Gut Capacity 112 6.2.1.3.2 Passage Rate, In Vivo Digestibility 112 6.2.1.3 .3 Laboratory Analysis 113 6.2.2 Vegetation Sampling 114 6.2.3 Model Predictions and Analyses 115 6.2.4 Statistical Analyses 118 6.2.4.1 Sensitivity Analyses 119 6.3 Results 120 6.3.1 The Foraging Model 120 6.3.1.1 Feeding Time Constraint 120 6.3.1.2 Energy Constraint 120 6.3.1.3 Digestive Capacity Constraint 121 6.3.2 Vegetation Sampling 126 6.3.3 Model Predictions and Analyses 128 6.3.3.1 Sensitivity Analyses 135 6.4 Discussion 140 6.4.1 Foraging Goal 141 6.4.2 Alternative Constraints 143 6.4.3 Environmental Variability and Diet Choice 144 6.4.4 Coevolution of Herbivores and their Food Source 145 6.4.5 Conclusion 146 viii

CHAPTER 7

The Optimal Body Size and Evolution of Sexual Dimorphism in Red Kangaroos. 7 .1 Introduction 147 7.2 Materials and Methods 149 7.2.1 The Foraging Model 149 7.2.1.1 Feeding Time Constraint 150 7.2.1.2 Energy Requirement Constraint 151 7.2.1.3 Digestive Capacity Constraint 151 7.2.2 Vegetation Sampling and Analyses 151 7.2.3 Estimating Model Parameters During Prolonged Drought 152 7.2.4 Model Predictions and Analyses 152 7.3 Results 153 7.3.1 The Foraging Model 153 7.3.1.1 Male Body Size 154 7.3.1.2 Female Body Size 156 7.3 .1.3 Optimum Body Size 160 7.3.2 Estimating Model Parameters During Prolonged Drought 161 7.3.2.1 Estimating Cropping Efficiency 161 7.3.2.2 Estimating Proportional Food Abundance. 163 7.3.2.3 Body Size During Drought 164 7.4 Discussion 166 7.4.1 Maximum and Minimum Body Size 166 7.4.2 Optimal Body Size 167 7.4.3 Evolution of Sexual Dimorphism 168 7.4.4 Conclusion 171

CHAPTERS

Is the concept of carrying capacity useful in variable environments? 8.1 Introduction 173 8.1.1 The Alternative Models 177 8.1.1.1 The rating system 177 8.1.1.2 Range succession 178 8.1.1.3 Key species 179 8 .1.1.4 Productivity-stocking rate models 180 8.1.1.5 Habitat use/availability models 183 8.1.1.6 The nutritional approach 184 8.1.1.7 The interactive model 185 8.2 Materials and Methods 191 8.2.1 The model 192 8.3 Results 195 8.4 Discussion 202

CHAPTER9

Summary of Results and Conclusions 9 .1 Introduction 205 9.2 Competition 205 9 .2.1 Inter- versus Intraspecific Competition 205 ix

9.2.2 Other Potential Competitors: Termites 207 9.2.3 Continuous versus Rotational Grazing 208 9.3 Foraging and the Evolution of Herbivores in Variable Environments 209 9.3.1 Foraging Goal and Optimal Diet Choice 209 9.3.2 Body Size 211 9.4 The Dynamics of Plant-Herbivore Systems in Variable Environments 211 9.5 Synopsis 212

References 213 X

List of Figures

Chapter 1 Fig. 1 a-c. The figures represent the hypothetical energy intakes for a diet. The frequency of alternative diets that offer different energy intakes to a forager are represent as a probability density function, in this case a normal distribution. If the forager maximises mean net energy intake then its energy intake will be X (la). If the forager has a minimum energy requirement (R) below X, then the forager will avoid variance in energy intake. The shaded area represents energy intakes that will not satisfy R. In this case, variance in energy intake only exposes the forager to an unnecessary risk of failing to meet its requirements, and the forager will be risk-averse (lb). If requirement falls above the mean, the forager will certainly die if it takes the mean energy intake. In this case the forager is sensitive to variance in energy intake and will be risk-prone (le). 9

Fig. 1.2. The number of published studies that have examined generalist mammalian herbivore diet choice, sorted by method. The groups were; 1) descriptive - includes studies that were simple dietary descriptions, 2) contingency - studies that used the contingency model of optimal foraging theory, 3) RSF - studies that used risk sensitive foraging models, 4) CPF - studies that used central-place foraging theory, 5) LP - studies that used the linear program of optimal diet choice, 6) structural defenses - studies that examined the effects of plant structural defenses, and 7) chemical defenses - studies that examined the effects of plant chemical defenses. 20

Chapter 2 Fig. 2.1. The distribution of present land use in Australia. Source Caughley (1987a). 24

Fig. 2.2. The distribution and seasonal incidence of rainfall in Australia. Isohyets are in mm. Source Robertson et al. (1987). 25

Fig. 2.3. The trend in sheep numbers in western New South Wales from first settlement to the mid 1980's. Source Caughley (1987a) 30

Figs 2.4 a-c. The distribution of a) red kangaroos, b) euros and c) eastern and western grey kangaroos in Australia. Source Dawson (1995). 32

Chapter 3 Fig. 3.1. The location of Fowlers Gap Research Station in far western New South Wales. 39

Fig. 3.2. The monthly rainfall (mm) recorded at Fowlers Gap's weather station from January 1986 to December 1991. 41 xi

Fig. 3.3. Mean monthly maximum and minimum temperatures at the study site. Source Bell (1973). 43

Fig. 3.4. The distribution of sheep in Australia. Source Caughley (1987a). 51

Chapter4 Fig. 4.1. The layout of the experimental treatments. Sympatric = sheep and red kangaroos, Sheep Allopatric = sheep only, and Red Allopatric = red kangaroos only. 55

Fig. 4.2. Layout of permanent transects within each paddock of the study site. 61

Fig. 4.3. The mean body mass of ewes measured at each sampling period. Masses are corrected for greasy fleece mass. Data are the means of 10 sheep per paddock with their standard errors. 63

Fig. 4.4. The mean annual clean wool mass from ewes measured after shearing of each year. Data are the means of 10 sheep per paddock with their standard errors. 64

Fig. 4.5. The mean number of foetuses conceived/ewe in each paddock. Data are means and error bars are standard deviations. 65

Fig 4.6. The proportion of lambs in each treatment surviving from ultrasounding to weaning of each year. 66

Fig. 4.7. The mean body mass of lambs measured at lamb marking and weaning of each year. Masses are not corrected for greasy fleece mass. Data are the means of 20 lambs per paddock and their standard errors. 68

Fig. 4.8. The proportion of all mature female red kangaroos captured that were reproductive (i.e. had either a pouch young or a young-at- foot). Captured females were divided into groups depending on whether they were sympatric or allopatric with sheep. 71

Fig. 4.9. The density of red kangaroos per treatment. Densities are treatment means and their standard errors. 72

Chapter 5 Fig. 5.1. A bivariate normal distribution. 85

Fig. 5.2 a Clipped plant biomass subdivided into the categories forb, grass and b. and shrub for a) Sympatric 1 and b) Sympatric 2. 91 xii

Fig. 5.3. The regression of a sheep's energy intake (kJ/day) as a function of total plant biomass (kg/ha). (y=1033o+4.57x, r = 0.894, Fl,2 = 7.93, P < 0.106). The winter 1990 data was not included in the regression because the model failed to predict a goal of energy maximisation at this time (cf. Chapter 6 for further details). 92

Figs 5.4 a-e. The zero-isoclines of sheep and red kangaroos at Sympatric 1 in; a) winter 1989, b) summer 1990, c) winter 1990, d) summer 1991, and e) winter 1991, (• the observed density of sheep and red kangaroos). Note that there was a change in the scale of the axes (density) from 0-10 (no.Iha) for 5.4 a-c, and 0-5 (no.Iha) for 5.4 d-e. 96

Figs 5.5 a-d. The zero-isoclines of sheep and red kangaroos at Sympatric 2 in; a) summer 1990, b) winter 1990, c) summer 1991, and d) winter 1991, (• the observed density of sheep and red kangaroos). Note that there was a change in the scale of the axes (density) from 0-10 (no.Iha) for 5.5 a-b, and 0-5 (no.Iha) for 5.5 c-d. 99

Fig. 5.6 a The regressions of predicted equilibrium allopatric and sympatric and b. densities of a) sheep (sheep allopatric with red kangaroos are open circles and dashed line, sheep sympatric with red kangaroos are closed circles and solid line) and, b) red kangaroos against total plant biomass (red kangaroos allopatric with sheep are open squares and dashed line, red kangaroos sympatric with sheep are closed squares and solid line). 101

Fig. 5.7. Correlation between sympatric equilibrium sheep density and red kangaroo density. ( open squares and dashed line are winter data, closed circles and solid line are summer data) 102

Chapter6 Fig. 6.1. The regression offorestomach capacity (g-wet mass) on body mass (kg) of red kangaroos, (yf= 210 + 78.6x, r2= 0.72, P < 0.001, N = 27). 122

Fig. 6.2. Regressions relating in vitro solubility (HCl + pepsin) to in vivo digestibility for red kangaroos ( circle and unbroken line) and sheep (triangle and broken line). 123

Fig 6.3. Clipped plant biomass at each sampling period from the study site. Plants were clipped from 0.25 m2 quadrats. 126

Figs 6.4 a-d. Sensitivity analyses of red kangaroo optimal diet choice, for a feeding goal of energy maximisation. Graphs are; a) summer 1990, b) winter 1990, c) summer 1991, and d) winter 1991. Winter 1989 analysis is not presented because the linear programming model failed to predict observed diet choice. 138 xiii

Figs 6.5 a-d. Sensitivity analyses of sheep optimal diet choice, for a feeding goal of energy maximisation. Analyses are a) winter 1989, b) summer 1990, c) summer 1991, and d) winter 1991. Winter 1990 analysis is not presented because the linear programming model failed to predict observed diet choice. 140

Chapter7 Fig. 7.1. The relationship between body mass and 1) metabolic requirement and 2) digestive capacity. 148

Figs 7.2 a- The predicted energy intakes and requirements of male red e. kangaroos across a range of body sizes for a) winter 1989, b) summer 1990, c) winter 1990, d) summer 1991, and e) winter 1991. 156

Figs 7.3 a - The predicted energy intakes and requirements of female red e. kangaroos across a range of body sizes for a) winter 1989, b) summer 1990, c) winter 1990, d) summer 1991, and e) winter 1991. In addition, the proportion of breeding females in the sizes classes 15.5-20 kg, 20.5-25 kg, 25.5-30 kg, and 30.5-35 kg are presented. The sample size of each lactational group is at the top of each column. 160

Figs 7.4 a The regression of cropping efficiency (min/g-dry) against food type and b. biomass (kg/ha} for a) grasses (y=l.30-0.0007x, r2=0.702, Fl,3=7.05, P=0.077), and b) shrubs (y=l.85-0.0025x, r2=0.659, Fl,3=5.79, P=0.095). The outlier data point marked with the arrow was winsorised before inclusion in the regression (Sokal and Rohlf 1981). 162

Fig. 7.5. The regression of shrub abundance (kg/ha} against total food abundance (kg/ha} (y=57.1 +0.24x, Fl,3=5.69, r2=0.656, P=0.097). 163

Fig 7.6. Simulated biomasses of the plant categories grass and shrub at 200, 250 and 300 kg/ha. 164

Figs 7.7 a- The simulated energy intakes and requirements of red kangaroos c. across a range of body sizes as drought intensifies from a) 300 kg/ha total plant biomass, to b) 250 kg/ha and c) 200 kg/ha. 166

Fig 7.8. The age structure of red kangaroos that died during a drought at K.inchega National Park. (From Robertson, 1986). 168

Chapter 8 Figs 8.1 a a) Phase-plane trajectory of a herbivore eruption in a deterministic and b. environment. The plant-herbivore system reaches a point equilibrium, and b) phase-plane trajectory of a herbivore eruption in an environment with some periodic time dependence. The plant- herbivore system reaches a limit-cycle. 175 xiv

Fig. 8.2 a Frequency distribution of seasonal rainfall recorded at the d. Tibooburra Post Office, a) summer, b) autumn, c) winter, and d) spnng. 194

Figs 8.3 a Modelled trajectory of red kangaroo density through time in a) a and b. stochastic system, and b) a deterministic system. Starting conditions were H = 0.1 kangaroos/ha, and V = 250 kg/ha. Data used in the figures are from one representative replicate of the simulations of each system. 196

Figs 8.4 a Modelled trajectory of vegetation biomass through time for a) a and b. stochastic system, and b) a deterministic system. Starting conditions were H = 0.1 kangaroos/ha, and V = 250 kg/ha. Data used in the figures are from one representative replicate of the simulations of each system. 197

Figs 8.5 a Phase-plane trajectories of a) a stochastic system, and b) a and b. deterministic system. Starting conditions were H = 0.1 kangaroos/ha, and V = 250 kg/ha. Data used in the figures are from one representative replicate of the simulations of each system. 199

Figs 8.6 a Plot of the rates of change of vegetation biomass (dV/dt) against red and b. kangaroo density (dH/dt) for a) a stochastic system, and b) a deterministic system. 201 xv

List of Tables

Chapter4 Table 4.1. ANOVA table of all effects for the analysis of sheep body mass. Some interactions could not be calculated because of nesting. 63

Table 4.2. ANOVA table of all effects for the analysis of wool growth per annum. Some interactions could not be calculated because of nesting. 64

Table 4.3. ANOVA of the mean number of foetuses produced per ewe. The interaction could not be calculated because of nesting. 65

Tables 4.4 a Log-linear analysis of the frequency oflambs in each treatment and b. surviving from ultrasounding to weaning; a) results of fitting all k- factor interactions, and b) tests of marginal and partial associations. 67

Tables 4.5 ANOVA of all effects for lamb body mass for; a) 1988, b) 1989, c) a-d. 1990, and d) 1991. 69

Table 4.6 ANCOVA of all effects for red kangaroo body mass. The main effect and interactions with the factor "Paddock" could not be calculated due to missing cells in the design. 70

Tables 4.7 a Log-linear analysis of the frequency of mature female red and b. kangaroos in each treatment that were reproductive; a) results of fitting all k-factor interactions, and b) tests of marginal and partial associations. 71

Table 4.8. ANOVA of all effects for the analysis of red kangaroos density. 73

Table 4.9. Randomisation test results of treatment comparisons for red kangaroo density. 73

Chapter 5 Table 5.1. The correlation between the predicted and observed minimum acceptable food type item size and solubility. Predicted item sizes and qualities were calculated using the algorithms of Belovsky (1981, 1984b, 1986a). Observed minimum values were assumed to be equal to the lowest 10% of measured bite sizes and qualities. 88

Table 5.2. The amounts (kg-dry mass/ha) of exclusive, overlapping food and total plant biomass. The calculated competition parameters ( ) are also presented. 93

Chapter6 Table 6.1. Digesta passage rates of red kangaroos and sheep. Data are means ( SD). 121 xvi

Table 6.2 a The parameters needed to solve the linear programming model of and b. optimal diet choice for a) a red kangaroo of 30 kg body mass, and b) a sheep of 60 kg body mass, at the study site. 126

Table 6.3. The within-distribution of plant types for each sampling period. The data are skewness coefficients of within plant type distributions. The test was one-sided because it was hypothesised that plant were patchily distributed (i.e. positively skewed). * P < 0.05, ** P < 0.01, *** P < 0.001. 127

Table 6.4. The between-distribution of plant types for each sampling period. Data are Spearman Rank correlation coefficients of between plant type association. The test was one-sided because it was hypothesised that plant were negatively associated (i.e. occurred in different patches).* P < 0.05, ** P < 0.01, *** P < 0.001. 127

Table 6.5. The predicted energy maximising (N = 100), time minimising (N = 100), null (N = 52 for winter 1989, N = 44 for all others) and observed (N = 8) mean ( SD) diets for red kangaroos and sheep for the each sampling period. The plant categories in the diet are forb, grass and shrub, and data are presented as percentage of a category in the diet. In addition, the energy intake (kJ/day) and feeding time (min/day) are presented for the energy maximising and time minimising diets. 129

Table 6.6. The results of the Monte Carlo test for similarities between the observed diet and the diet predicted by the linear programming model for the goals of energy maximisation and time minimisation, or a null diet (i.e. random diet choice). The probabilities (P) represent the probability that agreement between the predicted and observed diets was arrived at by chance. Predicted diets that were not significantly different from the observed diet are marked with an asterisk (*). 130

Table 6.7. The results of the Proportional Similarity Index measure of overlap between the predicted and observed diets. The within group overlap measures for the energy maximising, time minimising and null diets were the results of 4950 comparisons, while the within group measure for the observed diet was the result of 28 comparisons. The between group overlap between predicted diets and observed diets were the result of 800 comparisons. 135

Chapter 7 Table 7.1. Bite size calibration ratios of male and female red kangaroos relative to an individual of25 kg. Female red kangaroo bite size asymptotes after 30 kg body mass, while male bite size asymptotes after 50 kg body mass. 150 xvii

Table 7.2. The predicted optimum body sizes of male and female red kangaroos at each sampling period. 161

Chapter 8 Table 8.1. Seasonal rainfall recorded at the Tibooburra Post Office weather station. The stochastic standard deviation (SD) and coefficient of variation (CV) represent actual data, while the deterministic data were calculated by reducing SD to 1110th of the mean. Rainfall records represent 107 years of collection. 191

Table 8.2. Comparison of the simulation mean, mean standard deviation and coefficient of variation of the vegetation biomass and kangaroo density from stochastic and deterministic systems. Mean vegetation biomass, mean kangaroo density and standard deviations are the means of 10 simulations. 200 Chapter 1: Literature Review

The Feeding Strategies and Diet Choice of Generalist Mammalian Herbivores

1.1 Introduction

A generalist herbivore is one that subsists on a mix of the structural parts of plants, such as stems or leaves (Janis 1976), and does not include herbivores that are mainly granivorous or frugivorous. A consequence of being a generalist herbivore is that available food may be of low digestibility (Robbins 1983), have highly variable nutrient quality (Westoby 1974), contain defensive compounds that may reduce digestibility or be toxic (Freeland and Janzen 1974, Bryant et al. 1991), require a slow throughput to extract nutrients (Hungate 1966), and have a high bulk (wet/dry mass ratio) that may quickly fill the gut and restrict nutrient intake (Belovsky 1981 a, 1984a). Because of the anatomical, behavioural and physiological constraints to a herbivore's feeding all plants or parts of plants cannot be considered as food (Belovsky 1984b, 1986a), and as a consequence herbivores are often food limited (Robbins 1983). Consequently, there has been much interest in how generalist mammalian herbivores have made a successful living on such a potentially unfavourable food source (Rosenthal and Janzen 1979, Crawley 1983, Hughes 1990).

There have been several hypotheses to explain the feeding strategy and diet choice of mammalian herbivores (Schoener 1971, Covich 1972, Freeland and Janzen 1974, Westoby 1974, Owen-Smith and Novellie 1982). Not all models are mutually exclusive and some can be completely included within the theoretical framework of an alternative. For example, Westoby's (1974) diet choice model that hypothesises that generalist herbivores attempt to maximise nutrient balance whilst being constrained by a fixed total bulk of food can be incorporated into optimal foraging theory (Stephens and Krebs 1986). Two alternative models have received the most attention; Schoener's (1971) nutrient model and Freeland and Janzen's (1974) toxin model. Schoener (1971) derived a model of feeding strategies that was based on the predictions of optimal foraging theory (Stephens and Krebs 1986). Schoener hypothesised that feeding strategy was dependent upon the relationship of total feeding time and total net energy yield. 2

Furthermore, he hypothesised that the feeding goal of a forager would be either; 1) time minimisation, whereby an animal's fitness is maximised by spending just enough time to satisfy a given energy requirement, freeing time for other activities such as avoidance of predators, or nurturing young, or 2) energy maximisation, whereby an animal's fitness is maximised by maximising net energy intake for a given time spent feeding, potentially supplying stored energy reserves ( deposited fat) for times of food limitation. Freeland and Janzen (1974) argued that the main source of diet diversification in mammalian herbivores was the ubiquitous high toxin concentrations of plants. Physiological limitations on the ability of herbivores to detoxify and eliminate secondary compounds has forced mammalian herbivores to consume a variety of plant foods. Selection is a learned response to adverse physiological effects. The nutrient and toxin models remained distinct alternatives until recently, when Belovsky and Schmitz ( 1991, 1994) combined the two approaches.

The aim of this review is to examine the methods and hypotheses put forward to describe generalist mammalian herbivore feeding strategies and diet choice. Alternatives hypotheses are evaluated on the basis of their congruence with empirical studies and their potential to explain the determinants and consequences of diet choice from an autecological basis. In addition, the alternative hypotheses are discussed with respect to their ability to put diet choice into the broader ecological perspective of herbivore community dynamics.

1.2 Diet Choice Descriptions

Descriptive diet studies summarise the contribution of plant species or plant types to the diet. It has been common practice for descriptive diet studies to be devoid of testable hypotheses (Sinclair 1991), with authors simply basing their conclusions on the results of correlation methods (e.g. simple correlation or factor analysis). Even rudimentary hypotheses such as; herbivores select food types in proportion to their abundance (i.e. are non-selective), are commonly not tested (Sinclair 1991), but there are exceptions (e.g. Westoby 1980). Typically, the "inductive method" (Romesburg 1981) is used and consequently conclusions drawn from these studies are equivocal. 3

The levels of such factors as soluble carbohydrate, fibre, protein, secondary metabolites, organic acids, and vitamins and minerals have been used in correlation analyses of diet choice (Westoby 1974). However, correlation analyses cannot determine cause and effect (Romesburg 1981 ). Further complicating the interpretation of results is the fact that many of the factors listed above covary. For example, Vangilder et al. (1982) examined the diet choice of white-tailed deer (Odocoileus virginianus) by principal component analysis. They found that diet selection was positively correlated with variables such as plant digestibility, crude protein, phosphorus and potassium content, and negatively correlated with lignin, silica and cellulose content. They conclude that diet selection was not based on a single factor but upon multiple factors of the forage selected. However, digestibility and crude protein positively covaried, while digestibility negatively covaried with silica and cellulose. The simultaneous co-correlation and dependence of one factor on others may lead to conclusions being confounded. Vangilder et al. (1982) may have correctly concluded that forage selection was based on several factors, but their data could just as easily be interpreted as showing one factor ( e.g. digestibility) being important, and other factors simply being co-correlated. In addition, they cannot rule out that there was another important factor that they did not measure, which was the most important determinant of food choice. Explaining variation in diet choice by using correlation methods has led Robbins (1983) to conclude that very little has been learned from the hundreds of diet studies done on mammalian herbivores. This exposes one of the major weaknesses of the a postiori explanation of data by correlation analyses; that any pattern can be accounted for if enough variables are measured.

Descriptive diet choice studies have been useful in indicating patterns in herbivory, but the typical analysis of lists of plant species supplied in these studies has led to only a superficial understanding of herbivore feeding strategies. The need to understand the broader implications and mechanisms of diet choice has led to the analysis of herbivore diets based on theoretical frameworks, such as optimal foraging theory. Defining diet choice and herbivore feeding strategies from within a theoretical framework allows a priori predictions of the determinants ofherbivory, so that understanding may progress on the foundation of testable hypotheses. 4

1.3 Feeding Strategy and Diet Choice

There have been three main views of what determines mammalian herbivore diet choice; 1) nutrient maximisation, 2) selecting complementary nutrients, or 3) avoiding plant toxins (Stephens and Krebs 1986). Of these views nutrient maximisation and avoiding plant toxins have received the bulk of attention. Optimal foraging theory has been used to test hypotheses concerned with nutrient maximisation, while the proponents of plant defenses have relied upon measurement of defensive factors and correlation of these factors with diet choice. The following sections review these three alternatives, and discusses their contributions to the unravelling of the strategies and determinants of diet choice by generalist mammalian herbivores.

1.3 .1 Optimal Foraging Theory

Diet choice by mammalian herbivores has been examined using optimal foraging theory. Methods of predicting diet choice have included contingency models, central-place foraging models, risk-sensitive foraging models, linear programming models, and alternatives which do not neatly fit into the previous categories.

1.3 .1.1 Contingency Models The first mathematical formulation of an optimal foraging model is credited to MacArthur and Pianka (1966). Their model has since been referred to as the "contingency" (Schoener 1974a) or "classical" (Stephens and Krebs 1986) model of optimal foraging theory. The original model was subsequently refined and modified (Schoener 1969, 1971, 1974a, Pulliam 1974, Chamov 1976) and for generalist herbivores can be represented as (Belovsky 1981a);

(1.1)

where R is the rate of energy intake; for food type i; digestibility j; items of size

k; eiik is energy/item of i,j, k traits; aiik is items/m2 of foods included in the diet of i,j, k traits; sis horizontal search ability (m2/min); and t; is handling time for a food of type i. 5

The optimal diet is calculated by ranking the n food types in decreasing order of profitability (defined as the ratio of energy gained/time spent handling and consuming), and starting with the diet that includes only the most profitable food type, additional food types are added until R is maximised. Several predictions stem from this model; 1) the greater the absolute abundance of food, the more specialised the diet, 2) whether or not a food type is included in the diet is independent of its own abundance, but depends only on the absolute abundance of more profitable food types, and 3) partial preferences do not exist, either a food type is consumed when it is encountered or it is never taken (Schoener 1987).

Although the contingency model is one of the most frequently used optimal foraging models (Belovsky 1984c), there have been very few field tests of the model using generalist mammalian herbivores. Three typical examples of the use of the contingency model for predicting diet choice by mammalian herbivores are Belovsky (1981b, 1984a) and Owen-Smith and Novellie (1982). Belovsky (1981b) examined plant species diet choice of the moose (Alces alces) and found that the contingency model did not predict the observed diet choice, and moose had a lower net energy intake rate than predicted by the model. Similarly, Owen-Smith and Novellie (1982) found that kudu (Tragelaphus strepsiceros) selected a much wider dietary range than predicted by the model. Finally, Belovsky (1984c) comparatively tested three optimal foraging models; the contingency, linear programming and a model of food abundance weighted by net energy content. He found that the contingency model did not predict herbivore diet choice for two main reasons; 1) the model appears to lack important constraints to herbivore foraging. The only constraint implicit in the model is feeding time, and 2) the model assumes that food is searched for simultaneously (implying that food types are either randomly or uniformly distributed), whereas many plant species have clumped distributions (Belovsky et al. 1989).

Despite the lack of corroborative data, some authors (Owen-Smith and Novellie 1982, Owen-Smith 1993a, b) still claim that the contingency model is heuristically valuable for examining the diet choice of generalist mammalian herbivores. This peculiar point of view must be treated with scepticism, especially if the underlying model or assumptions of the model are inappropriate for examining the diet choice of 6

mammalian herbivores. This would appear to be the case because alternative models of the diet choice of mammalian herbivores ( cf. Linear Programming) have been spectacularly successful. While the contingency model has been significant in the development of optimal foraging theory, it would appear to be an unsuitable method of examining the diet choice of generalist mammalian herbivores.

1.3.1.2 Central-place Foraging Some animals search for food away from a nest or burrow, and instead of consuming harvested food where it is cropped return to their nest to consume the food. Central-place foraging (Orians and Pearson 1979) deals with animal's which forage in this manner, and four types of models have been proposed to describe their foraging behaviour (Schoener 1987, Stephens and Krebs 1986). First, Schoener's (1979) "encounter at a distance" model can be applied to foragers which consume food items from a range of sizes, and the model predicts the relationship between food item profitability and distance from the central-place. The second and third models were proposed by Orians and Pearson (1979) and deal with two different kinds of foragers, the single-prey loader and the multiple-prey loader. As the names of these models imply the single-prey loader returns to the central-place with a single food item, while the multiple-prey loader may carry several items. Lessells and Stephens (1983) later corrected a mistake in the single-prey loader model, the corrected model predicting that there is some critical travel time or distance below which a forager is unselective. The fourth central-place foraging model (Andersson 1978, 1981) is concerned with search time and distance from the nest and not food choice, so will not be considered further.

Although the Schoener and Orians-Pearson models share some common predictions there are also some important differences. Both models predict that if pursuit or provisioning time is independent of prey size, larger food items will be collected as the forager moves further from the nest. However, Schoener (1979) notes that this relationship may be reversed if pursuit or provisioning time increases with prey size. The predictions of the models differ mainly in the decision assumptions they make (Stephens and Krebs 1986). Schoener's model predicts which food items should be harvested when encountered at varying distance from the nest, while the Orians-Pearson model predicts how patches at varying distances from the nest should be exploited. 7

Field tests of central-place foraging models have concentrated mainly on birds (e.g. Houston 1985, Tamm 1989, Cuthill and Kalcenik 1990, Sodhi 1992, Korpimaeki et al. 1994), but other studies have examined granivorous mammals (Elliott 1988), carnivores (Lindstroem 1994), and invertebrates (Bailey and Polis 1987). Few studies have been done with mammalian herbivores, and then only two species have been examined. Beavers (Castor canadensis) have received the most attention (Jenkins 1980, Pinkowski 1983, Belovsky 1984d, McGinley and Whitham 1985, Basey et al. 1988, Fryxell and Doucet 1991); there has been one study on the pika, Ochotona princeps (Huntley et al. 1986).

The predictions ofSchoener's model have been most widely tested, and corroborated, in studies of the central-place foraging behaviour of beavers. A number of studies (Jenkins 1980, Pinkowski 1983, Belovsky 1984d) have shown that when provisioning time increases with tree size (the "prey" of beavers), beavers show greater selectivity for small trees at further distance from their nest. McGinley and Whitlam (1985) found that this size-distance relationship was reversed, as predicted by Schoener (1979), when provisioning time was independent of tree size. In this latter case beavers harvested only the branches of shrubs and small trees, so the difference in provisioning time between small and large branches was small (McGinley and Whitlam 1985), whereas in previous studies beavers harvested whole trees and cutting time tended to increase exponentially with tree diameter (Belovsky 1984d). While these tests of central-place foraging theory have shown that some beavers select diet based on maximising their net rate of energy gain, Basey et al. (1988) found that secondary plant metabolites may modify the size-distance relationship of diet choice by beavers. They found that when intensive tree harvesting induced chemical defenses in plant regrowth, small trees with low provisioning time but high levels of secondary metabolites were avoided in favour oflarger trees with higher provisioning time but low levels of metabolites. Thus, induced chemical defence could modify diet choice in a way not predicted by the conventional central-place foraging models. Belovsky and Schmitz (1991, 1994) have since shown that optimal foraging theory can incorporate the findings of Basey et al. (1988), by simply measuring the reduced profitability (e.g. digestible energy content) of plants with induced defenses or if the toxin has a cumulative effect by the inclusion of a further constraint that limits consumption of the defended food. 8

In summary, the small number of studies of central-place foraging by generalist mammalian herbivores have found good agreement between the predictions of the theory and observations. However, the behaviour of harvesting food away from a nest and then returning to the nest before consumption is an unusual feature of only a small number of herbivore species. Studies of central-place foraging by generalist herbivores suggest that maximisation of energy intake is the foraging goal, but that diet choice may be modified by other factors such as plant secondary metabolites.

1.3.1.3 Risk-sensitive Foraging The majority of optimal foraging models assume that a forager knows the expected mean and variance in energy intake for its next foraging period. These models assume that the variance associated with the mean is negligible to the fitness of the forager. But in a stochastic environment the expected net energy intake may not be not known and a forager may be sensitive to variance in expected energy intake. Risk sensitive foraging models deal with animals whose diet choice is affected by the mean and variance of expected food intake. Variation in expected energy intake introduces some risk that a forager will not achieve positive energy balance at the end of its foraging period. Negative energy balance reduces fitness by increasing the probability of starvation or decreasing reproductive output. Risk-sensitive foragers can maximise fitness by either; 1) minimising the probability of starvation (Stephens and Chamov 1982), 2) minimising the chance of failing to meet some threshold for reproduction (Caraco and Gillespie 1986, Gillespie and Caraco 1987), or 3) balancing both these goals (Schmitz and Ritchie 1991).

Risk occurs when there is a chance of not satisfying some requirement while foraging due to stochasticity in energetic reward per foraging period (Caraco 1981). This predicament can be explained graphically. The frequency of alternative diets available in an environment can be represented by a probability density function (Fig. 1.1 a). If a forager's minimum energy requirement falls below the mean energy intake available in the environment then the forager will avoid variance in energy intake (Fig. 1.1 b ). Selecting a variable energy intake only exposes the forager to the unnecessary risk of starvation. This is referred to as risk-averse behaviour (Caraco 1980). lfthe mean 9

quality of food items decreases, for example during a drought, a forager's energy requirement may exceed the mean for the environment (Fig. 1.1 c ). If the forager still selected a diet based on mean net energy intake, the forager's energy balance would be negative and it would eventually die of starvation. Selecting a variable energy intake does not guarantee survival, but offers some chance of avoiding starvation. In this case the forager should select the diet with variable energy intake. This is referred to as risk prone behaviour (Caraco 1980). 1.1 a) 1.1 b)

X R X

Energy Intake Energy lruke

1.1 c)

X R ' j

Fig. 1 a-c. The figures represent hypothetical probability density functions of food availability and energy intake. If the forager maximises mean net energy intake then its energy intake will be X (la). If the forager has a minimum energy requirement (R) below X, then the forager will avoid variance in energy intake. The shaded area represents energy intakes that will not satisfy R. In this case, variance in energy intake only exposes the forager to an unnecessary risk of failing to meet its requirements, and the forager will be risk-averse (lb). If requirement falls above the mean, the forager will certainly die if it takes the mean energy intake. In this case the forager is sensitive to variance in energy intake and will be risk-prone (le).

Caraco (1980) suggested "rules of thumb" to explain these different behaviours. If energy budget is positive be risk-averse. If energy budget is negative be risk-prone. 10

Stephens and Chamov (1982) extended the rules of thumb, and coined the "extreme variance rule of thumb", to include a special case where energy intake varies for all diets, but expected intake is identical. Foragers with positive energy balance should select low variance diets (risk-averse), while those with negative energy balance should select high variance alternatives (risk-prone).

While the theory of risk-sensitive foraging is well developed (e.g. Caraco 1980, Stephens and Chamov 1982, Regelmann 1984, Caraco and Gillespie 1986, Real and Caraco 1986, Gillespie and Caraco 1987, Real 1987, McNamara et al. 1991, Schmitz and Ritchie 1991), field tests of its predictions have generally been lacking with most tests being confined to artificial environments using either birds (Caraco et al. 1980, Stephens and Paton 1986, Caraco et al. 1990, Ha 1991) or insectivorous mammals (Barnard and Brown 1985a, 1985b, 1987, Barnard et al. 1985). There is especially a paucity of field tests of risk-sensitive foraging by generalist mammalian herbivores, with only two published field tests (Belovsky 1981a, Schmitz 1992). Belovsky (1981a) concluded that moose are risk averse when not threatened with starvation risk. Moose appeared to use a foraging strategy that implemented fixed thresholds of minimum item quality. For example, in summer moose only selected items that were > 1.3 kJ/item,

whereas including items ~ 0.84 kJ/item would have maximised the rate of energy intake. Thus, moose appeared to have a food item threshold that minimised the risk of selecting plants that did not satisfy energy requirements. Schmitz (1992) examined the winter diet choice of white-tailed deer in the Loring Deer Yard in Canada. He examined the consumption of two principal food types, coniferous and deciduous twigs, in two treatment areas that differed in their mean available food abundance. In one treatment (the natural wintering treatment) starvation risk was present (Schmitz 1990) since the only available food was natural browse, while in the other treatment (the supplemental feeding treatment) starvation risk was artificially eliminated by feeding deer ad libitum amounts of corn and oats. Schmitz found that in the presence of a starvation risk deer appeared to balance losses of fitness due to starvation with gains in fitness due to offspring production, as predicted by Schmitz and Ritchie (1991). In contrast, in the absence of a starvation risk deer were insensitive to variance in food availability and simply maximised their rate of energy intake. The close agreement between predictions and observations achieved by Schmitz (1992) indicates that risk-sensitivity may be an important determinant of diet choice by mammalian herbivores in environments where 11

nutrient availability is highly variable and there is a high probability of starvation. Given that these studies represent the only examples of field tests of risk-sensitive foraging by mammalian herbivores, the extent to which diet choice of other herbivores is affected by the expected mean and variance in nutrient intake remains unknown. This represents a major deficiency in our knowledge of foraging strategies of mammalian herbivores and warrants further tests of the theory.

1.3.1.4 Linear Programming The mathematical optimisation technique of linear programming has been used to predict diet choice by generalist mammalian herbivores (see Table 1 in Belovsky 1994, page 4 78). Linear programming is a method of finding the optimal solution to a constrained problem (Winston 1991). The use of linear programming to examine diet choice was first suggested by Schoener (1971). Westoby (1974) formalised the theoretical framework for using linear programming to examine diet choice and within a few years the first test of the model using a generalist mammalian herbivore (the moose) was published (Belovsky 1978). When applied to optimal foraging theory, the linear program of optimal diet choice predicts that a forager will be an energy maximiser or a time minimiser (sensu Schoener 1971), although alternative goals, such as toxin minimiser, protein maximiser or sodium maximiser, can be optimised (Belovsky and Schmitz 1991, Forchhammer and Boomsma 1995).

Belovsky (1978) hypothesised that moose feeding was limited by four constraints; 1) energy requirements for maintenance, growth and reproduction, 2) sodium requirement for reproduction, 3) available feeding time, and 4) daily digestive capacity. In the terminology oflinear programming energy and sodium requirements are lower constraints that must be exceeded, while feeding time and digestive capacity are upper constraints that cannot be exceeded. Belovsky (1978) predicted diet choice on the basis of three broad plant categories; deciduous leaves, forbs and aquatic plants. The energy maximising solution was the predicted dietary mix of the three plant types which provided the greatest amount of energy and satisfied an individual's sodium requirement. The time minimising solution was the mix which provided the energy and sodium requirements in the least amount of time. Specifically, Belovsky (1978) predicted that if a moose was to maximise its energy intake (be an energy maximiser) it 12

should consume in one day 853 g-dry mass of aquatics, 3585 g-dry of deciduous leaves and 342 g-dry of forbs, while a time minimising moose would consume 958 g-dry of aquatics, 3435 g-dry of deciduous leaves and no forbs. The observed average diet was 868 g-dry of aquatics, 3656 g-dry of deciduous leaves and 374 g-dry of forbs. Belovsky ( 1978) concluded that moose foraged as energy maximisers and not as time minimisers. The remarkable level of agreement between predicted and observed diets was unprecedented in studies of herbivore diet choice, and suggested that Belovsky had derived a simple and highly accurate optimisation model of herbivore foraging.

Since then more than 280 tests of the linear programming model of optimal diet choice by mammalian herbivores have been made, with the foraging goal of nutrient (energy or sodium) maximisation explaining 85% of the observed variation in diet composition (Belovsky and Schmitz 1994). The only exceptions to nutrient maximisation were found to be for males engaged in mating activities, for which a goal of time minimisation was found in two cases (Belovsky 1986b, Belovsky et al. submitted), while in a further five cases diet choice was found to be inconsistent with either energy maximisation or time minimisation (Forchhammer and Boomsma 1995). From these results it appears that a generalisation about mammalian herbivore feeding strategies can be drawn; be a nutrient maximiser unless you are a male actively searching for a mate, then be a time minimiser.

The linear programming approach to predicting optimal diet choice has been criticised on a number of grounds including incorrect formulation of the digestive constraint (Hobbs 1990), circularity in the formulation of constraints (Owen-Smith 1993a, 1993b), inappropriately tested foraging goals (Ward 1993), and incorrect statistical analysis of the results of the linear program (Huggard 1994). Each of these criticisms have been dealt with (Belovsky 1990, 1991, Belovsky and Schmitz 1993), and as Belovsky and Schmitz (1994) point out usually arise from misunderstandings of the linear programming approach and how it can be applied to herbivore foraging. Even though there is now a wealth of evidence to support the application of linear programming for examining herbivore diet choice, the criticisms listed above suggest that there is room for further validation and refinement. 13

The linear programming approach has been the most widely tested and successful method of examining diet choice by generalist mammalian herbivores (Belovsky 1994). Linear programming models have been used to examine temporal and spatial diet changes (Belovsky et al. 1989, Schmitz 1990); ontogenetic (Edwards 1992, unsubmitted MS), sexual (Belovsky 1978, 1984a) and reproductive (Belovsky 1984a, Belovsky et al. submitted, Forchhammer and Boomsma 1995) diet shifts; fitness and hereditary influences (Ritchie 1990, 1991); plant defensive strategies (Belovsky and Schmitz 1991, 1994, Schmitz et al. 1992); optimal body size selection (Belovsky 1978, 1984a, 1987); and the structure of herbivore guilds (Belovsky 1986b). Contrary to the critics of the linear programming approach (Hobbs 1990, Owen-Smith 1993a, 1993b, Ward 1993, Huggard 1994), who claim that the model has stifled research into diet selection and its consequences, the model has proven itself to be a highly accurate and powerful method of examining the constraints to herbivory on the diet choice and nutrient intake of generalist mammalian herbivores. Furthermore, the quantitative predictions of the model have provided the impetus for using optimal foraging theory to explore the ecological consequences of foraging behaviour (Green 1990).

1.3.1.5 Other Optimisation Models An alternative model of herbivore diet choice is based upon food type abundance weighted by net energy content (Stenseth et al. 1977, Stenseth and Hansson 1979, Stenseth 1981). The model (Eq. 1.2) predicts that a herbivore will select the optimum diet when it maximises LG;(x,y). j

(1.2)

where G;(x,y) is the net energy gain (kJ/day) for food class i and of energy contentx and abundancey; d;(y) is the inverse of cost of acquisition in terms of item at a given food abundance (y) for food class i (m2/min); F;(x) is the abundance of food type i of energy value x; x is the digestible energy value (kJ/g); and m(y) is the metabolic rate at food abundance y (kJ/min). 14

When all food types are abundant, herbivores are predicted to be highly selective, but as food becomes scarce a greater range of food types are predicted to be consumed. However, in contrast to the prediction of the contingency model, food types of low quality (low rank) but high abundance may be included in the diet (Stenseth and Hansson 1979). The contingency model predicts that the inclusion of lowly ranking foods in the diet is independent of their abundance and is dependent upon the absolute abundance of higher ranking foods. Therefore, when food type abundance is weighted by net energy content, diet choice is determined by both total food density and relative food density.

Belovsky (1984c) tested the Stenseth-Hansson model and provides an excellent critique. He found that the model did not predict herbivore diet choice and that it was also theoretically implausible. The Stenseth-Hansson model assumes that foods of only one rank are consumed, those with the highest product of energy content and abundance. This assumption of the model is likely to be commonly violated, especially when consumption of a variety of food types may produce a higher energy/time ratio (Belovsky 1984c). Furthermore, the model is not an optimal foraging model ( contrary to the claims of the authors) because it does not satisfy the mathematical criteria of optimisation (Belovsky 1984c, Stephens and Krebs 1986). In conclusion, the Stenseth Hansson model has been disproven as a hypothesis of generalist herbivore diet choice, and does not warrant further investigation.

1.3.2 Complementary Nutrients

The complementary nutrients hypothesis (Covich 1972, Rapport 1980, 1981) states that herbivores do not attempt to maximise intake of a nutrient, but rather choose food types on the basis of balancing a suite of complementary nutrients or anti-nutrients such as secondary metabolites. The dietary items in a complementary nutrient consuming herbivore can be predicted from "indifference" curves (Stephens and Krebs 1986) which are isoclines of prey combinations that contribute the same quantity of assimilated energy and metabolites (Rapport 1971).

To my knowledge the complementary nutrients hypothesis has never been field tested on generalist mammalian herbivores, so the extent to which the balancing of 15

complementary nutrients influences their diet choice remains unknown. However, on theoretical grounds the complementary nutrients hypothesis seems unlikely to be valid, especially given the wealth of evidence from optimal foraging theory studies that supports the hypothesis that generalist herbivores attempt to maximise their rate of energy intake. In addition, Stephens and Krebs (1986) point out that the evidence used to support the hypothesis of complementary nutrients could just as easily be interpreted in terms of the rate maximising hypotheses of optimal foraging theory.

1.3.3 Plant Defence

Plants use structural and chemical defences to discourage herbivores. Structural defences such as thorns, prickles and hairs can pierce or irritate the tongue and gums and generally act by slowing the rate at which food can be ingested (Belovsky et al. 1991). Chemical defenses can either reduce food digestibility, or have a cumulative toxic effect (Belovsky and Schmitz 1994). Chemical defences are collectively called secondary compounds ( or metabolites) and include such chemicals as tannins, phenols, alkaloids, cyanogenic glycosides, saponins and terpenoids. Because of their digestion reducing or toxic effects they must be degraded or eliminated from the body before they alter physiological systems (Robbins et al. 1987).

1.3.3.1 Spines and Thoms Spines and thorns can be effective in three ways (Belovsky et al. 1991 ). First, they can slow a herbivore's harvesting rate, forcing careful cropping to avoid painful spines. Second, a herbivore may take smaller bite sizes so that it can more easily manipulate the cropped item. Third, thomed plants often have fewer and smaller leaves for a given stem diameter than unthomed plants, reducing the amount that can be harvested per bite.

In an African savannaAcacia scrub, giraffes (Giraffa camelopardalis) selectively fed upon unthomed branches of Acacia seyal when thorns had been experimentally removed (Milewski et al. 1991). Unthomed branches lost 39% of their original length, while untouched control branches lost only five percent. Cooper and Owen-Smith (1986) found a similar result with other large mammalian herbivores. 16

Milewski et al. ( 1991) conclude that thorns affect harvesting of defended plants, but fail to state how. They go on to imply that some plants respond to herbivory by increasing thorn length and density. This response to herbivory has been termed "induced defence" (Karban and Myers 1989), and is an important anti-herbivore adaptation which suggests that plants actively control investment in defensive structures. At times of low herbivory it may be unprofitable to have a constant investment in defence, so produce fewer and smaller spines. When herbivory is higher, then invest more in defensive structures.

Spines can restrict herbivory over a wide range of herbivore body sizes. Belovsky et al. (1991) determined that the foraging behaviour of five shrub-steppe herbivores, ranging in size from 1.5 kg (European rabbit, Oryctolagus cuniculus) to 40.0 kg (domestic cattle, Bos taurus) were all affected by spines but to varying extents. They concluded that small herbivores are least affected because they can more easily manipulate cropped food to avoid being spiked. They note that native and introduced herbivores of similar size were equally influenced by thorns, which is in contrast to Cooper and Owen-Smith's (1986) conclusion that the effectiveness of thorns is related to the degree of coadaptiveness with thorny plants. Belovsky et al. ( 1991) conclude that thorns were effective by reducing the bite size but not the bite rate of the herbivores they studied. The presence of spines did not prevent a plant being fed upon, but only slowed the rate of consumption of the plant.

1.3.3.2 Secondary Compounds Food selection theories related to secondary compounds suggest that herbivores forage to satisfy their nutritional requirements with minimum ingestion of toxic secondary compounds (Freeland and Janzen 1974), or that food consumption is controlled by detoxification and elimination (Robbins et al. 1987). The evidence concerning the extent to which plant secondary compounds determine herbivore diet choice is contentious with some authors stating that toxins exert the greatest influence on diet (Cooper and Owen-Smith 1985), while others suggest they have a modifying effect and are one of several dietary influences (Basey et al. 1988, Belovsky and Schmitz 1991, 1994). 17

Soluble phenolics have been shown to reduce protein and cell wall digestibility by precipitating plant proteins and gastrointestinal enzymes (Zucker 1983). Yet many animals show adaptations that minimise protein precipitation and the toxic effects of secondary plant compounds (Freeland and Janzen 1974). Generalist herbivore stomaches are generally alkaline and contain diverse bacterial and protozoan microbes to digest plant cell walls. This type of gut also effectively degrades a variety of plant secondary compounds (Freeland and Janzen 1974). The extent to which the gut microorganisms can detoxify secondary compounds depends upon the experience of the microorganisms with the compounds, and it usually takes only a few days for the gut to adapt to a new diet (Warner 1962). The effectiveness of secondary compounds must be gauged after determining how toxins are combated, and not simply by measuring secondary compound concentration in the plant.

It would be misleading to assume that plant secondary compounds dominate diet choice for generalist herbivores. Cooper et al. (1988) conclude that the diet selection of kudus (Tragelaphus strepsiceros) and impalas (Aepyceros melampus) is controlled by

~ the relative concentrations of protein and condensed tannins. In the same study they report that several plant species that had highly unfavourable protein-tannin differences were often consumed, while some species with favourable differences were rejected. The inconsistency between their data and conclusions suggests that another factor is important, and warrants revaluation of their conclusions.

Basey et al. (1988) found that beaver (Castor canadensis) selected aspen trees (Populus tremuloides) using two different feeding strategies. The authors successfully predicted tree size selection of two beaver colonies by combining feeding strategies that minimised toxin intake and maximised energy consumption. At one site that had been occupied for twenty eight years they found that heavy herbivory had induced high concentrations of phenols in the bark ofjuvenile aspen. At this site beaver were observed to minimise phenol intake by avoiding juvenile aspen and taking larger trees that had lower concentrations of secondary compounds but were also energetically less profitable. Juvenile aspen at the recently occupied site had low concentrations of phenolic compounds. At this site beaver selected food that maximised their energy intake. The authors conclude that at any given time a herbivore may use either strategy depending on the state of its food source. 18

Schmitz et al. (1992) used the optimisation technique oflinear programming to examine the effect of plant chemical defenses on diet selection by a generalist herbivore the snowshoe hare (Lepus americanus). Their model included the three most common constraints to herbivore foraging used in other linear programs of optimal diet choice; 1) a feeding time constraint, 2) a digestive constraint, and 3) a nutrient constraint. Depending on their mode of action, having either a digestion inhibiting or toxic effect, chemical defenses were incorporated by modifying the nutrient constraint listed above (digestion inhibiting) or by the inclusion of another constraint which forms an upper limit to consumption (toxic effect) (Belovsky and Schmitz 1991, 1994). The two browse species that used as food in this study, the balsam poplar (Populus balsamifera) and the grey willow (Sa/ix g/auca), contain phenols which are thought to inhibit protein digestion in the snowshoe hare (Sinclair and Smith 1984). The two food types also differed in their relative amounts of phenols, with balsam poplar being the more heavily defended. Thus, the phenolic compounds modified the nutrient constraint of the linear program. They hypothesised that defence would be effective when the following condition was satisfied (Belovsky and Schmitz 1991),

(1.3)

where n is the digestible nutrient content of the comparatively less defended (u) and defended (d) plants; bis the wet/dry mass ratio (which is a measure of bulkiness in the gut); and p is the turnover rate of the plants in the gut (times/day).

They found that when this inequality was satisfied the defence was effective. But when the nutrient content of P. balsamifera was increased by fertilisation, or its bulkiness was reduced by drying the efficacy of the defence was reduced, and P. ba/samifera became the more preferred food. Schmitz et al. (1991) concluded that consumption of the alternative foods did not depend on the relative amounts of phenol, as suggested by the avoidance of plant toxins hypothesis, but rather on the interplay between the characteristics of defended plants, such as nutrient content and bulkiness, and the characteristics ofless defended plants. 19

The "paradox" of plant defence is that, under certain conditions, spines or toxins can increase consumption of defended plants (Robbins et al. 1987, Belovsky and Schmitz 1991). Belovsky and Schmitz (1991) model a case where spines can increase the consumption of the defended plant, to the ultimate exclusion of undefended plants. For example, if the harvesting rate of the undefended plant is lower than that of the defended plant, the herbivore will have less time to forage and may have to increase its consumption of the defended plant to meet its nutritional requirements. Robbins et al. (1987) give an example of how the addition of secondary compounds can increase herbivory. If a plant high in nutrients is being consumed by deer then the inclusion of tannin, an induced defence that reduces nutrient absorption, might lead to the deer eating more of the defended plant as it tried to meet the nutritional deficit.

Defensive structures or compounds do not guarantee reduced herbivory. As Belovsky and Schmitz (1991, 1994) point out, the efficacy of plant defence depends on the characteristics of the surrounding defended and undefended plants. These authors also suggest that future models should combine optimal foraging theory and plant defence to describe diet choice. They provide the first mathematical models that combine the two theories, and supply a framework from which further work should continue.

1.4 Field Studies of Mammalian Herbivore Diet Choice

I reviewed the literature of the past 10 years (1986-1995) on diet choice studies of mammalian herbivores. The purpose of the review was to identify areas that have received considerable attention, and more importantly areas that have not been adequately tested. The database of studies came from citations in the CD-ROM databases CAB, LifeScience and Biological Abstracts. If publications were not cited in these databases they were not included. My aim was to produce an unbiased sample of publications, that would accurately reflect the proportional contribution of each group. To this end the sample of publications is not exhaustive. I assigned studies to the groups (Fig. 1.2); 1) diet descriptions, 2) optimal foraging studies using the contingency model, 3) central-place foraging studies, 4) risk-sensitive foraging studies, 5) linear programming studies, 6) studies that examined the effects of structural defenses on diet 20

choice, and 7) studies of the effects of chemical defenses. The groups were not mutually exclusive, for example Schmitz et al. (1992) used linear programming to examine the influence of secondary plant metabolites on the diet choice of snowshoe hares. This study was therefore included in both the linear programming and the chemical defenses groups.

There were several criteria that the studies had to satisfy before they were included in the review. They had to be studies of diet choice by generalist mammalian herbivores. They had to involve experimentation or observation of diet choice. Purely theoretical studies and review papers were excluded. And finally, they had to be field studies using natural foods, although such things as the abundance or nutritional quality of the foods may have been manipulated.

en 35 ,:,-~ ::, u5 30 ,:, Q) 25 .c .!!1 :a ::, 20 .....a.. 0 15 c:i z 10

0 Q) >, lL lL a. (/) (/) > (J Q) Q) C en a. -' (/) (/) :-g_ Q) a:: u C C -~ Ol Q) -2! Q) (/) .!: ai Q) c 0 0 0 0

LP - studies that used the linear program of optimal diet choice, 6) structural defenses - studies that examined the effects of plant structural defenses, and 7) chemical defenses - studies that examined the effects of plant chemical defenses.

Dietary descriptions dominated the sample, and contributed 56% (43/77) of the papers sampled. The other groups could be lumped into the categories; optimal foraging theory studies, which made up 30% (23/77) of the total and studies examining the effect of plant defenses which made up 14% (11/77). The linear programming approach dominated the optimal foraging theory studies making up nearly 74% (17/23) of the category. The other groups within the optimal foraging theory category were roughly represented by a similar number of studies. In the plant defenses category chemical defenses were examined in nearly 82% (9/11) of the papers in the category, making chemical defenses more than four times more likely to be studied than structural defenses (2/11 ).

The number of papers in each group does not accurately reflect the contribution of that particular method to our understanding of feeding strategies and the determinants of diet choice by mammalian herbivores. One might mistakenly interpret the large number of descriptive studies as evidence that this method of examining diet choice is the most profitable and has contributed the most to our understanding. I believe that the dominance of descriptive studies belies their contribution. The descriptive studies are generally devoid of testable hypotheses, and their conclusions generally rely on correlation between diet choice and food nutrient or anti-nutrient content. While the method is undoubtedly useful for detecting patterns in diet choice, they have contributed the least amount to our understanding of what determines diet choice by mammalian herbivores.

In contrast, the other categories have contributed a great deal to our understanding of diet choice. While the proponents of each group have sometimes come to different conclusions regarding the mechanisms and determinants of herbivore diet choice, these conflicting ideas have stimulated discussion and continual refinement of hypotheses. The spectacular success of the linear programming model of herbivore diet choice is reflected in the number of optimal foraging studies that have used this method. In comparison, the lack of studies using the contingency model reflects the poor 22

quantitative predictions of this model. The small number of central-place foraging studies mirrors the small number of generalist herbivores that forage in this way. The single field test of risk-sensitive foraging marks a major deficiency in our knowledge of the response of mammalian herbivores to uncertainty and variance in food availability. This facet of optimal foraging theory needs to be addressed by further field tests.

In the studies sampled that examined plant defensive mechanisms, the conclusion of the authors in every study was that structural or chemical defenses affect diet choice. While this point was universally agreed upon, the magnitude of their effect was not. Some authors took the view championed by Bryant et al. (1991) that diet choice is regulated by chemical defenses, while others have taken the alternative view that nutritional factors (espoused by optimal foraging theory) and defensive mechanisms are both important (Haukioja and Lehtila 1992, Schmitz et al. 1992). In studies where both factors have been examined (Schmitz et al. 1992) the evidence suggests that the latter hypothesis is correct. The logical next step is then to examine the relative effects of nutrient or defensive factors in plant-herbivore systems where plant defenses are thought to be important at different spatial and temporal scales.

1.5 Synthesis

The main conclusion that can be drawn from the literature on the feeding strategies and determinants of diet choice is that most generalist herbivores attempt to maximise their net nutrient intake. The nutrient most likely to be maximised is energy, but others such as salt or protein are possible. Time minimisation is a far less common foraging goal, and has only been observed in sexually active males. Plant structural or chemical defenses may limit consumption of particular plant species or parts of a plant, but the foraging goal remains nutrient maximisation or time minimisation.

1.5.1 Why Linear Programming?

The linear programming model of herbivore diet choice has proven itself to be an ideal method of examining the foraging behaviour of mammalian herbivores. The method explicitly incorporates herbivore physiology and behaviour, plant characteristics and environmental parameters into a unified theory of diet selection (Belovsky and 23

Schmitz 1994). The linear programming model has attained the foremost position because it can incorporate the predictions of other conceptual models ( e.g. the efficacy of plant defenses) and also makes quantitative predictions of herbivore diet choice. This last point is most important as quantitative predictions permit the investigation of the ecological consequences of foraging behaviour (Green 1990), and not just its behavioural consequences. Chapter 2

Thesis Introduction

2.1 Introduction The semi-arid and arid zones of Australia occupy 5.32 million km2, or nearly 70% of mainland Australia. The extent of these climatic zones is defined by rainfall isohyets. The semi-arid zone receives 250-500 mm of rainfall per annum, while the arid zone receives less than 250 mm per annum {Leeper 1970). The semi-arid and arid zones are commonly referred to as the rangelands, and the dominant land use is extensive grazing of sheep and cattle on native pasture. Approximately 3.36 million km2 are used for pastoral enterprises, which support 20-25% of Australia's sheep and cattle (Woods 1984). Sheep are grazed mainly in the south while cattle are grazed in the north (Fig. 2.1).

Grain + sheep Other agriculture -~ Non-agricultural

Fig. 2.1. The distribution of present land use in Australia. Source Caughley (1987a). 25

• Summer dominant rainfall

~o 800 000 • Winter dominant rainfall •

• Non-seasonal rainfall 1000W.ooo

Fig. 2.2. The distribution and seasonal incidence of rainfall in Australia. Isohyets are in mm. Source Robertson et al. (1987).

The rangelands can be divided into three rainfall regions, a northern region that receives predominantly summer rainfall, a southern region that gets predominantly winter rainfall, and a belt in between with no clear seasonality (Fig. 2.2). The study site lies in the non-seasonal belt and is characterised by high variability in rainfall with a low annual total. Rainfall largely determines pastoral use, with cattle grazed mainly in the summer rainfall areas and sheep in the non-seasonal and winter rainfall areas.

Settlement of the range lands started in the 1850's and was completed throughout Australia by the 1890's (Shaw 1990). In that short time substantial changes took place. The most important were degradation of plant communities and soil erosion (Squires 1981 ). Plant communities throughout the settled areas suffered the loss of species diversity, and a change in community dominance from being shrub dominated to being annual grass and forb dominated. These changes were brought about by the excessive numbers of ruminant livestock which were introduced by graziers. The vegetation, 26 which had evolved under conditions of light, intermittent grazing, became heavily and continuously grazed by large numbers of introduced herbivores. Some native herbivores, in particular the large kangaroos, may have adapted to the new environment and increased in density (Newsome 1971, 1975), although this is disputed by Denny (1980). Many of the smaller native marsupials, rodents and birds did not adapt to the changes and their populations declined rapidly to remnants or became extinct (Strahan 1983, Burbidge and McKenzie 1989).

The increase in population sizes of eastern and western grey kangaroos, the red kangaroo and the euro led many graziers to believe that they were competing with domestic stock. The scientific data used to support the hypothesis of competition was based mainly on diet studies, and consequently the conclusions of these studies were equivocal and subjective. There was a clear need to examine their interaction experimentally, by controlled experiments which could provide unequivocal conclusions.

2.2 European settlement and the land laws The settlement of the pastoral zone of Australia was characterised by poor management. This was due to insufficient knowledge of the ecology of the arid and semi-arid zones, which led to unfounded optimism by settlers and administrators. To understand how the deterioration of the pastoral zone occurred, we must first understand the laws governing settlement and how they related to the problems that were later encountered.

Following the first European exploration of the West Darling in 1844, country with river frontage along the Darling River was settled on a more or less permanent basis. Pastoralism further west followed the ephemeral streams that ran from the Barrier Range, which were used opportunistically following rain (Mabbutt 1973). At this time the Waste Lands Occupation Act of 1846 declared that squatters could graze stock on "runs" ofland that could support up to 4000 sheep. After 1854 systematic surveys were made and runs were allocated to settlers. It was in the 1860's that the main settlement 27 west of the Darling River occurred. Favourable seasons encouraged settlement and it was in this decade that sheep were first grazed on Fowlers Gap (Mabbutt 1973).

The Crown Lands Occupation Act of 1861 optimistically suggested that carrying capacity could be 0.25-0.28 sheep/ha, through the provision of improvements such as fencing and watering points. Yet few squatters could afford the increasing land rentals and, with no capital for improvements, suffered badly in the second half of the 1860's when dry seasons prevailed. Low wool prices exacerbated their financial problems and eventually many were forced off the land. The large holdings bought the vacated blocks and some holdings swelled to over 400 000 ha.

The Crown Lands Act of 1884 was an attempt to provide some security for pastoralists in the Western Division of New South Wales, but largely failed because it did not recognise the special problems associated with an arid environment. The New South Wales government was also pursuing a policy of closer settlement, where large properties were resumed and subdivided into units that could support a family. The government hoped that closer settlement would lead to the land being fully developed, increasing population size in remote areas and strengthening regional economies (Young et al. 1984a). The Act divided the state into 3 regions, the Eastern, Central and Western Division. Leases in the Western Division were divided into Leasehold areas and Resumed areas. Leasehold areas were given 15 year leases, while leases on Resumed areas had to be renewed annually. Resumed leases could be taken back by the government on 6 months notice with no compensation for any improvements, and the uncertainty surrounding these leases led to a general hesitancy to build or maintain improvements on Resumed areas (Cunningham 1979). Consequently, many Resumed areas were neglected and became overrun by feral animals and noxious plants. The 1884 Act also resulted in many relatively secure Leasehold areas becoming over improved and over-stocked (Hardy 1969).

The 1890's were characterised by financial crises, rabbit plagues and widespread drought, and it was this setting that prompted the Royal Commission of 1901 (Anon 1901, op. cit. Cunningham 1979). The Commission concluded that over 2 million ha in the Western Division of New South Wales had been abandoned because of low rainfall, 28 rabbit infestation, overstocking, soil erosion, spread of noxious plants, declining wool and stock prices, insufficient land area for small selectors, dingoes, high marketing costs, and general problems in coping with arid land (Cunningham 1979). It is important to note that competition with kangaroos was not considered a problem for the grazing industry at this time. The government responded with the Western Lands Act of 1901. The government now realised that the land was unsuitable for close settlement, and provided relief by granting a 42 year extension on existing leases and reducing land rentals. As a consequence, more realistic stocking rates of between 0.10-0.17 sheep/ha were introduced. The grim picture of the 1890's improved slightly, but by 1934 the Western Division was in serious trouble again when it was swept by drought and economic depression.

At this time over 1000 settlers held Homestead Leases of between 2330 and 4140 ha, which were completely inadequate in size to support a family. To correct this the Western Lands (Amendment) Act, or Buttenshaw Act, was passed. In an effort to build-up the smaller holdings to economic size, the Act gave large leaseholders the option ofreducing their leases by one-half (114th straight away, 118th in 1943, and 118th in 1948) in return for a 25 year extension on their existing lease. Those who refused lost their whole lease in 1946 (Mabbutt 1973). Over 2 million ha became available when 78% ofleaseholders chose to come under the new Act (Hardy 1969). The Western Division is still governed by these land laws, although there have been some minor amendments.

Stock numbers have averaged 8.1 million sheep equivalents in the Western Division since 1950 (7.2 million sheep and 100 000 cattle) (Shepherd and Caughley 1987). A recent study of economic performance by Western Division pastoral leases (Hassan and Associates 1982) concluded that they performed poorly in comparison with other agricultural enterprises, and that this trend would continue. Their survey showed that 46% of lessees generated no disposable income over the survey period (1977-80). Hassan and Associates (1982) suggested a minimum property carrying capacity of 23000 sheep equivalents, thereby reducing the number of properties from nearly 1500 to 810. (For comparison, properties in the Broken Hill District presently average 4500 sheep equivalents, Mabbutt 1973). So far government administrators have 29 not acted on these recommendations, and are unlikely to do so for political and social reasons. As a consequence, chronic overstocking is still widespread due to small property size, declining income, and increasing costs.

In summary, settlement in the rangelands of New South Wales was characterised by overstocking, initially due to ignorance of the long term effects of high stock numbers and small property size, and later due to falling commodity prices for wool and meat. The policy of closer settlement was ecologically disastrous for the rangelands, and failed to recognise the need for management to adjust to changing circumstances (Young et al. 1984a). In New South Wales nearly all properties still fail to meet the criteria for the joint conservation and productivity objectives of pastoral enterprises, which are; maintaining productive potential, maintaining adaptive social structures, preserving genetic diversity, developing heritage and cultural values, encouraging joint and multiple landuse, and restoring degraded land (Young et al. 1984b).

2.3 Increasing sheep numbers The trend in sheep numbers in western New South Wales from first settlement to the mid 1980's is shown by Fig. 2.3. The fluctuations in sheep numbers are typical of a herbivore colonising a new environment (Caughley 1987a). The rapid rise in numbers from first settlement, followed by subsequent fluctuations at greatly reduced population size is remarkably similar to the pattern of other colonising ungulates (Caughley 1970). In the first three decades following settlement sheep numbers rose rapidly. Sheep flourished on vegetation that had up until then been grazed lightly by large herbivores. By the mid-1890's western New South Wales supported more than 14 million sheep, nearly twice the present number. At some waterpoints sheep density approached 12 times the number supported today (Robertson et al. 1987). It was during this period that large changes in vegetation communities were thought to occur (Beadle 1948, Perry 1977). Sheep numbers crashed dramatically in the late 1890's due to a combination of low food availability and widespread drought. Since then sheep numbers have followed an irregular cycle of peaks and crashes, but have never reached the high numbers of the 1890's. Caughley (1987a) hypothesises that the post-1900 peak and crash pattern represents an "uneasy truce" between consumer and food. This system is unlikely to 30 ever reach a stable equilibrium due to the vagaries of rainfall, upon which the growth of vegetation is dependent.

"'0 ~ 25. 0. 8 CU CU .s::...... ,, ...0 CU .0 § 4 z

0 1860 1900 1940 1980

Fig. 2.3. The trend in sheep numbers in western New South Wales from first settlement to the mid 1980's. Source Caughley (1987a)

2.4 The extent of land degradation Newman and Condon (1969) and Woods (1984) have documented the extent of land degradation in the arid areas used for pastoralism. Estimates of degraded land due to pastoralism range from 1.85 (Woods 1984) to 2.18 (Newman and Condon 1969) million km2• All these areas require treatment to prevent further degradation. The situation is particularly serious in New South Wales where 100% of the rangelands are degraded. These data are disturbing, given that the rangelands have been used for pastoralism for only 100-150 years. Woods (1984) concluded that much of the substantially degraded land will become desertified if landuse and management do not change, and treatment is not initiated. Unfortunately most treatments, such as erosion 31 control or destocking, are either too costly or impractical given the financial state of many lessees. It is also unlikely that the benefits of treatment, such as increased vegetation cover or reduced erosion, will cover the cost of the treatment. Therefore, there is little incentive to put treatments into practice.

2.5 Changes in native herbivore communities Coinciding with the 1890's crash in the sheep population was the disappearance of several native mammal species. The major contributing factor is believed to be habitat modification due to overgrazing by stock, but competition for food and shelter with rabbits and introduced predators such as foxes are also implicated (Newsome 1971, Newsome and Corbett 1977, Robertson et al. 1987).

At the time of European settlement the rangelands supported 38 species of marsupial mammals and 45 species of eutherian mammals. Presently within the rangelands, 12 of the original 38 species of marsupials are extinct and a further 8 are uncommon or rare. The present status of eutherians is no better with 6 species extinct and 10 uncommon (Robertson et al. 1987).

While European settlement spelt the demise of many smaller native mammals, some marsupials thrived in the modified environment. There is general consensus that the red kangaroo, the euro, and the eastern and western grey kangaroos have all increased in abundance due to habitat modifications associated with the introduction of stock (Shepherd and Caughley 1987), but note that Denny (1980) disputes that there have been large increases in the densities of the large macropodoids. The present distribution of these kangaroos is given by Figs 2.4 a-c. There are three modifications which are thought to have benefited these kangaroos the most, the creation of disclimax plant communities dominated by grasses and annual forbs; an increase in the number of waterpoints; and the removal of their main predators, the dingo and aboriginal man (Newsome 1971, 1975, Frith 1973, Leigh 1974). 32

2.4 a)

main distribution - Umits ol distribution 2.4 b)

B eastem wallaroo ~ northern wallaroo } AOBUSTUS GROUP O] euro

D barrow island wallaroo

• black wallaroo

2.4 c)

I I I NT I I I I I EASTERN GREY KANGAROO I I distribution I [IlJ main I ... I~------I ol distribution ,,.--1,~ I - limits WESTERN GREY KANGAROO g main distribution

-.- limits ot distribution

~TAS

b) euros and c) eastern and Figs 2.4 a) - c).The distribution of a) red kangaroos, (1995). western grey kangaroos in Australia. Source Dawson 33

2.6 Outline of the thesis I have chosen to examine the effect of food availability on the ecology and population dynamics of these herbivores. A number of studies have concluded that food limitation is an important determinant of fitness (survival and reproduction) in these herbivores (Squires 1982, Barker 1987, Short 1987), but with few exceptions (e.g. Caughley 1987b) the mechanisms by which food limitation affects the population dynamics of these herbivores have not been examined. In this thesis I attempt to address some of these problems.

2.6.1 The Study Site In Chapter 3 I present a general introduction to the study site, covering the study site location, land systems, climate, soils, vegetation and fauna.

2.6.2 Competition between sheep and kangaroos Many studies have hypothesised that competition occurs between sheep and kangaroos (Griffiths and Barker 1966, Newsome 1971~ 1975, Bayliss 1985, 1987, Caughley 1987b, Dawson 1989, Edwards 1990, Wilson 1991a, Dawson and Ellis 1994, Edwards et al. 1995, 1996); however, confusion still remains regarding the conditions under which competition occurs and the biological effect of each species on the other. Competition occurs when two or more individuals try to acquire a resource that is in short supply, and their interaction results in harm to at least one of the individuals (Schoener 1983). Harm is ultimately a reduction in population size, but often loss of body weight, change in population distribution or some other variable is used as a proxy measurement of harm. The general consensus is that competition between sheep and kangaroos in the rangelands is for food, since water is no longer a limiting resource (Edwards 1990). The hypothesis of competition between sheep and kangaroos has been mainly based on the data of diet studies, while spatial distribution studies have been used to a lesser extent. While these methods may provide useful insights into the interactions of competing species, they cannot provide data to unequivocally test hypotheses of competition. For example, dietary overlap between these herbivores has been equated with competition (Griffiths and Barker 1966, Squires 1982, Wilson 1991b, Dawson and Ellis 1994), but overlap may indicate resource sharing and not competition (Vandermeer 1972, Strong 1983). An essential requirement of competition 34 is harm to one or more individuals, and if harm cannot be measured a hypothesis of competition cannot be unequivocally tested. More often these studies correlate dietary overlap with population variables, which may or may not be related to the presence of the hypothesised competitor. In these cases, cause-and-effect and correlation cannot be differentiated and any conclusions must be tentative at best (Romesburg 1981 ). Spatial distribution studies suffer from similar problems of identifying causality.

Methods of examining competition are well documented (Underwood 1986, Hurlbert 1984). The basic requirements of a field experiment on competition between two potentially competing species, A and B, is as follows. The potential competitor (species B), is removed from some areas it shares with species A, and the performance of species A in these areas is compared with untouched, control areas that contain both species (Underwood 1986). Additionally, the manipulated and control areas must be adequately replicated to account for confounding effects that cannot be controlled during the experiment. For example, food resources differing slightly between replicates or the effect of a predator in some replicates. but not others. The replicates must also be interspersed, either randomly or systematically, again to account for differences that cannot be controlled. The densities of both species must be representative of natural populations; experiments that artificially increase population densities beyond natural densities are not representative of any populations ( except the ones in the experiment), and do not add to our knowledge of competitive interactions. The uncritical acceptance of poorly designed or executed experiments is worse than useless, because they are misleading and may incorrectly support or reject the existence of important ecological processes (Connell 1983).

A review by (Edwards 1989) dealt with the subject of competition between sheep and macropodoids based on diet and distribution studies. Two important studies (Wilson 1991a, Edwards et al. 1995, 1996) have been completed since this review was published. These two studies stand out from the others because they are the first experiments to manipulate populations of sheep and kangaroos. In the following section I will review the contributions of the Edwards et al. (1995, 1996) and Wilson (1991a) studies. 35

Edwards et al. 's (1995, 1996) study was done on the arid, shrub steppe plains of New South Wales and examined competition between red kangaroos and merino sheep. The design of the experiment used the controlled removal procedure recommended above. Each treatment was replicated twice, and each replicate was approximately 600 ha in area, which was an attempt to represent the large size of paddocks that occur on pastoral holdings in the area. The density of sheep was maintained at a level which was representative of the conservative stocking rates in the district. Kangaroo populations in the kangaroo only and sheep and kangaroo treatments were uncontrolled and allowed for the free movement of kangaroos throughout these treatments. A potential weakness of the study was the uncontrolled movement of kangaroos; as the density of kangaroos could potentially be below average for the duration of the experiment. As it turned out, this was not the case and the density of kangaroos was representative of naturally occurring kangaroo density throughout the area. The justification for using uncontrolled kangaroo populations was that kangaroo population densities are rarely constant, and kangaroos have virtually unrestricted movement throughout the rangelands. A more serious problem was the nonrandom allocation of replicates to treatments, because logistical constraints forced the two sheep only replicates to be placed adjacently. The confounding effect that this might have had on the results is unknown. Edwards et al.

(1995, 1996) concluded that above a plant biomass threshold of 50-60 g/m2 there was little evidence of competition, but below the threshold kangaroos reduced the liveweight of sheep. Despite the fact that replicates were not assigned to treatments randomly, the results of this experiment are likely to be representative of what occurs in usual populations of sheep and kangaroos throughout the shrub-steppe rangelands.

Wilson's (1991a) study was done in the semi-arid woodlands of New South Wales, and examined competition between kangaroos (western grey and red kangaroos) and merino sheep. The design of the experiment used six levels of grazing intensity of two treatment types; sheep only, and sheep and kangaroos. There was no replication of treatments, and treatments ranged in area from 7 .5-30 ha. There are problems with the design of this experiment, and in the interpretation and presentation of the results. Although the design of the experiment is more appropriate for assessing the productivity of stock at different stocking rates (Bransby et al. 1988) the design could nevertheless be used to examine interspecific competition. The most serious problem 36 with Wilson's experiment was the use of animal densities higher than those naturally occurring in the semi-arid woodlands of New South Wales. The average density of sheep in the area surrounding the study site was 0.25 sheep/ha (range 0.2-0.35 sheep/ha; data from the Soil Conservation Service of New South Wales and Condon (1968)), but Wilson used sheep densities starting at 0.3 sheep/ha and rising to 1.0 sheep/ha. Thus, only the lowest density, for the sheep only treatment, was representative of sheep densities grazed in the area. A similar problem exists with the sheep and kangaroo treatments. Only the density of the lightly stocked treatments were representative of the natural kangaroo densities in the surrounding area. Furthermore, the design of the experiment did not take into account the local fluctuations in kangaroo density, which are a typical feature of kangaroo populations (Bailey 1971). Experimental treatments must be representative of the system that they are examining, and using animal densities higher than those found naturally to force a result is an invalid method of examining competition. Wilson (1991a) also presented incomplete data for the experiment, making it difficult to fully evaluate his results. Wilson's claim that the study provides unequivocal evidence of direct competition between sheep and kangaroos should be treated with scepticism.

There is obviously a need for further studies of competition between sheep and kangaroos. In Chapter 4 of this thesis I describe a controlled removal experiment which was used to study competition between sheep and kangaroos. This study follows on from Edwards et al. (1995, 1996) and uses the treatments established during that study. Additionally, another method of studying competition using by mathematical modelling is described in Chapter 5. Mathematical has provided insights into the conditions under which competition occurs, the mechanism involved, and the effect it has on the population dynamics of the competitors (Belovsky 1984b, 1986a). The modelling approach was used to complement the results of the controlled removal experiment. In a variable environment, such as the arid zone, fluctuations in resource abundance may prevent consumer populations from reaching equilibrium. The stochastic nature of resource abundance may dominate the dynamics of consumer populations so that the results of interactions between consumers can be unpredictable. Changes in body condition or population dynamics of consumers may simply reflect a response to varying resource abundance that is unrelated to competition. Mathematical modelling of 37 consumer interactions can allow us to predict the occurrence of competition and its affect on population dynamics. The controlled removal experiment was then used to test the predictions of the model. Used in this way, the combination of methods became a powerful tool for understanding competition between these species.

2.6.3 Optimal diet selection and the evolution of arid zone herbivores The results of Chapters 4 and 5 suggest that the population dynamics of both sheep and red kangaroos are closely linked to food availability. The implication of this is that these herbivores are food limited. In Chapter 6 I used optimal foraging theory to examine the relationship between temporal variability in food resources and diet choice by sheep and red kangaroos. Specifically, I used the optimisation technique of linear programming (Belovsky 1978) to model the diet choice and energy intake of these two herbivores. I hypothesised that their foraging was limited by three constraints; 1) daily feeding time, 2) daily digestive capacity, and 3) daily energetic requirements. Linear programming has been used successfully to predict the diet choice of a wide range of generalist herbivores (see Belovsky 1994), but there have been no published studies of the optimal diet choice of any macropodoids, or sheep in an arid environment.

If the dynamics of these herbivores are related to spatio-temporal variability in food abundance, then predicting their energy intake may also shed light on the evolution of herbivore morphology and life history strategies, such as the evolution of body size and sexual dimorphism. In Chapter 7 I examined the hypothesis that the evolution of maximum, minimum and optimal body size in red kangaroos is a function of their rate of energy intake. Furthermore, I hypothesised that the evolution of sexual dimorphism and the different life history strategies used by male and female red kangaroos could be explained by the relationship between food availability and rate of energy intake as a function of body size.

2.6.4 Carrying capacity One of the greatest problems facing continued agricultural use of the rangelands is land degradation caused by overgrazing. Overgrazing is directly attributable to poor management, and results when a grazier and land administrators fail to meet the joint conservation and productivity objectives recommended by Young et al. (1984b). 38

Grazing at animal densities beyond the carrying capacity of an area can result in a long term reduction of primary productivity through a reduction in plant species abundance and diversity, and increasing soil erosion (Woods 1984). The main method of assessment in current use in the rangelands of New South Wales relies on scaling an area for which a carrying capacity is sought, against another area where the carrying capacity is "known" (Condon 1968, Condon et al. 1969). The method uses rating scales based on soils, topography, tree density (as an inhibitor of pasture growth), density of palatable trees and shrubs (as drought forage), pasture composition, condition and rainfall. This system of estimating carrying capacity has been used by the Soil Conservation Service throughout the Western Division of New South Wales, and the rangelands of the Northern Territory (Condon 1968).

This system of determining carrying capacity has some major deficiencies. In Chapter 8 I review the underlying bases of this method, and alternative methods that are in current use. Their failure to deal with a stochastically fluctuating environment such as the rangelands of Australia is discussed. I propose an alternative method that can incorporate stochasticity and, using this alternative, I critically examine the concept of carrying capacity and its application in variable environments.

2.6.5 Conclusion Chapter 9 reviews and attempts a synthesis of the findings of Chapters 4 to 8. I discuss the limitations of our present level of understanding of sheep and red kangaroo ecology in particular, and semi-arid and arid zone herbivores in general. I suggest avenues of further research and how they might improve our understanding and management of Australia's arid ecosystems. Chapter 3

General Description ofStudy Site

This chapter provides a general description of the study site, including its location, land systems, climate, soils, and flora and fauna. Detailed descriptions of particular aspects of the study site will be given where they are relevant to later chapters.

3.1 Location

The study site was located within the University of New South Wales' Fowlers Gap Arid Zone Research Station. Fowlers Gap is located 110 km's north of Broken Hill in western New South Wales (latitude 31° 05' S, longitude 141° 43' E) (Fig. 3.1). Fowlers Gap is leased by the University of New South Wales, which maintains a commercial flock of sheep to help offset the station's running costs.

30•-

35•-

I 150"

0 200 400 kilometres Fig. 3.1. The location of Fowlers Gap Research Station in far western New South Wales. 40

3.2 Land Systems

There are 14 land systems recognised on Fowlers Gap. A land system is ' ... an area or group of areas throughout which there is a recurring pattern of topography, soils and vegetation.' (Corbett 1973). The study site had 2 land systems; Conservation land system, and Caloola land system, of which Conservation land system formed the bulk.

Conservation land system is classified as creek frontage habitat. Consisting of Quaternary alluvial plains and floodplains, it is extensively scalded and traversed by shallow drainage channels. Scalding occurs when the topsoil is removed, leaving an area with a hard-packed clay surface and no vegetation. The stable alluvial plains are up to 8 km wide and carry some sandy hummocks and isolated gravelly rises. The land system has low drought resistance, and is subject to extensive erosion if overgrazed (Corbett 1973).

Calloola land system is classified as Mitchell grass habitat. It consists of Quaternary alluvial floodplains with many gilgais (wavy surface) and crabholes (shallow depressions). Gilgais and crabholes are caused by swelling and drying of clay soils during wet and dry periods. Shallow drainage channels occur throughout the area, and after flooding there is abundant ephemeral plant growth (Corbett 1973).

3.3 Climate

Fowlers Gap Station lies well within the arid zone and, following Meig's (1953) classification, is arid with mild temperatures and no distinct rainfall season. Fowlers Gap is influenced all year by the belt of prevailing anti-cyclones that circulate from west to east around the Southern Hemisphere. There are three main factors that contribute to the aridity of central Australia and they are: 1) the tropical continental air mass over inland Australia; 2) the remoteness from ocean influences; and 3) the absence of high mountains which might cause orographic precipitation.

3. 3 .1 Rainfall

The main origins of rain are the Tropical Maritime sources to the north and east, and the Southern Maritime sources to the south and south-west. Summer rains come 41

from tropical depressions to the north and east, and occasionally tropical cyclones bring heavier falls. Winter rain is associated with extra-tropical cyclones and accompanying frontal activity. Moderate intensity rain can fall in any season (Foley 1956), but generally rain is either a result of spasmodic local convective storms or prolonged drizzle.

3.3.1.1 Annual and Seasonal Rainfall

The mean annual rainfall at Fowlers Gap Station is 242 mm (based on data from 1966-1992) with a coefficient of variation of 50%, which makes it one of the most unreliable in New South Wales. There is 20% more rainfall in the summer half of the year (October to March) than in winter. But winter rain is slightly more reliable than summer rain, with coefficients of variation of 51 % and 55% respectively. Monthly rainfall measurements recorded at Fowlers Gap's weather station in the years relating to this study, and two preceding years, are given by Fig. 3.2.

140

120

E 100 _§_

=(I] 80 -C (I] Cl::'. ..::!' 60 - .c - 'E 0 ~ 40 - f- f-- - - 20 - '] - - - -- J n 0 ~ .r I ll . ~. r, il,~ 1 n fh, 1986 1987 1988 1989 1990 1991

Year

Fig. 3.2. The monthly rainfall (mm) recorded at Fowlers Gap's weather station from January 1986 to December 1991. 42

3.3.1.2 Wet Spells

High intensity rain of one days duration due to local thunderstorms accounts for 45% of summer rain and 65% of winter rain. Wet spells of 3 or more days duration occur on average less than once per year but are responsible for large rainfalls of greater than 40 mm. One year in 10 may be expected to have rainfall in excess of 400 mm.

3.3.1.3 Droughts

Gibbs and Maher (1967) suggest using the lowest decile of annual rainfall as an index of drought. For Fowlers Gap this is about 100 mm. By this criterion, in the last 60 years, there have been severe droughts in the area in 1938, 1940, 1965, and 1982. Less severe droughts occur more frequently and their onset is unpredictable.

3.3.2 Temperature

The subtropical latitude, low altitude and lack of moisture for latent heat exchange ensure a high average daily temperature, even in winter. The dry, cloudless atmosphere allows high rates of incoming solar radiation during the day and high rates of outgoing infrared radiation during the night. These factors combined with the area's remoteness from the ocean are responsible for the moderate to high diurnal temperatures in both summer and winter (Fig. 3.3).

3.3.2.1 Summer Temperatures

Summer daytime temperatures are hot (mean approximately 35°C) while nights are warm to mild (mean approximately 20°C). The diurnal range is often greater than 15°C. Frost has never been recorded in summer and on average 40 days per year have a maximum temperature of greater than or equal to 3 7. 7°C.

3.3.2.2 Winter Temperatures

In winter the daytime temperatures are mild to warm (mean approximately 18°C), while nights and early mornings are cool (mean approximately 5°C). The mean diurnal range is about 13°C. Frosts are common during the coldest winter months. 43

40,------.. ---· MAXIMUM

O .__J___._F___.__M_.___A___._M__.__J---'--J----'-A---'--s---'---:o:----'--:-N ...... ---:-D ~

MONTH

Fig. 3.3. Mean monthly maximum and minimum temperatures at the study site. Source Bell (1973).

3.3.3 Humidity and Evaporation

The relative humidity is highest in winter (50-70%) and lowest in summer (25- 35%). Mean annual evaporation is 2300 mm, which makes the evaporation rate among 44

the highest in New South Wales. Mean evaporation is much greater than mean rainfall for every month, and is approximately 10 times average annual rainfall.

3.4 Soils

Soils on the plains and lowlands ofFowlers Gap are classified as texture contrast, crusted, loamy soils with red clay sub-soils. In Conservation land system the lower lying tracts are characterised by texture-contrast unleached soils. Higher lying tracts and drainage tracts are differentiated loam, leached to at least 20 cm. Caloola land system's alluvial fans and drainage tracts have unleached, differentiated loamy soils.

3.5 Vegetation

The vegetation on the plains is representative of the shrub-steppe vegetation of southern arid Australia. These low shrub lands form a broken mosaic of perennial vegetation caused by run-on and run-off microtopographic variation in soil structure.

The high evaporation rate and low rainfall have resulted in low, open communities of perennial vegetation that are floristically poor. Effective rainfall during any season results in the growth and germination of perennials and annuals, and the germination of ephemerals. The quantity of ephemeral growth depends on the amount of rain and the temperature, with more rain required in summer than winter for germination and growth. In general, grasses are the most abundant ephemerals after summer rain, while winter rain favours forbs.

Based on Specht's (1970, op. cit. Burrell 1973) classification, Conservation land system is, in decreasing order of dominance, a mixture of; 1) low shrub land, 2) perennial grasslands, 3) areas lacking perennial vegetation, and 4) tall-open shrubland.

3.5.1 Low Shrubland

Perennial bladder saltbush (Atrip/ex vesicaria) dominates the low shrubland association and occurs on areas with low infiltration rates. Associated with A. vesicaria 45

are the smaller and semi-perennial chenopods Sc/erolaena spp. Effective rain supports abundant ephemerals between bushes.

The cottonbush-berry saltbush-bladder saltbush (Mairiana aphylla-Rhagodia spinescens-Atriplex vesicaria) association is also common on the lowlands, with M aphylla being the most prominent. This association occurs on alluvial plains that frequently border tussock grassland or prickly wattle (Acacia victoriae) tall open shrubland.

The copperburr (Sc/erolaena spp.) association is dominated by S. divaricata and S. ventricosa. Other semi-perennial chenopods and the occasional perennial shrub or tussock grass are found in this association, which supports dense growths of ephemerals after heavy rain. The copperburr association probably represents overgrazed bladder saltbush or cottonbush-berry saltbush-bladder saltbush associations (Milthorpe 1973).

3.5.2 Perennial Grasslands

Tussock grasslands are composed of a mixture of perennial grasses, with neverfail (Eragrostis setifolia) and Mitchell grass (Astrebla pectinata, As. lappacea) being the most common. Other grasses (Sporobolus spp., Chloris spp. and Enneapogon avenaceus) and the occasional shrub may be present.

Tussock grasses tend to occupy low lying alluvial areas that are subject to occasional flooding. Following heavy summer rain good growth of tussock grasses occurs and is generally associated with the germination and growth of ephemerals in the inter-tussock spaces. In winter the tussock grasses are dormant and effective rainfall stimulates the growth of annual and ephemeral species. During dry periods the tussock grasses are grazed down to the ground and remain as dormant butts until the next effective rainfall. The tussock grasses persist well into drought but once seeded become rank and relatively indigestible. This community can withstand heavy grazing and can carrying high stocking rates (Milthorpe 1973). 46

3.5.3 No Perennial Vegetation

These areas can be separated into areas with no vegetation, or ephemeral vegetation only. Scalds and claypans contain no vegetation as their soils exhibit limited water penetration, are usually highly pedal, saline and calcareous. Areas with ephemeral vegetation only, appear to be the result of past overgrazing. These areas provide only short lived herbaceous forage following good rains, but do not persist and are susceptible to overgrazing even at low stock densities (Milthorpe 1973). The floristic composition of this association is highly variable with the most common families being the Graminaceae, Chenopodiaceae, Asteraceae, Cruciferae, Solonaceae and Malaceae.

3.5.4 Tall Open-Shrubland

In Conservation land system prickly wattle (Acacia victoriae) forms tall open shrublands along minor drainage tracts, but is never extensive and occurs in discontinuous narrow strips. Acacia victoriae is a short lived shrub that provides valuable shade, but is not an important forage species.

3.6 Fauna

The extant mammalian fauna ofFowlers Gap is represented by 11 marsupials, 20 eutherians and one monotreme. Eleven of the 20 eutherian species were introduced during European settlement, and have to varying degrees been implicated in the demise of approximately 40% of the terrestrial mammals native to this area. The following section will list the mammalian fauna ofFowlers Gap, but only the biology of red kangaroos and sheep will be discussed in detail. These two species are described in detail because they form the focus of this study. The distributions of bats were derived from Strahan (1983). The avian and invertebrate faunas will not be discussed.

3.6.1 Monotreme Mammals

The echidna (Tachyglossus aculeatus) is the only monotreme that occurs on Fowlers Gap. The echidna is not abundant in the area and individuals are usually well dispersed. 47

3.6.2 Marsupial Mammals

Fowlers Gap and the surrounding area once contained a diverse marsupial fauna, but large scale regional extinctions that coincided with European settlement reduced their number from an estimated 17 species to the present 9 species. The species that became locally extinct were between 0.5 and 7 kg in body mass. The locally extinct species include the numbat (Myrmecobiusfasciatus), the bilby (Macrotis lagotis), the common brush-tailed possum (Trichosaurus vulpecu/a), the brush-tailed bettong (Bettongia penicillata), and the burrowing bettong (Bettongia /eseur). The yellow footed rock-wallaby (Petrogale xanthopus) is now restricted to a small population 100 km to the east ofFowlers Gap. The pig-footed bandicoot (Chaeropus ecaudatus) is now globally extinct. The reasons why these species became extinct in the region are unknown but are likely to be related to habitat modification by sheep and rabbits, competition with these species, and predation by foxes and cats (Morton 1990).

The extant species include the red kangaroo (Macropus rufus), the eastern grey kangaroo (Macropus giganteus), the western grey kangaroo (Macropus fuliginosus), the euro (Macropus robustus), the common dunnart (Sminthopsis murina), the fat-tailed dunnart (Sminthopsis crassicaudata), the stripe-faced dunnart (Sminthopsis macroura), the narrow-nosed planigale (Planigale tenuirostris), the paucident planigale (Planiga/e gilesi), the wongai ningaui (Ningaui ridei), and the kultarr (Antechinomys /aniger). Adults of these species are either less than 30 g or greater than 15 kg in body mass. It is interesting to note that while species with body masses between 30 g and 15 kg have become extinct in the arid rangelands of New South Wales, species with body masses outside this range have either not suffered or have increased in abundance.

3.6.3 Eutherian Mammals

Eleven extant terrestrial species of eutherians occur in the region. Of these, Forrest's mouse (Leggadinafo"esti) is the only remaining native eutherian; however, it is likely that Gould's mouse (Pseudomys gouldii) and the greater stick-nest rat (Leporillus conditor) also occurred in the region prior to European settlement. The introduced eutherians include sheep (Ovis aries), cattle (Bos taurus), the horse (Equus cabal/us), the house mouse (Mus muscu/us), the European rabbit (Oryctolagus cunicu/us), the red fox (Vulpes vulpes), the feral cat (Fe/is catus), the pig (Sus scrofa), 48

and the goat (Capra hircus). Dingoes (Canisfamiliaris dingo) are thought to have been introduced by Australian Aborigines sometime in the last 4000 years (Corbett 1995), and rarely occur on the study site. Of these species only sheep and the red fox occur in significant numbers on the study site.

On the study site bats are represented by two Families, the Molossidae (mastiff bats) and the Vespertilionidae ('ordinary' bats), of the Suborder Microchiroptera. There are two mastiff-bats, the white-striped mastiff-bat (Tadarida australis) and the little mastiff-bat (Moropterus p/aniceps); and six 'ordinary' bats, the lesser long-eared bat (Nyctophilus geoffroyi), Gould's wattled bat ( Chalinolobus gou/dii), the little pied bat (Chalinolobus picatus), the little broad-nosed bat (Nycticeius greyii), the western broad nosed bat (Nycticeius balstoni), and the little forest eptesicus (Eptesicus vulturnus).

This study concentrates on the ecology of two species of mammals, the native red kangaroo and the introduced domestic sheep. Their general biology is described in more detail in the following two sections

3.6.4 The Biology of Red Kangaroos

Red kangaroos are thought to have evolved during the rapid differentiation of macropodine genera that occurred in the late Pleistocene (Flannery 1989). The evolution ofred kangaroos appears to coincide with the increase in aridity of the Australian continent (1-2 million years BP), which resulted in the spread of grasslands (Dawson 1995).

3.6.4.1 Distribution and Abundance

Red kangaroos are the largest of the extant macropodoids (Frith and Calaby 1969). They are largely confined to the arid and semiarid interior of Australia (Fig. 2.4 a), and the study site is situated in an area where red kangaroos approach their highest average density of approximately 0.2 red kangaroos/ha (Caughley 1987a). During a previous study (Edwards 1990, Edwards et al. 1996) at the study site density was observed to fluctuate widely from 0.01-1.6 red kangaroos/ha around a long term average of approximately 0.35 red kangaroos/ha. 49

3.6.4.2 Reproduction

In good seasons, red kangaroos breed continuously, and at any one time can maintain three young; 1) a young-at-foot, which still suckles but is independent of the pouch and may forage, 2) a pouch young, which stays in the pouch and is dependent upon milk for essentially all its nutrient intake, and 3) a blastocyst, which remains in embryonic diapause in the uterus. When the pouch is evacuated by the pouch-young, the blastocyst resumes development and becomes the new pouch young (Russell 1982). The cycle takes, from birth to weaning, about 360 days (Sharman and Calaby 1964).

The effect of limited nutrient intake on the survivorship ofjuveniles is most pronounced during drought (Newsome 1965). Mortality ofjuveniles between permanent pouch exit and weaning is typically high with 15% mortality in good seasons, and up to 83% during drought (Frith and Sharman 1964). During severe drought females may become anoestrus and no breeding will occur (Newsome 1965). However, following drought breaking rains the dormant blastocyst will resume development, and within 31 days a new young may be born (Sharman and Calaby 1964).

3.6.4.3 Body Size and Growth Rate

Red kangaroos are sexually dimorphic in body mass (Jarman 1989), with mature males averaging 66 kg (range 22-85 kg) and females averaging 26.5 kg (range 17-35 kg) (Sharman 1983). Male red kangaroos appear to increase in mass throughout their life, whereas females reach maximum body size after about five years (Edwards 1990).

3.6.4.4 Movement, Social Organisation and Home Range

Red kangaroos free-range throughout the rangelands since conventional domestic stock fences do not pose a barrier to their movement. Populations are made up of a sedentary component (usually mature animals) and a mobile component (usually immature) (Edwards et al. 1994). On a daily basis red kangaroos may have a home range of between 28.2 (Croft 1991) and 158 ha (Priddel 1987). At the study site, 50

Edwards (1990) recorded an average daily home range of28.4 ha and a weekly home range of 92.4 ha. Group size in red kangaroos is not variable and is typically between 1.54-2.2 animals/group (Croft 1980, Johnson 1983).

3.6.4.5 Management

The management of red kangaroos has largely been directed by the perception that they are a pest in the rangelands (Shepherd and Caughley 1987). The main complaint of pastoralists is that red kangaroos are competitors of livestock for native pasture. Testing this assertion has been the subject of two recent studies (Edwards et al. 1996, Wilson 1991a), and forms a major part of this thesis (Chapter 4 and 5). Red kangaroo populations are presently culled for "damage mitigation" (Shepherd and Caughley 1987), the level of control being set by the relevant wildlife authorities in each state and is dependent on population size and environmental conditions.

The alternative management strategy of harvesting populations as a renewable resource is not a new one (Frith and Calaby 1969), but it has received renewed interest recently (Lunney and Grigg 1988). A major feature of this strategy is the replacement of domestic stock with kangaroos, which then become the main source of pastoral revenue. While this option has ecological benefits, it requires a major change to the perception of Australia's wildlife as an exploitable resource and not just a part of our natural heritage.

3.6.5 The Biology of Sheep

Sheep were introduced to Australia in 1788 as part of the first fleet, but it wasn't until 1805 that the first Merinos were brought to Australia (Cottle 1991). The merinos used in this study were derived from a strong wooled, South Australian breed that is widely grazed in the arid and semiarid rangelands of Australia (Cottle 1991). Sheep are commercially bred for wool and meat in Australia, but in the arid and semiarid rangelands they are bred almost exclusively for their wool (Squires 1981 ). 51

3.6.5.1 Distribution and Abundance

The distribution of sheep in Australia is given in Fig. 3.4. In western New South Wales the distribution of sheep overlaps that of red kangaroos (Fig. 2.4 a). In New South Wales sheep density ranges between 0.40 sheep/ha in the wetter, semiarid areas in the east, to 0.10 sheep/ha in the arid regions in the west and northwest. Rainfall is the main determinant of stock density (Condon 1968). Only about 20% of Australia's sheep are run in the arid rangelands (Bureau of Agricultural Economics, 1976).

ct:;J

• 40,000 sheep and lambs ---- Limit of sheep range lands

Fig. 3.4. The distribution of sheep in Australia. Source Caughley (1987a).

3.6.5.2 Reproduction

Sheep breed once a year producing one or two lambs per ewe, the timing of breeding being controlled by the stock manager. At the study site, joining (placing rams in a flock of ewes) was done in February, with parturition occurring about 145-150 days later (Miller 1991). Nutritional status has been found to be closely linked to reproductive success. Ovulation rate is correlated with liveweight (Fletcher 1971, Restall 1976), and lamb birth weight and perinatal mortality are sensitive to the ewe's 52

nutritional status (Miller 1991). In addition, nutrient intake by ewe's during lactation may affect milk yields and consequently lamb growth rates and survival.

3.6.5.3 Body Size and Growth Rate

The body size and growth rate of sheep are dependent on breed. Merinos reach maximum body size after about 2-3 years, but nutrient intake is a major determinant of growth rate (Thompson 1991). Adult body mass in strong woolled merinos ranges between 45-100 kg. The mean body mass of sheep during this study was about 60 kg.

3.6.5.4 Movement, Social Organisation and Home Range

Sheep are allowed to graze within large paddocks, that range in area from 500- 4000 ha. The sheep within each paddock at the study site usually grazed as a single mob, but would form a number of smaller mobs as vegetation biomass declined. The paddocks used in this study were approximately 600 ha in area and sheep would forage over the whole paddock, regardless of season or vegetation biomass.

3.6.5.5 Management

The management of sheep in the arid and semiarid rangelands is characterised by low capital input and minimal handling. Sheep are essentially free-ranging and management is ''very extensive" (Wilson 1982). Handlings are limited to musters at 3 to 6 month intervals for practices such as crutching, lamb marking and shearing. Predators such as dingoes and feral pigs either do not occur on the study site, or occur in low numbers and have minimal impact on sheep survivorship. Foxes may prey on lambs (Miller 1991), but their numbers were not controlled at the study site. Survival of animals in extensive grazing systems largely depends on an individual's ability to physiologically and behaviourally adapt to the harsh environment (Squires 1984). Chapter 4

Experimentally Examining Competition Between Sheep and Red Kangaroos.

4.1 Introduction

Sheep and red kangaroos occur sympatrically through much of the arid and semi-arid rangelands of Australia. They can have a high degree of dietary overlap (Griffiths and Barker 1966, Storr 1968, Griffiths et al. 1974, Dawson et al. 1975, Ellis et al. 1977, Dawson and Ellis 1994, Edwards et al. 1995), and have been hypothesised to compete for food (Edwards 1989, Dawson and Ellis 1994). Up until recently the scope of competition and its potential effect on individual productivity and community dynamics has been based on suggestive rather than conclusive evidence (Caughley 1987b). Two recent studies (Wilson 1991a, Edwards et al. 1996) sought to address this gap in our knowledge.

Both studies found that sheep and red kangaroos compete for food. Edwards et al. (1996) found that competition was intermittent and occurred when food availability was low and there was a high density of kangaroos. When these conditions occurred there was a small (but significant) reduction in the body mass of sheep, but no effect on wool growth. Red kangaroos favoured paddocks destocked of sheep, which Edwards et al. (1996) interpreted as a competitive effect. However, Edwards et al. (1996) were unable to detect any other competitive effect of sheep on red kangaroos. In contrast, Wilson (1991a) concluded that competition between sheep and kangaroos markedly diminished sheep productivity (body mass and wool growth). Neither study examined the effect of competition on the reproductive output of these herbivores. Since competition is ultimately a population process, this is an obvious deficiency of both studies and there is a need for further work, with emphasis on the effect of interspecific competition on the population dynamics of these herbivores.

The aim of this chapter was to evaluate whether sheep and red kangaroos compete. Specifically, the competitive effect of red kangaroos on sheep was examined by testing the following hypotheses: 54

1) that sheep sympatric with red kangaroos have lower body mass than sheep allopatric with red kangaroos, 2) that sheep sympatric with red kangaroos have lower wool growth than sheep allopatric with red kangaroos, 3) that ewes sympatric with red kangaroos have lower fecundity than ewes allopatric with red kangaroos, 4) that lambs sympatric with red kangaroos have lower body mass than lambs allopatric with red kangaroos, 5) that lambs sympatric with red kangaroos have lower survivorship than lambs allopatric with red kangaroos.

The competitive effect of sheep on red kangaroos was examined by testing the following hypotheses: 1) that red kangaroos sympatric with sheep have lower body mass than red kangaroos allopatric with sheep, and 2) that red kangaroos sympatric with sheep have lower fecundity than red kangaroos allopatric with sheep, and 3) that red kangaroos will tend to avoid areas used by sheep.

4.2 Materials and Methods

I used a controlled removal experiment to examine the hypothesis that sheep and red kangaroos compete. The experimental treatments were of three types; 1) sheep and red kangaroos present (referred to as the Sympatric treatment), 2) sheep present and red kangaroos removed (the Sheep Allopatric treatment), and 3) red kangaroos present and sheep removed (the Red Allopatric treatment). Each treatment was replicated twice. The Sympatric treatment represented the naturally occurring situation over the majority of the rangelands where sheep and red kangaroos occur sympatrically and can be thought of as an untouched control for the manipulation treatments.

The study site covered an area of 3718 ha. The layout of the experimental units is given in Fig. 4.1. Each replicate was approximately 600 ha in area, and the experimental treatments were first imposed in December 1985 (Edwards 1990). I allocated replicates to treatments by following the design of Edwards (1990), who 55

assigned replicates to reduce the initial cost of setting up the experiment. A full discussion of the potential problems in assigning replicates in this way is given by Hurlbert (1984). The most serious problem was that there was partial but inadequate interspersion of treatments, which increases the probability that chance events impinge to different extents on different treatments. Edwards et al. (1995, 1996) discuss this limitation on the experimental design used here and the potential effect it may have had on the results of their experiment.

Red Allopatric 2

SCRLE 1 km

Fig. 4.1. The layout of the experimental treatments. Sympatric = sheep and red kangaroos, Sheep Allopatric = sheep only, and Red Allopatric = red kangaroos only. 56

4.2.1 Sheep

Adult sheep were stocked at the district average of 0.19 sheep/ha for the duration of the experiment (the district average stocking rate was determined by the Soil Conservation Service of New South Wales, which is the government department responsible for monitoring domestic stock densities and range condition). In each replicate that contained sheep, only ewes (female sheep) were used since the effect of competition on wethers (castrated males) had been examined in a previous study (see Edwards 1990, Edwards et al. 1996). All ewes were bred at Fowlers Gap Station and came from the 1985 cohort of lambs. Individual sheep were randomly assigned to experimental replicates. Individuals were maintained in the same experimental unit for the duration of the experiment.

The experimental treatments were initially imposed in December 1985 (Edwards 1990), and were maintained until the conclusion of the experiment reported here in November 1991. The sheep were placed in their experimental units in January 1988. Adult sheep productivity was measured twice a year, in winter (May or June) and again in summer (November or December), and was timed to coincide with normal management practices such as crutching or shearing. After I had assigned individual sheep to an experimental unit, 20 randomly chosen ewes in each unit were individually ear tagged. At the conclusion of the experiment I took a sub-sample of 10 ewes from the remaining tagged individuals in each replicate, some having died or lost their tags. From these individuals I measured annual wool growth and body mass at each sampling period. For lambs, the survivorship of all individuals within a replicate were measured. For body mass comparisons a randomly selected sub-sample of 20 lambs was chosen from each paddock at each sampling period.

During May all the ewes within a replicate were ultrasounded to determine the rate of pregnancy resulting from the February to March mating period. The diagnosis of pregnancy and litter size were made by a veterinarian (Mr G. Curran) employed by New South Wales Agriculture. The diagnoses were made with a real-time ultrasonic scanning device, which is the only reliable and practical method presently available for determining litter size (Fowler and Wilkins 1982, Miller 1991). The real-time scanner produces a high resolution image of the foetuses in the uterus, and in the hands of an 57

experienced operator diagnoses of foetus number are 96-99% accurate (G. Curran pers. comm.). In addition, the individually tagged ewes were weighed in the field shortly after being mustered, on a portable electronic platform scale accurate to 0.5 kg, and dye banded. Dye-banding (Chapman and Wheeler 1963) involves permanently staining a section of the fleece at skin level with a dye. The rate of wool growth over a period of time can be measured from the difference between two dye-bands. Prior to shearing, the dye-bands were removed. I measured the growth of greasy wool between the summer (shearing of the previous year to winter of the present year) and winter (winter of the present year to shearing of the present year) samples by taking a 100 g sub-sample of the dye-banded wool and cutting the wool at the bottom of the stain left from the winter sample dye-band, and separately weighing the samples. I measured clean wool growth by reweighing the samples after scouring the greasy wool in a series of petroleum baths to remove wool grease and contamination such as soil or vegetative matter. Any visible contamination not removed by the baths was removed with tweezers. All wool samples were weighed to the nearest 0.001 g. From the calculated rates of greasy wool growth I was able to correct body mass measurements for wool-growth, and from the scoured samples I was able to determine wool yield from which I later calculated clean wool growth.

The number and body mass of lambs in each experimental unit was determined during lamb marking in September, and again at shearing in November or December of each year when lambs were weaned. Lamb marking is the practice of tail docking and mulesing male and female lambs to reduce the incidence of blowfly strike in later years, and also castrating male lambs. Mulesing is the practice of removing two crescent shaped pieces of skin from around breech of a sheep. The resulting scar tissue that forms as a result of the operation is smooth and hairless, thus reducing the likelihood of blowfly strike (Bell 1991). Weaned lambs were removed from the experimental units and played no further role in the experiment.

In 1989 two separate chance events effected the lamb data from Sympatric 1 and Sheep Allopatric 2. In Sympatric 1 two rams from a nearby holding paddock managed to break through several fences and enter the treatment before the scheduled joining period. The rams were not detected until about two weeks later and it was unknown how many ewes had been inseminated. I decided to not include the data from this joining 58

with the data from the scheduled mating period in February-March. In Sheep Allopatric 2 the two rams joined with the ewes at the start of the scheduled mating period were not recovered from the paddock at the end of the mating period. It was subsequently discovered that no ewe from the treatment had been inseminated, and it was suspected that the rams had either died soon after being placed in the treatment (this occasionally occurs due to injuries sustained from fighting with other rams), or that they escaped through the fence to an adjoining paddock. Consequently, there was no lamb data from this paddock in 1989.

4.2.1.1 Statistical analyses

I used three-factor, fixed effects, nested ANOVA with repeated measures (Lindman 1974) to analyse treatment effects on ewe body mass, lamb body mass and annual wool growth by ewes. The factors of the ANOVA were treatment, paddock and individual sheep. The individual sheep were specified as a level because they were repeatedly measured (Sokal and Rohlf 1981 ). The fact~r "paddock" was nested within treatment for all analyses. For lambs, I had initially intended to analyse their data by following the same ANOVA model that was used for ewes. However, the lamb body mass ANOVA was incomplete due to the absence oflamb data from Sympatric 1 and Sheep Allopatric 2 in 1989, so it was necessary to analyse each year separately.

The average number of lambs produced per ewe, as determined by ultrasound examination, was compared by two-factor ANOVA with the factors being treatment and paddock. I compared lamb survivorship between treatments by log-linear analysis (Bishop et al. 1975). The factors of the log-linear analysis were sample, treatment and survivorship. The number of lambs not surviving to weaning was calculated as the difference between the ultrasound estimate and the number alive at weaning. The data from paddocks nested within treatments were pooled to remove empty cells from the analysis. Although this represents sacrificial pseudoreplication (Hurlbert 1984) it is a requirement of the analysis (Bishop et al. 1975). 59

4.2.2 Red Kangaroos

With the exception of the Sheep Allopatric treatment, red kangaroos were able to move freely about the study site. This represents the natural situation across the sympatric range of sheep and red kangaroos, since the standard fencing used to contain domestic stock does not form a significant barrier to the movement of red kangaroos (Edwards et al. 1994). The immigration of red kangaroos into the Sheep Allopatric treatment was minimised by a 1.2m high electric fence. The electric fence did not completely stop the movement of red kangaroos into this treatment, and regular culling was required to keep their number significantly below that seen in the other treatments.

The body mass and reproductive status of red kangaroos was determined from live capture samples taken in summer (December to January) and winter (June to July) of each year. The first sample of red kangaroos was taken in winter 1988. Kangaroos were captured by either "stunning" (Robertson and Gepp 1982) or by cannon netting at a water trough. Stunning involves capturing an individ:ual at night that has been dazzled by a combination of a high powered spotlight shone in its eyes and a small calibre (.22 LR) supersonic bullet fired between its ears. "Stunned" animals are momentarily disoriented allowing a capturer to tackle the animal to the ground to be (hopefully) subdued. Cannon-netting was only done in summer when kangaroos would come to drink at one of the permanent water troughs located in each paddock of the study site. Cannon-netting involved remotely firing a 20 x 20 m net over kangaroos that were drinking at the trough. Animals captured by either technique were injected with Valium (Roche) to help calm them, at a dose rate of 1 mg to every 10 kg of body mass. Measurements were made as quickly as possible to minimise stress to the animals and reduce the incidence of capture myopathy (Shepherd 1984). Captured animals were sexed, weighed to the nearest 0.5 kg, and had their limb lengths measured. In addition, female's had their pouch examined to assess their reproductive status. In particular, the presence or absence of a pouch young, long-teat (which indicates suckling of a young at-foot) or "capped" teats (which indicates sexual immaturity) were noted. All captured animals were tagged with identifying eartags and released. During each sampling period I attempted to catch (with the help of a large number of volunteers) at least 15 individuals from each replicate. 60

Following the method of Edwards et al. (1996), I used regressions oflimb dimension ratios on age for red kangaroos (Edwards et al. 1994) to age all captured animals. Before analysis I truncated the data to include only adult red kangaroos. Adult males were 3 to 15 years old, and adult females were 1. 7 to 15 years old. Males less than 3 years old and females less than 1. 7 years old were considered to be immature (Sharman and Calaby 1964). Including the data of young animals, which may be highly transient (Edwards et al. 1994) and not resident in the experimental unit, or old animals that may be in "poor condition" due to old age may have biased the analysis. The regressions that I used to estimate age were those of Edwards et al. (1994); logy = 9.76o{logx)+ 2.192 (4.1) for females, where y is age in years, and x is the arm/foot ratio {r=0.87), and logy = 3.707(1ogx}+ 1.016 (4.2) for males, parameters as previously defined (r=0.93).

I estimated the density of red kangaroos in each replicate at each sampling period by strip transect analysis. Spotlight transect counts of kangaroos were made by an observer standing on the back of a four wheel drive truck driven at about 15 kph. Permanent transects within each replicate (Fig. 4.2) were spaced approximately 500 m apart, and were between 5.5-8 km in length. When a kangaroo was sighted its distance from the vehicle was estimated to the nearest 10 m and its angle from the transect line was estimated to the nearest 15°. For each replicate, three counts were usually made over successive nights. Edwards et al. (1996) found that the sightability of kangaroos at the study site declined markedly beyond 120 m from the transect. Consequently, I truncated data to 120 m either side of the transect, which resulted in a strip width of240 m. The densities of red kangaroos per treatment were calculated from these data. 61

4.2.2.1 Statistical Analyses

I analysed treatment effect on kangaroo body mass by a three-factor, nested ANCOVA. The factors of the ANCOV A were sample, treatment and paddock, with paddock nested within treatment. Leg length was used as the covariate to control for the effect of body size. Treatment effect on female reproductive success was compared by log-linear analysis. The factors of the log-linear analysis were sample, treatment and reproductive status. Females captured within a treatment were classified as either reproductive or not reproductive. Females were defined as reproductive if they had either a pouch young or a young-at-foot (determined by the presence or absence of a long teat), or both. The data from paddocks nested within treatments were pooled to remove empty cells from the analysis. I determined treatment effects on the density of red kangaroos using two-factor ANOVA with the factors being sample and treatment.

- Red J\l\opatric 2 -

SCALE 1 km

Fig. 4.2. Layout of permanent transects within each paddock of the study site. 62

4.3 Results

4.3.1 Sheep

The pattern of change in body mass of sheep was similar across all paddocks (Fig. 4.3). The analysis of all eight ewe body mass samples indicated that there was no treatment effect on mean ewe body mass (F1•36=0.0532, P > 0.8)(Table 4.1 ). There were also no paddock differences (F2•36=1.42, P > 0.2). There were significant differences between the repeated measurements of sheep body masses (F7_252=64.5, P << 0.001), and a significant interaction between treatment and body mass (F7•252=2.77, P < 0.01). To examine the interaction effect further, I analysed each winter-summer pair separately to see if there was an annual treatment effect. There was no treatment effect on ewe body mass for any winter-summer pairing (winter 1988/summer 1989, F 1•36=2.36, P > 0.1; winter 1989/summer 1990, F 1•36=0.432, P > 0.5; winter 1990/summer 1991, F 1•36=0.113,

P > 0.7; winter 1991/summer 1992, F 1•36=2.33, P > 0.1). There were also no interactions between treatment and body mass (winter 1988/summer 1989, F 1•36=0.333, P > 0.5; winter 1989/summer 1990, F 1•36=1.59, P > 0.2; winter 1990/summer 1991, F 1•36=3.80, P

> 0.05; winter 1991/summer 1992, F 136=2.89, P > 0.09). The treatment X paddock interaction cannot be determined because of the nesting of paddock within treatment. 63

-~00

rJ) -rJ) 50 ro a Syrrpatric 1 ~ 40 >, •Syrrpatric 2 -0 OAJlcµrtric 1 3) s OAJlcµrtric 2

0 (X) a, a, 0 0 C'I (X) (X) (X) a, a, ;:;; ;:;; a, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ai ai .Sl ai ai ai ., ., c E C E c E c E E E E E ~ ::, ~ ::, ~ ::, ~ ::, (J) (J) rJ) (J) Sarµe

Fig. 4.3. The mean body mass of ewes measured at each sampling period. Masses are corrected for greasy fleece mass. Data are the means of 10 sheep per paddock with their standard errors.

Effect dfEffect MS Effect dfError MS Error F p Treatment 1 9.21 36 173 0.0532 0.819 Paddock 2 247 36 173 1.42 0.254 Sample 7 1074 252 16.6 64.5 <0.0001 T*P T*S 7 46.1 252 16.6 2.77 <0.01 P*S 14 111 252 16.6 6.65 <0.0001 T*P*S

Table 4.1. ANOVA table of all effects for the analysis of sheep body mass. Some interactions could not be calculated because of nesting.

The pattern of wool growth (Fig. 4.4) showed a small increase from 1988 to a peak in 1989, followed by a small decrease in 1990 and a larger decrease in 1991. The 64

ANOVA analysis of mean annual wool growth indicated that there was no treatment effect on the wool growth of sheep (F,.36=0.0281, P > 0.8)(Table 4.2), nor a treatment X wool mass interaction (F3.J08=1.45, P > 0.2). However, there were significant differences between the mass of wool grown by sheep each year during the experiment (F3.108=85.9, P < 0.0001).

5 -Ol ~ V) 4 V) a Syrrpatric 1 <1l ::!E •Syrrpatric 2 0 3 D Aliqlatric 1 0 s: D Aliqlatric 2 2

0 1988 1989 1900 1991 Yea

Fig. 4.4. The mean annual clean wool mass from ewes measured after shearing of each year. Data are the means of 10 sheep per paddock with their standard errors.

Effect dJEffect MS Effect df Error MS Error F p Treatment 1 0.0190 36 0.674 0.0281 0.868 Paddock 2 1.24 36 0.674 1.84 0.174 Sample 3 26.3 108 0.306 85.9 <0.0001 T*P T*S 3 0.444 108 0.306 1.45 0.231 P*S 6 0.641 108 0.306 2.10 .0595 T*P*S

Table 4.2. ANOVA table of all effects for the analysis of wool growth per annum. Some interactions could not be calculated because of nesting. 65

The mean number of foetuses produced per ewe in each paddock was similar (Fig. 4.5). The two-factor ANOVA indicated that there was no treatment effect on the mean number of foetuses conceived per ewe (F1.9=0.0122, P > 0.9), and that there were

also no differences between paddocks (F1_9=0.440, P > 0.6)(Table 4.3).

Q) ~ 1.75

--~ 1.5 ;------r------t------. (/) ::::, a5 1.25 E -....0 Q) E o.75 ::::, C 0.5 C ro ~ 0.25

0 +----'-=a::.;.J,--+---1 Sympatric 1 Sympatric 2 Allopatric 1 Allopatric 2 Treatment and Replicate

Fig. 4.5. The mean number of foetuses conceived/ewe in each paddock. Data are means and error bars are standard deviations.

Effect dfEffect MS Effect dfError MS Error F p Treatment 0.000379 9 0.0312 0.0122 0.915 Paddock 2 0.0137 9 0.0312 0.440 0.657 T*P

Table 4.3. ANOVA of the mean number of foetuses produced per ewe. The interaction could not be calculated because of nesting.

The proportion of lambs in each treatment surviving from ultrasounding to weaning (Fig. 4.6) showed no consistent treatment pattern. For two of the four years of sampling, the lambs within the allopatric treatment had higher mean survivorship than 66

lambs sympatric with red kangaroos. For the other two years the lambs in the sympatric treatment had higher mean survivorship. However, both treatments appeared to respond to year to year changes in survivorship in a similar manner. The log-linear analysis of lamb survivorship indicated that the model that best fitted the observed frequencies included the three-factor interaction between sample, treatment, and survival (Tables 4.4a and b).The significance of the three-factor interaction indicated that significance between any two factors depended on the level of the third factor (Bishop et al. 1975, Sokal and Rohlf 1981 ). Therefore, I examined two-way tests of independence between the factors treatment X survival separately for each sampling period, as recommended by Sokal and Rohlf (1981 ).

I tested for independence using ML Chi-square. There were no differences between treatments in the frequency of lambs surviving from ultrasounding to weaning in 1988 (X2 = 0.81, DF= 1, P > 0.36), in 1989 (X2 = 1.97, DF= 1, P > 0.16), or 1991 (X2

= 3 .32, DF = 1, P > 0.068). There was a significant treatment difference in 1990 (X2 = 13.4, DF = 1, P < 0.001), when the lambs sympatric with red kangaroos had higher survivorship than lambs allopatric with red kangaroos.

g1 0.9 ·c ~ 0.8 $'. 0 7 .9 . g1 0.6 Csympatric :~ 0.5 •Ano atric ::I CJ) 0.4 C ~ 0.3 0 e 0.2 a.. 0.1

0 1988 1989 1990 1991 Year

Fig 4.6. The proportion of lambs in each treatment surviving from ultrasounding to weaning of each year. 67

4.4 a)

k- actor d ML Chi-s uare 1 5 519.542 <0.0001 2 7 143.194 <0.0001 3 3 15.636 0.002

4.4 b)

Partial Partial Marginal Marginal Effect df Association Association p Association Association p Chi-s uare Chi-s uare Sample (S) 3 68.8 <0.0001 68.8 <0.0001 Treatment (T) 1 12.9 0.0004 12.9 0.0004 Survival (Sur) 1 438 <0.0001 438 <0.0001 S*T 3 6.19 0.103 5.04 0.169 S*Sur 3 136 <0.0001 134 <0.0001 T*Sur 1 3.75 0.0528 2.60 0.107

Tables 4.4 a and b. Log-linear analysis of the frequency oflambs in each treatment surviving from ultrasounding to weaning; a) results of fitting all k-factor interactions, and b) tests of marginal and partial associations.

The pattern of change in lamb body mass from lamb marking to weaning was similar for all paddocks for the first three years of the study (Fig. 4.7). Lamb mass generally increased by about 5-10 kg from marking to weaning. In 1991, the increase in body mass was much less for most paddocks (approximately 2.5 kg), while in Sympatric 2 lamb mass declined from lamb marking to weaning by a mean 0.2 kg. The ANOVA of lamb mass change indicated that there were no treatment effects for the years 1988 to 1990 (1988; F 1•76= 0.801, P > 0.3: 1989; F 1•38 = 0.829, P > 0.3: 1990; F 1•76

= 0.022, P > 0.8). However, in 1991 there was a treatment effect (F1•76 = 5.53, P < 0.05), where lambs sympatric with red kangaroos had higher mean body mass than lambs allopatric with red kangaroos. In addition, lambs showed a significant increase in body mass from lamb marking to weaning in all years (1988; F 1•76= 905, P < 0.0001: 1989;

F1•38 = 180, P < 0.0001: 1990; F 1•76 = 756, P < 0.0001: 1991; F 1•16 = 23.6, P < 0.0001). The summary of all effects for the ANOVA's of lamb body mass are presented in Tables 4.5 a) - d) for 1988 to 1991, respectively. 68

~ 35 Cl .Y. -; 3) aSyrrµitric 1 Cl) ro 25 •Synµiric2 ~ oAJlcµtric 1 >, "C 2) D AJlcµitric 2 0 CD 15

0 0) 0) 0) 0) 0) 0) Ca, .E co CO> .!: 0) .!:o .!:T :g~ Ca, :g a, Ca, CO> c a, ro ~ "'a, "'a, "'a, "'a, "' a, :::; Q)~ :::;~ Q)~ Q) ~ Q)~ ~ ~ ~ ~

Fig. 4.7. The mean body mass oflambs measured at lamb marking and weaning of each year. Masses are not corrected for greasy fleece mass. Data are the means of 20 lambs per paddock and their standard errors.

4.5 a) 1988

Effect df Effect MS Effect dfError MS Error F p Treatment 33.7 76 42.1 0.801 0.374 Paddock 2 75.4 76 42.1 1.77 0.177 Sample 4805 76 5.31 905 <0.0001 T*P T*S 1 30.8 76 5.31 5.81 0.0184 P*S 2 72.0 76 5.31 13.6 <0.0001 T*P*S

4.5 b) 1989

Effect dfEffect MS Effect dfError MS Error F p Treatment 1 46.5 38 56.1 0.829 0.368 Sample 1075 38 5.97 180 <0.0001 T*S 1.25 38 5.97 0.209 0.650 69

4.5 c) 1990

Effect dfEffect MS Effect dfError MS Error F p Treatment 1 1.02 76 46.2 0.022 0.883 Paddock 2 14.0 76 46.2 0.303 0.740 Sample 1 3286 76 4.35 756 <0.0001 T*P T*S 1 0.070 76 4.35 0.0161 0.899 P*S 2 45.0 76 4.35 10.4 <0.001 T*P*S

4.5 d) 1991

Effect dfEffect MS Effect df'Error MS Error F p Treatment 1 125 76 22.5 5.53 0.021 Paddock 2 82.8 76 22.5 3.67 0.030 Sample 1 83.7 76 3.54 23.6 <0.0001 T*P T*S 1 2.55 76 3.54 0.721 0.399 P*S 2 22.7 76 3.54 6.42 0.00266 T*P*S

Tables 4.5 a)- d). ANOVA of all effects for lamb body mass for; a) 1988, b) 1989, c) 1990, and d) 1991.

4.3.2 Red Kangaroos

The design of the ANCOVA analysis of red kangaroo body mass was incomplete, so I examined univariate, specific effects within the design (Table 4.6). The analysis indicated that there was no sampling period effect (F4.IU = 0.583, P > 0.65), treatment effect (F1,IU= 1.57, P > 0.2), or treatment X sample interaction (F014 = 0.90, P> 0.4). 70

Effect dfE.lfect MS Effect dfError MS Error F p Treatment 1 10.35 124 6.60 1.57 0.213 Paddock Sample 4 3.85 124 6.60 0.583 0.675 T*P T*S 4 5.99 124 6.60 0.90 0.462 P*S

Table 4.6. ANCOVA of all effects for red kangaroo body mass. The main effect and interactions with the factor "Paddock" could not be calculated due to missing cells in the design.

With respect to treatment, there was no consistent trend in the proportion of adult female red kangaroos that were reproductive (Fig. 4.8). Within a treatment, the proportion reproductive was variable from one sample to the next, but was always greater than 0.73. The log-linear analysis of the frequency ofreproductive females indicated that the factors of the model (sample X treatment X reproductive status) were independent of one another (ML Chi-square= 12.3, DF = 19, P < 0.87), and that no interactions were significant {Tables 4. 7 a and b ). The result that the treatment X reproductive status interaction was insignificant is particularly relevant to this study because it indicates that there was no difference in the frequency of reproductive versus non-reproductive females between treatments. 71

Q) :g> ::::, 0.9 "O 0 0.8 c.L... Q) a::: 0.7 en Q) 0.6 ro asympatric E 0.5 Q) •Allopatric lL 0.4 0 - 0.3 C 0 t 0.2 0 c. 0 0.1 a..L... 0 a:, Cl Cl 0 0 a:, a:, a:, Cl Cl ;;; ;;; Cl Cl Cl ?2 ~ ~ ?2 ?2 ~ ?2 ~ Q) ai ai ai Q) ai Q) c E c E c E c -~ E -~ E -~ E -~ ::, ::, ::, "' "' "' Sarµe

Fig. 4.8. The proportion of all mature female red kangaroos captured that were reproductive (i.e. had either a pouch young or a young-at-foot). Captured females were divided into groups depending on whether they were sympatric or allopatric with sheep.

4.7 a)

k- actor d ML Chi-s uare I 8 151.790 <0.0001 2 13 7.122 0.896 3 6 5.208 0.517

4.7 b)

Partial Partial Marginal Marginal Effect df Association Association p Association Association p Chi-s uare Chi-s uare Sample (S) 6 38.476 <0.0001 38.476 <0.0001 Treatment (T) 1 9.869 0.002 9.869 0.002 Reproductive (R) 1 103.445 <0.0001 103.445 <0.0001 S*T 6 4.143 0.657 4.217 0.647 S*R 6 2.823 0.831 2.897 0.822 T*R 1 0.009 0.926 0.083 0.774

Tables 4.7 a) and b).Log-linear analysis of the frequency of mature female red kangaroos in each treatment that were reproductive; a) results of fitting all k-factor interactions, and b) tests of marginal and partial associations. 72

The general trend in the density of red kangaroos was an increase across all treatments as the experiment progressed (Fig. 4.9). The Red Kangaroo Allopatric treatment had higher mean densities of red kangaroos than the Sympatric treatment in all but one sampling period (summer 1990), but these means were usually associated with large variance. The two-factor ANOVA ofred kangaroo density indicated that there were significant sample effects (F6_21 = 4.18, P < 0.01) and treatment effects (Fv , =

15.9, P < 0.0001), but no sample X treatment interaction (F, 2_21 = 0-:-555, P > 0.8)(Table 4.8). The significant sample effect indicates that red kangaroos did not maintain a stable population size over the course of the experiment. I examined the treatment effect in further detail by a Randomisation test (Manly 1991), using the mean density ofred kangaroos within each treatment for each sampling period. The Randomisation test indicated that over the course of the experiment there were significant differences in the density ofred kangaroos in all treatments (Table 4.9). Red kangaroos preferred paddocks with no sheep over paddocks with sheep. It proved impossible to completely exclude red kangaroos from the Sheep Allopatric treatment, but their mean density was kept lower than the other treatments at all times.

6() ,------,

- oo ~------~ "'E .:.:: ---ci ~~ ~ ------~ ------~~~ £ (/) C []Sympatric Q) 030 ~ ------+------t • Red Allopatric o O Sheep Allopatric eco Cl c~ ~ - ---~ --~± --~~- - ro ::x:: "O Q) 0::: 10

0 winter summer winter summer winter summer winter 1988 1989 1989 1990 1990 1991 1991 Sarµe

Fig. 4.9. The density ofred kangaroos per treatment. Densities are treatment means and their standard errors. 73

Effect df MS Effect dfError MS Error F p Sample 6 311 21 74.4 4.18 0.0064 Treatment 2 1185 21 74.4 15.9 <0.0001 S*T 12 41.3 21 74.4 0.555 0.853

Table 4.8. ANOVA of all effects for the analysis ofred kangaroos density.

Treatment Red Allopatric Sheep Allopatric Sympatric 0.02 0.01 Red Allopatric 0.01

Table 4.9. Randomisation test results of treatment comparisons for red kangaroo density.

4. 4 Discussion

The competitive effect of red kangaroos on sheep was tested by measuring the body mass, wool growth and reproductive output of ewes, together with the growth and survivorship oflambs in the presence and absence ofred kangaroos. In a similar way, the competitive effect of sheep on red kangaroos was tested by measuring the body mass and reproductive status of red kangaroos in the presence and absence of sheep. There was no evidence of a competitive effect of red kangaroos on sheep. Whilst I was not able to detect an effect of sheep on red kangaroo productivity, red kangaroos appeared to avoid sympatric areas in favour of paddocks destocked of sheep. This result suggests that there may be interference competition between sheep and red kangaroos.

Sheep sympatric with red kangaroos did not have a lower body mass than sheep allopatric with red kangaroos. Similarly, sympatric sheep did not grow less wool or have lower levels of fecundity than allopatric sheep. Significant treatment effects on the body mass and survivorship of lambs were measured, but they were not consistent with a hypothesis of competition. In 1991, lambs sympatric with red kangaroos had higher 74

mean body weights than those allopatric with red kangaroos. In 1990, lambs sympatric with red kangaroos had higher survivorship than those allopatric with red kangaroos. These treatment effects are intriguing and also difficult to explain. The cause of these results could be due to any stochastic difference between the paddocks but, since I have no data to test hypotheses on stochastic differences, I will not discuss it further. The importance of these results are that these anomalies are not consistent with the hypothesis of interspecific competition. Therefore, I conclude that there was no competitive effect of red kangaroos on the body mass or survivorship of lambs.

Red kangaroos sympatric with sheep did not have lower body masses than red kangaroos allopatric with sheep. Female red kangaroos did not have lower levels of fecundity than females allopatric with sheep. Red kangaroos tended to avoid areas with sheep. These results are consistent with an hypothesis of interference competition between sheep and red kangaroos.

The environmental variation experienced during this study was considerable. Plant biomass, which has been identified as the proximate influence of the dynamics of red kangaroos and to a lesser extent of sheep (Caughley 1987b), varied between a high of 1550 kg/ha and a low of367 kg/ha. These levels of plant biomass can be equated with conditions of superabundant food to moderate drought, respectively. As noted previously, this study follows on from a similar study using the same treatments (Edwards 1990, Edwards et al. 1995, 1996). Therefore, the results and conclusions of that study supplement the results of the study described here. During these studies , competition between sheep and red kangaroos was detected once. Edwards et al. (1996) found a competitive effect of red kangaroos on the body mass of sheep for one three month period. This is equivalent to approximately 5% of the time covered by the two experiments. During this period no competitive effect was detected on the red kangaroos in the study site. Close examination of Edwards et al. 's (1996) data reveal that the period ofinterspecific competition coincided with a large influx of red kangaroos from neighbouring properties, apparently due to a localised rain event on the study site when the district was generally dry. At this time, red kangaroo density underwent a dramatic increase from approximately 10-20 individuals/km2 to a maximum of 105 individuals/km2 (Edwards et al. 1996). The onset of competition was probably triggered by this unusual increase in red kangaroo density and when red kangaroo density 75

returned to previously recorded levels (10-20/km2) competition was no longer detected. If this is a general pattern, competition rarely occurs between these herbivores in the arid chenopod shrublands of New South Wales and when it does occur it is linked to unusual circumstances.

The results of Edwards et al. (1996) suggested that the competitive effect ofred kangaroos on sheep was exploitative, as it was directly related to food availability and diet choice. The period of competition coincided with a decrease in total pasture biomass from 540 kg/ha to 430 kg/ha. However, these levels of total pasture biomass are well above the minimum recorded during the present study (367 kg/ha) and the level suggested by Caughley (1987b) as the threshold for exploitative competition between sheep and red kangaroos (300 kg/ha). If the pasture biomass threshold for exploitative competition between sheep and red kangaroos is about 500 kg/ha, as suggested by Edwards et al. (1996), then a competitive effect of red kangaroos on sheep should have been detected in the winter 1991 sample. In winter 1991 there was no detectable effect ofred kangaroos on sheep productivity. The discrepancy between the pasture value suggested by Edwards et al. (1996) and the results of the present study suggest that some other factor may be involved. The design of the present study was very similar to the design used by Edwards et al. (1996), so direct comparisons between theses studies can be made. Edwards et al. (1996) noted that the competitive effect ofred kangaroos on sheep coincided with a large influx of red kangaroos into the study site which resulted in a five-fold increase in red kangaroo density. Taking into account the results of the present study, these data suggest that the competitive effect recorded by Edwards et al. (1996) was due to interference competition and not exploitative competition.

The trend for red kangaroos to favour paddocks destocked of sheep was observed in this study and has been recorded in a number of other studies on the habitat preference ofred kangaroos (e.g. Andrew and Lange 1986, Norbury and Norbury 1993, Edwards et al. 1996). In only one sample, summer 1990, was the mean density of red kangaroos in sympatry with sheep higher than the density when allopatric. This result may be interpreted as a competitive effect if it can be demonstrated that red kangaroos suffered some type of harm as a result of their habitat choice. In this case, harm would be equated with a drop in the level of fecundity, an increase in mortality, or a lower rate of change of red kangaroos sympatric with sheep when compared to the levels of these 76

factors in red kangaroos allopatric with sheep. It must be remembered that competition is a population process and is ultimately expressed as a reduction in population size. Rate of change in a population is a function of its exponential rate of increase (r) and population size (Caughley 1977). I did not explicitly measure the exponential rates of increase of red kangaroos in the experimental treatments but assuming that they will be similar for kangaroos in both treatments, as other aspects of their biology seem to be, then the rate of change of red kangaroos in allopatry will be higher-than the rate of red kangaroos in sympatry. This result suggests that sheep are having a competitive effect on red kangaroos.

In a study examining competition between sheep and kangaroos (mainly western grey kangaroos) in the semi-arid woodlands of New South Wales, Wilson (1991a) concluded that at times of food shortage, kangaroos exert a significant competitive effect on sheep. While I discussed Wilson's (1991) study in Chapter 2, some points warrant reiteration. In some treatments, Wilson used densities of herbivores that were higher than naturally occur in his study area. Experimental manipulations which use densities of putative competitors that are higher than those which naturally occur are not representative of any natural system, and the results of such experiments cannot be interpreted unambiguously (Underwood 1986). There are also problems in interpreting the results of the grazing intensity design, which Wilson used, with respect to the extent and nature of competition. Any analysis of the results will be confounded because comparison of the treatments (sheep only, and sheep plus kangaroos) involves two differences, the increase in density of sheep and the simultaneous increase in density of kangaroos. Comparisons of the productivity of sheep in the presence and absence of kangaroos were confounded, because for every increase in sheep density, there was a similar increase in kangaroo density. Thus, it is essentially impossible to interpret Wilson's results unambiguously. If the species studied suffer from intra- and interspecific competition, the grazing intensity experimental design will be of doubtful value for examining the effects of competition on the biology of the species. Since the intraspecific competitive effects of both species are unknown, the results and conclusions of Wilson's (1991) study are open to question. Finally, the experimental treatments studied by Wilson were not replicated and consequently, it is not possible to determine if treatment effects were due to competition or heterogeneity between the experimental units that may have affected sheep productivity. 77

Edwards et al. ( 1996) discussed in detail the limitations of their experimental design, which are also applicable to this study. First, there was inadequate interspersion of treatments. A potential consequence is the increased likelihood that chance events , which Hurlbert (1984) colourfully describes as "nondemonic intrusion", will produce spurious treatment effects if they impinge on some treatments and not others. If the replicates of treatments are adequately interspersed then it is safe te assume that one type of treatment will be not be biased by a chance event, since its effect is likely to be spread over a number of treatments. The chance event most likely to impinge on the treatments was rainfall. Differential rainfall across treatments could not be controlled and consequently its potential effect across treatments could not be determined.

Second, Edwards et al. (1996) argue that the allocation ofreplicates to treatments was not properly blocked with respect to sheep productivity. Edwards (1990) found that before the imposition of experimental treatments, sheep productivity varied between paddocks. Sheep from the paddocks which were to become the Sheep Allopatric treatment replicates had greater wool growth and body mass than sheep from the paddocks which were to become the Sympatric treatment replicates. However, according to stocking rate estimates made by Soil Conservation Service of New South Wales (SCS) the experiment was blocked. The SCS estimate was based on the "rating system" (used for assessing carrying capacity or stocking rates) and ranked the paddocks from highest to lowest productivity as Sympatric 2, Sheep Allopatric 1, Sheep Allopatric 2, and Sympatric 1 (op. cit. Edwards 1990). The difference between the productivity estimates of Edwards (1990) and SCS remain unresolved, but are probably due to the different methods of assessment. Edwards' (1990) estimate was based on animal productivity over a relatively short time (six months), while the SCS's estimate was based on a range of factors including primary productivity, topography, soil fertility and rainfall (Condon 1968, Condon et al. 1969).

Third, only two replicates per treatment were used, resulting in only a small number of degrees of freedom and an overall lack of power in some analyses. The correct way to address this problem would be to increase the number of replicates per treatment (Sokal and Rohlf 1981). Increased spatial replication of this experiment was not possible because of financial and labour constraints and, because of the problem 78

associated with maintaining experimental replicates on the limited area covered by the principal land system (Conservation land system).

Fourth, it proved impossible to completely exclude kangaroos from the Sheep Allopatric treatment. The potential effect of this problem would be to confound the results of the experiment, since the difference between the treatments was not maintained. However, their density was always below that of kangaroos in the Sympatric treatment, and over the course of the experiment they were kept at significantly lower density than the other treatments. Fifth, red kangaroos were able to free-range during the experiment, which helped the experiment mimic the natural situation. Edwards et al. (1996) suggest that this is a potential problem because red kangaroo grazing pressure is not constant. I interpreted this feature of the experiment differently. Spatio-temporal variance in grazing pressure is a natural feature of red kangaroo populations. I suggest that allowing red kangaroos to free-range was an appropriate method of examining competition between an animal naturally constrained in its movements (sheep) and an animal that can distribute itself in an ideal-free manner (sensu Fretwell and Lucas 1970, Fretwell 1972). Constraining populations of red kangaroos may indicate if competition is possible, but is so divorced from the natural situation that it would make unambiguous interpretation of the results very difficult. An assumption of my analyses relating to red kangaroo was that, prior to capture, the kangaroos had been in the same paddock for six months. Studies suggest that this is probably a valid assumption for adult red kangaroos, which tend to be relatively sedentary (Croft 1991, Edwards et al. 1994). Nevertheless, this assumption was not tested during this study.

Sixth, the experimental design was unable to detect intraspecific competition. Alternative designs that can detect intra- and interspecific competition are discussed by Underwood (1986), and they all involve the establishment of at least one more allopatric treatment per species. The new treatment is kept at a different density from the other, and the relative strengths of intra- and interspecific competition can be gauged by comparisons between the performance of a target species in the allopatric treatments and the sympatric treatment. Establishment of two more treatments to examine the extent of intraspecific competition in sheep and red kangaroos would have involved at least four more paddocks and was not possible due to financial and labour constraints. It 79

is important to point out that unlike Wilson's (1991) analysis, my analysis of interspecific competition, and also that of Edwards et al. (1996), was not confounded by intraspecific interactions but hypotheses of intraspecific competition could not be tested.

Edwards et al. (1996) finally point out that the short duration of their experiment would limit the generality of their conclusions. This potential problem has been in part overcome since the treatments established by Edwards (1990) were maintained for the duration of the experiment described here. The treatments have now been imposed for six and one half years, more than doubling the duration of the original study. The environmental conditions experienced by the combined studies range from super abundance of food resources to moderate drought. With the exception of severe drought, such as that described by Caughley et al. (1987) or Dawson and Ellis (1994), the results of these two studies largely cover the gamut of environmental conditions experienced in this environment.

I conclude that exploitative competition for food between sheep and red kangaroos rarely occurs and is not a major factor affecting productivity of sheep in the arid rangelands of New South Wales. Of greater consequence is the effect of interference competition on the biology of these herbivores. A reanalysis of the data of Edwards et al. (1996) indicates that red kangaroos interferentially compete with sheep when red kangaroos are at extremely high densities. At normal densities there was no longer a competitive effect. In contrast, the interferential competitive effect of sheep on red kangaroos is essentially continuous, and red kangaroos tend to avoid areas used by sheep. Whether these competitive effects are due to agonistic interactions, simple avoidance or indirect modification of the environment that make it unsuitable for other species are unresolved and awaits further study. In addition, the long term effects of prolonged and severe drought on the dynamics of these herbivores remain unresolved and also awaits further experimentation. Chapter 5

Mechanistically Modelling Competition Between Sheep and Red Kangaroos.

5.1 Introduction The extent to which competition influences the structure of:.animal communities has received much attention (Law and Watkinson 1989), and prompted much debate (Connell 1983, Schoener 1983). In particular, the mathematical modelling of competitive interactions has greatly contributed to our understanding of how resource availability, competitive ability and the density of competitors contribute to the dynamics of populations. Early work concentrated on applying the Lotka-Volterra competition equations (Lotka 1932, Volterra 1926) to laboratory communities; some successfully (Gause 1934, Crombie 1947, Vandermeer 1969), others unsuccessfully (Ayala et al. 1973, Gilpin and Ayala 1973). The Lotka-Volterra model assumes that species interactions can be described in terms of linear. equations, but this model was found to inadequately describe the dynamics of some populations which demonstrated non-linear dynamics. Ecologists attempted to derive better models that were mechanistically based and which could incorporate the non-linear nature of competitive interactions (Belovsky 1984b). It was in this setting that Schoener (1973, 1974b, 1976, 1978) developed a series of mechanistic models that could examine intraspecific, and interspecific, exploitative and interference competition; and it is the application of these models to a sheep-red kangaroo assemblage that forms the focus of this chapter.

By definition, competition occurs when two or more individuals try to acquire a resource that is in short supply. By their interaction in trying to acquire the resource at least one of the individuals is harmed (Schoener 1983). Harm is ultimately a reduction in population size, therefore competition is a population process that ultimately reduces the rate of increase of a species affected by competition. Modelling the dynamics of a population in the presence of its putative competitor potentially allows us to examine how resource limitation and the density of the competitors can influence competitive processes and ultimately community structure. 81

Red kangaroos have been hypothesised to be a competitor of sheep (Wilson 1991a, Dawson and Ellis 1994, Edwards et al. 1996). The main mechanism being exploitative competition for food (Edwards et al. 1996), but interference has also been suggested (Edwards 1989). However, the extent to which competition influences the population dynamics of these species is unclear. To date, the study of competition between sheep and kangaroos has concentrated on indirect means of measuring competition, such as dietary overlap. While the results of these studies suggest competition for food, unequivocal tests require the experimental manipulation of populations in controlled experiments (Underwood 1986, Caughley 1987b). In a highly variable environment, such as the one that includes the study site, competition may only occur sporadically and may be linked to infrequent episodes of resource depletion (Wiens 1977). In such situations the results of experimental manipulations of populations designed to measure competition may be dependent on chance events that may or may not occur during the experiment. Under this scenario the generality of the conclusions of the experiment could be severely weakened. The approach I have adopted here is to model the competitive interaction of sheep and red kangaroos in such a way that the results of the modelling exercise may be combined with the results of a controlled removal experiment (Chapter 4). This approach should yield robust predictions of the conditions under which these herbivores compete and the influence of competition on community structure.

The aim of this chapter is to present a mechanistically derived model of exploitative competition between sheep and red kangaroos. Schoener (1973, 1974b, 1976, 1978) developed a series of mechanistic models that predict the rate of change in populations that are hypothesised to be undergoing competition. These models have been successfully used to predict the effect that competition has on the community structure of island lizard populations (Schoener 1974b, 1975), and terrestrial vertebrate (Belovsky 1984b) and invertebrate (Belovsky 1986a) communities. Using Schoener's models I examined the hypothesis that sheep and red kangaroos compete exploitatively for food. This approach enabled me to make a priori predictions about the population dynamics of both herbivores if they are influenced by competition; predictions that could be directly compared with the results of the controlled removal experiment described in Chapter 4. 82

5.2 Materials and Methods A model was constructed to examine competition for food between the red kangaroo and domestic sheep in an arid rangeland in Australia. The model was solved from parameters derived from two study sites that contained a fixed number of sheep and free-ranging kangaroos. The competition model was solved five times at six monthly intervals starting winter 1989 and finishing winter 1991. These times covered conditions ranging from highly abundant food (winter 1989) to moderate drought (winter 1991).

5.2.1 Modelling

Schoener's (1973, 1974b, 1976, 1978) mechanistic models of competition were used to test the hypothesis of competition between sheep and kangaroos. The general form of the model for two species competition is;

(5.1)

where R1 is the number of offspring resulting from the intake and assimilation of one unit of resource intake by species 1; N1 is the number of individuals of species 1; N2 is the number of individuals of the competing species 2; and M 1 is the amount of resource per unit time available to a single individual of species 1 for reproduction beyond replacement. M can include parameters for exploitative and interference competition and when explicitly formulated the two species system of differential equations becomes;

(5.2a)

(5.2b) 83 where NR is the population size (or density) ofred kangaroos; Ns is the population size

(or density) of sheep; IER is the amount of resource exclusively available to red kangaroos per unit time; !Es is the amount of resource exclusively available to sheep per unit time; 10 is the amount of resource that is available to red kangaroos and shared with sheep; y RR is the cost of interaction for an individual red kangaroo with a conspecific

(intraspecific interference); y ss is the cost of interaction for an individual sheep with a conspecific (intraspecific interference); y Rs is the cost of interaction for an individual red kangaroo with an individual sheep (interspecific interference); y SR is the cost of interaction for an individual sheep with an individual red kangaroo (interspecific interference); CR is the density-independent maintenance and replacement cost for an individual red kangaroo; Cs is the density-independent maintenance and replacement cost for an individual sheep; and ~ is the likelihood of an individual sheep getting an item of resource relative to an individual red kangaroo.

For a specific system the parameters of equations (5.2a) and (5.2b) are evaluated individually and if they are greater than zero are incorporated into the model. Since I wished to examine exploitative competition only the interference terms y RR , y RS , y ss and y sR were not included in the final model. The differential equations reduced to pure exploitation models with resources partially overlapping, and a fixed resource input to the populations;

(5.3a)

(5.3b)

This system of differential equations produces nonlinear zero-isoclines that intersect once. The equilibrium formed by the intersection is stable and provided each species has sufficient exclusive resource to allow dN/dt > 0 neither species can be driven to extinction by exploitative competition alone. Importantly, no closed 84 trajectories can be formed in the first quadrant by this family of models, so no limit cycles exist (Schoener 1974b, 1976).

5.2.2 Parameterising the Model

I solved the competition model for the zero-isocline of each species at each sampling period. The solution was made for a six month time periQd. I chose this period because it reflects the time over which domestic stock managers typically make management decisions in this environment, and because it would potentially highlight the effect of seasonal differences on competition. The amount of total, exclusive and overlapping resources and J3 parameters were measured at the study site during each sampling period, and the density-independent maintenance and replacement costs were taken from the literature or estimated using my own data.

Total vegetation biomass was measured by clipping 0.25 m2 plots at each sampling period. Clipped vegetation was separated into the categories forb, grass or shrub. Forbs were classified as dicotyledonous broad-leaved non-woody plants other than grass and grass-like plants, grasses were monocotyledonous narrow-leaved non woody plants, and shrubs were dicotyledonous woody plants capable of growing to about 2 m in height (Cunningham et al. 1992). Clipped plots were chosen systematically at 500 m intervals along transect lines that ran through the study sites. With the exception of the winter 1989 sample, 44 plots in Sympatric 1 (cf Fig. 4.1, Chapter 4) and 38 plots in Sympatric 2 were clipped at each sampling period. In winter 1989 52 plots were clipped from Sympatric 1 only. Clipped plants were separated at collection and later oven-dried at 70°C for 48 hours. Samples were weighed after drying to the nearest 0.1 g.

The probability density functions of food types were modelled as bivariate normal distributions (Fig. 5.1) from which exclusive and overlapping resources were calculated. The variates used to construct the distribution were; 1) plant quality, and 2) available bite size. Because the variates of the distribution are not independent, the distribution of foods cannot be simply calculated from the product of their unidimensional distributions (May 1975, Pianka 1981). The construction of the distribution for a given plant type requires five parameters to be determined; mean plant 85

quality µd and standard deviation cr d, mean available bite size µ 5 and standard

deviation cr s, and the product-moment correlation coefficient p between variates. Each

variate tended to be right skewed and were log transformed to approximate a normal distribution. The bivariate normal distribution can be described by the relation (Winer et al. 1991);

1 -[( x::·r +(ytr +zp( x::,)(yt)] f (x,y) = ~ 2 exp 21t 1-p 2(1- p 2 )

(5.4)

Fig. 5.1. A bivariate normal distribution. (Source Sokal and Rohlf 1981). 86

For all sampling periods I measured a minimum of20 bite sizes from both study sites for each plant type and herbivore species. I measured individual bite sizes, the product of item dry mass and items per bite, following the method ofBelovsky et al. (1991 ). Sheep and red kangaroos were observed during feeding periods and forbs, grasses and shrubs which were fed upon were collected. The diameter of the remaining stub of an eaten twig or the remaining width of an eaten leaf was measured, using callipers, as close as possible to the point of consumption. A similar sized uneaten twig or leaf was collected from the same plant where possible, or from an adjacent plant. A 'matched bite' of equivalent diameter or width was then clipped and kept, along with the bite-stub of the consumed plant and the stub of the matched bite. The matched bite was oven-dried at 70°C for 48 hours. The mass of the matched bite was used as an approximate measure of bite size.

Determining the frequency of food item sizes in the environment presented a particular problem. A plant stem or leaf is essentially a fractal that can potentially be broken into an infinite range of smaller items. Consequently, there is no a priori way of determining available item size from direct measurement of the vegetation. I therefore made an indirect measurement of available food item sizes by assuming that measured bites were representative of the range and frequency of item sizes available in the environment. In essence I let the herbivores determine the frequency of available food item sizes. For each sampling period and plant type I pooled the red kangaroo with the sheep data but kept each study site separate, and then calculated mean available bite size ( µ s) and standard deviation ( er s) for each study site. If herbivores are not biased toward taking a particular bite size from a food type more often than its proportional abundance in the environment, then the method I used will produce an unbiased estimate of available bite size frequency. There is some evidence that herbivores do select food items within a food type based on minimum nutrient content-item size criteria and their relative abundance (Belovsky 1978, 1981, 1986a). Therefore, the assumption seems justified.

I analysed clipped plot samples and bite sizes to determine the plant quality in the environment and selected by herbivores, respectively. I assumed that plant quality was directly related to plant solubility, which was measured using the hydrochloric acid 87

(HCl) in pepsin technique (Tilley and Terry 1963). After drying, plant samples were ground to pass through a 1 mm sieve. A 0.1 g subsample was added to 1O ml of acid/pepsin solution (2.0 g of 1: 10 000 pepsin in 1 L of 0.1 N HCl) and incubated at 38°C for 48 hours with occasional shaking. The residual was filtered onto tared Whatman No. 4 filter paper and thoroughly washed. The filter paper and residue were then dried at 70°C for 24 hours. The percent digested was then calculated. This method was not intended to mimic in vivo digestibility of forage by sheep or kangaroos, but was used as an approximate measure of plant quality. The absolute digestibility of plant parts was not needed to solve the model, only the relative solubility of each group. An estimate of bite quality was calculated using the formula;

(5.5)

where Eb is the solubility of the eaten bite; Er is the solubility of the eaten stub; Mb is the solubility of the matched bite; and Mt is the solubility of the matched stub. Again I assumed that these samples were representative of the range and frequency of plant qualities available in the environment, and pooled the data to estimate mean food item solubility ( µd ) and standard deviation ( cr d) in the environment.

I calculated the product-moment correlation coefficient ( p ) from the correlation of matched bite mass and solubility. For each sampling period and plant type the red kangaroo and sheep matched bites were pooled. The product-moment correlation coefficient was calculated from the pooled data.

Using the algorithms derived by Belovsky (1981, 1984b, 1986a), I found that the theoretical minimum bite sizes and the minimum quality of bites were not correlated with the observed data, although the test had low power (error df= 3) (Table 5.1). (The respective observed minima were assumed to be equal to the mean of the lowest 10% of measured bite sizes and bite qualities) Therefore, I used the observed values to estimate minimum bite sizes and qualities. In a similar way, maximum bite sizes and qualities were taken to be the mean of the highest 10% of each variable. 88

Herbivore Species Plant TyPe Selection Parameter Fu r p

Red Kangaroo Forb Solubility (%) 3.79 0.747 NS Item Size (g-dry/bite) 1.78 0.610 NS

Grass Solubility(%) 0.133 0.206 NS Item Size (g-dry/bite) 0.003 0.030 NS

Shrub Solubility (%) 0.218 - 0.260 NS Item Size (g-dry/bite) 0.158 0.224 NS

Sheep Forb Solubility(%) 1.04 0.506 NS Item Size (g-dry/bite) 20.7 0.934 <0.02

Grass Solubility(%) 0.081 0.162 NS Item Size (g-dry/bite) 0.0448 0.126 NS

Shrub Solubility(%) 4.21 0.764 NS Item Size !g-!!!l'.:lbite} 0.126 0.201 NS

Table 5.1. The correlation between the predicted and observed minimum acceptable food type item size and solubility. Predicted item size~ and qualities were calculated using the algorithms ofBelovsky (1981, 1984b, 1986a). Observed minimum values were assumed to be equal to the lowest 10% of measured bite sizes and qualities.

The amounts of exclusive, overlapping and total resource were calculated as a volume of the bivariate normal distribution using Fubini's Theorem (Thomas and Finney 1988), giving;

Volume= Jdm.ax Jsm.axf(x,y)dxdy (5.6) dm1n smtn

where dmax is the maximum plant quality available; dmin is the minimum plant quality accepted or available; smax is the maximum bite size accepted or available; smin is the minimum bite size acceptable or available; and the other variables have been previously defined.

The total volume of the bivariate normal distribution was calculated first, and equated with the measured total biomass from the clipped plots. The volumes of 89 exclusive and overlapping resource amounts were calculated and converted into proportions of the total resource base and then into plant biomass (kg/ha). For each solution of the isoclines, food types were summed for each herbivore species to calculate the total amount of exclusive and overlapping resources. The ~ term was calculated following the method ofBelovsky (1984b) as,

(5.7)

where a is a red kangaroo's proportion of the diet made up by shared resources, bis a sheep's proportion of the diet made up by shared resources, MR is a red kangaroo's per capita resource intake per unit time, and Ms is a sheep's per capita resource intake per unit time. Using Short's (1987) functional response equations that relate food intake rate to total plant biomass, I calculated the food intake rate (kg-dry mass/(6 months)) of an individual sheep and red kangaroo for each sampling period at each site.

Schoener (1974b, 1978) discusses the assumptions of the model that may be biologically unrealistic in some systems. First, at low population densities an individual's capacity to use resources must be very large if available resource abundance (IE; + 10 ) is very large (Schoener 1978). However, for a species at low population density, the amount of overlapping food (10 ) approaches zero as the density of a competitor species increases and takes a proportionally larger amount of the overlapping resource. Ultimately the competitors will have only exclusive resources available. At no time in this study was the density of either competitor large enough to totally consume the overlapping food resource, and the amount of exclusive resource was always proportional to the to the level of consumption of resource by the herbivore. Essentially, if population size was low then food availability was also low. For these reasons it was unnecessary to algebraically modify Schoener's (1974b) original model. Second, the interaction of the herbivores with their food supply assumes that the generation of food for the populations per unit time is unaffected by consumption (Schoener 197 4b ). The generation of food and its consumption by herbivores are independent, and herbivore dynamics are reactive (sensu Caughley and Lawton 1981 ). Schoener's (1974b, 1976, 1978) models assume that the system is continuous, but I 90 have specifically modelled the dynamics of the herbivores over a six month time period, the dynamics of one period being independent from the next since the model was reparameterised at the start of each six month period. Changing the system from a continuous one to a discontinuous one makes this assumption unimportant, and the measured resource availability represents the minimum available per unit time. The sheep-red kangaroo system described here does not invalidate these assumptions, and I conclude that the model produces biologically meaningful results. -

5.3 Results

5.3.1 Parameterising the Model

The clipped plant biomasses are present in Fig. 5.2 a and b. The general trend was a decline in the amount of plant biomass from a maximum in winter 1989 to a minimum in winter 1991. This decline corresponded with prevailing rainfall, with above average rainfall at the start of the study and below average rainfall for the second half of the study. Both study sites produced similar amounts of plant biomass, with the exception of summer 1990 when Sympatric 1 produced 920 kg/ha and Sympatric 2 produced 1335 kg/ha.

5.2 a)

700

600 mForb ro -£. Cl 500 •Grass ::=, DShrub Cl) 400 Cl)ro E 0 300 in 1: 200 a:ro 100

0 Winter 1989 Summer 1990 Winter 1990 Summer 1991 Winter 1991 Sampling Period 91

5.2 b)

700

ro 600 El Farb .c. Cl 500 •Grass 6 DShrub Cl) Cl) 400 ro E 0 300 iii -C 200 a:ro 100

0 Winter 1989 Summer 1990 Winter 1990 Summer 1991 Winter 1991

Sampling Period

Fig. 5.2 a) and b).Clipped plant biomass subdivided into the categories forb, grass and shrub for a) Sympatric 1 and b) Sympatric 2.

The parameters needed to solve the model are presented in Table 5.2. I equated the density-independent maintenance and replacement costs ( C;) with an individual's food intake rate (kg-dry mass/6 months) when the population's exponential rate of increase (r) is zero. For red kangaroos in this environment r = 0 when plant biomass is 230 kg/ha (Bayliss 1987, Caughley 1987b). At this plant biomass the amount of food eaten by a 25 kg red kangaroo in six months is 172 kg-dry mass (Short 1987). There are no published data on the numerical response of sheep as a function of plant biomass, so I could not calculate the density-independent costs for sheep using the same methods. As an alternative method I regressed the rate of energy intake by a sheep against total plant biomass (Fig. 5.3) using data from chapter 6, assuming a goal of energy maximisation. Although the regression is not significant it closely approaches significance, and represents the best data available. The density-independent costs of a sheep are satisfied when energy intake is 11359 kJ/day (Kleiber 1947, 1961, Blaxter 1967, Moen 1973), which is the maintenance and reproductive replacement energy requirement of a 60 kg sheep. From the regression, this rate of energy intake is satisfied when total plant biomass is at least 225 kg/ha. I then used Short's (1987) functional response for sheep to estimate food intake rate when plant biomass is 225 kg/ha. Using these methods I calculated the density-independent costs (the amount of food consumed) of a 60 kg sheep over six months to be 271 kg-dry mass. 92

~ ~ 19000,--~---.--~----.----~-----.-~--....--~...,.....-----.---.....--, --, ~ a, ~ 18000 0 C: >, C) ~ 17000 wC "ffi :§ 16000 =c> -= £ 15000

14000 0

13000 0

12000

11000 .____ _.______._ ____.______._ __~~-~~-----___, 200 400 600 800 1000 1200 1400 1600 1800 Plant Biomass (kg/ha)

Fig. 5.3. The regression of a sheep's energy intake (kJ/day) as a function of total plant biomass (kg/ha). (y= 1033o+4.57x, r = 0.894, F1•2 = 7.93, P < 0.106). The winter 1990 data was not included in the regression because the model failed to predict a goal of energy maximisation at this time (cf Chapter 6 for further details). 93

Available Plant Biomass (!g_lha2 Total Plant Herbivore Site Sampling Exclusive Overlapping Biomass Species Period (kg/ha) (kg/ha) (kg/ha)

Red Kangaroo Sympatric 1 Winter 1989 78 962 1556 1.68 Summer 1990 13 824 920 1.68 Winter 1990 105 585 1004 1.80 Summer 1991 56 94 500 2.04 Winter 1991 26 104 380 1.54

Sympatric 2 Summer 1990 19 1127 1335 1.62 Winter 1990 113 601 1034 1.81 Summer 1991 60 137 522 1.78 Winter 1991 20 118 367 1.36

Sheep Sympatric 1 Winter 1989 127 962 1556 1.68 Summer 1990 49 824 920 1.68 Winter 1990 90 585 1004 1.80 Summer 1991 41 94 500 2.04 Winter 1991 41 104 380 1.54

Sympatric 2 Summer 1990 116 1127 1335 1.62 Winter 1990 91 601 1034 1.81 Summer 1991 56 137 522 1.78 Winter 1991 55 118 367 1.36

Table 5.2. The amounts (kg-dry mass/ha) of exclusive, overlapping food and total plant biomass. The calculated competition parameters ( ~ ) are also presented.

Comparison of the zero-isoclines with the observed densities (cf Chapter 4) of the herbivores indicates that interspecific competition for food between sheep and red kangaroos was unlikely to have occurred during this study. The plots of the zero isoclines (Figs 5.4 a-e and 5.5 a-d) indicate that sheep and red kangaroos had sufficient resources to allow positive rates of increase at all times. Consistently, there was a large overlap in the available food resource of both herbivores; however, both herbivores were also able to procure exclusive resources. The herbivores partitioned food on the basis of minimum item size and minimum solubility, with no partitioning of either maximum item size or solubility. Red kangaroos were usually able to make use of small items that were unavailable to sheep, whereas the exclusive resources of sheep were usually of lower solubility than were acceptable to red kangaroos. Therefore, even if the populations were able to go to equilibrium, the herbivores would be unable to exclude one another on the basis of competition for food alone. 94

5.4 a) Sympatric 1, winter 1989

10.------,..---~------.------,------.---~--~ cu ,E .sci ~ 8 C Cl) 0 0

e111 g> 6 111 ~ "C a:Cl)

dR/dt = 0

2 4 6 8 10 Sheep Density (no.Iha)

5 .4 b) Sympatric 1, summer 1990

10.--.----~--~------.------,------.---~----. cu ,E dS/dt = 0 .sci ~ 8 C Cl) 0 ~ 111 g> 6 ~ "C a:Cl)

dR/dt= 0

2 4 6 8 10 Sheep Density (no.Iha) 95

5 .4 c) Sympatric 1, winter 1990

10r---r------~--.....------.------.------, 'ii, ,E dS/dt = 0 .s0 t 8 C: Q) 0

m~ g> 6 ~ 'O Q) 0::

2 dR/dt= 0

2 4 6 8 10 Sheep Density (no.Iha)

5 .4 d) Sympatric 1, summer 1991

5 ,--,.------.....-----.------.------.------....------, 'ii, ,E dS/dt= 0 .s0 f4 C: Q) 0

m~ g> 3 m ~ 'O Q) 0::

1~_,LI ...._ \ ______dR/dt=O~ o.______.. ___...... ______.______.~ ______. 0 2 3 4 5 Sheep Density (no.Iha) 96

5.4 e) Sympatric 1, winter 1991

5 .----...------.------..------~------.------

dS/dt = 0

1,.\i -~ ------J _ dR/dt=O o~-~~-...... --~-- ...... ----~------0 2 3 4 5 Sheep Density (no.Iha)

Figs 5.4 a) - e).The zero-isoclines of sheep and red kangaroos at Sympatric 1 in; a) winter 1989, b) summer 1990, c) winter 1990, d) summer 1991, and e) winter 1991, (• the observed density of sheep and red kangaroos). Note that there was a change in the scale of the axes (density) from 0-10 (no.Iha) for 5.4 a-c, and 0-5 (no.Iha) for 5.4 d-e. 97

5.5 a) Sympatric 2, summer 1990

10.------....----.------~-----~------. ni' ,E 0 dS/dt = 0 s ~ 8 C: Q) 0e I'll g> 6 ~ "C a::Q)

• dR/dt = 0 O L:______~=:::::::::::::'.:~==~;;;~d 0 2 4 6 8 10 Sheep Density (no.Iha)

5.5 b) Sympatric 2, winter 1990

10.----.------.------.------~------.---~----, (0 ,!:; s0 dS/dt= 0 ~ 8 C: Q) 0e I'll g> 6 ~ "C a::Q)

2 dR/dt = 0

2 4 6 8 10 Sheep Density (no.Iha) 98

5.5 c) Sympatric 2, summer 1991 5..-----.------~----~-----~--~-----.---~---, dS/dt = 0

1 dR/dt = 0

2 3 4 5 Sheep Density (no.Iha)

5.5 d) Sympatric 2, winter 1991

5.---...... ------~----~-----~--~---~------, IQ ,E .sci dS/dt = 0 i 4 C: Cl) C e0 CU g> 3 CU ~ "O Cl) 0:::

dR/dt= 0

1 2 3 4 5 Sheep Density (no.Iha) 99

Figs 5.5 a) - d). The zero-isoclines of sheep and red kangaroos at Sympatric 2 in; a) summer 1990, b) winter 1990, c) summer 1991, and d) winter 1991, ( • the observed density of sheep and red kangaroos). Note that there was a change in the scale of the axes (density) from 0-10 (no.Iha) for 5.5 a-b, and 0-5 (no.Iha) for 5.5 c-d.

The isocline analysis also indicates that this consumer-reso_}lrce system would reach a stable equilibrium if it were not constantly buffeted by the environment. The equilibrium density of the herbivores would be equal to the intersection of the two isoclines. Furthermore, the variability in the equilibrium densities exemplifies the highly dynamic nature of the food resource. For example, in the six month period from winter 1990 to summer 1991, total plant biomass approximately halved in both study sites (Sympatric 1, 1004 kg/ha to 500 kg/ha; Sympatric 2, 1034 kg/ha to 522 kg/ha). Associated with this drop in total plant biomass was an even greater drop in food availability (Table 5.2). A consequence of this drop in food availability was that the predicted equilibrium density (number/ha) of sheep and red kangaroos dropped from (1.52, 2.08) (sheep, red kangaroos) to (0.31, 0.59) in Sympatric 1; and from (1.53, 2.21) to (0.47, 0.72) in Sympatric 2. This degree of variation makes long-term predictions of productivity in this environment almost meaningless.

The calculated J3 terms for each sampling period suggest that sheep would have a potentially greater competitive effect on red kangaroos, than red kangaroos would have on sheep. This occurs because an average sheep has a higher per capita resource intake than an average kangaroo. The proportion of food for each species that is overlapping with that available to the other species cannot account for the effect because the proportions are more or less evenly divided between red kangaroos and sheep. The effect of the competition parameter on population dynamics is most clearly seen by examining the rate of change in the slope of the zero-isocline as the density of the potential competitor increases. At all times the rate of change in the red kangaroo zero isocline is greater than the change in the sheep zero-isocline. Belovsky (1984b) points out that the calculation of the J3-term depends on two assumptions; 1) items of resource are perceived equivalently by sheep and red kangaroos, and 2) the total amounts of resources available to the herbivores are equivalent. Both of these assumptions are essentially satisfied in this system. 100

I regressed the theoretical equilibrium densities of sheep and red kangaroos against total plant biomass when the herbivores were allopatric or sympatric with their hypothesised competitor (Figs 5.6 a and b).There were significant relationships between the equilibrium densities of both herbivores and total plant biomasses: sheep in allopatry; F1,1 = 23.63, P < 0.002, r = 0.878: sheep in sympatry; F1,1 = 64.71, P < 0.0001, r = 0.950. (Fig. 5.6 a); red kangaroo in allopatry; F1,1 = 9.36, P < 0.018, r =

0.756: red kangaroo in sympatry; F17 = 82.52, P < 0.0001, r = 0.960 (Fig. 5.6 b).At plant biomasses greater than 500 kg/ha the equilibrium densities of red kangaroos when sympatric with sheep are greatly reduced from their allopatric densities. In comparison, sheep show only a small reduction in sympatric equilibrium density compared with their allopatric density. At plant biomasses less than 500 kg/ha, the sympatric and allopatric densities of both herbivores converge and there was only a marginal reduction in equilibrium density when a competitor was present compared with when the competitor was absent.

Fig. 5.6 a) Sheep

5 -~-~--~--~~--~--~~~-~---~-.,-~., ., ., ., ., 0 .," ., .," ., ., ni' 4 ., ,E • ., .," 0 ci ., ., s ., ., ., ., ·w~ ., ., C: 0 ., .," ~ 3 ., ., a. .,.," Q) ., Q) . . .r:. .,.,"00 (J) ., ., ., ., ., 2 ., ., ., ., ., ., .,.-" ., ., .. ., ., .," 1 ., ., ., ., oo.,""

0 ..__"""'----'---~~----'------'----...... --___._- __...... _ ____, 200 400 600 800 1000 1200 1400 1600 1800 Total Plant Biomass (kg/ha) 101

Fig. 5.6 b) Red Kangaroo

8 ,. ,.,."' "iu ,E ,. ,."' ci ,."' 7 ,."' .s D ,."' ~ ,. ,. "iii ,. C ,," D Cl) 6 ,. ,. 0 ,. ,. 0 ,. ,. ...0 ,. ,. ~ 5 D ,.,."' C ,. 111 ,. ~ ,. "'O Cl) 4 ,. ,.~ri a::: ,. ,. ,. ,. ,. ,. 3 ,. ,. ,."' ,. ,. ,. ,. ,,"' 2 ,. ,. .. ,. ,. ,."' ,. ,. 1 ,. ,."' . ,. • ,. ,. 0 200 400 600 800 1000 1200 1400 1600 1800 Total Plant Biomass (kg/ha)

Fig. 5.6 a) and b).The regressions of predicted equilibrium allopatric and sympatric densities of a) sheep (sheep allopatric with red kangaroos are open circles and dashed line, sheep sympatric with red kangaroos are closed circles and solid line) and, b) red kangaroos against total plant biomass (red kangaroos allopatric with sheep are open squares and dashed line, red kangaroos sympatric with sheep are closed squares and solid line).

The correlation of sheep equilibrium density and red kangaroo equilibrium density was not significant (t = 1.16, P > 0.25, r = 0.400, N = 9). However, after I separated and replotted the data into summer and winter equilibrium densities, a pattern emerged (Fig. 5.7). In winter there was a significant correlation between the equilibrium densities (t = 3.41, P < 0.05, r = 0.891, N = 5). In summer the correlation was not significant (t = 2. 750, P = 0.111, r = 0.889, N =4), although the correlation coefficient between the variates was nearly as strong as in winter and the null result may simply have been due to the small number of degrees of freedom (DF = 2). 102

2.6 ...... ---.---...,...... -~---...... --~- ...... /~~~-~-~~- ...... - ...... / / 1G / .t:; / 0 / D C / D / i 2.2 / / "iii D / C / G) / / 0 / 0 / e 1.a / (I) / C) / C / (I) / / ~ / "C / / ~ 1.4 / / / / / / / / 1 / • / / / •

D 0.2 ...___ __....______....._ __._._ ____ ~----~----- ..... 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Sheep Density (no.Iha)

Fig. 5. 7. Correlation between sympatric equilibrium sheep density and red kangaroo density. ( open squares and dashed line are winter data, closed circles and solid line are summer data)

5.4 Discussion The mechanistic competition model (Schoener 1974b, 1976, 1978) used in this study indicates that competition for food between sheep and red kangaroos in the arid rangelands is rare. Even under drought conditions, such as the winter of 1991 when the study region was officially declared drought stricken by the New South Wales Government, the model predicted that there was no competition between sheep and red kangaroos; a conclusion that was corroborated by the results of a controlled removal experiment (cf Chapter 4) that was run in conjunction with this study.

Sheep and red kangaroos had a high degree of food resource overlap, averaging 81 % for sheep (range 68.2-94.4%) and 84% for red kangaroos (range 62.7-98.4%). A high degree of resource overlap between these herbivores has been observed on a number of occasions (Wilson 1991 b, Dawson and Ellis 1994, Edwards et al. 1995), with some authors suggesting that such a high degree of overlap must lead to competition for 103

food (e.g. Wilson 1991a). This conclusion is incorrect. Equating resource overlap with competition can be misleading (Colwell and Futuyma 1971). A high degree of resource overlap may equally be interpreted as an absence of competition (Vandermeer 1972, Strong 1983), which leads to the sharing of the common resource (Belovsky 1986a). One of the conditions of competition is that a resource needed by competitors is in limited abundance, or if resource abundance is not limited then access to the resource must be limited in some way (Schoener 1983). The results of this study indicated that at the herbivore densities recorded, each species was not food limited and that interspecific competition for food did not occur.

At all times sheep and red kangaroos had exclusive resources. A consequence of this is that on the basis of exploitative competition for food alone, neither herbivore can competitively exclude the other from a sympatric area. This conclusion is supported by the observation that red kangaroos occur sympatrically throughout the range of sheep (Caughley 1987a). For competitive exclusion to occur the available resources of one species must completely overlap that of the other, in essence producing an included niche. In this case the herbivore species with the included niche has no exclusive food resources, while the other species has overlapping and exclusive resources. The zero isocline of the species with the included-niche is linear and if the isoclines of the two species fail to intersect, their competitive interaction will result in the competitive exclusion of the included species (Schoener 1974b).

Sheep are potentially the dominant competitor in this assemblage. Although I did not observe competition between sheep and red kangaroos, the modelling approach allows conclusions to be drawn on the relative competitive abilities of the herbivores. Comparing the theoretical allopatric equilibrium densities with the sympatric equilibrium densities for each sampling period indicates that on average sheep are able to potentially reduce the density of red kangaroos by 52.4% (range 29.4-84.8%), while red kangaroos can potentially reduce sheep density by an average 29 .1 % (range 12.5- 38.5%). However, these potential influences must be viewed as theoretical levels, since the density of herbivores needed to produce these changes far exceed the naturally occurring densities of either herbivore under most circumstances. The exception to this last statement may occur when plant biomass is low and at least one of the herbivores is at high density. These conditions occurred during the sheep-red kangaroo competition 104 study of Edwards et al. (1996). During their study localised rainfall fell on their study site (Fowlers Gap Station), while the surrounding properties received little or no rain and remained dry. The rain stimulated the growth of ephemeral forbs and grasses, which consequently attracted large numbers of kangaroos from neighbouring areas. The density of red kangaroos swelled to 35-105 kangaroos/km2, which was a marked increase on the average red kangaroo density of 10-20 kangaroos/km2• During this time mean pasture biomass dropped to 430 kg/ha. Edwards et al. (1996)-found that at this time sheep sympatric with red kangaroos suffered a larger drop in body mass than sheep allopatric with red kangaroos. They concluded that the combined affects of low food abundance and high red kangaroo density culminated in exploitative competition for food.

Although I did not observe competition between sheep and red kangaroos, competition for food between these herbivores may occur. Close examination of the zero-isoclines indicates the density of the herbivores, relative to resource availability, necessary for exploitative competition to occur. Essentially, at plant biomasses greater than 500 kg/ha the potential of competition for food between sheep and red kangaroos is negligible because the density of the herbivores necessary to produce competition approaches unrealistic levels. At plant biomasses between 500 kg/ha and approximately 370 kg/ha competition is more likely to occur, but one of the herbivores must be at higher than average density. At average densities, both species have sufficient resources to allow coexistence without exploitative competition. At plant biomasses less than 370 kg/ha exploitative competition becomes more likely as biomass declines, however the competitive effect will only be small since the dynamics of allopatric and sympatric populations closely converge as plant biomass reaches very low levels.

Based on food intake rates, Caughley (1987b) predicted that exploitative competition for food between sheep and red kangaroos only occurred at plant biomasses less than about 300 kg/ha, because at higher plant biomasses the species are able to satisfy their food requirements. While Caughley predicted competition at similar biomasses to the present study, this method of predicting competition must be used with caution. The model that Caughley used did not take into account the amount of exclusive and overlapping resources of each herbivore, or the likelihood of a competitor gaining a unit of overlapping resource. These factors are the major determinants of 105 exploitative competition (Schoener 1974b, 1976). Similarly, Caughley's (1987b) hypothesis that competition between sheep and red kangaroos would reduce the long term density of kangaroos to about half that attainable when sheep are removed, potentially overestimates the intensity of interspecific competition and its affect on kangaroo population dynamics. The interactive model that Caughley (1987b) used did not take into account overlapping and exclusive resources, and did not include interference competition which will tend to lessen the intensity of competition at low food availability.

In the sheep-red kangaroo system described in this chapter competition for food is most likely to occur at low plant biomass (less than 370 kg/ha}. It is important to note that the predicted allopatric and sympatric equilibrium densities of each herbivore closely converge at plant biomasses less than 500 kg/ha. This implies that phenomena that may be interpreted as evidence of interspecific competition, such as drop in body condition or fecundity, may be more closely related to an individual's ability to harvest food as plant biomass declines regardless of the presence or absence of a putative competitor. Furthermore, it suggests that the measurement of competition using an established technique, such as the controlled removal experiment described in Chapter 4, may require a large number of replicates to increase the power of detecting a competitive effect. In addition, the prevailing conditions probably have a dominant influence on the results of any experiments run in the arid rangelands. This may severely weaken the generality of conclusions if the experiment does not sample the full range of conditions that can be experienced in this environment. This problem must always be kept in mind when interpreting the results of experiments from highly variable environments.

At high plant biomasses (greater than 850 kg/ha), the equilibrium density of sheep that were sympatric with red kangaroos was relatively unaffected by season (Fig. 5.6 a). In contrast, sympatric red kangaroo equilibrium density was much lower in summer than in winter (Fig 5.6 b).This was most likely to be a consequence of the small amount of exclusive food that red kangaroos were found to have in summer. This suggests that during summer, if sheep densities are kept at high levels red kangaroos may suffer from interspecific competition for food. In this study, the density of sheep required to produce a competitive effect exceeded naturally occurring densities, and so 106 no competitive effect was observed (cf Chapter 4). At low plant biomass the equilibrium densities converge, so that there is no longer a seasonal difference in red kangaroo equilibrium density. Regardless of seasonal effects, at times of low food abundance red kangaroos have only a small amount of exclusive resources.

The current justification for culling red kangaroos in the rangelands is to minimise the effect of competition between domestic stock and kangaroos for native pasture (Shepherd and Caughley 1987). The present study indicates that under most conditions, red kangaroos have a negligible effect on the productivity of sheep and that culling at these times is unjustified. During times of drought, culling is justified but significant increases in sheep productivity should not be expected.

This study represents the first attempt to mechanistically model competition between these herbivores. Many of the parameters needed to solve the model are time consuming to measure and difficult to quantify, and consequently make the model too difficult to routinely examine competition between generalist herbivores. This may explain why the model has only been applied to natural populations a few. times (Schoener 1975, Belovsky 1984b, 1986a). Despite these reservations, the theoretical advantages of examining competition using this model allowed me to predict the conditions under which these herbivores compete. I conclude that competition for food between sheep and red kangaroos is rare, and under most conditions does not affect the population dynamics of these herbivores. However, competition may occur during drought when both herbivores are severely food limited. At these times competition is asymmetric with sheep dominating. This conclusion was also reached by Caughley (1987b) and Edwards (1990). However, in contrast to Caughley (1987b ), I conclude that the competitive effect on both species is not severe.

5.5 Appendixes

1. The following appendix gives the solution to the zero-isoclines of the mechanistic model of exploitative competition with partially overlapping resources and a fixed energy input (Schoener 1974b, 1976, 1978). Solving the differential equations (eq.'s 3a and b) for their zero-isoclines gives; 107

(5.8a)

(5.8b)

Using the quadratic formula, the roots are;

(5.9a)

(5.9b)

2. The sympatric equilibrium densities were found by solving the simultaneous equations;

NI=------_..;..(!EI +lo -C1~N2}+~(IE1______+lo -C1~N2}2 +4ClE1~N2_

2C1 and,

(5.10) Chapter 6

Optimal diet choice by sheep and red kangaroos.

6.1 Introduction

Diet choice studies of sheep and kangaroos have largely concentrated on simple descriptions of the proportions of different plant types in the diet. Diet descriptions explain little of the ecology of the studied herbivore, and conclusions about the relationship between diet choice and community ecology are usually unsubstantiated best guesses (Sinclair 1991 ). Predicting diet choice using optimal foraging theory (Stephens and Krebs 1986) is an alternative method of examining diet choice. Optimal foraging theory makes specific predictions of the limits to foraging, and how they may interact to determine diet choice by an individual. In this chapter I have used the technique of linear programming to predict the optimal diet selection of red kangaroos and sheep.

The linear programming model of optimal diet choice (Belovsky 1978) has been used to predict optimal diet choice of generalist herbivores in environments ranging from boreal forest (Belovsky 1978, Schmitz 1990) to prairie grasslands (Belovsky 1986b, Ritchie 1988) and arid shrublands (Belovsky et al. submitted). The linear programming model of optimal diet choice is a well established technique (Belovsky 1994) that can be used to examine the effects of food limitation and environmental variance on diet selection. The model predicts the energy intake of a forager and the amount of each food type consumed. Determining energy intake may provide insights into the fitness of organisms living in an unpredictably variable environment such as the Australian arid zone.

The aims of this chapter were to examine the optimal diet choice of red kangaroos and sheep in an arid shrubland habitat, and determine the effects of temporal and spatial variance in food abundance and quality on optimal diet choice. The herbivores were hypothesised to have a common foraging goal of energy maximisation, and that the diet choice of both herbivores would be sensitive to variation in the same 109 foraging parameters. Furthermore, I hypothesised that domestic sheep would be able to select an optimal diet even though they did not evolve in the Australian arid zone.

6.2 Materials and Methods

6.2.1 The Foraging Model

The optimisation technique of linear programming (Belovsky 1978) was used to predict the diet selected by sheep and red kangaroos. Optimal foraging theory (Stephens and Krebs 1986, Pyke 1984) predicts that the foraging goal of an animal will be either energy maximisation, or time minimisation (sensu Schoener 1971). Accordingly, these herbivores are predicted to select a diet that either maximises energy intake or minimises the time spent feeding. Energy maximisation is the hypothesised goal if fitness (survival and reproduction) is maximised by consuming the greatest amount of energy possible per foraging period. The alternative goal of time minimisation is hypothesised if fitness is maximised by satisfying minimum nutrient requirements as quickly as possible, thereby freeing time for other activities such as caring for young, or searching for mates (Belovsky 1984c).

I hypothesised that sheep and kangaroo foraging was limited by three constraints; feeding time, digestive capacity, and energy requirement. These constraints have been identified as major influences on the diet selection of many other generalist herbivores (Belovsky 1986b, see citations in Table 1 Belovsky 1994). Daily feeding time was the maximum time available per day for an individual to find and crop food. Daily digestive capacity was the maximum wet mass of food that could be passed through the gut per day (Belovsky 1978). Digestive capacity was limited by the size of the digestive organ (the rumen-reticulum of sheep, or the forestomach of red kangaroos), plant bulkiness (wet mass/dry mass ratio), and gut turnover rate. Daily energy requirement was the minimum energy required for growth and reproduction (Belovsky 1984a, 1986b), and was equated with field metabolic rate (FMR). Daily feeding time and daily digestive capacity were upper constraints to the diet selection of these herbivores and could not be exceeded, while daily energy requirement was a lower constraint that had to be exceeded if the herbivores were to satisfy their maintenance, production and reproduction requirements. 110

The constraints were formed into a system of linear equations that could be solved using the mathematical techniques of linear programming (Winston 1991 ). The constraints took the general form,

n C ~ Lll;X; (6.1) i=I

for the feeding time and digestive capacity constraints, or

n C::;; Lll;X; (6.2) i=I for the energy requirement constraint, where C is the constraint value; X; is the amount of food i; a; transposes Xi into the units of the constraint C; and n is the number of food types available.

The linear program of optimal diet choice was solved from data collected from the Sympatric 1 treatment (cf Fig. 4.1, Chapter4).

6.2.1.1 Feeding Time Constraint

Daily feeding time values (min/day) were taken from the literature for red kangaroos (Watson and Dawson 1993) and from unpublished data for sheep (Watson and Dawson in prep.). The feeding time data for both species were collected during a study of diel time-use by these herbivores at Fowlers Gap.

6.2.1.1.1 Cropping Efficiency

Bite sizes (g-dry mass/bite) were collected during the sampling periods (cf Section 5.2.2, Chapter 5). Individual bite sizes, the product of item dry mass and items per bite, were measured following the method ofBelovsky et al. (1991).

Biting efficiency (min/bite) was measured during observation periods. I observed the feeding behaviour of individual herbivores, using either 10X50 binoculars 111 or a 15-60X spotting scope, from between 10 to 100 m away. Biting efficiency was defined as the time taken to harvest 10 consecutive bites of one plant category (i.e. min/10 harvesting bites). This measurement was then converted to min/bite. If an individual switched plant categories before 10 bites were made the data were discarded. Biting efficiency reflects the time taken to find and crop a particular plant category. Cropping efficiency (min/g-dry mass) was then calculated as the quotient of biting efficiency and bite size.

6.2.1.2 Energy Requirement Constraint

Daily energy requirements were estimated using allometric relationships from the literature. Energy requirement always included reproductive requirements because sheep and red kangaroos were breeding at the time of the study. The daily energetic requirement of a red kangaroo was estimated using Green's (1989) regression of field metabolic rate (FMR) on body mass for macropodoids. Sheep daily energetic requirements were estimated using Kleiber's (1947, 1961) estimate of eutherian basal metabolic rate times 1.88 (Blaxter 1962, Moen 1973).

Energy, rather than protein was considered to be the constraining nutrient. While protein intake may be limiting juvenile and subadult growth, adults require relatively less protein as their growth rate slows or asymptotes (McDonald et al. 1988). In most cases an adult's requirements for specific nutrients, such as protein, can be satisfied while foraging for energy (Robbins 1983).

The digestible energy content of each food category was determined from clipped plant biomasses collected during each sampling period. A subsample of 20 samples was taken from each food category. The gross energy content (kJ/g-dry) of each of the subsamples was measured to the nearest 0.1 kJ using a ballistic bomb calorimeter. The in vivo digestibility of each subsample was also estimated using the methods described in Section 6.2.1.3.3. Digestible energy content (kJ/g-dry) of a food type for each sampling period was determined by calculating the quotient of the in vivo digestibility and gross energy content for each subsample. 112

6.2.1.3 Digestive Capacity Constraint

6.2.1.3.1 Gut Capacity

The rumen-reticulum wet mass capacity of sheep was derived from the literature (Parra 1978). Forestomach capacity ofred kangaroos was measured by weighing the contents of the forestomach from individuals shot soon after a feeding period. Nematodes were often present in the stomach contents and were re!lloved before the contents were weighed. The wet mass capacity of the rumen-reticulum of sheep and the forestomach of red kangaroos were chosen because the passage of digesta through these organs is slower than through any other part of the digestive tract (Hume 1982). Thus, the digestive capacity of these herbivores is limited by the capacity of these organs to hold food, and the rate at which digesta is passed through them.

6.2.1.3.2 Passage Rate, In Vivo Digestibility

Food passage rate and in vivo digestibility were measured for three plant species; (i) Medicago polymorpha, a forb, (ii) Eragrostis setifolia, a grass, and (iii) Atriplex vesicaria, a shrub. These species were chosen to represent the three major plant groups eaten by these herbivores, and all have been recorded in significant amounts in the diets of both herbivores (Ellis et al. 1977, Barker 1987, Dawson 1989, Edwards et al. 1995). Red kangaroos and sheep were housed individually in cages (2.0 m W. x 2.0 m D. x 1.5 m H.) with a slatted floor to allow faeces to fall through onto nets laid underneath. The cages were kept under cover in a large shed. Windows in the shed allowed normal light/dark cycles and the ambient temperature was not regulated.

Four sheep (wethers) and four red kangaroos (males) were housed in the pens at Fowlers Gap for the turnover rate study. Sheep were randomly selected from one of the Fowlers Gap flocks. The red kangaroos were raised in captivity in Sydney and were transported to the study site one month before the experiment began. Wild kangaroos were thought to be unsuitable for this type of experiment since they would suffer high levels of post-capture stress, especially in the confines of the cages. If the body mass of an experimental animal dropped by more than 10% of their initial body mass, their data were not included. 113

The three plant species were clipped daily, or every other day, from the study site. The experimental animals were fed a monospecific diet of freshly clipped plants. If there was an excess of food clipped the excess would be kept in plastic bags in a refrigerator and used the next day, otherwise it was discarded. A pre-feeding period of 14 days was made prior to the measurement of passage rate and in vivo digestibility. This period was long enough to allow the gut microbes to adjust to the new diet (Mothershead et al. 1972, Robbins 1983). Feed and water were available ad libitum throughout the experiment, and were checked several times per day. Following the pre feeding period a chromium marker was fed to the herbivores and faeces collected at 2 to 4 hourly intervals over the next five days. From these samples gut passage rate and digestibility were measured.

The chromium marker was made by mordanting sodium di chromate ( VI) dihydrate (N~Cr2O7.2H20) onto approximately 100 g of the freshly clipped vegetation, following the method ofUden et al. (1980). The mordanted feed was mixed with an equivalent mass of fresh feed and presented to the herbivores for one hour. The start of this one hour period was referred to as time zero. Collected faecal samples were dried to constant weight at 100 °C. Mass of feed consumed (g-dry/day) was calculated from the difference between the amount fed and the amount spilled or not eaten per day. Wet mass was converted to dry mass by dividing by the wet mass/dry mass ratio for each plant species (n = 10). In vivo dry matter digestibility (IVDMD) was calculated from;

dry mass of food-dry mass of faeces IVDMD = ------ (6.3) dry mass of food

Subsamples of dried faeces were taken from each sample and chromium concentration was measured by atomic absorption using a Varian Spectra AA-20 (Varian Techtron Pty Ltd, Springvale, Australia).

6.2.1.3.3 Laboratory Analysis

I determined the in vitro solubilities of clipped plots and bite sizes using the hydrochloric acid (HCl) in pepsin technique (Tilley and Terry 1963) described in Section 5.2.2 of Chapter 5. In vitro solubilities were converted to in vivo digestibilities 114 using the regression equations derived from the in vitro solubility values of Mpolymorpha, E.setifolia and A. vesicaria.

To account for any potential differences in quality between the eaten bite (which is no longer available) and the matched bite, an estimate of eaten bite quality was calculated by;

(6.4)

where Eb is the solubility of the eaten bite; Er is the solubility of the eaten stub; Mb is the solubility of the matched bite; and Mr is the solubility of the matched stub.

6.2.2 Vegetation Sampling

I measured vegetation biomass by clipping 0.25 m2 plots at each sampling period. Fifty two quadrats were clipped during the winter 1989 sampling period, and 44 quadrats were clipped for all other sampling periods. Clipped vegetation was separated into the categories forb, grass or shrub. Forbs were classified as dicotyledonous broad leaved non-woody plants, other than grass and grass-like plants. Grasses were classified as monocotyledonous narrow-leaved non-woody plants, and shrubs were dicotyledonous woody plants capable of growing to about 2 m in height (Cunningham et al. 1992). Clipped plots were chosen systematically at 500 m intervals along transect lines that ran through the study site. Clipped plants were separated at collection and later oven-dried at 70°C for 48 hours. Samples were weighed after drying to the nearest 0.1 g.

Plant wet mass/dry mass ratios were measured from clipped plants which were weighed before and after drying at 70°C for 48 hours. Plants species selected were those seen to be eaten during the observation periods. The wet to dry mass ratio represents the "fill" of a plant category in the stomach or rumen. Belovsky et al. (submitted) noted that some plants in this environment may absorb water from the gut once they have been consumed by a herbivore. If a correction for the increase in plant wet mass/dry mass ratio is not made then the fill of that plant category will be underestimated. Belovsky et al. (submitted) soaked plants in a water bath for 24 hours. After the plants were removed from the water, blotting paper and air drying were used to remove surface 115 water. The plants were then weighed to determine wet mass, and subsequently dried to determine dry mass. The wet/dry mass ratio was then calculated in the normal way. Belovsky et al. (submitted) determined that rehydrated forbs had a mean wet/dry mass ratio of 1.59 ( ± 0.35 (SD), N = 4), grasses a mean of 1.90 ( ± 0.42, N= 4) and shrubs a mean of2.24 (± 0.38, N= 4). Following the methods ofBelovsky et al. (submitted), I assumed that these plants would absorb water from the gut if its wet/dry mass ratio were less than the rehydrated ratio. Consequently, if the respective ratios of plants clipped fresh from the field were less than the ratios of rehydrated plants, then the wet/dry mass ratio used in the linear program of optimal diet choice was increased to the rehydrated amount.

The spatial distribution within and between plant categories was determined each time the linear program of diet choice was solved. It was important to determine the distribution of food types as this has a major influence on the searching strategy of the forager (Belovsky et al. 1989). The skewness coefficient of each plant type was determined from clipped plot samples. A positive skewness coefficient indicates a patchy distribution within each plant type (Belovsky 1986b). I also calculated Spearman Rank correlations for association between plant types within each clipped plot. A negative correlation indicates that plant types tend to occur in different areas or patches.

6.2.3 Model Predictions and Analyses For each sampling period I calculated the diet of an energy maximising herbivore, a time minimising herbivore and an unselective herbivore. These predicted diets were compared with the observed diet determined by identification of undigested plant fragments in the faeces of these herbivores after each plant category was corrected for its relative in vivo digestibility (see below).

The linear program of diet choice was solved using the simplex algorithm (Winston 1991). The solution of the algorithm predicts the amount (g-dry mass) of each food category that should be consumed by an average sized adult of each species, if the herbivores are to satisfy their foraging goal. In addition, the algorithm predicts the digestible energy content of the diet if the foraging goal is energy maximisation, or feeding time if the goal is time minimisation. A new linear program was parameterised for each herbivore at each sampling period. 116

The solution to the simplex algorithm does not include an estimate of variance in predicted diet choice. The solution assumes that foragers select their diet based only on the mean of each parameter, and that the variance surrounding the mean is unimportant. However, it has been found that generalist herbivores will select a range of items from a food type if they exceed a minimum nutrient or size limit (Belovsky 1981a), rather than just the mean value for a particular food type. In addition, Ritchie (1988) found in an optimal diet choice study of ground squirrels that there was considerable variance in the ability of individual's to select an optimal diet. Therefore, the solution of the linear program should reflect environmental and individual herbivore variance.

It was also important to solve the model over an appropriate time scale. For each solution the parameters of the model were measured or derived over approximately one month of data collection. The parameter means and standard deviations reflect the large amounts of uncontrollable spatial and temporal variance between such things as the feeding behaviour of individual animals which were observed, the mix of plant species that made up each food category, and variation in food abundance over different parts of the study site. In addition, the faecal samples from which the observed diet was estimated were taken from different individuals over the month in which the model's parameters were collected. Therefore, the solution to the model must also include environmental and individual heterogeneity over an appropriate time scale. Consequently, I solved the diet on the basis of a herbivore's average daily diet over a one month time period.

The linear program model of optimal diet choice was solved using Monte Carlo simulation methods to incorporate environmental and individual heterogeneity in the model's parameters, and followed the method of Ritchie (1988) with some small modifications. Used in this way Monte Carlo methods can generate a mean and confidence interval for the predicted diets (Manly 1991, 1992). For each iteration of the simulation new parameter estimates were taken as a random draw from a normal distribution of one standard deviation around the mean of each variable. The steps in the algorithm (Ritchie 1988, Schmitz 1990) can be summarised as: 117

1. Form a normal distribution around the mean of each parameter value using one standard deviation of the mean. 2. Take one random sample from each distribution as the parameter value to use in the simplex algorithm. 3. Solve the linear program. 4. Repeat Steps Two and Three 30 times to estimate diet choice over one month. 5. Calculate the mean of each food category from the 30 simulations (i.e. the mean daily diet over the month). 6. Repeat step Four 100 times to form 100 predicted diets. 7. Repeat steps One to Four for each species and sampling period.

I made a sensitivity analysis of the linear program to determine which constraints had the greatest influence on optimal diet choice. This was done by making the parameter values of all constraints, except the one of interest, invariant; while the parameters of the constraint of interest were allowed to vary according to a random draw from its standard deviation around the mean. I again used the Monte Carlo method to generate a mean for the optimal diet.

I compared the solution of the linear program with the actual diet selected by each herbivore species for each sampling period. The actual diet was determined by measuring the frequency of each food type in the faeces of the herbivores. Eight independent faecal samples were collected from each herbivore species at each sampling period. I only collected fresh faeces that had been passed on the day of collection. The sampled faeces were prepared by following the method described by Ellis et al. (1977), with one modification. I reduced the time that samples were bleached in domestic bleach (5% sodium hypochlorite) from overnight to two hours. This modification reduced the chance of the bleach differentially digesting plant fragments with thin cells walls {T .J. Dawson pers. comm.), which would consequently be underestimated when the samples were analysed. The frequency of each plant category was measured using the point-quadrat technique suggested by Norbury (1988). Two replicate slides were made from each diet sample, from which at least 100 plant fragments were identified.

The null diet is the expected diet choice of a herbivore that feeds unselectively and consumes food items at random from the environment. The proportion of plant 118 categories in the diet of a herbivore that feeds unselectively will be equal to the relative abundance of each plant category in the environment. The null diet for each sampling period was equated with the relative proportion of each plant category in the clipped plots. Using Monte Carlo methods I generated a set of 100 null diets for each sampling period. The null diet set was formed from 100 random draws from a normal distribution around the mean ( ± lSD) biomass of each plant category. The simulated plant biomasses of each iteration were then converted into percentages of total plant biomass.

6.2.4 Statistical Analyses For each sampling period I used Monte Carlo methods to compare the level of agreement between the observed diet of each herbivore with the diet predicted by the linear programming model, and the null diet. However, this time the Monte Carlo methods were not used to determine the mean and confidence interval of the predicted diet, but to compare the level of agreement of the predicted diet and the observed diet against a randomly chosen diet and the observed diet. I hypothesised that if five percent, or more, of the randomly selected diets provided a closer fit to the observed diets than the predicted diets, then there was a high probability that the level of agreement between the predicted and observed diets was arrived at by chance. Alternatively, ifless than five percent of the randomly chosen diets provided a closer fit to the observed diets than the predicted diets, then I concluded that there was a high probability that the predicted diet was not arrived at by chance. The random diet was created by selecting the percentage of each food category ( forb, grass or shrub) in a diet selected from a random draw from a uniform distribution. For each herbivore species and each sampling period I generated a new set of 1000 random diets. The steps of the test can be summarised as;

1. Calculate the difference between each food category of the first individual of the observed diet and the first diet predicted by the linear programming model, or the null diet set. 2. Calculate the difference between each food category of the first individual of the observed diet and the first diet of the randomly generated diet set. 3. Compare the differences between observed/predicted and observed/random diets. 4. Repeat step Two for every random diet (N = 1000). 119

5. Tally the number of random diets that provide an equal or closer fit to the observed diet than the predicted diet. (Note that the difference between the observed/random diet must be less than or equal to the difference between the observed/predicted diet for all food categories). 6. Repeat steps One to Five for each observed diet (N = 8) and predicted diet (N = 100).

In total 800 000 comparisons were made between the observed diet and the predicted and random diets for each herbivore species at each sampling period. The calculated significance level of the test represents the probability that agreement between the predicted diet and the observed diet was arrived at by chance.

In addition to the Monte Carlo test, I used the Proportional Similarity Index (PS; Feinsinger et al. 1981) to measure dietary overlap between the predicted diets and the observed diet for each herbivore at each sampling period. The PS index measures the degree of association between two data sets that share a common basis (i.e. plant categories). This analysis should indicate if there was a dominant feeding strategy. The index ranges between 1 (complete overlap) and O (no overlap), and can be represented as· '

P s = 1 - o.s I: (I Pi - Qi I) (6.5)

where P; is the proportion of food category i in the observed diet; and Q; is the proportion of food category i in the predicted diet.

6.2.4.1 Sensitivity Analyses

The purpose of the sensitivity analyses was to determine which constraint or constraints had the greatest influence on the optimal solution. The optimal diet was defined as the energy maximising diet for both herbivore species because energy maximisation seemed to be the dominant feeding goal. From left to right the bars (Figs 6.6 and 6.7) represent; 1) the observed diet, 2) energy maximising diet; 3) the diet predicted when all parameters of the three constraints are held constant; 4) the diet 120 predicted when the feeding time constraint was allowed to vary while the energy and digestive capacity constraints were held constant; 5) the diet predicted when the digestive capacity constraint was allowed to vary while energy and feeding time constraints were held constant; and 6) the diet predicted when the energy constraint was allowed to vary while the feeding time and digestive capacity constraints were held constant.

6.3 Results

6.3.1 The Foraging Model

6.3.1.1 Feeding Time Constraint

The daily feeding time of a red kangaroo in summer and winter was 459 ( ± 69) and 727 {± 109) min/day respectively (Watson and Dawson 1993). The daily feeding time, excluding time for rumination, of a sheep in summer and winter was found to be 276 {± 41) and 581 {± 87) min/day respectively (Watson and Dawson in prep.). Watson and Dawson (1993, in prep.) did not supply an estimate of the standard deviation of the mean of daily feeding time. I assumed that the standard deviations were equal to 15% of the mean. This level of deviation was assumed to be representative of a moderate level of variance in the parameter, and was intended to be a modest estimate that would not strongly bias the solutions of the model. As Belovsky (1994) pointed out, care must be taken to accurately represent uncertainty in the model's parameters, since a conservative (large) variance estimate may overwhelmingly bias the solution of a linear program.

6.3.1.2 Energy Constraint

Using Green's (1989) equation for the prediction ofFMR as a function of body mass, I predicted that a 30 kg red kangaroo would have daily energy requirement of 5534 {± 830) kJ/day. Using Kleiber (1961) and Blaxter (1962) I predicted that a 60 kg sheep would have a daily energy requirement of 11359 ( ± 1704) kJ/day. It was not possible to make an accurate estimation of the standard deviation of the mean of each FMR so, I assumed that the standard deviations were equal to 15% of the mean. 121

6.3.1.3 Digestive Capacity Constraint

The time taken from ingestion to 50% excretion of the chromium marker was taken as the mean passage rate of the gut. The passage rate data are summarised in Table 6.1. In summary, sheep had a mean passage rate of 33.3 hours that was approximately 20% faster than red kangaroos, which had a mean passage rate of 41.5 hours. These rates are equivalent to gut turnover rates of 0. 72 time's/day and 0.58 time's/day respectively for sheep and red kangaroos.

Time (h) taken to excrete Sample Size Herbivore Body Mass (kg) Diet 50% ofmarker 90% ofmarker Red Kangaroo 4 29.5 ( ± 11.9) Forb 32.7 (± 9.2) 47.5 (± 9.8) 3 37.5 (±0.7) Grass 59.3 (± 7.8) 76.9 (± 1.4) 1 34.2 Shrub 32.6 47.3 3 33.7(±4.0) Mean 41.5 ( ± 15.4) 57.2 (± 17.0)

Sheep 4 46.7 (± 3.8) Forb 41.0 (± 7.9) 69.0 (± 5.8) 4 42.9 ( ± 4.1) Grass 36.5 (± 2.9) 56.1 (± 5.4) 4 38.8 (± 1.6) Shrub 22.5 (±4.1) 37.2 (± 8.9) 3 42.8 (+ 4.0) Mean 33.3 (± 9.6) 54.1 ( ± 16)

Table 6.1. Digesta passage rates of red kangaroos and sheep. Data are means ( ± SD).

The plot of forestomach capacity (g-wet mass) against body mass (kg) for red kangaroos is presented in Fig. 6.1. A linear regression;

y1 = 210 + 78.6x (6.6)

where y1 is forestomach capacity and x is body mass fitted to the data indicated that the variates were significantly correlated (r= 0. 72, P < 0.001, N = 27). Using this equation, I predicted that a 30 kg red kangaroo would have a forestomach capacity of 2568 ( ± 443) g-wet mass.

The rumen-reticulum capacity of a sheep was predicted using Parra's (1978) regression of total capacity of the gut against body mass, assuming that the rumen reticulum makes up 71.5% of the total capacity wet mass (Parra 1978). Using Parra's equation; 122

Yr= 89.6x1.041s (6.7) where Yr is rumen-reticulum capacity I predicted that a 60 kg sheep will have a total gut capacity of 6530 g-wet mass, and a rumen-reticulum capacity of 4670 ( ± 701) g-wet mass.

rn rn 111 4500 E 4) 14000

~ ·g 3500 a. 111 (.) • .c • 0 3000 111 E • • .s • t/l 2500 • ~ 0 • u. • • 2000 ••

1500 •

1000 •

500

0 0 10 20 30 40 50 60 Body Mass (kg)

Fig. 6.1. The regression of forestomach capacity (g-wet mass) on body mass (kg) of red kangaroos, (y1= 210 + 78.6x, r= 0.72, P < 0.001, N= 27).

Daily digestive capacity was calculated from the product of the rumen-reticulum or forestomach and digesta turnover rate. For a 30 kg red kangaroo I calculated daily digestive capacity to be 1489 (± 609) g-wet mass per day, and for a 60 kg sheep I calculated daily digestive capacity to be 3362 ( ± 1095) g-wet mass per day.

I used regression equations to convert percent in vitro (V1) solubility values into percent in vivo (VV) values. For red kangaroos the regression was VV = 59.2 + 0.44VT, 123 and for sheep the regression was VV = 48.0 + 0.41 VT. The regressions are plotted in Fig. 6.2.

90.------.------,---~--.-----~~------.-----, 85 • • -~ • ~ 80 :0 • ~ 75 l--~~---i:------i CJ 0 §? 70 t 5 = • 65 • ------t------..: ------t 60 • •

55 • 50 45~---~------~---~----~ 34 36 38 40 42 44 46 HCI + Pepsin Digestibility (%)

Fig. 6.2. Regressions relating in vitro solubility (HCl + pepsin) to in vivo digestibility for red kangaroos (circle and unbroken line) and sheep (triangle and broken line).

The parameters that I measured or derived from the literature to solve the linear program of optimal diet choice are presented in Table 6.2 a) and b ). Table 6.2 a Winter Summer Winter Summer Winter Herbivore Parameter 1989 1990 1990 1991 1991 mean SD N mean SD N mean SD N mean SD N mean SD N

Red Forestomach 2568 443 27 2568 443 27 2568 443 27 2568 443 27 2568 443 27 Kangaroo Capacity (g-wet mass)

Gut Turnover Rate 0.58 0.215 3 0.58 0.215 3 0.58 0.215 3 0.58 0.215 3 0.58 0.215 3 (X's/day)

Plant Bulk (g-wet/g-dry) Forb 2.27 0.97 34 1.90 0.65 27 4.30 0.65 14 1.69 0.21 33 2.50 0.97 20 Grass 2.10 0.52 28 1.90 0.42 20 3.61 2.34 9 1.90 0.42 20 2.50 0.68 15 Shrub 3.50 0.90 19 2.24 0.38 20 4.60 1.27 11 2.47 0.83 71 2.52 0.43 30

Feeding Time 727 109 na 459 69 na 727 109 na 459 69 na 727 109 na (min/day) I

Cropping Rate (minlg-dry) Forb 0.459 0.390 20 0.710 0.356 20 0.599 0.489 20 2.66 1.47 16 1.70 0.050 28 Grass 0.906 0.748 20 0.630 0.493 20 1.01 0.483 20 0.991 0.613 20 1.22 0.304 20 Shrub 1.13 0.765 20 0.655 0.531 20 1.03 0.776 11 1.25 0.694 21 1.64 0.460 20

Energy Requirement 4867 730 na 4867 730 na 4867 730 na 4867 730 na 4867 730 na (kJ/day) 2

Digestible Energy of Food (kJ/g-dry) Forb 13.l 3.78 20 13.5 4.61 20 13.5 2.13 20 11.0 3.64 20 13.5 3.12 20 Grass 11.2 4.08 20 12.7 2.71 20 11.9 3.04 20 12.6 1.99 20 11.1 3.34 20 Shrub 13.7 3.57 20 12.4 6.79 20 13.4 3.06 20 13.5 2.56 20 13.5 4.04 20

124 Table 6.2 b Winter Summer Winter Summer Winter Herbivore Parameter 1989 1990 1990 1991 1991 mean SD N mean SD N mean SD N mean SD N mean SD N

Sheep Forestomach 4670 701 na 4670 701 na 4670 701 na 4670 701 na 4670 701 na Capacity 3 (g-wet mass)

Gut Turnover Rate 0.72 0.208 3 0.72 0.208 3 0.72 0.208 3 0.72 0.208 3 0.72 0.208 3 (X's/day)

Plant Bulle (g-wet/g-dry) Forb 2.27 0.97 34 1.90 0.65 27 4.30 0.65 14 1.69 0.21 33 2.50 0.97 20 Grass 2.10 0.57 28 1.90 0.42 20 3.61 2.34 9 1.90 0.42 20 2.50 0.68 15 Shrub 3.50 0.90 19 2.24 0.38 20 4.6 1.27 11 2.47 0.83 71 2.52 0.43 30

Feeding Time 581 87 na 276 41 na 581 87 na 276 41 na 581 87 na (min/day) 4

Cropping Rate (min/g-dry) Forb 0.252 0.164 20 0.307 0.203 20 0.235 0.132 20 0.300 0.208 20 0.711 0.392 101 Grass 0.527 0.224 15 0.268 0.167 20 0.531 0.453 20 0.250 0.160 20 0.807 0.436 20 Shrub 0.383 0.250 19 0.271 0.312 20 0.537 0.407 20 0.260 0.176 21 0.601 0.346 14

Energy 11359 1704 na 11359 1704 na 11359 1704 na 11359 1704 na 11359 1704 na Requirement (kJ/day) s

Digestible Energy of Food (kJ/g-dry) Forb 11.6 2.07 20 11.5 5.97 20 9.8 1.81 20 10.5 3.13 20 11.4 3.47 20 Grass 9.8 6.31 20 10.2 4.67 20 10.2 2.68 20 11.l 2.03 20 10.5 2.63 20 Shrub 11.9 2.71 20 10.9 3.13 20 11.4 2.85 20 11.7 4.17 20 11.5 3.18 20

125 126

Table 6.2 a and b. The parameters needed to solve the linear programming model of optimal diet choice for a) a red kangaroo of 30 kg body mass, and b) a sheep of 60 kg body mass, at the study site.

I Feeding time derived from Watson and Dawson (1993). 2 Energy requirement derived from Green (1989). 3 Forestomach (rumen) capacity derived from Parra (1978). 4 Feeding time derived Watson and Dawson (in prep.). 5 Derived from Kleiber (1947, 1961 ), Blaxter (1962) and Moen (1973).

6.3.2 Vegetation Sampling The clipped plant biomasses for each sampling period are presented in Fig. 6.3. There was a seasonal effect on the abundance of forbs, with winter months favouring forb growth. Grasses and shrubs did not appear to follow this pattern, the abundance of both categories generally declining from winter 1989 to winter 1991.

700

600 DForb -Cll .c •Grass ---Ol 500 c DShrub (/) (/) 400 Cll E 0 300 iii C 200 -Cll a: 100

0 Winter 1989 Summer 1990 Winter 1990 Summer 1991 Winter 1991 Sampling Period

Fig 6.3. Clipped plant biomass at each sampling period from the study site. Plants were

clipped from 0.25 m2 quadrats.

The skewness coefficients for within plant type distribution indicates that all plant types were patchily distributed(Table 6.3). All plant types had positive skewness coefficients. The distributions of grasses and shrubs were always highly patchy. Forbs were less patchily distributed but were not uniformly or randomly distributed. 127

Plant type Sampling period N Forb Grass Shrub Winter 1989 52 0.37 0.73* 1.15** Summer 1990 69 0.58* 1.01*** 0.92** Winter 1990 82 0.35 0.72** 1.14*** Summer 1991 81 0.72** 0.62* 1.07*** Winter 1991 62 0.90** 0.74** 0.96**

* P < 0.05, ** P < 0.01, *** P < 0.001.

A Spearman Rank correlation of between plant type distribution indicated that all plant types were negatively associated {Table 6.4). These data indicate that all plant types tend to occur in different patches. At most times the negative association between plant types was significant. The skewness coefficient and the Spearman Rank correlation analyses indicate that plant types were patchily distributed, and that patches did not occur together. Therefore, herbivores had to use a spatial non-simultaneous search pattern if they were to feed on all plant types.

Correlation Sampling period N Forb vs Grass Forb vs Shrub Grass vs Shrub Winter 1989 52 -0.69*** -0.19 -0.36** Summer 1990 69 -0.25* -0.27** -0.21 * Winter 1990 82 -0.31 ** -0.30** -0.40*** Summer 1991 81 -0.47*** -0.12 -0.29** Winter 1991 62 -0.19 -0.27* -0.26*

6.3.3 Model Predictions and Analyses The dietary percentages ( ± SD) predicted and observed for each herbivore at each sampling period are presented in Table 6.5.

Herbivore Sampling Plant category Energy Time minimiser Null diet Observed diet species period maximiser

Red kangaroo Winter Forb 76.4(± 7.6) 60.9(± 9.1) 3~5(± 5.0) 46.1(± 6.8) 1989 Grass 23.6(± 7.6) 0.1(± 0.5) 41.4( ± 7.9) 40.4(± 7.7) Shrub 0 39.0(± 9.1) 23.4( ± 7.6) 13.5(± 3.9) Energy intake 9091(± 161) 4993(±46) (kJ/day) Feeding time 400(± 27) 269(± 22) (min/day)

Summer Forb 37.3( ± 7.8) 45.0(± 8.9) 12.3(± 3.8) 33.5(± 4.5) 1990 Grass 47.0(± 7.7) 31.8(± 8.8) 44.6( ± 14.0) 53.3(± 6.3) Shrub 15.6(± 5.1) 23.2(± 8.1) 43.2(± 15.5) 13.3(± 4.5) Energy intake 9984( ± 147) 4893(± 56) (kJ/day) Feeding time 501(± 7) 241(± 5) (min/day)

Winter Forb 27.2(± 7.2) 60.9(± 7.9) 28.5( ± 5.9) 25.5( ± 10.2) 1990 Grass 69.1(± 7.36) 31.7(± 7.5) 41.7(± 6.7) 59.7( ± 12.6) Shrub 3.7( ± 3.0) 7.4( ± 4.4) 29.9(± 9.1) 14.8(± 7.8) Energy intake 5267(± 95) 4869(± 51) (kJ/day) Feeding time 378(± 19) 286(± 16) (min/day)

Summer Forb 0 0 5.8( ± 1.8) 6.9(± 3.0) 1991 Grass 87.0(± 5.7) 45.8( ± 8.7) 71.0(± 9.2) 77.2( ± 7.3) Shrub 13.0(± 5.7) 54.2(± 8.7) 23.2(± 8.3) 15.9( ± 7.3) Energy intake 6168(± 110) 5008( ± 44) (kJ/day) Feeding time 495( ± 10) 426(± 11) (min/day)

Winter Forb 4.9(± 2.5) 25.6(± 7.6) 18.8(± 8.9) 17.9(± 4.3) 1991 Grass 76.6(± 5.0) 44.5(± 8.3) 49.5( ± 13.2) 56.7(± 3.2) Shrub 18.5(± 5.2) 29.9(± 7.7) 31.7(± 10.5) 25.4(± 4.2) Energy intake 6825(± 73) 4945(± 49) (kJ/day) Feeding time 760(± 7) 580(± 8) min/da 129

Herbivore Sampling Plant category Energy Time minimiser Null Observed diet se.ecies e.eriod maximiser diet

Sheep Winter Forb 86.8(± 4.0) 67.3( ± 8.0) 35.2(± 5.0) 79.2(± 12.8) 1989 Grass 13.2(± 4.0) 2.1(± 2.7) 41.4( ± 7.9) 9.9(± 12.9) Shrub 0 30.6(± 8.2) 23.4(± 7.6) 11.0( ± 3.4) Energy intake 18026(± 243) 11592( ± 106) (kJ/day) Feeding time 452( ± 19) 295(± 12) (min/day)

Summer Forb 23.3(± 7.7) 54.3(± 9.0) 12.3(± 3.8) 28.6( ± 13.8) 1990 Grass 27.0(± 7.3) 14.9(± 6.2) 44.6( ± 14.0) 38.9(± 7.9) Shrub 49.7(± 7.7) 30.8(± 8.5) 43.2(± 15.5) 32.5( ± 12.4) Energy intake 13003( ± 377) 11326( ± 142) (kJ/day) Feeding time 324(± 9) 286(± 8) (min/day)

Winter Forb 2.2(± 1.6) 2.1(± 1.9) 28.5(± 5.9) 80.6(± 8.9) 1990 Grass 84.1(± 6.2) 84.8(± 5.6) 41.7(± 6.7) 6.8(± 6.4) Shrub 13.7(± 5.7) 13.l(± 5.4) 29.9( ± 9.1) 10.6( ± 4.7) Energy intake 9926( ± 164) 9913(± 181) (kJ/day) Feeding time 500(± 11) 507(± 17) (min/day)

Summer Forb 3.81(± 3.4) 3.24( ± 3.3) 5.8(± 1.8) 3.0(± 2.5) 1991 Grass 46.3(± 8.8) 28.3(± 8.8) 71.0(± 9.2) 48.8( ± 6.4) Shrub 49.9(± 8.6) 68.4(± 9.0) 23.2(± 8.3) 48.2( ± 6.7) Energy intake 13909( ± 240) 11528( ± 113) (kJ/day) Feeding time 310(±6) 254(± 6) (min/day)

Winter Forb 10.2( ± 5.2) 35.2(± 8.0) 18.8(± 8.9) 22.3( ± 6.0) 1991 Grass 0.3(± 0.9) 3.1(± 3.0) 49.5( ± 13.2) 3.4(± 3.8) Shrub 89.5(± 5.3) 61.6(± 8.37) 31.7(± 10.5) 74.3(± 3.8) Energy intake 11748( ± 217) 11492( ± 105) (kJ/day) Feeding time 622( ± 11) 643(± 15) min/da

Table 6.5. The predicted energy maximising (N = 100), time minimising (N = 100), null (N= 52 for winter 1989, N= 44 for all others) and observed (N= 8) mean(± SD) diets for red kangaroos and sheep for the each sampling period. The plant categories in the diet are forb, grass and shrub, and data are presented as percentage of a category in the diet. In addition, the energy intake (kJ/day) and feeding time (min/day) are presented for the energy maximising and time minimising diets. 130

The results of the Monte Carlo test for similarities between the predicted (energy maximising, time minimising and null) diets and the observed diets {Table 6.6) indicated that the energy maximising was most commonly not different from the observed diet. However, when plant biomass approached low levels{< 500 kg/ha) the energy maximising strategy became indistinguishable from the alternative strategies of time minimisation or selecting a null diet. At this time the predicted diets converged for both herbivore species and suggests that this may be a general phenomena faced by generalist herbivores when available food becomes rare.

Herbivore Sample Period Energy Maximiser Time Minimiser Null Diet Diet Diet

Red Kangaroo Winter 1989 P= 0.143 P= 0.166 P= 0.127 Summer 1990 P= 0.017 * P=0.066 P= 0.122 Winter 1990 P= 0.049 * P= 0.124 P=0.072 Summer 1991 P= 0.029 * P= 0.144 P= 0.027 * Winter 1991 P= 0.059 P=·0.032 * P= 0.041 *

Sheep Winter 1989 P= 0.044 * P=0.063 P= 0.355 Summer 1990 P= 0.058 P= 0.100 P=0.111 Winter 1990 P=0.186 P= 0.179 P=0.418 Summer 1991 P=0.010* P=0.032 * P= 0.027 * Winter 1991 P= 0.022 * P= 0.027 * P=0.047 *

On one occasion for each herbivore no predicted diet provided a close match for the observed diet. In winter 1989 there was no agreement between observed and predicted diets for red kangaroos, while at this time there was close agreement between the energy maximising and the observed diet for sheep. In winter 1990 there was no 131 agreement between the observed and predicted diets for sheep, while for red kangaroos the energy maximising diet was not different from the observed diet. Closer examination of the constraints at these times may reveal the bases of these anomalous results.

For red kangaroos in winter 1989 the majority of the predicted energy maximising and time minimising diets consisted of forb, 76.4% and 60.9% respectively. At this time the cropping efficiency of forb (0.459 min/g-dry) was much more efficient than for grass (0.906 min/g-dry) or shrub (1. 13 min/g-dry). At the same time there was only a relatively small difference between the bulk values of forb (2.27 g-wet/g-dry), grass (2.10 g-wet/g-dry) and shrub (3.50 g-wet/g-dry). These differences might explain why the alternative feeding strategies predicted a large amount of forb consumption. If energy maximisation were the goal then forbs do not limit feeding time (they can be cropped efficiently), have a relatively low bulk value, and have a much higher digestible energy content than grass (13.1 kJ/g-dry for forb, 11.2 kJ/g-dry for grass) and while not as energy rich as shrub (13.7 kJ/g-dry) forbs are not handicapped by a relatively weak cropping efficiency and a high bulk value. For the alternative feeding strategy of time minimisation the large amount of forb in the diet can be explained from the basis that they could be quickly cropped and were relatively energy rich. The lack of agreement between the null diet and the observed diet indicates that red kangaroos were not selecting food randomly from the environment. There are three main reasons why neither the energy maximising or time minimising solutions explained diet choice of red kangaroos in winter 1989. First, red kangaroos do not attempt to optimise their diet choice. This potential reason can be rejected because for all other sample periods red kangaroos appeared to follow a goal energy maximisation or time minimisation. Second, that I did not include an important constraint to red kangaroo foraging in the linear program. I also reject this explanation for the reasons given previously. Third, that I overestimated the cropping efficiency of forb. Including an overestimate of any parameter would potentially bias the solution to the linear programming model of diet choice. In this case any overestimation of forb cropping efficiency would strongly bias the solution to the model because of its associated low bulk and high energy content. While the failure of the linear programming model at this time remains unresolved, I suspect that the overestimated cropping efficiency was due to the inclusion of too many measurements of the bite mass of a rare plant. 132

The linear programming model of diet choice failed to predict sheep diet choice in winter 1990. In addition, sheep did not randomly select their diet. At this time the solutions to the alternative goals of the linear programming model were extremely similar {Table 6.5). It is also important to note that neither solution provides an energy intake sufficient to satisfy an individual's requirements for maintenance, growth and reproduction. Of the three potential reasons listed in the previous paragraph to explain these anomalous results I again rejected the first two reasons because of the close agreement at other times between the predictions of the linear programming model and the observed diet. However, at this time the forb cropping efficiency parameter did not appear to be biased. Instead it appeared that the digestible energy content of forb was underestimated. Comparing the digestible energy content of forb from the winter 1990 sample (9.8 kJ/g-dry) with the digestible energy content of forb during the other winter samples (1989, 11.6 kJ/g-dry; 1991, 11.4 kJ/g-dry) indicates that I may have underestimated the energy content of forb for winter 1990. Another unusual feature of the constraint parameters during winter 1990 was the very high bulk values of all plant categories. The bulk values were higher than at any other sampling time and would have had the effect of rapidly filling the rumen, and potentially limiting food intake and ultimately energy intake. The concurrence of the daily energy intakes and feeding times of the energy maximising and time minimising solutions suggests that this may have occurred. In constructing the digestive capacity constraint I assumed that plant bulk was independent of herbivore species (after Belovsky 1986b), therefore I could use the same values for both herbivore species. Under most conditions this assumption appears to be realistic, however under extreme conditions this assumption may no longer be valid. During winter 1990 sheep may have selected against plants with high food bulk. The method I used to construct the food bulk values in the digestive capacity constraint would have overestimated the bulk value of food chosen by sheep, leading to a bias in the solutions to the linear programming model. Why the linear programming model did not work on these occasions, when it did at other times, remains unresolved and awaits further experimentation. The problems I encountered at these times highlights the need to carefully measure all parameters of the model.

The results of the PS index {Table 6.7) support the conclusion that under most circumstances red kangaroos and sheep follow a feeding strategy of energy maximisation. The energy maximising solution provided the greatest overlap between 133 predicted and observed diet for both herbivores from winter 1989 to summer 1991. In the last sampling period, winter 1991, the time minimising solution provided the greatest degree of overlap with the observed diet for both herbivore species. However, the energy maximising solution also had a high degree of overlap with the observed diet and was only marginally less than the time minimising diet overlap. 134

Herbivore Sample Period Diet Overlap Within Overlap Between

Red Kangaroo Winter 1989 Emax 0.909( ± 0.063) 0.688( ± 0.089) Tmin 0.891( ± 0.070) 0.585( ± 0.063) Null 0.861 ( ± 0.077) 0.500( ± 0.077) Observed 0.889( ± 0.054) na

Summer 1990 Emax 0.878( ± 0.063) 0.881(± 0.054) Tmin 0.850( ± 0.077) 0. 767( ± 0.089) Null 0.824( ± 0.141) 0.475( ± 0.083) Observed 0.907( ± 0.044) na

Winter 1990 Emax 0.895( ± 0.054) 0.827( ± 0.100) Tmin 0.882( ± 0.063) 0.628( ± 0.114) Null 0.813(±0.141) 0.584( ± 0.083) Observed 0.821( ± 0.094) na

Summer 1991 Emax 0.931( ± 0.044) 0.873( ± 0.063) Tmin 0.897( ± 0.058) 0.611(± 0.104) Null 0.829( ± 0.122) 0.709(± 0.144) Observed 0.903( ± 0.070) na

Winter 1991 Emax 0.922( ± 0.031) · 0.790( ± 0.044) Tmin 0.860( ± 0.063) 0.844( ± 0.063) Null 0.808(± 0.109) 0. 725( ± 0.077) Observed 0.926( ± 0.031) na

Sheep Winter 1989 Emax 0.950( ± 0.031) 0.837(± 0.083) Tmin 0.891( ± 0.089) 0. 768( ± 0.089) Null 0.861 ( ± 0.077) 0.173( ± 0.130) Observed 0.844( ± 0.126) na

Summer 1990 Emax 0.866(± 0.063) 0.778(± 0.114) Tmin 0.861(± 0.070) 0.683(± .0104) Null 0.824(±0.141) 0.582( ± 0.122) Observed 0.801(±0.100) na

Winter 1990 Emax 0.919(±0.044) 0.185( ± 0.077) Tmin 0.922( ± 0.044) 0.183( ± 0.077) Null 0.813(±0.141) 0.159( ± 0.089) Observed 0.886( ± 0.063) na

Summer 1991 Emax 0.876( ± 0.063) 0.891( ± 0.054) Tmin 0.876( ± 0.070) 0. 773( ± 0.100) Null 0.829(± 0.122) 0.771(± 0.063) Observed 0.904( ± 0.044) na

Winter 1991 Emax 0.932( ± 0.031) 0.839( ± 0.054) Tmin 0.877( ± 0.063) 0.842( ± 0.083) Null 0.808( ± 0.109) 0.619(± 0.118) Observed 0.913(± 0.031) na 135

6.3.3.1 Sensitivity Analyses

I made a graphical analysis of the results from the linear program sensitivity analysis. The analyses are presented as stack histograms, for red kangaroos Figs 6.4 a-d, and for sheep Figs 6.5 a-d.

Sensitivity analyses of the constraints of the linear programming model can be used to indicate which constraints are exerting the greatest influence on diet choice. Sensitivity of the solution of the model to a particular constraint indicates that the constraint has a dominant affect on the solution, and that changes in the parameters of the constraint will be expressed as a change in predicted diet choice. Just as importantly sensitivity analyses can show which constraints have no effect on optimal diet choice. In this case, variance in the parameters of the constraint do not change the optimal solution of the model. For example, we might expect that in summer when the daily feeding time of both herbivores is at a minimum that the feeding behaviour of herbivores will be most sensitive to the time constraint. In summer plant bulk values may also be low due to the drying effect of the sun, so that herbivore diet choice is less likely to be limited by digestive capacity. At this time a sensitivity analysis would indicate that the feeding time constraint exerted a dominant affect on diet choice, while the digestive capacity constraint had no effect on diet choice. The sensitivity of the herbivores feeding behaviour to these constraints is likely to be reversed in winter when daily feeding time is at a maximum and foods often have high bulk values. While sensitivity of the optimal solution of the model to the time and digestive capacity constraints might be expected to change on a seasonal basis, variance in the energy constraint would always be expected to exert an effect on the solution to the model. The optimal solution is always dependent 136 on the slope of the energy constraint plane. The only exception to this occurs when the energy constraint is "anchored" by an intersection with one of the upper constraints and the slopes of the upper constraint and the energy constraint are very different (e.g. in summer 1991 for red kangaroos, Fig. 6.4 c).For red kangaroos in summer 1991 the time constraint intersects the energy requirement constraint because of the very low cropping efficiency of forbs at this time (2.66 min/g-dry). The result of this intersection is to discount the affect of variance in the energy constraint on the solution to the model. A similar result emerged from the sensitivity analysis of sheep optimal diet choice in winter 1991 (Fig. 6.5 d). This time the insensitivity of the model's solution to the energy constraint occurred because the time and energy constraints were very close to one another. The close proximity of the constraints led to virtually identical energy maximising and time minimising solutions. However, these situations can be regarded as exceptions to the norm. In most situations variance in the energy constraint will affect the optimal solution to the model.

A common pattern emerged from the sensitivity analyses; both herbivore species were sensitive to the time constraint in summer and sensitive to the digestive capacity constraint in winter. In addition, the optimal solution (for a feeding strategy of energy maximisation) was nearly always sensitive to variance in the energy constraint. These results suggest that these herbivores are sensitive to seasonal changes in the constraints to their foraging, and that they can adjust their diet choice to optimise their energy intake during foraging periods. Frequently, only one of the upper constraints to diet choice acts at any one time, but even when all three constraints exert a equal affect on diet choice (e.g. red kangaroos in winter 1991) herbivores can still approach optimal diet selection. 137

6.4 a) red kangaroo, summer 1990

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6.4 b) red kangaroo, winter 1990

100%

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6.4 c) red kangaroo, summer 1991

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6.4 d) red kangaroo, winter 1991

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Figs 6.4 a)-d). Sensitivity analyses of red kangaroo optimal diet choice, for a feeding goal of energy maximisation. Graphs are; a) summer 1990, b) winter 1990, c) summer 1991, and d) winter 1991. Winter 1989 analysis is not presented because the linear programming model failed to predict observed diet choice. 139

6.5 a) sheep, winter 1989

100%

90%

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70% ~ 0 60% 0 50% oShrub C -Q) ~ •Grass Q) 40% a. aForb 30%

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6.5 b) sheep, summer 1990

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0% (I) Ill c i:S cc ·ro !: Q) ~~ 11) - C Ill c ..0 0 C 0 .~ ~Q) U 0 Ill u"' ..0 u Q) > 0 E i= 140

6.5 c) sheep, summer 1991

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70% .; c 60% 0 c., 50% oShrub •Grass .,~ 40% C1. aForb 30%

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6.5 d) sheep, winter 1991

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20%

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0% (I) c cc "iii s -~ !:; Q) ~ en ~:o 0 C 0 -~ l) 0 l) l) "' Q) > E i=

Figs 6.5 a)-d). Sensitivity analyses of sheep optimal diet choice, for a feeding goal of energy maximisation. Analyses are a) winter 1989, b) summer 1990, c) summer 1991, and d) winter 1991. Winter 1990 analysis is not presented because the linear programming model failed to predict observed diet choice. 141

6. 4 Discussion This study examined the diet selection and foraging goals of two arid zone generalist herbivores; the native red kangaroo and the introduced domestic sheep. I hypothesised that the foraging behaviour and diet selection of these herbivores would be consistent with the predictions of optimal foraging theory, and that they would attempt to either maximise energy intake or minimise feeding time while satisfying minimum energy requirements during foraging periods. I examined optimal diet selection over three winters and two summers. Food abundance varied greatly from a maximum of 1556 kg/ha in winter 1989 to a minimum of 380 kg/ha in winter 1991. Using optimal foraging theory I was able determine the effects of the constraints on the diet choice of both herbivores under extreme temporal variability in food resources. Furthermore, I hypothesised that domestic sheep would be able to select an optimal diet even though they did not evolve in the Australian arid zone.

6.4.1 Foraging Goal At most times red kangaroos and sheep followed or closely approached a foraging goal of energy maximisation. This finding supports the conclusion of many other tests of optimal diet choice by generalist herbivores (Belovsky 1978, 1984a, 1986b, Ritchie 1988, 1990, Schmitz 1990, Forchhammer and Boomsma 1995). One potential reason for sheep and red kangaroos to follow a goal of energy maximisation in this environment is that food abundance varies unpredictably (Caughley 1987b). A herbivore that could exceed its energy requirements and store the excess would be able to draw on that reserve of energy during times when food abundance and quality were so low that energy requirements could not be met. However, it was not possible to determine whether this was the objective for following a goal of energy maximisation, and elucidating the reason behind the feeding goal of these herbivores requires further work.

As food abundance declined the predicted diet of the alternative feeding goals of energy maximisation, time minimisation or selecting foods in proportion to their abundance, converged toward a diet where the diet choice predicted by all three strategies was not different from the observed diet. It appears that when food abundance approaches low levels the dietary niche breadth of these arid zone herbivores narrows, leaving them with very few dietary options. 142

Convergence in predicted diet choice based on the alternative strategies of energy maximisation and time minimisation has also been described by Schmitz (1990) who examined the diet choice of white-tailed deer during winter in Ontario, Canada. Schmitz (1990) found that white-tailed deer diet choice consistently followed a goal of energy maximisation. However, the combined effects of accumulating snow and browse depletion reduced food availability in late winter to the point where the energy maximising diet choice of deer was identical to the time minimising diet choice. At this point the diet breadth of the deer was extremely narrow and any deviation from the optimal solution would have resulted in an individual failing to satisfy its energy requirements.

The results of Schmitz's (1990) study and the study reported in this chapter support Belovsky's (1984c) suggestion that the alternative feeding strategies of energy maximisation and time minimisation should not be viewed as a dichotomy, but as endpoints of a continuum. Under most situations the endpoints are separate, not only in energy intake but also in the mix and amounts of plants that make-up the energy maximising and time minimising diets. When conditions change and food intake becomes limited, the optimal solutions to the alternative strategies converge. Thus, classifying a herbivore as an energy maximiser or a time minimiser must always be qualified by the environmental conditions at the time when the feeding strategy was determined.

I can offer no rational explanation for the finding that sheep and red kangaroos followed a goal of random diet choice, i.e. selecting foods in proportion to their abundance in the environment. There is no evolutionary advantage, that I am aware of, that explains why this feeding strategy offers a selective advantage in increased fitness over the alternative feeding goals of energy maximisation or time minimisation. Crawley (1983) suggested two reasons that sought to explain apparent 'suboptimal' diet choice. First, that it is not worth being too choosy, because the costs of discriminating between foods are greater than the rewards. Second, that foods do not differ sufficiently for animals to discriminate between them. I reject both of these hypotheses because they fail to explain why, at other times, both sheep and red kangaroos were choosy and were able to discriminate between foods that supplied the maximum amount of energy and those that did not. I tentatively conclude, in the absence of further data, that this result 143 was due to the limited dietary choices available toward the end of the study when plant biomass was at its lowest recorded levels. Consequently, the diets predicted for all strategies converge to the point where they are no longer distinguishable.

6.4.2 Alternative Constraints Only one other nutrient constraint has been included in other studies that used linear programming to predict optimal diet choice, and that was a sodium constraint (Belovsky 1978, 1984a, Forchhammer and Boomsma 1995). This constraint was included in environments that had very low concentrations of sodium in the vegetation. Sodium is a mineral needed for the regulation of body fluid volume and osmolarity, acid-base balance and tissue pH, muscle contraction, and nerve impulse transmission (Robbins 1983). It is necessary for growth and reproduction. Herbivores in sodium poor environments actively seek out plants with the highest levels of sodium (Robbins 1983). This nutrient is not limiting in the arid zone of Australia, and many plants that are commonly consumed in an energy maximising diet have high concentrations of sodium in their leaves (Wilson 1966). If there is another important nutrient constraint on the foraging of generalist herbivores, it has not been identified in 400 published tests of the linear programming model of optimal diet choice (Belovsky 1994).

It appears that the diet choices of sheep and red kangaroos in the chenopod shrublands of the study area are only constrained by the initial three constraints proposed; the daily feeding time constraint, the digestive capacity constraint, and the energy requirement constraint. It was not necessary to include an additional constraint to explain the diet choice and feeding goal of these herbivores. The two times when the linear program of optimal diet choice did not predict diet choice were probably due to incorrectly formulated parameters within the constraints. Therefore, these constraints have now been shown to be important in a wide array of environments ranging from prairie grasslands (Belovsky 1986b, Ritchie 1988) and boreal forests (Schmitz et al. 1992), to alpine tundra (Ritchie and Belovsky 1990) and desert shrublands. Only in environments where there has been an essential nutrient in relatively low concentrations in food plants (e.g. sodium, Belovsky 1978, 1984a, Forchhammer and Boomsma 1995) has it been necessary to include an additional constraint. I conclude that the hypothesised constraints of feeding time, digestive capacity and energy requirement are 144 general constraints of most generalist herbivores regardless of the type of environment in which they live.

6.4.3 Environmental Variability and Diet Choice Owen-Smith (1993a, b) criticised the use of the linear programming approach for examining the diet choice of generalist herbivores. He suggested that previous studies have implicitly assumed, but not demonstrated, that herbivores respond to variation in the parameters of the constraints to diet choice. Furthermore, he suggested that the constraints of the linear program were not likely to be limiting feeding behaviour. These criticisms were recently addressed by Forchhammer and Boomsma (1995) who used a linear program of diet choice to show that muskoxen (Ovibos moschatus) adjusted their foraging behaviour and feeding goals in response to seasonal changes in the parameters of the linear programming model's constraints. The study reported in this chapter offered another chance to examine Owen-Smith's criticisms.

Red kangaroos and sheep were highly sensitive to temporal variability in their food resources. Both herbivores were able to adjust their diet selection as their food resources changed. The seasonal changes in food parameters were most evident in the wet mass/dry mass ratio of food types, with high ratios in winter and lower ratios in summer. Consequently, the diet selection of both herbivores was highly sensitive to the digestive capacity constraint in winter when food types had the highest wet mass/dry mass ratios, and insensitive in summer when all food types had lower bulk values. In contrast, the time constraint was most important in summer. Red kangaroos suffered a 37% drop in available feeding time from winter to summer. Sheep suffered an even larger drop of 52%. These drops in available feeding time in summer were enough to constrain diet choice so that the digestive capacity of the animal's was not reached. This switching in importance of the feeding time and digestive capacity constraints on a seasonal basis highlights one of the major strengths of the linear programming approach; any number of potential constraints can be included in the model, but only those acting will affect the solution (Belovsky and Schmitz 1993). Following on from this discussion, it would be likely that at times of high food bulk (winter) and low cropping efficiency (low food abundance) that both the time and energy constraints would influence diet choice. The sensitivity analysis of red kangaroo optimal diet choice in winter 1991 (Fig. 6.4 d), a time ofrelatively high food bulk and low cropping 145 efficiency, indicated that indeed both the time and digestive capacity constraints acted upon diet choice. The results of my study of the diet choice of red kangaroos and sheep indicate that both herbivores can successfully adjust their feeding behaviour on a seasonal basis, so that they may maintain optimal diet choice. I conclude that Owen Smith's (1993a, b) criticisms of the linear programming approach for examining herbivore diet choice are not supported by the results of the present study.

6.4.4 Coevolution of Herbivores and their Food Source McNaughton (1984, 1986) hypothesised that introduced and indigenous herbivores do not have similar foraging behaviours, because introduced herbivores have not coevolved with the plant communities upon which they feed. Westoby (1985, 1986) was sceptical of McNaughton's hypothesis, claiming that such a difference may exist but that there was no data to support or reject the hypothesis. Belovsky and Slade (unpublished data) attempted to address McNaughton's hypothesis by comparing the foraging behaviour of taxonomically related introduced and indigenous herbivores grazing native Palouse prairie vegetation in Montana (USA). Belovsky and Slade (unpublished data) found that introduced and indigenous herbivores were able to select an optimal diet that maximised energy intake during foraging periods. Belovsky and Slade's (unpublished data) results indicate that the hypothesis that introduced and indigenous herbivores have different foraging behaviours is incorrect. However, the herbivores used in Belovsky and Slade's tests were taxonomically related and their foraging behaviour may have been related to similarities in the herbivore's physiology, anatomy or behaviour. Further testing of the hypothesis was warranted. The results of the present study offer another opportunity to test McNaughton's hypothesis. Red kangaroos and sheep are taxonomically distinct and do not share many similarities in their physiology, anatomy or behaviour. The results of the present study indicate that despite striking differences in the components of their feeding behaviour, such as cropping efficiency and feeding time, sheep and red kangaroos shared the common foraging goal of energy maximisation. I conclude that McNaughton's (1984, 1986) claim that indigenous and introduced herbivores have different foraging behaviours is only true on a superficial basis. On the superficial basis of comparing, for example, cropping efficiencies indicates that there are clear differences between sheep and red kangaroos. But when these differences are taken in the context that they are simply different routes to the same feeding goal of energy maximisation, it is clear that these 146 herbivores are functionally equivalent. McNaughton's (1984, 1986) claim that introduced herbivores that have not coevolved with the plants upon which they feed are not the functional equivalent of indigenous herbivores is incorrect. Energy (or nutrient) maximisation appears to be the universal feeding goal of most generalist herbivores, regardless of their evolutionary history.

6.4.5 Conclusion In conclusion, sheep and red kangaroos appeared to follow a feeding goal of energy maximisation. This finding supports the conclusions of many other studies examining the feeding strategies of generalist herbivores, which found that the goal of energy (or nutrient) maximisation explained 85% of the observed variance in dietary choice (Belovsky and Schmitz 1994). In addition, I found that red kangaroos and sheep could adjust their diet choice on at least a seasonal basis to track extreme temporal changes in the constraints to their diet choice. Furthermore, the alternative feeding goals of energy maximisation and time minimisation should not be viewed as a dichotomy, but as the endpoints of a continuum. Finally, it appears that the ability of a herbivore to select an optimal diet is independent of the coevolution of that herbivore with the plants upon which it feeds. Instead, it appears that energy maximisation is a feeding strategy pursued by most, if not all, generalist herbivores.

Contrary to the claims of some of its detractors (Hobbs 1990, Owen-Smith 1993a, b, Ward 1993, Huggard 1994), the linear programming model of optimal diet choice has not stifled investigation of the constraints to foraging. The linear programming approach has revealed the constraints and how, by their interaction, generalist herbivores balance potentially conflicting factors when making dietary choices. Furthermore, the quantitative accuracy of the linear programming model allows its predictions of energy intake to be used in a ecological context (Green 1990). The linear programming model can then be used to examine the population dynamics and life-history strategies of species that are potentially limited by energy intake. Chapter 7

The Optimal Body Size and Evolution ofSexual Dimorphism in Red Kangaroos.

7.1 Introduction

The evolution of body size in generalist herbivores has usually been explained through the interaction of digestive capacity constraints and metabolic requirements (Demment and Van Soest 1985, Illius and Gordon 1992). Demment and Van Soest (1985) argued that because metabolic rate scales with mass (W) as W°·75 and digestive capacity scales isometrically with mass (Fig. 7 .1 ), larger animals are more tolerant of food of low digestibility due to their relatively lower metabolic requirements than are small animals, which must seek out rare, high quality foods. Under this hypothesis, the upper limit to body size is set by either rumination rate or marginal increase in digestibility with increasing body size (Demment and Van Soest 1985). At the other end of the spectrum minimum size body size is set by maximum fermentation rates. Contrary to the arguments ofDemment and Van Soest (1985), Illius and Gordon (1992) predicted from the results of a model of the digesta kinetics offoregut and hindgut fermenters that the upper limit to body size of ungulates is set by their ability to extract nutrients from low quality foods at times of resource depletion. While this approach has met with some success in predicting the general increase in ungulate body size during times of abundant food (Demment and Van Soest 1985, Illius and Gordon 1992), the qualitative nature of the predictions has prevented rigorous tests of the hypotheses. A more rigorous approach would involve making quantitative predictions with respect to the limits to upper and lower body size and the evolution of body size in generalist herbivores.

Few studies have attempted to quantitatively predict the upper and lower limits to herbivore body size of a particular species, nor what might be an optimal body size for that species (Reiss 1989). Belovsky (1978, 1984a, 1987) used an optimal foraging model to examine the hypothesis that herbivore foraging is directly related to the evolutionary selection ofbody size. He demonstrated that the maximum, minimum and optimal body sizes of moose (Alces a/ces) (Belovsky 1978), snowshoe hare (Lepus americanus) (Belovsky 148

1984a) and Microtus pennsylvanicus (Belovsky 1987) could be quantitatively predicted by examining the relationship between body size and foraging efficiency.

--Metabolic Requirement -- -Oigestiw Capacity

Body Mass

Fig. 7.1. The relationship between body mass and 1) metabolic requirement and 2) digestive capacity.

Belovsky' s model (1987) may be a general model that describes body size selection in generalist herbivores, but so far it has only been tested in boreal forest and prairie grassland habitats. In Chapter 6 I demonstrated that red kangaroos usually follow a foraging strategy of energy maximisation. Therefore, energy intake is probably an important determinant of survival and reproductive success for this species and it may also be a factor in the evolution of body size. In this chapter I will test the generality ofBelovsky's (1987) model using it to predict body size selection in a generalist herbivore, the red kangaroo, in an arid shrubland environment.

There are many hypotheses that attempt to explain the evolution of sexual dimorphism in body size. With respect to mammals the current hypotheses are; 1) that dimorphism arises through intermale conflict and competition for mates, 2) that environmental factors, and their effect on the timing of reproduction by females, allows some males to limit access to females by other males, and 3) that delayed maturation of 149 males relative to females increases either the early survivorship or mature fecundity of males, and that these phenomena lead to extreme polygyny and dimorphism (Jarman 1983). While these hypotheses may explain the evolution oflarge body size in males, they fail to explain why the females of some species do not reach large body size, especially when there is evidence that females with larger body size often have greater reproductive success (Clutton-Brock 1988, Moss 1995).

The aim of this chapter is to examine the hypothesis that maximum, minimum and optimal body size in red kangaroos can be predicted from the relationship between their rate of energy intake and metabolic requirements. I also examine the hypothesis that energy intake rates can be used to explain the evolution of sexual dimorphism in red kangaroos. I predict that the body size of female red kangaroos has evolved to maximise survivorship, while the body size of male red kangaroos has evolved to maximise their dominance in intraspecific contests. Consequently males will attempt to grow as large as possible while females will approach optimal body size, defined as the body size with the greatest surplus of energy. I tested these hypotheses by comparing the actual body sizes of red kangaroos to those predicted by optimal foraging theory.

7.2 Materials and Methods

The linear programming model of optimal diet choice (cf Chapter 6) was solved for the goal of energy maximisation over five sampling periods; winter 1989, summer 1990, winter 1990, summer 1991 and winter 1991. The model was solved for red kangaroos across a range of body sizes (5-100 kg) by reparameterising the constraints of the model for each body size at 5 kg increments. The 5 kg lower limit was set because it is close to the mass of juveniles when they emerge permanently from the pouch (4.6 kg, Frith and Calaby 1969), and the upper limit of 100 kg was set because it is slightly above the mass of the largest males (Denny op. cit. Jarman 1989). The model predicts the amount of energy (kJ/day) consumed by a forager following a goal of energy maximisation. 150

7.2.1 The Foraging Model For a detailed description of the model's parameters and constraints see Chapter 6.

7.2.1.1 Feeding Time Constraint Daily feeding time and food bite rates have been found to be independent of body size (Watson and Dawson 1993). However, bite size (g-dry mass/bite)is dependent on body size since it is a function of the size of the incisors and the volume of the mouth (Illius and Gordon 1987, 1993). It was not possible to measure the bite size for all body sizes since at times there were no individuals of certain body sizes present in the study site, or they were in such low numbers that obtaining bite sizes was extremely difficult. Therefore, I sought an alternative method of estimating bite size across the range of body sizes. Belovsky et al. (submitted) measured the bite size of red kangaroos across a range of body sizes. They found that maximum bite size was 1.88 times that of an average individual of 25 kg body mass. Furthermore, Edwards (1990) found that while male red kangaroos increase in body mass over their life span, their bones stop growing after eight years of age (cf. Figs 8.4 and 8.6, Edwards 1990). Females show a similar pattern, but their bones stop growing after five years of age (cf Figs 8.3 and 8.5, Edwards 1990). These ages correspond to average male and female masses of approximately 50 kg and 30 kg respectively (Edwards 1990). Skeletal growth in male and female red kangaroos is approximately linear up to their maxima, and then rapidly asymptotes (Edwards 1990). By using these two studies I estimated the relative bite sizes of male and female red kangaroos for a range from 5 to 50 kg body mass {Table 7.1 ). The change in bite size with body size was assumed to follow the same linear pattern up to the respective maxima, after which bite size asymptotes.

Body Mass (kg)

5 JO 15 20 25 30 35 40 45 50

Males 0.30 0.47 0.65 0.82 1.0 1.18 1.35 1.53 1.70 1.88

Females 0.30 0.47 0.65 0.82 1.0 1.18 1.18 1.18 1.18 1.18

Table 7 .1. Bite size calibration ratios of male and female red kangaroos relative to an individual of25 kg. Female red kangaroo bite size asymptotes after 30 kg body mass, while male bite size asymptotes after 50 kg body mass. 151

I calculated the bite size of each food type for each body mass as the product of the bite size of a 25 kg individual and the respective calibration ratio. Food cropping efficiencies were calculated as the quotient of bite rate and the adjusted bite size. The feeding time constraint was then constructed following the methods discussed in Chapter 6.

7.2.1.2 Energy Requirement Constraint I assumed that net energy gain (kJ/g-dry mass) from all food types was independent of body size, and food type digestible energy was equal to the mean of each group. However, daily energy requirement (kJ/day) is dependent on body size, with energy requirement increasing logarithmically with body mass. I derived the energy requirement of each body mass using Green's (1989) regression of field metabolic rate on body mass for macropodoids. I was then able to construct the energy requirement constraint for each body mass.

7.2.1.3 Digestive Capacity Constraint Food wet mass/dry mass ratios were assumed to be independent of body size (Belovsky 1986). I assumed that digesta turnover rate was also independent of body size. Forestomach capacity is dependent on body size. The forestomach capacity of each body size was derived from the linear regression;

y1= 210 + 78.6x (7.1)

where y1is forestomach capacity and x is body mass (cf Chapter 6, Fig. 6.1 ). The digestive capacity of each body size was then calculated as the product of forestomach capacity and digesta turnover rate. I was then able to construct the digestive capacity constraint for each body mass.

7 .2.2 Vegetation Sampling and Analyses The vegetation sampling methods and analyses are the same as those described in Chapter 6. 152

7 .2.3 Estimating Model Parameters During Prolonged Drought

I estimated the cropping efficiencies of red kangaroos at plant biomasses lower than those experienced during this study to examine the consequences severe food limitation might have on the evolution of body size in red kangaroos. I assumed that as plant biomass drops or food item size decreases, cropping efficiencies (min/g-dry) generally become less efficient (i.e. they increase in value). I estimated the cropping efficiencies of grasses and shrubs at 300, 250 and 200 kg/ha total plant biomass. The estimates were made by regressing the cropping efficiencies of each food category against its respective biomass measured during the sampling periods. These predicted cropping efficiencies were used to simulate the cropping efficiencies of red kangaroos during a prolonged drought. I did not include forbs since they generally make up an insignificant proportion of the diet and available plant biomass during drought (Dawson 1989, Dawson and Ellis 1994). The wet mass/dry-mass ratios of grass and shrub were assumed to be at very low levels and once consumed would rehydrate to the minimum wet-mass/dry-mass ratios of 1.90 for grass and 2.24 for shrub (cf Chapter 6 for a full discussion). The other parameters of the model were assumed to be unaffected by prolonged drought.

I estimated the proportional mix of total plant biomass that grass and shrub made up at 300, 250 and 200 kg/ha. I did this by regressing grass or shrub biomass against total plant biomass for each sampling period. From these predicted plant biomasses I used the regressions relating cropping efficiency to plant biomass and estimated food cropping efficiencies during a drought. The model was reparameterised for each body size, and solved following the methods outlined above.

7 .2.4 Model Predictions and Analyses

The linear programming model of diet choice was only solved for the foraging goal of energy maximisation, which red kangaroos have been shown to follow (Chapter 6). The solution to the model predicts diet choice and, most importantly, energy intake by a forager. Energy intake was predicted across all body masses, for all sampling periods. 153

If variance estimates are included in the parameters of the linear program of optimal diet choice they must be accurately determined, otherwise the solution to the model may be biased (Belovsky 1994). I was not able to accurately determine the amount of variance in each parameter of the model, and consequently decided to make the parameters of the model invariant. The optimal solution to the linear program was found by using the simplex algorithm (Winston 1991).

The predicted maximised energy intakes were plotted against energy requirements, and from these plots it was possible to predict the minimum, maximum and optimal body size ofred kangaroos ifbody size is constrained by energy intake. The predicted body size limits and optima were tested by comparing the predicted limits and optima with the observed values from individuals caught in the study area A body size was defined as optimum if it had the largest proportional (to requirement) difference between energy intake and energy requirement. Minimum and maximum body size were defined as the lower and upper intersection of the predicted energy intake curve with the energy requirement curve. In addition, the evolution of body size in red kangaroos was examined, with emphasis on the evolution of sexual dimorphism.

7.3 Results

7.3.1 The Foraging Model

The energy intakes for the feeding goal of energy maximisation across all body sizes are plotted in Figs 7.2 a-e for males and 7.3 a-e for females. Against energy intake, I plotted energy requirement predicted from Green's (1989) regression of field metabolic rate against body weight. In addition, I plotted the proportion of females lactational in the body mass ranges; 15.5-20 kg, 20.5-25 kg, 25.5-30 kg, 30.5-35 kg. A female was defined as lactational if she had either a pouch young or an elongated teat, which indicated she was still suckling a young-at-foot. The lowest observed body mass of a lactational female in the studied population was 15.5 kg, and no females weighing over 35 kg were captured during the sampling periods. The optimum body sizes of males and females for each sampling period are presented in Table 7.2. 154

7.3.1.1 Male Body Size The maximum body size of male red kangaroos cannot be explained from the basis of energy limitation alone. For three sampling periods (winter 1989, summer 1990 and winter 1990) the predicted maximum fell outside the limit of the analysis, exceeding the observed maximum body size of any male red kangaroo. On the other two sampling periods, there was closer agreement between the predicted and observed maximum body sizes. In summer 1991, the maximum body mass was predicted to be approximately 66.5 kg. At this time the mean mass of the largest five males was 68.9 kg (range 60-81 kg). In winter 1991, the predicted maximum body mass was approximately 89 kg, with the largest captured male having a mass of 71 kg.

In four of the sampling periods there was reasonable agreement between the predicted and observed minimum body size (winter 1989, winter 1990, summer 1991 and winter 1991), and although the curves did not intersect in winter 1989 and winter 1991 they closely approach one another. In summer 1990, there was a relatively large deviation between predicted and observed minimum size, indicating that at this time minimum size may not have been limited by energy intake.

7.2 a) Male red kangaroo, winter 1989

30000~------~ i 32 25000 ~ Cl) -a 20000 -.E ~ 15000 E ·s~ c-10000 ~ >, _.,_ Energy Requirement (kJ/day) ~ 5000 C w ---Energy Intake (kJ/day)

0 +----+----i,---+---+-+---+---+--+----+-+---+---+-+----+----+---+--+-----t 10 20 30 40 50 60 70 80 90 100

Body Mass (kg) 155

7 .2 b) Male red kangaroo, summer 1990

18000 ~------

i16000 32 ~14000 Q) 1612000 ~ ::: 10000 C: Q) E 8000 ·s~ O' 6000 ~ ei 4000 -e-Energy Requirement (kJ/day) Q) ffi 2000 -II-Energy Intake (kJ/day)

0 ...____,.__--+---+---+-----+---+---+------L--1--....__,...____.__ _.__..,__.....___._ _, 10 20 30 40 50 60 70 80 90 100 Body Mass (kg)

7 .2 c) Male red kangaroo, winter 1990 20000~------~

'>:18000 <11 "'C i 16000 ~ 14000 j!l -.f: 12000 ~ 10000 E -~ 8000 ::, O' ~ 6000 >. e 4000 -e-Energy Requirement (kJ/day) Q) C: W 2000 -II-Energy Intake (kJ/day)

0 +--+----+------+----+--+---1--+-----1---1---1---1-----,,..._--I 10 20 30 40 50 60 70 80 90 100 Body Mass (kg) 156

7 .2 d) Male red kangaroo, summer 1991

14000 -,------,

~ Cl3 12000 32 ~ ~ 10000 :§ - 8000 i: G) ~ 6000 ·5 O" & 4000 >. e> ---Energy Requirement (kJ/day) ~ 2000 w ---Energy Intake (k.Vday)

0 +---+-+---+-+---+-+---+-+---+-+----+--+----+--+---+--+---+--+----f 10 20 30 40 50 60 70 80 90 100 Body Mass (kg)

7.2 e) Male red kangaroo, winter 1991

14000 ~------, -->. Cl3 12000 32 ~ ~ 10000 :§ - 8000 C: -G) E 6000 ·5e O" & 4000 >. e> ----Energy Requirement (kJ/day) ~ 2000 w ---Energy Intake (k.Vday)

0+----+-+----+--+----+--+------t----t----r----. 10 20 30 40 50 60 70 80 90 100 Body Mass (kg)

Figs 7.2 a) - e).The predicted energy intakes and requirements of male red kangaroos across a range of body sizes for a) winter 1989, b) summer 1990, c) winter 1990, d) summer 1991, and e) winter 1991.

7.3.1.2 Female Body Size

The pattern of the limits to female body size predicted by the foraging model are similar to that of males. In two sampling periods the predicted maximum body mass of 157 females fell outside the limits of the analysis (winter 1989 and winter 1990). The predicted maximum body size of summer 1990 (70 kg), whilst falling within the limits of the analysis, was far greater than the maximum body size recorded for females (39 kg, captured at the study site in summer 1988). The winter 1991 sample approached a closer fit between predicted and observed, but the predicted upper limit of 47.5 kg was much larger than the observed upper limit of 31.5 kg. However, the sampling period in summer 1991 provided a close fit between predicted and observed maximum body size. In summer 1991, the predicted maximum body mass was approximately 35 kg, which was closely matched by the observed maximum of 34 kg.

The minimum predicted body size for females is identical to that of males, the predicted body sizes of the sexes only separating after about five years of age. Thus the results for males are also applicable to females.

The proportion of females that are lactating in the four body size categories indicates that as body size increases, the proportion of females breeding within each body size group increases. The smallest group (15.5-20 kg) consistently had a lower proportion of breeding females than the other groups. This may have been due to delayed onset of sexual maturity or simply failed conceptions as Ashworth (1995) found for euros in the study area. This group also had the smallest net difference between energy intake and requirement. The largest group (30.5-35 kg) had the highest proportion breeding, and was followed by the 20.5-25 kg and the 25.5-30 kg groups which had marginally lower proportions breeding. 158

7.3 a) Female red kangaroo, winter 1989

25000 1 -----.n~.------~~:.==.i- >, 0.9 CU -,~ c 20000 0.8 Q) ni .><: 0.7 C s 0 £ = 15000 0.6 ~ C j -Q) 0.5 C E 0 11! :e ·s 10000 0.4 0 O" c. Q) 0::: 0.3 a.e >, e> -Proportion Lactational Q) 5000 0.2 C --Energy Requirement (kJ/day) w ...... _ energy Intake (kJ/day) 0.1

0+--+-+--+--+---+---+-a.+-+--+-+--+-+--+-+--+-+---+--+---+-----1-0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Body Mass (kg)

7.3 b) Female red kangaroo, summer 1990

14000

>, 0.9 CU 12000 -,~ c 0.8 Q) ni .><: 10000 0.7 C s 0 £ 0.6 8000 ~ -i: j Q) 0.5 C E 0 11! 6000 :e ·s 0.4 0 O" c. Q) e 0::: 4000 0.3 a. >, -Proportion Lactational e> 0.2 Q) --Energy Requirement (kJ/day) wC 2000 ...... _ Energy Intake (kJ/day) 0.1

0+--+-+--+---+---+--+-a.+-+--+-+--+-+--+-+--+-+---+--+---+----1-0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Body Mass (kg) 159

7.3 c) Female red kangaroo, winter 1990

18000

>, 0.9 Ill 16000 :i::? -, 0.8 c 14000 Iii ~ 0.7 C 0 .l!l 12000 :;:, ..!: 0.6 ~ 10000 Ill c ...I Q) 0.5 C E 0 I!! 8000 :e ·s 0.4 0 C" c. Q) 6000 0:: 0.3 Q..e >, 4000 -Proportion Lactational e> 0.2 Q) Energy Requirement C -e- (kJ/day) w 2000 -+-Energy Intake (kJ/day) 0.1

0 +--+-+--+--+-a+--+-a+-+--+-+--+-+--+-+----+--+----+--+----+-----1- 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Body Mass (kg)

7.3 d) Female red kangaroo, summer 1991

14000

>, 0.9 Ill 12000 -,:i::? c 0.8 Q) Iii .:.: 10000 0.7 C 0 .l!l :;:, ..!: 0.6 ~ -- 8000 j cQ) 0.5 C E 0 I!! 6000 :e ·s 0.4 0 C" c. Q) e 0:: 4000 0.3 Q.. >, -Proportion Lactational e> 0.2 Q) -e-Energy Requirement (kJ/day) C 2000 w -+-Energy Intake (kJ/day) 0.1

0 -r---+--r---+-+--+-+--+---t-----t---t-----t---t-----t---t-----t--+-----t--+---+---+ 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Body Mass (kg) 160

7.3 e) Female red kangaroo, winter 1991

14000

>, 0.9 I'll 32 12000 c""') 0.8 1'ij Q) 10000 ~ 0.7 !5 .1!l :;:, 0.6 ~ -= 8000 -C: ~ Q) 0.5 c E 0 e 6000 ·5 0.4 '§ O" Q) ~ 0:: 4000 0.3 a_ >, -Prcpoltlon Lactational e> 0.2 Q) --Energy Requirement (kJ/day) C 2000 w -+-Energy Intake (k.l/day) 0.1

o------.__------+-+->--+--+---+-~o5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Body Mass (kg)

Figs 7.3 a)-e).The predicted energy intakes and requirements of female red kangaroos across a range of body sizes for a) winter 1989, b) summer 1990, c) winter 1990, d) summer 1991, and e) winter 1991. In addition, the proportion of breeding females in the sizes classes 15.5-20 kg, 20.5-25 kg, 25.5-30 kg, and 30.5-35 kg are presented.

7.3 .1.3 Optimum Body Size

The optimum body size of male and female red kangaroos is not constant. However, a pattern is present. In winter 1989 and 1990, when food is abundant and has high wet mass/dry mass ratios, optimum body size is largely dependent upon digestive capacity, which increases linearly with body mass. At these times diet choice and energy intake are not time limited and energy intake is a function of digestive capacity, i.e. its fill by food types and the digestible energy content of food. When diet choice by red kangaroos was time limited (summer 1990, summer 1991 and winter 1991) the optimum body size was constrained to 30 kg for females and 50-55 kg for males. 161

Optimum Body Size (kg) Sampling Period Female Male Winter 1989 90 100 Summer 1990 30 55 Winter 1990 100 100 Summer 1991 30 50 Winter 1991 30 50

Table 7.2. The predicted optimum body sizes of male and female red kangaroos at each sampling period.

7.3.2 Estimating Model Parameters During Prolonged Drought

7.3.2.1 Estimating Cropping Efficiency

The regressions used for the estimation of cropping efficiencies at biomasses lower than observed during this study are presented in Figs 7.4 a and b. While the regressions are not significant at the 0.05 level, they approach significance, and provide representative estimates of cropping efficiency as plant biomass declined. The important trend of cropping efficiency becoming less efficient (i.e. increased in value) as plant biomass declined was observed. 162

7.4a)

1.25 ~ '9 -e> 0 C: I 1.2 ~ C1I 0:: 1.15 Cl .5: c. c. ..0 1.1 (.) UI UI ~ (!) 1.05

0.95

~o 0.9

0.85 150 250 350 450 550 650 750 Grass Biomass (kg/ha)

7.4 b)

2 ~ "O I -e> 0 C: I 1.8 ~ C1I 0:: 1.6 Cl 'a.C: c. e 1.4 (.) .c :::, .c.. en 1.2

0.8

0 0.6

0.4 80 140 200 260 320 380 440 Shrub Biomass (kg/ha)

Figs 7.4 a) and b).The regression of cropping efficiency (min/g-dry) against food type

biomass (kg/ha) for a) grasses (y=l.30-0.0007x, r2=0.702, F1_3=7.05, P=0.077), and b) 163

shrubs (y=l.85-0.0025x, r=0.659, Fu=5.79, P=0.095). The outlier data point marked with the arrow was winsorised before inclusion in the regression (Sokal and Rohlf 1981).

7.3.2.2 Estimating Proportional Food Abundance.

The regression of shrub abundance as a function of total plant biomass is presented in Fig. 7.5. This regression was used to generate the likely mix in the abundance of grasses and shrubs as biomass declined from 300 to 200 kg/ha. Although the regression was not significant the object was to estimate the "likely" mix, and for the purpose of this exercise represents a reasonable estimate. I calculated grass abundance by subtracting the estimated shrub biomass from total plant biomass ( excluding forbs ). The predicted mixtures are presented in Fig. 7 .6.

440

ci, 380 .r:. 0 --Cl '=- U) U) ro 320 E 0 i:ii .c 2 .r:. en 260

200

140 0 0

SOL----~~~~--~~--~~-~-~-_.__-~~~-...... 200 400 600 800 1000 1200 1400 1600 1800 Total Plant Biomass (kg/ha)

Fig. 7.5. The regression of shrub abundance (kg/ha) against total food abundance

(kg/ha) (y=57 .1 +0.24x, F 1,3=5.69, r=0.656, P=0.097). 164

160

140 ro .c 120 Cl ~ 100 CJ Grass VJ :(l 80 •shrub E .Q 60 co 40

300 kg/ha 250 kg/ha 200 kg/ha

Total Plant Biomass (kg/ha)

Fig 7 .6. Simulated biomasses of the plant categories grass and shrub at 200, 250 and 300 kg/ha.

7.3.2.3 Body Size During Drought

The simulation of energy intake by red kangaroos during drought indicates that the optimal body size for red kangaroos is independent of sex and is approximately 50 kg. As plant biomass declines the range of body sizes that are able to maintain positive energy balance drops (Figs 7.7 a-c).At 300 kg/ha the range is approximately 28 to 56 kg body mass, dropping to 35 to 54 kg at 250 kg/ha, and dropping further to 42.5 to 52.5 kg at 200 kg/ha. Throughout this decline in plant biomass the optimum body size remains 50 kg. However, the closeness of the energy intake and requirement curves across the range of body sizes is important. Below the maximum predicted body size the energy intake curve lies very close to the requirement curve. In contrast, above the maximum any increase in body mass leads to a larger deviation between intake and requirement. This suggests that individuals with large body mass (> 50 kg) are at a severe disadvantage during drought, or at any time when diet choice and energy intake are time limited. Individuals below 50 kg body mass are not at such a great disadvantage, and while they may not satisfy their reproductive requirements, they may be able to satisfy subsistence requirements. 165

a) 300 kg/ha total plant biomass

14000 ,------~

~ , e> -----Energy Requirement (kJ/day) ~ 2000 w -a-Energy Intake (kJ/day)

0 +----+--+---+----+r---+--+--r---+--+--+----+--+--+----+--+--+------1--+------i 10 20 30 40 50 60 70 80 90 100

Body Mass (kg) b) 250 kg/ha total plant biomass

14000 ,------,

~ m 12000 ~ ~ ~ 10000 ~ -. 8000 C: -Cl) E ~ 6000 ·s C" &_ 4000 >, e> -----Energy Requirement (kJ/day) ~ 2000 w -a-Energy Intake (kJ/day)

0 +------l--+--+----+---+--+----+---+---l---11----+--l--+----+--+--+----+--+---l 10 20 30 40 50 60 70 80 90 100

Body Mass (kg) 166 c) 200 kg/ha total plant biomass

14000 ...------~ -;:: co 12000 J2 l ~ 10000 ~ - 8000 1= Cl) ~ 6000 ·s O'" ~ 4000 >- e> -+-Energy Requirement (kJ/day) ~ 2000 w ---Energy Intake (k.Jlday)

0 +----+----1--+---+-+----+----+----+--l---+---+-+----+-----,f---+---+-+-----i 10 20 30 40 50 60 70 80 90 100 Body Mass (kg)

Figs 7.7 a) - c).The simulated energy intakes and requirements ofred kangaroos across a range of body sizes as drought intensifies from a) 300 kg/ha total plant biomass, to b) 250 kg/ha and c) 200 kg/ha.

7. 4 Discussion

7.4.1 Maximum and Minimum Body Size When food availability and feeding time do not limit energy intake, the model fails to predict the maximum body size of either male or female red kangaroos. This indicates that at most times the upper body size limit of red kangaroos is not set by energy intake. However, in summer 1991 when there was relatively low food abundance and limited time for foraging, the model gave reasonably close estimates of observed maximum body size for both male and female red kangaroos. From these data it appears that maximum body size may be constrained by infrequent episodes of food limitation.

In contrast, there was close agreement between minimum body size and the prediction of the model, indicating that body mass and age ofjuveniles at pennanent-pouch emergence (PPE) are probably closely related to energy intake. In addition, the closeness of the energy intake and requirement curves at body masses between 4.6 kg (PPE) and weaning (12 kg) might explain the high rates of mortality, which range between 15% in good seasons up to 83% in drought (Frith and Sharman 1964), seen in these groups. The closeness of the 167 two curves for young animals indicates that even small deviations from the energy maximising diet may lead to a rate of energy intake that fails to satisfy requirements.

7.4.2 Optimal Body Size The optimal body size of male and female red kangaroos depends on the limits to food intake. If energy intake is limited by digestive capacity alone, optimal size becomes a function of digestive capacity. Since digestive capacity scales isometrically with body mass and requirements scale with mass (W) as w

For a body size to be optimal it must confer some advantage over other body sizes. I predicted that the optimal body sizes of males and females would have greater reproductive success and survivorship than other body sizes. Therefore, the survivorship of five year old females and eight year old males should be highest at times of food limitation, such as during prolonged drought. Red kangaroo populations can suffer high rates of mortality during drought with population declines ofup to 52% (Bayliss 1987). Robertson's (1986) study of mortality in a red kangaroo population in western New South Wales provides a test of this hypothesis. Robertson (1986) determined the age structure ofkangaroos that died in a prolonged drought (Fig 7.8). The low frequency of dead individuals in 3-8 year old cohorts suggests that these age classes had higher survivorship than other cohorts. The optimal body sizes I predicted for male and female red kangaroos lie within this range. While this result does not represent an unequivocal test of the hypothesis, it does provide support. 168

~ 10 >, u C: Q) 8 :::, a l1? 6 u. 4

0 0 4 8 12 16 20 24 Age (years)

Fig 7.8. The age structure of red kangaroos that died during a drought at Kinchega National Park. (From Robertson, 1986).

It is not clear from the results that the predicted optimal body size of females had higher reproductive success than other body sizes, but they were certainly no lower. The smallest size class of mature females (15.5-20 kg) consistently had the lowest proportion of breeding females and this size class also had the lowest swplus of energy. Thus, there appears to be a positive correlation between swplus energy intake and reproductive status, but a conclusive test will need to be done on a population that is severely food limited.

Male red kangaroos of optimal size are not likely to have the highest reproductive success. Size related dominance over other males and access to females produces intrasexual selection for large body size (Clutton-Brock and Harvey 1978, Jarman 1983, Maynard Smith 1991 ). Thus, males with the largest body size have the highest reproductive success and this has been established for male red kangaroos in the study area (Moss 1995).

7.4.3 Evolution of Sexual Dimorphism

In the introduction I presented a hypothesis to explain the evolution of sexual dimorphism of body size in red kangaroos. I hypothesised that female body size evolved to maximise survivorship, which would in turn maximise reproductive output. In contrast, I hypothesised that males would maximise their reproductive output by being as large as possible, foregoing long term survivorship for short term dominance over other males and access to females. This is because one dominant male can achieve many matings in a relatively short time, while females can produce at most 1.4 young per year (Russell 1982). 169

The simulations of available food and energy intake during drought indicated that the largest females (30-35 kg) were able to exceed energy requirements when plant biomass was greater than or equal to 250 kg/ha When plant biomass dropped to 200 kg/ha they could no longer maintain intake above requirement. However, energy intake by individuals with body sizes within the range shown by mature females (15-35 kg) never deviate far from the energy requirement curve. While these individuals may not be reproductive at these low levels of food availability they still exceed their minimum energy requirements for survival.

The simulations indicated that the overall optimal body size of red kangaroos is 50 kg. The model failed to explain why female red kangaroo maximum body size is approximately 35 kg, when they would maximise survivorship and meet reproductive requirements by approaching the male optimum of 50 kg. There are two possible explanations for this anomaly; 1) that energy intake is not the main determinant of female body size, or 2) that the parameters of the simulation were not representative of conditions during drought.

A recently published hypothesis by Flannery (1994) provides a possible reason why the observed maximum body size of female red kangaroos does not reach the predicted optimum of 50 kg. Flannery (1994) points out that almost all of the larger extant Australian mammals have decreased in body size over the past 40 000 years. "Dwarfing" in body size has been restricted to the larger species, while smaller species (5 kg and less in body mass) have shown no reduction in size. Flannery suggests that Aboriginal hunting may have caused the observed decline in body size, and that the more popular explanation based on climatic change contains some anomalies. In particular, the climate change hypothesis suggests that dwarfing had something to do with the last ice age and the concomitant drop in the quality and quantity of forage (Flannery 1994). However, this hypothesis fails to explain why dwarfing continued long after the last ice age, about 15 000 years ago. The theory also fails to explain why dwarfing has occurred in only the last ice age, when there have been 17 ice ages in the past two million years. The overexploitation hypothesis proposed by Flannery (1994) suggests that intense hunting pressure and preferential selection for the largest individuals by Aboriginal hunters led to dwarfing by large mammalian species. According to this hypothesis there would have been evolutionary selection against having a large body size, while there would have been selection for the onset of early maturity at a lower body size. Flannery cites many examples of dwarfing, but one of particular relevance to the 170 present chapter is the data of Marshall and Corruccini (1978), which indicates that the teeth of the red kangaroo have declined by 30-35% in length in the last 40 000 years. Assuming that this decline has been mirrored by body mass Flannery predicts that body masses of present day species would have been about twice as heavy 40 000 years ago. Presently, female red kangaroos have a maximum body mass of approximately 35 kg, but 40 000 years ago this maximum would have been closer to 70 kg. Therefore, 40 000 years ago the range of female body masses would have encompassed the 50 kg optimum. These figures suggest that maximum female body size may have been closer to the optimal body size of red kangaroos before the intense hunting pressure of Aboriginal man. Thus, Flannery' s (1994) overexploitation hypothesis offers one explanation as to why female red kangaroos do not reach the predicted optimum body size of red kangaroos.

Explanations for the selection of body size have been based on predation, competition or metabolic arguments (Roff 1981 ). Predation may be an important constraint on the evolution of body size of red kangaroos. Under this hypothesis individuals within the body size range of mature females would have a greater chance of escaping predation than individuals closer to the 50 kg optimum of males. However, the available evidence contradicts this hypothesis. Shepherd (1981) found that dingoes selectively preyed upon juveniles and adult females to the exclusion oflarge adult males. In addition, Clutton-Brock and Harvey (1983) note that increasing body size is generally associated with reduced predation rates (but probably not by man). Consequently, females would evolve larger body size to escape predation, which was not observed. Intrasexual competition for mates occurs in male red kangaroos and leads to the selection of larger body size (Moss 1995). It is not clear if intrasexual competition occurs in female red kangaroos, but if it did there would again be selection for large body size which was not observed. Interference competition for other resources such as food or water might occur, but with one exception (Croft 1985), has not been demonstrated. Croft (1985) examined inter and intraspecific conflict between kangaroos at a watering point within the study site. He found that there was size related dominance of access to water, with the largest and most aggressive male euros dominating all other species and size classes. Large male red kangaroos were the next most dominant group. If interference competition is exerting selective pressure on the evolution of female body size it would favour large size over small, since dominance in contests is usually correlated with increasing size (Ralls 1976). Exploitative competition may be an important determinant of body size in red kangaroos. Some observations suggest that when food 171 availability is limiting, small grazers tend to exclude larger ones (Clutton-Brock and Harvey 1983). In the Serengeti, large grazers are the first to leave as available plant biomass declines. They move to areas ofhigher food abundance but lower quality (Bell 1970, Jarman and Sinclair 1979). Illius and Gordon (1987) report a similar pattern for red deer in England. Ifthis pattern also occurs in red kangaroo populations, small body size would be selected. However, it is not clear if these phenomena are the result of competition or simply the failure of large animals to satisfy their energetic requirements as food availability declines, and that even in the absence of small grazers the larger grazers would be unable to satisfy their requirements. This last point overlaps the metabolic requirement argument of body size selection. These two hypotheses are intrinsically linked and cannot be separated without further experimentation that could control for the effect of small grazers on larger ones.

The second explanation for the failure of the model to predict the evolution of female body size requires an examination of the assumptions used in the simulations. I assumed that as cropping efficiency worsened, the bite size component of cropping efficiency remained in the ratios presented in Table 7 .1. This assumption presumes that any decline in available item size is independent of body size. Ifbite size is limited by available item size so that a larger grazer can take a bite no larger than a smaller grazer, then smaller body sizes will be favoured as plant biomass drops and energy intake is time limited, and there is evidence that this occurs in some ungulate communities (lllius and Gordon 1987). Consequently, the optimal body size of red kangaroos will be lower than 50 kg and will approach the female optimum of 30 kg. Plant biomass did not reach these low levels during this study, so I was unable to test this hypothesis. However, it is a reasonable assumption that food item size will decrease during a prolonged drought. Further work is required to test this hypothesis.

7.4.4 Conclusion

In conclusion, it appears that male and female red kangaroos follow different routes to attain the same goal of maximising their reproductive success. Male red kangaroos attempt to grow as large as possible, thereby dominating other males and reducing their access to females. This is a risky strategy that puts them at a severe disadvantage if food availability falls, since they can no longer satisfy their energetic requirements for survival. In contrast, females take a conservative strategy that attempts to maximise survival, thereby maximising reproductive output. I hypothesise that these alternative routes evolved because 172 of a combination of an unpredictably variable food resource and the fact that females cannot achieve as many successful matings as males in the same amount of time. Chapter 8

Is the concept of carrying capacity useful in variable environments?

8.1 Introduction

How many animals can an ecosystem support? This is a fundamental question for range and wildlife managers of plant-herbivore ecosystems. One of the biggest problems facing the semiarid and arid regions of the world is sustainable landuse by domestic herbivores. Range managers have attempted to quantify the density of domestic herbivores that would provide maximum productivity without permanent damage to the range. Their failure to accurately predict sustainable herbivore density is highlighted by the past, and current, trend of land degradation caused by overgrazing (Breman and de Wit 1983, Woods 1984). Wildlife managers usually have different goals. Wildlife management objectives include th~ conservation of species and biological processes in natural areas, using wildlife for a sustained yield, or control if it is a pest (Shepherd and Caughley 1987b). Quantification of carrying capacity is usually an important part of these objectives.

The dynamics of a plant-herbivore system can be represented by three components (Caughley 1979); 1) the functional response of the herbivore, which describes plant biomass intake by herbivores as a function of standing plant biomass, 2) the numerical response of the herbivore, which describes the rate of increase of herbivores as a function of standing plant biomass, and 3) the plant growth response, which describes the rate of increase of plant biomass as a function of plant density. Following the nomenclature of Noy-Meir (1975), let us assume that, in the absence of grazing, vegetation increases at a rate described by some function of vegetation biomass G(V), where Vis total vegetation biomass. Total vegetation biomass is depleted by herbivores at a mean rate of c(V) per herbivore. If His the density of herbivores, then net consumption by herbivores is Hc(V). The rate of change of vegetation can then be described by the relation; 174

dV dt = G(V)- Hc(V) (8.1)

In deterministic ecosystems, the interaction between plant growth, and plant consumption by herbivores and herbivore growth will eventually lead to an equilibrium. At this point the rate of growth of plants equals the rate of consumption by herbivores. Carrying capacity is the name given to the equilibrium eventually reached between herbivores and plants (Caughley 1979). Therefore, herbivores are at their carrying capacity when;

dH dV ----0 (8.2) dt - dt -

A phase-plane trajectory of herbivore density and vegetation biomass in a deterministic environment is illustrated in Fig. 8.1 a. In this example the plant herbivore system reaches a point equilibrium. Alternatively, the system can reach a stable limit cycle ifthere is some periodic time dependence~ such as seasonal variation in the rate of plant growth (Fig. 8.1 b).In this last case, the herbivore's functional and numerical responses will tend to destabilise the system, while plant growth rate will have a stabilising effect (May 1973). 175

8.1 a)

0.5

~ 0.4 C QI 0 ~ g € 0.3 QI J:

0.2

0.1

0 0 500 1000 1500 2000 2500 3000 3500 Vegetation Biomass

8.1 b)

0.8

0.7

~ 0.6 ·0 C QI 0 QI 0.5 ...0 .2: .0 ...QI J: 0.4

0.3

0.2

0.1

0 0 500 1000 1500 2000 2500 3000 3500 Vegetation Biomass

Figs 8.1 a and b. a) Phase-plane trajectory of a herbivore eruption in a deterministic environment. The plant-herbivore system reaches a point equilibrium, and b) phase- 176 plane trajectory of a herbivore eruption in an environment with some periodic time dependence. The plant-herbivore system reaches a limit-cycle.

Although carrying capacity might seem to be a simple concept, it has had a very confusing history. As Dhondt (1988) points out in his recent review of the definitions and usage of carrying capacity, it is rarely defined. Hadwen and Palmer (1922, in Edwards and Fowle 1955) originally introduced the term carrying capacity to describe the relationship between domestic stock and their environment, and it was then applied to wild herbivores (Leopold 1933). Hadwen and Palmer (1922) defined carrying capacity as the density of stock that could be grazed for a definite period without damage to the range, although this definition is conditional on the definition of"damage". Leopold (1933) defined carrying capacity as the density reached by a population at a particular site, when the population is limited by some external factor such as food. Range managers followed Hadwen and Palmer's (1922) definition, while wildlife managers followed Leopold's (1933). Thus, range and wildlife managers applied the concept in different ways, the distinction between the two definitions being rarely explained, and confusion over the concept became entrenched.

Caughley (1979) distinguished the separate meanings and introduced the terms "ecological carrying capacity" for the equilibrium that results from the unmanipulated interaction of plants and herbivores, and "economic carrying capacity" for the equilibrium imposed by sustainable harvesting of the herbivore population. An undisturbed plant-herbivore system is at ecological carrying capacity when dH/dt = dV/dt = 0. An economic carrying capacity can be imposed upon this system if the herbivore population is sustainably harvested. Under sustainable harvesting a new equilibrium will be formed, the density of herbivores will be lower and the biomass of plants will be higher than the equilibrium in the unharvested system. The confusion between these different meanings probably arises because even though the rate of change of plants and herbivores equals zero in both cases, ecological carrying capacity and economic carrying capacity refer to different densities of plants and herbivores.

An implicit feature of all definitions is the assumption that the system will approach or reach equilibrium, if given enough time. While this may be true for slightly variable environments, it is certainly invalid for highly variable environments 177 where plants and herbivores rarely, if ever, reach equilibrium (Shepherd and Caughley 1987).

The aim of this chapter is to review models and methods presently used to determine the carrying capacity of domestic and wild herbivores. In addition, a general model for calculating carrying capacity in slightly stochastic and highly stochastic environments is presented, with particular focus on the concept of carrying capacity in stochastic environments and how this model relates to the management of wild and domestic herbivores.

8.1.1 The Alternative Models

A review of the literature revealed six main methods of determining carrying capacity. Each method was examined on the basis of three criteria; 1) the method had to be objective, 2) it had to produce quantitative estimates of carrying capacity and, 3) it had to be suitable for deterministic and stochastic environments. If any criterion was not satisfied the method was rejected.

8.1.1.1 The rating system

The rating system (Condon 1968, Condon et al. 1969) was developed to determine the carrying capacity of domestic herbivores in the arid rangelands of Australia. The method involves determining the productivity of an area based on its soils (fertility and moisture storing ability), topography, hilliness and areas unsuitable for grazing, tree density, condition (pasture deterioration and soil erosion), and rainfall. Each of these factors is given a rating scale derived from a comparison with an area of "known" grazing capacity, referred to as the reference area. The authors do not discuss the precision of the "known" carrying capacity estimate, and its value must be accepted with caution. The rating of each factor is a multiplier given unity if it has the same value as the reference area, less than one if in poorer condition and greater then one if in better condition. The ratings are then summed and compared with the value of the reference area. If the sum of the ratings falls below that of the reference area the grazing capacity estimate is proportionally reduced, and if the sum 178 falls above then the estimate is proportionally increased. If the sum equals the value of the reference area then the two areas have the same grazing capacity.

The rating system does not meet any of the criteria set out above. The method uses some subjective judgements, and because of this is open to bias. Although the rating system produces an estimate of animal density, this estimate is not a measure of carrying capacity. The estimate produced by the rating system is a conservative stocking rate estimate, that is more akin to the notion of safe capacity d[scussed by Noy-Meir (1978). Finally, the method cannot incorporate stochasticity and the stocking rate estimate does not reflect the variance in productivity inherent in stochastic systems such as the arid zone.

8.1.1.2 Range succession

The range succession model (Stoddart and Smith 1943, 1955) was developed as a range management system in response to land degradation caused by overgrazing by domestic herbivores in the U.S.A. The main concepts of the model are that; 1) any plant community has a single stable equilibrium, or climax, that the community will tend to approach after disturbance; 2) a disturbance, such as grazing, creates a disturbance climax or disclimax; 3) the successional tendency of the plant community and the destabilising effect of the grazers act in opposing directions; 4) the disclimax becomes a new stable equilibrium; 5) a range manager can set the disclimax by adjusting herbivore stocking rate (Westoby 1979/80, Westoby et al. 1989). The object of management using the range succession model is to set a stocking rate which maximises animal productivity while maintaining pasture condition. This stocking rate has been referred to as the carrying capacity of the range (Stoddart et al. 1975), and matches Caughley's (1979) concept of economic carrying capacity.

There are now a large number of studies that have found that the assumptions of the range succession model do not hold in all environments. Westoby (1979/80) and Westoby et al. (1989) cite many of these studies and detailed discussion can be found in these papers. Essentially, in areas where the concept ofClementsian succession (i.e. all successional pathways in the same climatic region lead to a single common climax) does not hold, the range succession model appears to be invalid. 179

The range succession model satisfies only one of the criteria of a generalised model for calculating carrying capacity, since it produces quantitative estimates. The model fails the first and third criteria because the inventory of range condition is often subjective, and stochasticity cannot be incorporated into its methods.

8.1.1.3 Key species

The key species concept (Standing 1938) was developed as a method for determining grazing capacities for domestic stock on rangelands. The concept was developed further by Smith (1965) to determine common use grazing capacities (i.e. use by two or more animal species). The characteristics of a key species include high palatability, resilience to grazing and competition, and they are nutritious, abundant and productive (Standing 1938). The plant species that meet these requirements provide the basis for decisions on the level of usage and stocking rate of the range. The method hinges on determining "proper use" for each plant species by each animal species. Smith (1965) does not clearly define proper use, but it seems to be a function of dietary intake and pasture biomass, where animal use of a plant species is not allowed to exceed some minimum plant species biomass. For each plant species in the diet a "forage factor" is calculated that is the product of a species' proper use and its relative contribution to pasture composition. The forage factors are then summed to provide an estimate of total permissible use. Stocking rate is then set by adding stock to the range until the intake equals total permissible use. The method Smith (1965) presented can calculate common use grazing capacities for two herbivore species, and the technique was extended by Connolly ( 197 4) using linear programming to include n species.

The key species approach follows three assumptions; i) the key species are abundant so that food intake of any plant species is not limited, ii) common use of the range does not alter dietary preference, and iii) food consumption is proportional to herbivore population density (Smith 1965). There is a potential problem with these assumptions. If food intake becomes limited, which is likely to occur in a highly variable environment, all of these assumptions are likely to breakdown. Since a period 180 of low plant biomass is a critical time for the preservation of range condition, a method that fails at this time would not be of much use.

The method only passes the second criterion of producing quantitative carrying capacity estimates. The first criterion is failed because the method involves subjective setting of parameter values. As Smith (1965) points out, proper use values are often set by convenience. The method cannot incorporate stochasticity into its methods. It assumes that the environment is purely deterministic and that parameters will not change through time. This is an unrealistic assumption and it is difficult to imagine under what conditions it would hold.

8.1.1.4 Productivity-stocking rate models

Mathematical relationships between animal productivity and stocking rate have been proposed by several authors (Harlan 1958, Mott 1960, Petersen et al. 1965, Jones and Sandland 1974). Although the relationships differ in form, some are exponential (Mott 1960) others linear (Jones and Sandland ·1974), a common aspect is that productivity per animal declines as stocking rate (animals per unit area) increases. This is hypothesised to occur because competition for food will reduce intake per animal. In all models, productivity per unit area is assumed to be a curvilinear function of stocking rate. Initially from infinitely small stocking rates, productivity per unit area increases as stocking rate is increased. A point is reached after which productivity per unit area decreases as stocking rate is increased. The stocking rate at the point of maximum productivity per unit area, or maximum productivity per animal, or a combination of these two measures is referred to as the optimum stocking rate, or carrying capacity (Mott 1960). The models of Mott (1960) and Jones and Sandland (1974) are the most widely cited in the literature, and the remaining discussion of this group of models will be restricted to these two papers.

Mott (1960) proposed that gain per animal (ya) and stocking rate (x) could be related by the function;

(8.3) 181

where d, a and b are constants. (Mott originally used k to represent the y intercept, but I have changed this constant to d to avoid confusion with K, carrying capacity, used in models such as the logistic). The model was derived from eight stocking rate trials in six studies. From each trial, the stocking rate which gave the highest animal gain was deemed the optimum. The separate trials were unified by representing stocking rate as a ratio of actual stocking rate and optimum stocking rate. Thus, the optimum rate had a ratio of 1.0 and ratios less than, or greater-than, 1.0 were respectively sub-optimal or super-optimal. Productivity per animal, and productivity per unit area were transformed in a similar way. When productivity per animal and productivity per unit area are plotted on the same graph against stocking rate, the stocking rate at the intersection of these two curves represents the optimum stocking rate, or carrying capacity of the pasture.

Jones and Sandland (1974) present a similar model to Mott (1960), but suggest that animal productivity is a linear function of stocking rate where;

Ya =e-mx (8.4)

(y0 and x are the same as before and e and mare constants). Productivity per unit area (yh) can then be easily calculated by multiplying (8.4) by x, giving;

(8.5)

Maximum productivity per unit area occurs when x = e/2m. Substituting this x

value into (8.4) we find that productivity per unit area is maximised wheny0 = e/2, which is half the stocking rate at which productivity per animal= 0. Jones and Sandland (1974) found that the data from a large number (144) of stocking rate trials fitted their model tightly. In their study they applied a similar transformation to the one used by Mott (1960) thereby scaling each stocking rate, productivity per animal and productivity per unit area by its respective actual to optimum ratio. But unlike Mott (1960), Jones and Sandland (1974) equate maximum productivity per unit area with optimum stocking rate. 182

Both models share some common assumptions, but two are of particular relevance to this analysis; 1) optimum stocking rate can be sustained without substantial adjustment to animal density, and 2) stocking rate and forage productivity are independent (Norton 1986). These assumptions would probably hold for the temperate and tropical, grass and grass-legume pastures on which the data to support the models were collected. Plant production in these environments is relatively reliable. But in environments such as the semiarid and arid zones, that can have high variance both within and between seasons, these assumptions would not hold.

The models have been criticised for the productivity-stocking rate relationship they use. Jones and Sandland (1974) suggest that a linear relation provides a better fit to the data than the modified exponential relation suggested by Mott (1960). Connolly (1976) points out that it is statistically difficult to distinguish between a linear and a more complex association when only a few stocking rates are used. If the form of the productivity-stocking rate relationship is not known, assuming linearity, or some other association, can lead to under- or overestimating optimum stocking rate. For example, if linearity is assumed and the true productivity-stocking rate relationship is curvilinear, and the assumed optimum is much less than the true optimum, the linear estimate will lead to over-estimation of the true optimum stocking rate and underestimation of animal productivity at the true optimum (Connolly 1976). The opposite will occur if the true optimum is less than the assumed optimum.

The productivity-stocking rate models pass the first two criteria for a generalised model of carrying capacity. The methods are objective and they produce quantitative estimates of carrying capacity. However, because the models are empirically derived they cannot incorporate stochasticity in a biologically meaningful way. Furthermore, the assumptions of the models breakdown in a variable environment. The concerns expressed by Connolly (1976) regarding the form of the productivity-stocking rate relationship must also be taken into account when evaluating the validity of these models. 183

8.1.1.5 Habitat use/availability models

Habitat evaluation models (Verner et al. 1986) have been used to indirectly measure the carrying capacity of an environment (Hobbs and Hanley 1990). These models rely on habitat use and availability data to explain differences in the spatial use patterns of animals in relation to vegetation communities, topography and other factors that may influence animal distribution and abundance (Hobbs and Hanley 1990). An implicit assumption of this approach is that these data reflectihe value of different habitat types for animal populations. This assumption is based on the argument that animals will seek out areas that can best supply their requirements, and this will result in greater use in higher quality habitats (Schamberger and O'Neil 1986). Habitat use/availability indices will be directly related to habitat value (Fagen 1988) when animal distribution is ideal free (Fretwell and Lucas 1970, Fretwell 1972). According to the habitat evaluation models carrying capacity will be directly proportional to the use/availability indices.

The habitat evaluation approach to determining carrying capacity has been criticised for its lack of generality and restrictive assumptions. From a simulation study, Hobbs and Hanley (1990) found that the method did not predict habitat use in a non-deterministic environment. Even small, infrequent changes in natality resulted in large temporal variation in simulated habitat use/availability indices. Hobbs and Hanley's (1990) simulations indicate that animal distribution will reflect carrying capacity only when; 1) animals follow an ideal free distribution, 2) the environment permits long-term stable equilibria between animals and plants, and 3) the use/availability data are obtained after the populations reach equilibrium. Hobbs and Hanley (1990) suggest that these conditions will rarely be satisfied and that indices of animal density may not lead to reliable estimates of habitat value, and consequently density indices will not reflect habitat carrying capacity.

The habitat evaluation method passes the first two criteria of a generalised model for calculating carrying capacity. The method is objective and produces quantitative estimates of habitat carrying capacity. The method fails the third criterion because it fails to be predictive in a variable environment. 184

8.1.1.6 The nutritional approach

Food, or nutrient, based predictions of carrying capacity relate an individual animal's nutrient requirement to the nutrient's availability in a habitat. This approach is prevalent in the wildlife literature (Potvin and Huot 1983, Hobbs et al. 1982, Moen 1973, Hobbs and Swift 1985, Rowe-Rowe and Scotcher 1986, Mentis and Duke 1976). Nutrients such as nitrogen (Hobbs et al. 1982, Hobbs and Swift 1985), energy (Hobbs et al. 1982, Potvin and Huot 1983, Hobbs and Swift 1985) or plant dry-matter (Christie and Hughes 1983, Crete 1989) have been used as the constraining nutrient upon which carrying capacity is calculated. Algorithms for estimating carrying capacity are similar but vary in sophistication. Hobbs et al. 's (1982) (Eq. 8.6) model for elk is representative of this group of models;

i:(B; X F;) k- i (8.6) - (Rq x Days)-En where k is the number of animals that can be supported per unit area; n is the number of principal foods; B; is the consumable biomass of principal forage species i; F; is the nutrient content of principal forage species i; Rq is the individual elk requirements per day; Days is the number of days animals occupy the habitat; and En is the endogenous reserve of nutrient per herbivore.

There are a number of implicit assumptions of this group of models. The method assumes that an individual's nutrient intake is temporally and spatially constant, but optimal foraging models have found that animals facing spatio-temporal variability in food quality and abundance can quickly vary their foraging behaviour to maximise nutrient intake. Furthermore, many of the models assume that an animal will forage to satisfy some minimum nutrient requirement, when nutrient maximisation is the most common goal for generalist herbivores (Belovsky 1986a, b, 1994). The nutrient approach also assumes that the plant-herbivore system has reached a stable equilibrium. In disequilibrium communities, food availability will not match food consumption and the method will fail to predict herbivore density, for the same reasons given for the failure of the habitat use/availability models. Betraying 185 this method's general use as a method of calculating carrying capacity is the poor agreement in some studies between predicted carrying capacity estimates and measured animal densities. For example, Wallmo et al. (1977) measured the abundance of mule deer (Odocoileus hemionus) on a North American range in summer and winter as 10,200 and 9,000 deer respectively, but their calculated carrying capacity ranged from 350,000 deer in summer to no deer in winter. Their method was clearly inaccurate. Similar disagreement between predicted and observed animal density was recorded by Hobbs et al. (1982) and Crete (1989) using similar methods.

The nutrient based approach passes the first and second, but fails the third criterion of a general model for calculating carrying capacity. The method is objective and produces quantitative estimates of carrying capacity. In theory, stochasticity can be incorporated into the model using the variance of the mean of each variable, and then solving for carrying capacity. However, an implicit assumption of the nutrient approach not formally stated in the literature, is stability in the plant-herbivore interaction (i.e. the system is at, or close to, equilibrium). This assumption would rarely hold in a highly variable environment, where plants and herbivores are commonly not at equilibrium. Evidence of the method's failure to cope with environmental stochasticity is highlighted by a number of studies in variable environments, with severe winters and mild summers, which fail to make accurate predictions of carrying capacity (Wallmo et al. 1977, Hobbs et al. 1982, Crete 1989).

None of the methods reviewed in the preceding sections were able to incorporate stochasticity in a biologically meaningful way, without invalidating the assumptions of the model. For this reason these methods were collectively rejected and an alternative was sought.

8.1.1. 7 The interactive model

The interactive model (Caughley 1976, Caughley and Lawton 1981) relates plant biomass to the rate of increase and food intake of herbivores. The model has four components; plant growth response, herbivore functional response, herbivore numerical response, and herbivore intrinsic response (Caughley and Gunn 1993). The 186 interactive model can be divided into two classes; 'interferential systems' in which herbivores may reduce one another's ability to harvest food and 'laissez-faire systems' where there is no interference between individual herbivores (Caughley 1976). Thus, in the interferential system, herbivore functional, c(V,H), and numerical response, N(v,H), are dependent on plant biomass and herbivore number;

dV dt = G(V) - Hc(V, H) _ (8.7a)

dH -=HN(V H) (8.7b) dt '

Whereas, in the laissez-faire system, herbivore functional, c(V), and numerical response, N(V), are independent of herbivore number (May 1981);

dV dt = G(V) - Hc(V) (8.8a)

dH -=HN(V) (8.8b) dt

The components of the model can be represented as response functions (Caughley and Gunn 1993):

1. Plant growth response is the rate of increase of edible forage as a function of standing plant biomass and environmental variables such as rainfall and temperature;

LiV = G(V,E;) (8.9)

where Li Vis the plant growth increment or decrement; Vis plant biomass; E; is the ith environmental variable; and G is the growth function that relates V and E;, The form of the relationship (Eq. 8.9) for a specific plant community must be established by measurement, and cannot be chosen a priori from the numerous forms available. However, the general shape is convex upward with a single maximum (Noy-Meir 1975). 187

2. Herbivore functional response is the rate of forage intake per herbivore as a function of plant biomass. a) Laissez-faire system: this function has many alternative forms (see May 1981: Chapter 5, Table 5.1), and the inverted exponential form (Ivlev 1961, Short 1986) chosen here has been widely used in models of grazing systems (Noy-Meir 1978);

[-(v-v,)/ J} I= Is { 1-e /(v,-v,) (8.10)

where I is food intake rate at plant biomass V; Is is the maximum food intake rate; V, is the ungrazable residual plant biomass; and ~ is the plant biomass at which a fraction (1-e-• ~ 0.63) of the maximum intake rate is attained (Noy-Meir 1978, Short 1986).

b) Interferential system: this function is modelled i~ a similar way to the laissez-faire system except that there is an interference factor which limits food intake rate at high herbivore density (May 1975, 1981);

[-(v-v,)/(v,-v,)]} I= Is { 1-e +H (8.11)

where cl> measures the strength of the interference, per herbivore, between herbivores and cl> > 0, and the other variables are as previously defined. [Note that the functional response presented by Caughley and Lawton (1981) is incorrect because by definition, in an interferential system herbivore's reduce one another's food intake rate, and their function is independent of herbivore density. This problem is discussed in more detail in Barlow (1985)]. 188

3. Herbivore numerical response is the rate of increase of the herbivore population as a function of plant biomass. a) Laissez-faire system: again the form is the inverted exponential (Bayliss 1987), which has been widely used in models of grazing systems (Caughley 1976, Caughley and Lawton 1981, Caughley 1987b);

(8.12) where r is the yearly exponential rate of increase; a is the maximum rate of decrease in the absence of food; c is the rate at which a is ameliorated at high plant biomass; d is the demographic efficiency of the herbivore (its ability to multiply at low plant biomass), and the other variables are as previously defined.

b) Interferential system: the form taken is again similar to the laissez-faire but modified by the inclusion of an interference factor which reduces the intrinsic rate of increase of the herbivores at high herbivore density;

(8.13)

where Y is a proportionality constant that represents the amount of food needed to sustain a herbivore at equilibrium; rm is the intrinsic rate of increase, and the other variables are as previously defined (Caughley and Lawton 1981 ).

4. Herbivore intrinsic response is the rate of increase of the herbivore population as a function of its own density. The herbivores have some sort of spacing behaviour, for example territoriality, which reduces their rate of increase as population density increases. The intrinsic response can be easily incorporated into the numerical response of either the laissez-faire or the interferential systems, since it reduces r as H increases, but will only affect the functional response of the interferential system. Therefore, it may be considered a special case of the interferential system. 189

The interactive model can then be formed. This example models a laissez-faire system, which has been found to be appropriate for red kangaroo populations (Caughley 1987b, Caughley and Gunn 1993). The rate of change of the plant population is represented by;

dV = /lV - HC (1- e[-/(v,)J) (8.14) dt s (where vr = 0)

The rate of change of the herbivore population is represented by;

(8.15)

The interactive model has been used to examine the mechanisms of change through which a plant-herbivore system reaches equilibrium (Caughley 1976, Caughley and Lawton 1981), or why a system does not reach equilibrium (Caughley 1987b). The interactive model has not been used previously to estimate the carrying capacity of herbivores. But by definition the equilibrium density reached by the herbivore is the carrying capacity of that herbivore. The mechanisms that produce equilibrium density and carrying capacity density are identical (Caughley 1979).

A problem exists in trying to calculate carrying capacity when the plant herbivore system does not reach equilibrium. Most definitions equate carrying capacity with the density of animals that can be sustained for a long period of time (Dasmann 1964, Collier et al. 1973, McCullough 1979, 1992). lfwe apply this definition to a plant-herbivore system, we are implying that the system will reach an equilibrium, at which point the rate of forage production equals the rate of forage consumption (Caughley 1979). If the destabilising forces of environmental and intrinsic stochasticity dominate, the system will not reach a stable equilibrium and the method discussed in the preceding paragraph will no longer work. Therefore, we need to remove the "long time" component from the definition of carrying capacity. Caughley's (1979) definition does not include a time component and states that a herbivore's carrying capacity is reached when the rate of change of the herbivore 190 population and the plant population equals zero. So, Caughley's (1979) is a general definition which applies to deterministic and stochastic systems.

Ifwe examine the rate of change of plants and herbivores in a stochastic system on a short time scale, for example one season, the dynamics will approximate a deterministic system. It is only when we study the stochastic system over a much longer period of time that the true dynamic nature of the system is revealed. Using the herbivore numerical response we can calculate the plant biomass at which the herbivore population will have a rate of increase (r ) of zero. Giving;

(8.16)

solving for V* and substituting this value into Eq. 8.14 gives herbivore density when dV /dt = O;

(8.17)

solving for H* when V, = V* gives the carrying capacity.

It should be noted that stochastic systems can be highly labile. H* will not be a constant, but will rise or fall according to ll. V. There is a similarity between this method of calculating carrying capacity and the method outlined in the preceding section, "The nutritional approach". There is, however, a fundamental difference between the two methods. The nutritional approach sets the level of available resources arbitrarily, the value of the level being derived from an estimate of appropriate use (e.g. Christie and Hughes 1983, Potvin and Huot 1983), or minimum nutrient content (Hobbs et al. 1982, Hobbs and Swift 1985). The level of appropriate use may or may not be related to the dynamics of the plant and herbivore populations, as it is in the interactive model. But the greatest advantage that the interactive model has over the nutritional approach, and all the other approaches, is its ability to 191 examine the effect of stochasticity on the rates of change of the plant-herbivore system and hence on carrying capacity.

The interactive model is the only method that passes all the criteria of a general model for calculating carrying capacity in deterministic and stochastic plant herbivore systems. The method is objective and it produces quantitative estimates of carrying capacity. Most importantly, environmental and intrinsic stochasticity can be incorporated into the interactive model.

8.2 Materials and Methods

The remainder of this chapter will examine the use of the interactive model for determining carrying capacity in stochastic and deterministic environments. The modelled system uses variables determined in a shrubland-red kangaroo assemblage from western New South Wales. The shrubland varies in composition from monospecific stands of black bluebush (Maireana pyramidata) or pearl bluebush (M sedifolia), to mixed stands of both species. The interbush areas support a mixed cover of annual and perennial grasses and forbs (Cunningham et al. 1992), and can be highly productive after rain. The population dynamics of this assemblage have been modelled before (Caughley 1987b, Caughley and Gunn 1993), and found to exhibit a high degree of environmental and intrinsic stochasticity and will be used to represent a stochastic system. The slightly variable system will be represented by the same assemblage, but with stochastic variation reduced to levels representative of a stable environment. For the purpose of this study environmental stochasticity, in this case rainfall, will be reduced to 10 percent of the mean (Table 8.1).

SD SD CV CV Season Months Mean (mm) Stochastic Stable Stochastic Stable S stem S stem S stem S stem Summer Dec.-Feb. 78 80 7.8 1.03 0.10 Autunm Mar.-May 57 66 5.7 1.16 0.10 Winter Jun.-Aug. 43 34 4.3 0.79 0.10 Spring Sep.-Nov. 43 34 4.3 0.79 0.10 Annual Dec.-Nov. 221 136 22.1 0.62 0.10

Table 8.1. Seasonal rainfall recorded at the Tibooburra Post Office weather station. The stochastic standard deviation (SD) and coefficient of variation (CV) represent 192 actual data, while the stable system data were calculated by reducing SD to 1110th of the mean. Rainfall records represent 107 years of collection.

Although on average more rain falls during the summer-autumn seasons, the winter-spring rains are more reliable. Thirty-five percent of the annual total falls in summer, and the serial correlation in summer between successive years was only r = 0.0004. Of the remainder, 26 percent fell in autumn (r between successive years of 0.0016) and 19.5 percent fell equally in winter (r = -0.11) and spring (r = 0.29). The coefficient of variation within any season ranges from 1.16 in autumn to 0. 79 in winter/spring. Serial correlation between years is very weak (r = 0.06). The low serial correlation between successive years and in the same season across years indicates that rainfall is highly unpredictable from one year to the next. These high levels of variance and aseasonality are characteristic of the rainfall over much of Australia's semiarid and arid areas, and ranks these environments amongst the most unpredictably variable in the world.

The red kangaroo was chosen as the herbivore species because its functional and numerical response have been thoroughly studied (Bayliss 1987, Short 1985, 1987) and are well understood (Caughley 1987b, Caughley and Gunn 1993).

8.2.1 The model

The response functions are represented by the following equations:

Plant growth response;

'1.V =-55.12-0.01535V-0.00056V2 +25R (8.18) where '1. Vis the standing biomass growth increment (kg/ha), or decrement, for three months; Vis the standing biomass at the start of the three months; and R is the rainfall (mm) over the three months. The coefficient of R used here is different from Robertson's (1987) coefficient of 3.946 for the reasons given by Caughley (1987b). I 193 assumed that each three month fl. V could be subdivided into 13 equal intervals (13 weeks= 3 months), so all calculations were made on a weekly basis.

Red kangaroo functional response;

(8.19)

where I is the per capita intake of food over one week, assuming a mean body mass of 35 kg; from Short (1987).

Red kangaroo numerical response;

r = -1.6 + 2[ l-/-<>.007V)] (8.20) where r is the exponential rate of increase, from Bayliss (1987) as modified by Caughley (1987b).

Intrinsic stochasticity was incorporated into the plant growth increment or decrement as a random draw from a normal distribution with a mean equal to the solution of the regression (Eq. 8.18) and one standard deviation. The standard deviation, of 52 kg/ha, was calculated from the residual of the regression (Robertson 1987). Intrinsic stochasticity was considered to represent demographic stochasticity and sampling error, and was treated equally in the highly stochastic and slightly stochastic systems.

Environmental stochasticity was incorporated as a random draw from a lognormal distribution with two standard deviations. Seasonal rainfall was found to follow a lognormal distribution (Figs 8.2 a-d). Seasonal means from 100 year simulations (n=lO) oflognormal rainfall were not significantly different (P > 0.05) from recorded seasonal means. In contrast, seasonal means taken as random draws from a normal distribution were significantly different (P < 0.05) from the recorded rainfall. 194

8.2 a) 8.2 b)

Summer Autumn JO so

25 ••

20 JO

Frequency 15 Frequency

20 10

75 150 225 300 375 450 525 600 75 150 225 300 375 450 525 600 Rainfall (mm) Rainfall (mm)

8.2 c) 8.2 d)

W inter Spring so ••

" JO

25 JO

Frequency Frequency 20

20 15

10 10

75 150 225 300 375 450 525 600 75 150 225 300 375 450 525 600 Rainfall (mm) Rainfall (mm)

Fig. 8.2 a-d. Frequency distribution of seasonal rainfall recorded at the Tibooburra Post Office, a) summer, b) autumn, c) winter, and d) spring.

Simulations were run for 100 years, and each system was replicated 10 times. Vegetation biomass and herbivore density were calculated for each week of the simulation. The starting conditions for all simulations were H = 0.1 kangaroos/ha and V = 250 kg/ha.

Solving Eq. 8.14 for dV/dt = 0 gives a vegetation biomass of approximately 230 kg/ha. Carrying capacity (H*) could then be calculated on a seasonal basis from Eq. 8.17 and V=230 giving; 195

2.5R-88.27 H*= 85.9 (8.21)

8.3 Results

The highly dynamic nature of the highly stochastic system is exemplified by the non-periodic behaviour of the kangaroo density-time trajectory (Fig. 8.3 a), and the vegetation biomass - time trajectory (Fig. 8.4 a). The system is characterised by high amplitude fluctuations. In contrast, the slightly stochastic system is characterised by low amplitude fluctuations (Figs 8.3 band 8.4 b).A feature shared by both systems is the high frequency of fluctuations. The similarity in the frequency of plant herbivore fluctuations for the two systems suggests that stochasticity has a similar effect on all systems, regardless of its magnitude. The low level of environmental variance in the slightly stochastic system did not dampen the frequency of plant herbivore fluctuations, only its amplitude.

8.3 a)

'ii E 0 .s i 0.8 C Cl) 0 e0 ~ 0.6 C., :.::

0.4

0.2

o~------__.0 20 40 60 80 100 Year 196

8.3 b)

co ,E 0 .s ~ 0.8 "iii C: ~ ~ ~ 0.6 C: ~

0.4

0.2

o.__------~0 20 40 60 80 100 Year

Figs 8.3 a and b. Modelled trajectory ofred kangaroo density through time in a) a highly stochastic system, and b) a slightly stochastic system. Starting conditions were H = 0.1 kangaroos/ha, and V = 250 kg/ha. Data used in the figures are from one representative replicate of the simulations of each system. 197

8.4 a) ., .r. CJ ~ 800 "' "'E .Q ID C: .Q.; 600 Q) CIJ G) > 400

200

0 0 20 40 60 80 100 Year

8.4 b)

1000

'iu t ;. 800 :g Ill E .Q Ill C 0 600 '""'J!l G) Cl ~ 400

200

o~----~------0 20 40 60 80 100 Year

Figs 8.4 a and b. Modelled trajectory of vegetation biomass through time for a) a highly stochastic system, and b) a slightly stochastic system. Starting conditions were

H = 0.1 kangaroos/ha, and V = 250 kg/ha. Data used in the figures are from one representative replicate of the simulations of each system. 198

The slightly stochastic and highly stochastic systems are centripetal sensu Caughley (1987b ), in that they try to reach equilibrium. Neither system reaches equilibrium because of the constant buffeting they receive from the environment. However, the degree of deviation from equilibrium is an important difference between the systems. The slightly stochastic system never deviates far from equilibrium (Fig. 8.5 b), and the trajectory of the phase-plane converges rapidly to aperiodic cycles around the equilibrium within well defined limits. Ifwe ignore the tail formed by the starting conditions, the population trajectory oscillates between 0.45 - o:67 kangaroos/ha and 155 - 350 kg/ha of vegetation. In contrast, the highly stochastic system is rarely near equilibrium, its phase-plane following a random walk (Fig. 8.5 a) between 0.06 - 0.99 kangaroos/ha and 0 - 840 kg/ha of vegetation.

8.5 a)

(II ,E ci 5 i 0.8 C: G) C e0 ig, 0.6 C: (II ~

0.4

0.2

o~------~------~------'0 200 400 600 800 1000 Vegetation Biomass (kg/ha) 199

8.5 b)

ro € ci .s b 0.8 "iii C G) 0 ~ ig, 0.6 C ~

0.4

0.2

0'------~----~-----~--~-~------' 0 200 400 600 800 1000 Vegetation Biomass (kg/ha)

Figs 8.5 a and b. Phase-plane trajectories of a) a highly stochastic system, and b) a slightly stochastic system. Starting conditions were H = 0.1 kangaroos/ha, and V = 250 kg/ha. Data used in the figures are from one representative replicate of the simulations of each system.

Environmental stochasticity reduces mean herbivore density, and as a consequence increases mean plant biomass (Table 8.2). But associated with the stochasticity is greatly increased variance. In comparison, the slightly stochastic system has only about one-third the variance of the highly stochastic system. In both systems vegetation biomass is less variable than herbivore density. This occurs because of the asymmetry in the numerical response of kangaroos. Their maximum rate of increase (rm) is 0.4, while their maximum rate of decrease (a) is 1.6. In addition, the slope of the numerical response becomes increasingly steeper as vegetation biomass falls. A given increment in vegetation biomass results in a smaller population increase than an equivalent decrement will reduce it. Or as Caughley and Gunn ( 1993, p. 50) clearly put it "kangaroos decrease much faster than they increase." 200

Vegetation Kangaroos System SD CV no.Iha SD CV Stochastic 299 t 148 0.49 0.33 t 0.23 0.70 Stable 241 t 38 0.16 0.54 t 0.10 0.19

Table 8.2. Comparison of the simulation mean, mean standard deviation and coefficient of variation of the vegetation biomass and kangaroo density from highly stochastic and slightly stochastic (stable) systems. Mean vegetation biomass, mean kangaroo density and standard deviations are the means of 10 simulations. (t significantly different at 0.001 level).

As a system approaches equilibrium, the rate of change of the players in the system will tend toward zero. In the plant-herbivore system this means dH/dt ---+ 0 and dV/dt---+ 0. We can use these criteria to examine how far a given system deviates from equilibrium, and consequently from carrying capacity. Figs 8.6 a and b show plots of dH/dt against dV/dt. In the slightly stochastic system (Fig. 8.6 b) the rates of change never deviate far from zero, and the plot shows a dense cluster of points around the equilibrium point (0,0). This implies that this system is at or close to carrying capacity most of the time. In contrast, the highly stochastic system (Fig. 8.6

a) has a large amount of scatter, particularly along the axes dH/dt = 0 and dV /dt = 0. The concentration of points along the two axes suggests that if one component, for example vegetation biomass, is changing rapidly the rate of change in the herbivore population will be close to zero. This will then switch and herbivores will change rapidly, while vegetation change will be close to zero. This occurs because of asymmetry in the numerical response of the kangaroos. The kangaroos cannot increase quickly when there is a flush of plant growth and abundant food, so the vegetation can increase at a much faster rate than the herbivores can consume it. At a later stage when the vegetation is not increasing, either due to drought or the negative effect of standing biomass on growth, the herbivores continue to graze and deplete standing biomass. In the absence of rain they may rapidly deplete plant biomass and undergo a spectacular population crash when they over-exploit their food source. When the rain comes and the plants start growing there are too few herbivores to prevent another flush of growth and the cycle starts anew. This system is seldom, if ever, close to equilibrium. 201

8.6 a)

0.008 . . . . ········· ...... 0.004 -

-0.004 ~- I -0 -0.008

-0.012

-0.016

-0.02 -40 -20 0 20 40 60 dV/dt

8.6 b)

0 .01

0.005

0 .

~- -0.005 I -0 •

-0.01

-0.015

-0.02 .__----~------~------~ -40 -20 0 20 40 60 dV/dt

Figs 8.6 a and b. Plot of the rates of change of vegetation biomass (dV/dt) against red kangaroo density (dH/dt) for a) a highly stochastic system, and b) a slightly stochastic system. 202

8. 4 Discussion Vegetation based methods such as the rating system and range succession model cannot take into account the rapid rate of change of vegetation and variable plant biomass inherent in highly stochastic environments. In applying these models the manager sets a constant herbivore density. Ignoring the highly dynamic nature of the environment may lead to plant extinctions and soil erosion (Harrington et al. 1984, Woods 1984). The other models such as the key species, productivity-stocking rate, habitat use/availability and the nutritional approach use a combination of vegetation measurements and animal requirements to calculate carrying capacity. While some have had limited success in deterministic or slightly variable environments, they were found to be unsuitable in highly stochastic environments. Although the interactive model has not been used previously to calculate carrying capacity, it could be modified to estimate carrying capacity and it was the only model that could incorporate biologically meaningful stochasticity into its methods.

The concept of carrying capacity has been applied to the management of domestic and wild herbivores in a wide range of habitats. The analysis of carrying capacity in this chapter indicates that the concept is useful in deterministic and slightly variable environments, but is misleading in highly stochastic environments. In environments where plant-herbivore dynamics do not reach or closely approach equilibrium levels, carrying capacity is more a mathematical abstraction than a measurement of sustainable population size (Macnab 1985). In systems that are insensitive to variation, or any system that reaches or closely approaches equilibrium, carrying capacity is a useful measure of sustainable density. The dichotomy of pure deterministic and completely stochastic systems is in reality a continuum, in which these alternatives form the endpoints. The job of the manager is to determine where an environment lies on this continuum, and whether carrying capacity is a realistic measure of sustainable herbivore density, or a theoretical value.

The interactive model of the shrubland-red kangaroo assemblage never reaches equilibrium. Does this mean that from a management perspective the concept of carrying capacity has no meaning in this environment? The answer to this question lies in the degree of variation surrounding the equilibrium. In the highly variable 203 system the concept has little meaning because of the extreme deviation from the equilibrium. In contrast, in the slightly variable system the concept is still valid and useful for determining sustainable herbivore density.

The analysis of carrying capacity in a highly variable environment indicates that plant-herbivore equilibrium cannot be maintained in some environments, and in others only by very frequent, almost constant adjustment of herbivore density. A similar prediction has been made by Noy-Meir (1975) in his analysis of stability in grazing systems. This type of management is unrealistic in the extensive grazing systems that dominate in highly variable environments. Domestic stock management in this type of environment is characterised by low labour input and infrequent stock handling. More importantly, the current practice in many extensive grazing systems of maintaining a constant stocking rate will ultimately lead to plant extinction unless there are plant refugia (Noy-Meir 1975). Similar conclusions apply to wild herbivore populations, such as red kangaroos in Australia's arid zone.

The idea of a "safe capacity" defined as the maximum herbivore density at which the plant-herbivore system has a stable equilibrium (Noy-Meir 1978), will not hold in all environments. In the highly stochastic version of the shrub land-red kangaroo assemblage, there was no herbivore density that produced a stable equilibrium. The concept of safe capacity is close to the range managers concept of carrying capacity when there is food limitation, such as a drought. It is invalid to assume this environment has a safe capacity and the notion that there is a sustainable herbivore density in all environments should be dispelled.

Although carrying capacity in variable environments does not represent sustainable herbivore density, it is still useful in other models of population dynamics in these environments. Measurement of carrying capacity is an implicit part of some competition models (e.g. Schoener 1973, 1974b, 1976, 1978) and maximum sustainable yield models (Caughley 1976). Carrying capacity can then be calculated on a time scale of interest to the researcher, over which the potential dynamics of the population are studied. In this sense, carrying capacity is not a measurement of long- 204 term equilibrium density but of short-term potential density as a function of resource availability. Chapter 9

Summary ofResults and Conclusions

9.1 Introduction

In this section I will briefly summarise the major findings of Chapters 4 to 8, and present a synthesis of the results and conclusions. I discuss the findings in the context of how they relate to the dynamics of herbivore populations in arid ecosystems, and how they may be used profitably to extend our knowledge along new avenues of research. I also discuss the limitations of some of the methods used, and possible ways to remedy these limitations.

The aim of this study was to examine the effect of temporal variability in food availability on the biology of sheep and red kangaroos·in an arid ecosystem of eastern Australia. Specifically, I examined the effect of interspecific competition on the biology of both herbivores, by a controlled removal experiment (Chapter 4) and by mechanistically modelling exploitative competition for food (Chapter 5). In Chapter 6 I examined the optimal diet choice of both herbivores, and later used the same methods to examine the evolution of body size and sexual dimorphism in red kangaroos (Chapter 7). Finally, I considered the usefulness of the concept of carrying capacity for herbivores in environments where plant biomass is unpredictably variable (Chapter 8).

9 .2 Competition

9.2.1 Inter- versus Intraspecific Competition

Exploitative competition between sheep and red kangaroos occurs rarely in the rangelands of eastern Australia, and under most conditions will have a negligible effect on the biology of both species. The effects of interference competition are more pronounced. The effect of sheep on red kangaroos is continuous with red kangaroos avoiding areas used by sheep. The interference effect of red kangaroos on sheep is less common and appears to be linked to times of low food abundance and high kangaroo 206

density. Thus, competition between sheep and red kangaroos is not due to exploitative consumption of common resources but due to interference mechanisms such as avoidance. Competition between these herbivores is asymmetric with sheep dominating.

The long-term effects of competition on the population dynamics of these herbivores remain unclear, but I caution against acceptance ofCaughley's (1987b) conclusion that sheep reduce the long-term density of red kangaroos in the rangelands by half. Without taking into account the exclusive amounts of food available to both herbivores, Caughley's modelling approach could have produced spurious results. In addition, Caughley's approach only considers exploitative competition which probably is linked to infrequent times of severe drought. I am not suggesting that the long-term density of red kangaroos will not be reduced, but the effect may not be as great as suggested by Caughley (1987b ).

The results of Chapter 4 indicated that under the conditions experienced, exploitative interspecific competition had a negligible .effect on the productivity and population dynamics of these herbivores. The plant biomass at which exploitative interspecific competition becomes an important influence on the population dynamics of these herbivores remains unknown. However, the productivity of sheep declined in the last year of the experiment, and while interspecific competition can be ruled out, the hypothesis that intraspecific competition produced the decline cannot be rejected. The importance of intraspecific competition to the population dynamics of these herbivores remains unresolved and warrants further study.

Underwood (1986) discusses four reasons why intraspecific competition is important to study. First, the detection ofintraspecific competition provides a good starting point for building hypotheses about interspecific competition. Since exploitative competition is related to resource overlap, the similarities of resource requirements among individuals of the same species will be at least as great, if not greater, than between species. Thus, intraspecific competition is a prerequisite of interspecific competition. Second, intraspecific competition is important in the development of competition theory and community theory. Third, the magnitude ofinterspecific competition and ultimately its effect on community dynamics, will probably depend on the relative strengths of intra- and interspecific competition. Intraspecific competition 207

may play a regulatory role, preventing a competitively superior species from excluding an inferior (Creese and Underwood 1982). Fourth, the extent of interspecific competition detected in experiments will probably depend on the starting densities of the potential competitors. If the starting densities invoke intraspecific competition, then partitioning competitive effects into intra- and interspecific components will allow unambiguous conclusions to be drawn from the results.

9.2.2 Other Potential Competitors: Termites

Termites have been found to be a major consumer of dead plant parts in the Chihuanhuan desert rangelands, their consumption ranging between 40-90% of annual standing crop which included annual and perennial forbs, grasses and shrubs (Whitford 1991 ). If invertebrate herbivores in the rangelands of eastern Australia consume similar levels of plant biomass, then there is the potential for competition between invertebrate and vertebrate herbivores, especially during times of low food availability. Unfortunately, there is a paucity of data on the offtake of invertebrate herbivores in the arid shrublands of eastern Australia, and the question of competition for food remains unresolved.

With a few exceptions, the ecology of termites in Australia has concentrated on the northern savanna ecosystems (Holt 1987, Coventry et al. 1988, Braithwaite et al. 1988, Spain and Mcivor 1988, Anderson and Lonsdale 1990), while the rangelands have been relatively neglected. Exceptions to this trend include a small number of studies examining the ecology of termites in the mulga woodlands of semi-arid eastern Australia (Noble et al. 1989, Noble and Tongway 1989, Whitford et al. 1992, Noble 1995).

The potential importance of these herbivores as consumers in chenopod shrublands, similar to those occurring at the study site, is suggested by the results of Robertson (1987). Robertson (1987) modelled the quarterly rate of change in above ground plant biomass, and found that in the absence of rain and vertebrate herbivores, vegetation biomass would sharply decline. Robertson (1987) did not partition the lost plant biomass into the sources ofloss, but labelled it simply as "dieback". Given the low rates of microbiotic decomposition in arid areas (Meentemeyer et al. 1982), a 208

reasonable assumption is that the major source of dieback was consumption by invertebrate herbivores, such as termites. Thus, the potential for competition between invertebrate and vertebrate herbivores is high. There is clearly a need for closer examination of the interaction between invertebrate and vertebrate herbivores in the arid rangelands of Australia.

9.2.3 Continuous versus Rotational Grazing

Traditionally, the grazing management of Australian rangelands have been based on year-long continuous grazing of native plant communities (Squires 1991). Under this grazing system domestic herbivores are stocked at low densities, relative to other grazing systems, and survival usually depends on the animal's ability to adapt to the environment. The alternative system of rotational grazing, where stock densities are closely monitored and frequently adjusted, has been widely used in rangelands outside of Australia, and is the recommended grazing system in North America (Sampson 1951) and Africa (Roberts 1974). Under rotational grazing, stock are grazed at relatively high densities and frequently moved from one paddock to another, with a proportion of the paddocks spelled from grazing at any one time to allow plant regrowth. The theoretical advantages of rotational grazing are; 1) increased herbage yield and quality, 2) increased animal production, and 3) long term rangeland productivity (Roberts 1986). In a major review of grazing management, Gammon (1978) concluded that while rotational grazing did not offer consistent productivity advantages over continuous grazing, there is sufficient evidence to conclude that rotational grazing facilitated rangeland stability, while continuous grazing usually resulted in pasture deterioration. The disadvantages of a rotational system are essentially economic since they require more capital for fences and watering points, in addition to increased labour costs associated with the frequent handling of stock.

The greatest challenge facing continued use of Australia's rangelands is land degradation caused by the grazing of domestic stock (Woods 1984). lfrotational grazing offers advantages in the sustainable use of the rangelands, then changes in the grazing management of stock from continuous to rotational grazing should be pursued. The results of the isocline analysis (Chapter 5) indicate that under most conditions significantly higher densities of herbivores can be sustained for short periods of time, 209

suggesting that these rangelands would be suitable to use on a rotational basis. I suggest that the traditional approach to grazing stock in the Australian rangelands requires significant review in light of the demonstrated advantages associated with rotational grazing systems. Australian rangelands are suitable for rotational grazing management, and if land administrators and managers are serious about addressing the issues of land degradation and sustainable use, then they must look closely at modifying the present grazing system in favour of a rotational based system.

9.3 Foraging and the Evolution of Herbivores in Variable Environments

9.3.1 Foraging Goal and Optimal Diet Choice

Sheep and red kangaroos, like most generalist herbivores (Belovsky 1994), appear to follow a goal of energy maximisation (Chapter 6). Red kangaroos and sheep show a degree of seasonality in their foraging behaviour, being constrained by plant bulk and digestive capacity in winter and feeding time.and food cropping efficiency in summer. However, at times of low food abundance all constraints act upon diet selection. At this time the herbivores were able to maintain or closely approach optimal diet choice, which emphasised the "plasticity" in diet choice by these herbivores in response to heterogeneity in the constraints to their foraging.

The predicted diets for the alternative feeding strategies of energy maximisation, time minimisation and random selection of food converged when food was in low abundance. I was unable to resolve any differences in the feeding strategies at this time since the consumption of each food category was determined as a percentage of the diet and not quantified as mass consumed per day. An alternative method of determining diet choice that could potentially distinguish between the alternative feeding strategies would involve measurement of actual consumption of each food category. This method was used successfully by Schmitz (1990) to determine the observed diet choice of white-tailed deer over winter in a deciduous forest. This method was not possible during my study because of the difficulty in finding plants from which a known amount of forage had been consumed over a set time. (Schmitz's (1990) system was much simpler and deer basically had to make dietary choices between two different types of twigs). Resolving any differences, with respect to the amount of each food type consumed, 210

between the alternative feeding strategies at times of low food abundance will require further work.

The results indicate that red kangaroos and sheep are able to track changes in food quality and quantity. This may have far reaching consequences for herbivore energy intake and ultimately population dynamics, in an environment where plant biomass varies unpredictably (Caughley 1987b). However, at times of low food abundance red kangaroos appear to be able to achieve higher net energy intake, relative to requirements, than sheep. In addition, at times of low food abundance group foraging may be imposing penalties on sheep fitness, since costs associated with grouping such as resource competition (Sih 1993), may not be balanced by benefits such as increased predator vigilance (Krebs and Davies 1993) when predators are no longer a threat.

I suggest that examining the optimal diet choice of individuals at a much smaller time scale would be a profitable approach for further research. The results of this study indicate that sheep and red kangaroos can track resource fluctuations and select an optimal diet on at least a seasonal basis, but their ability to track resources on a shorter time scale ( e.g. daily) remains unresolved. Determining the time scale over which these herbivores can discriminate changes in forage parameters may also explain differences in resource tracking. Dynamic programming would be a suitable method of examining daily diet selection or diet choice over different parts of the day. However, dynamic programming models are more difficult to solve and require a greater number of more complex parameters than linear programming (Belovsky and Schmitz 1993). The influence of group foraging by sheep could be examined by comparing the diet choice and energy intake of group foragers with individual foragers. There is a paucity of risk sensitive foraging studies of mammalian herbivores. The convergence in the diets of both sheep and red kangaroos suggests that these herbivores may become sensitive to the risk of not meeting their energy requirements at times of low food abundance. It would be timely and profitable to study the risk-sensitive foraging of these herbivores. These hypotheses have important implications for understanding the evolution of and constraints to herbivore diet choice, and ultimately the effect that diet choice and energy intake have on herbivore population dynamics. 211

9.3.2 Body Size In Chapter 7 I used the linear program of optimal diet choice (Belovsky 1978) to examine the evolution of body size and sexual dimorphism in red kangaroos. I concluded that sexual differences in body size arose through a combination of red kangaroos living in an unpredictable environment and the sexes pursuing different life history strategies. Assuming that an individual's fitness is a function of survival and reproduction, males attempt to maximise reproductive output, while females attempt to maximise survivorship. Thus, males try to get as big as possible as fast as possible, thereby dominating other males and access to females. Alternatively, females stop growing after reaching about 35 kg, a body size that permits them to maintain positive energy balance when food availability approaches very low levels.

Future research could investigate the reasons why females do not approach the hypothesised optimum size of 50 kg. The linear program was not solved during a time of severe food limitation, and the parameters I used to examine body size at times of severe food limitation were simulated. There is clearly- a need to examine the accuracy of the simulated parameters.

9.4 The Dynamics of Plant-Herbivore Systems in Variable Environments

Caughley (1987b) used a laissez-faire version of the interactive model (Caughley and Lawton 1981) to simulate the population dynamics of a shrubland-red kangaroo assemblage. He showed that although the short term dynamics of the plant herbivore assemblage appeared to be chaotic, they were in fact tightly deterministic, the apparent chaos caused by the high level of unpredictable variation in rainfall. In Chapter 8 I demonstrated that the same methods could be used for examining the carrying capacity of herbivores, and how the concept relates to population dynamics in a unpredictably variable environment. I concluded that measurements of ecological or economic carrying capacity (sensu Caughley 1979) could be used in slightly variable environments, but were misleading in highly variable environments such as the rangelands of eastern Australia. Consequently, approximations of carrying capacity based upon deterministic models (currently used in rangelands management) are invalid in systems sensitive to environmental variance, and should not be used as a basis for long term stocking rates or "sustainable" densities of wild and domestic herbivores. 212

9. 5 Synopsis A common theme running through each chapter of this thesis was the effect of food, and ultimately energy, limitation on the dynamics of generalist herbivores. While other factors such as behaviour, physiology or anatomy may all impinge on the autecology of a species at any one time, it is the transfer of energy through trophic levels that ultimately limits all ecological systems (Odum 1971). In this thesis I have demonstrated that simple measurements of available food or energy, and their rate of harvest by herbivores, can be used to test hypotheses about; 1) exploitative competition, 2) optimal diet choice, 3) coevolution of herbivores and plant communities, 4) the evolution of body size, 5) the evolution of sexual dimorphism, and 6) the long term population dynamics of herbivores in variable environments.

Sheep and red kangaroos responded to temporal variation in food availability in similar ways. They both attempt to maximise energy intake during foraging periods. Although these herbivores occur sympatrically throughout most of their range and have a high degree of dietary overlap, they rarely compete exploitatively for food. Consequently, I conclude that falling herbivore productivity as food becomes limiting is initially due to an individual's ability to harvest energy, and not due to interspecific exploitative competition. The point at which interspecific competition becomes important to the population dynamics of these herbivores remains unknown, and awaits further experimentation. 213

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