chiversEtAl-supplementary material

Predator-prey systems depend on a prey refuge1

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Supplementary material3

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W. J. Chivers, W. Gladstone, R. D. Herbert and M. M. Fuller5

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Contents6

1 Model behaviour across initial condition and parameter value ranges 37

1.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

1.2 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

1.3 Predator initial population . . . . . . . . . . . . . . . . . . . . . . . . 710

1.4 Predator initial resources . . . . . . . . . . . . . . . . . . . . . . . . . 1011

1.5 Predator metabolic cost per time step . . . . . . . . . . . . . . . . . . . 1312

1.6 Predator trophic efficiency . . . . . . . . . . . . . . . . . . . . . . . . 1613

1.7 Predator chances of eating . . . . . . . . . . . . . . . . . . . . . . . . 1914

1.8 Predator trapping rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 2215

1.9 Predator generalist rate . . . . . . . . . . . . . . . . . . . . . . . . . . 2716

1.10 Predator generalist resources added . . . . . . . . . . . . . . . . . . . . 3417

1.11 Prey initial population . . . . . . . . . . . . . . . . . . . . . . . . . . . 4118

1.12 Prey initial resources . . . . . . . . . . . . . . . . . . . . . . . . . . . 4419

1.13 Prey metabolic cost per time step . . . . . . . . . . . . . . . . . . . . . 4720

1.14 Prey resource consumption per time step . . . . . . . . . . . . . . . . . 5021

1.15 Prey hidden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5322

2 Predator functional response 5623

3 Appendix 1: Model description in pseudo-code 5824

3.1 Initialisation and main loop . . . . . . . . . . . . . . . . . . . . . . . . 5825

3.2 Method definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5926

4 Appendix 2: The agent-based model implemented in the Python program-27

ming language 6128

4.1 Using the model graphical interface . . . . . . . . . . . . . . . . . . . 6129

4.2 Python version and additional packages . . . . . . . . . . . . . . . . . 6230

4.3 Running the ABM on Microsoft Windows . . . . . . . . . . . . . . . . 6231

4.4 Running the ABM on Linux or BSD . . . . . . . . . . . . . . . . . . . 6332

4.5 Running the ABM on Apple OSX . . . . . . . . . . . . . . . . . . . . 6333

4.6 The model code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6434

4.6.1 main.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6435

4.6.2 gui.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6536

4.6.3 simulation.py . . . . . . . . . . . . . . . . . . . . . . . . . . . 7337

4.6.4 default_values.py . . . . . . . . . . . . . . . . . . . . . . . . . 8438

4.6.5 animal.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8539

4.6.6 predator.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8740

4.6.7 prey.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8841

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1 Model behaviour across initial condition and param-42

eter value ranges43

This section presents an analysis of the sensitivity of the model to variation in the default44

initial condition and parameter values. The behaviour of the model with this parameter45

set is typical of all parameter sets observed.46

This analysis illustrates47

1. For all initial conditions or parameters:48

• the ranges over which each initial condition or parameter value can be ad-49

justed while maintaining population cycling,50

• the ranges over which each initial condition or parameter value can be ad-51

justed without causing extinctions,52

• suggested correlations between initial condition or parameter values and53

– population means,54

– population cycle period length and55

– population cycle amplitude.56

2. For the parameters predator trapping rate (ptr), predator generalist rate (pgrate)57

and predator generalist resources added (pgres) this analysis also illustrates58

• correlation between population amplitudes and the predator trapping rate,59

ptr and60

• correlations between population amplitudes and the generalist predator pa-61

rameters, pgrate and pgres.62

3

3. Finally for the parameters predator generalist rate (pgrate) and predator generalist63

resources added (pgres) this analysis illustrates the effects of these parameters on64

the predator functional response.65

1.1 Method66

The approach taken was to start with the default set of parameters (which usually results67

in the two populations reaching 1000 time steps without an extinction) and to vary each68

parameter while holding the others constant. The graphs produced were:69

1. For all initial condition or parameters:70

• mean populations and mean number of time steps before an extinction (up71

to 1000 time steps) graphed against the initial condition or parameter and72

• predator and prey populations per time step for eight executions of the model73

(up to 500 time steps) using different values of the initial condition or pa-74

rameter.75

2. For the parameters predator trapping rate (ptr), predator generalist rate (pgrate)76

and predator generalist resources added (pgres) the following are added:77

• mean predator population peaks graphed against the parameter and78

• mean prey population peaks and graphed against the parameter.79

3. Finally for the parameters predator generalist rate (pgrate) and predator generalist80

resources added (pgres) the functional response of the predators for eight execu-81

tions of the model using different values of the parameter are graphed and the82

intercepts and slopes of lines of best fit on these graphs are tabulated.83

4

For the purposes of this analysis the upper and lower limits for each initial condition84

or parameter were found by manual experimentation. These limits were identified by85

• increasing failure of one of the populations (usually the predator population) to86

reach 1000 time steps and/or87

• stabilisation of the apparent trend in the data.88

The ranges over which cycling populations were evident were judged by observation89

of the output of individual model executions.90

Population and time step mean graphs91

The data collected over 50 simulations at each initial condition or parameter value were92

• the mean populations over 1000 time steps,93

• the mean number of time steps (up to 1000) before extinction of either of the94

populations and95

• the mean maximum and minimum levels of each population.96

Individual simulations at selected parameter levels97

The data collected for each time step were98

• the time step,99

• the predator population and100

• the prey population.101

5

1.2 Summary of results102

Without formal statistical analysis, the graphs presented below suggest the following103

effects within parameter ranges which result in population cycling and few extinctions.104

Note: not tabulated was the observation that per capita predation rates may rise slightly105

as pgrate and/or pgres rise.106

SM Table 1: a) Ranges over which initial conditions and parameters produce popula-tion cycling and populations persistent to 1000 time steps and b) correlations betweeninitial condition or parameter levels and population means, population cycle periodlength and population cycle amplitude within these ranges. These correlations have notbeen formally tested—these results are suggested only by the trends evident in SM Fig-ures 1a to 13b.Key:— no correlation or no extinctions recorded? relationship not clear∗ positive correlation† negative correlation†? possible negative correlation, separates predator and prey resultsts: time steppop: population

Name Symbol Pop cycling Persistent Pop Pop cycle Pop cyclerange to 1000 ts means period amplitude

PredatorInitial population pn ≥ 0 — — — —Initial resources pir 20− 1700 ≥ 140 † ∗ ?Energy cost per ts pmc 14− 40 ≤ 37 ∗ † ∗Trophic efficiency pte 10− 40 ≥ 16 † — †Chance of eating pce 0.01− 0.06 ≥ 0.02 † — †Trapping rate ptr 0− 50 ≤ 25 ?,∗ †? ∗Generalist rate pgrate 0− 45 — † ∗ †Generalist resources pgres 0− 60 — † ∗ †PreyInitial population bn ≥ 0 — — — —Initial resources bir ≥ 60 ≥ 60 † ∗ †Energy cost per ts bmc 0− 70 ≤ 60 † ∗ †Resource consumption bminr,bmaxr 90− 700 ≥ 120 ∗,†? † †Prey hidden bph 5− 20 ≥ 6 † ∗ †

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1.3 Predator initial population107

Summary108

The initial population of predators (pn) is the size of the population used to start a simu-109

lation. In the simulations reported in this parameter sensitivity analysis, this parameter110

has a default value of 35 individuals—this value chosen because it is the mean predator111

population level which emerges over many time steps with this parameter set.112

With the default parameter set, values of pn ≥ 0 individuals result in population cy-113

cling and no extinctions were observed while adjusting this parameter. Higher values of114

the parameter do result in transient dynamics at the start of a simulation as the predator115

population falls to a sustainable level. SM Figure 1a graphs mean population levels and116

mean time step reached over 50 simulations at each parameter level.117

Eight individual executions of the model are illustrated in SM Figure 1b at eight118

different parameter levels. These figures do not suggest any correlation between pn and119

population cycle period length or between the parameter and population cycle ampli-120

tudes.121

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Predator initial population: Population levels, population persistence and range in122

which population cycling is evident123

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SM Figure 1a: Mean populations and mean number of time steps before an extinctiongraphed against predator initial population (pn). To avoid any confounding effect ofincreasing the initial predator number, these data are from time steps 201–1000 only astransient dynamics at the start of a simulation very rarely persist for 200 time steps. Thedefault value for the simulations reported here was 35 individuals. The error bars repre-sent one standard deviation. No extinctions were observed and population cycling wasevident in the range 1 to > 500 individuals. This graph indicates the lack of importanceof the initial predator population size—the level of the predator initial population maycause transient dymanics at the start of a simulation, but the peaks, troughs and meanpopulations then settle to levels which are dependent on the model parameters.

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Predator initial population: Eight individual simulations at differing parameter124

levels125

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SM Figure 1b: Predator and prey populations per time step for eight executions of themodel using different values of the predator initial population (pn). The values of pn are10 (a), 80 (b), 150 (c), 220 (d), 290 (e), 360 (f), 430 (g) and 500 (h) individuals.The number of population peaks over 500 time steps are 27 (a), 26 (b), 26 (c), 25 (d),26 (e), 26 (f), 26 (g) and 26 (h). These figures do not suggest any correlation betweenthe parameter and population cycle period length or population cycle amplitudes.

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1.4 Predator initial resources126

Summary127

The predator initial resources parameter (pir) represents the energy resources a predator128

individual is born with. At the start of a simulation all predators have this resource129

level and all individuals born during the simulation have the same resource level in their130

first time step. This parameter also specifies the cost of reproduction for a parent—it131

is the number of resources subtracted from a parent when it bears one offspring. In the132

simulations reported in this parameter sensitivity analysis, this parameter has a default133

value of 220.0 resource units.134

With the default parameter set, values of 20 ≤ pir ≤ 1700 resource units result in135

population cycling and extinctions are observed when pir ≤ 140 resource units. Mean136

populations of both species are negatively correlated with pir in this range of values, as137

illustrated by SM Figure 2a which graphs mean population levels and mean time step138

reached over 50 simulations at each parameter level.139


different parameter levels. These figures suggest a positive correlation between pir and141

population cycle period length; the relationship between the parameter and population142

cycle amplitudes is not clear.143

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Predator initial resources: Population levels, population persistence and range in144


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SM Figure 2a: Mean populations and mean number of time steps before an extinctiongraphed against predator initial resources (pir). The default value for the simulationsreported here was 220.0 resource units. The error bars represent one standard deviation.Extinctions were observed when pir <= 140 resource units and population cycling wasevident in the range 20(approx.) to 1700(approx.) resources (bounded by the dottedvertical lines).

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Predator initial resources: Eight individual simulations at differing parameter lev-146

els147

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SM Figure 2b: Predator and prey populations per time step for eight executions of themodel using different values of the predator initial resources (pir). The values of pirare 40 (a), 320 (b), 600 (c), 880 (d), 1160 (e), 1440 (f), 1720 (g) and 2000 (h) resourceunits. Note the predator extinction at time step 467 in (a) and the breakdown of popula-tion cycling in (h).The number of population peaks over 500 time steps, where they can be visually iden-tified, are 20 (b), 13 (c), 10 (d), 7 (e), 6 (f) and 5 (g), suggesting a positive correlationbetween pir and population cycle period length. The relationship between the parameterand population cycle amplitudes is not clear from these figures

12

1.5 Predator metabolic cost per time step148

Summary149

The predator metabolic cost per time step parameter (pmc) represents the energy cost150

of metabolism in a living organism over time, this cost is subtracted from the resource151

total of each predator each time step. If after the subtraction a predator does not have152

enough resources to live another time step, it dies of starvation and is removed from153

the simulation. In the simulations reported in this parameter sensitivity analysis, this154

parameter has a default value of 30.0 resource units.155

With the default parameter set, values of 14 ≤ pmc ≤ 40 resource units result in156

population cycling and extinctions are observed when pmc ≥ 37 resource units. Mean157

populations of both species are positively correlated with pmc in this range of values, as158

illustrated by SM Figure 3a which graphs mean population levels and mean time step159

reached over 50 simulations at each parameter level.160


different parameter levels. These figures suggest a negative correlation between pmc162

and population cycle period length and a positive correlation between the parameter and163

population cycle amplitudes.164

13

Predator metabolic cost per time step: Population levels, population persistence165

and range in which population cycling is evident166

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SM Figure 3a: Mean populations and mean number of time steps before an extinctiongraphed against predator metabolic cost per time step (pmc). The default value for thesimulations reported here was 30.0 resource units. The error bars represent one standarddeviation. Extinctions were observed when pmc => 37 resource units. Populationcycling was evident in the range 14(approx.) to > 40 resources (bounded by the dottedvertical line and the RH y-axis).

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Predator metabolic cost per time step: Eight individual simulations at differing167

parameter levels168

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SM Figure 3b: Predator and prey populations per time step for eight executions of themodel using different values of the predator metabolic cost per time step (pmc). Thevalues of pmc are 5 (a), 10 (b), 15 (c), 20 (d), 25 (e), 30 (f), 35 (g) and 40 (h) resourceunits. Note the breakdown of population cycling at lower values of pmc and the differingy-axis scales.The number of population peaks over 500 time steps, where they can be visually iden-tified, are 20 (d), 23 (e), 26 (f), 28 (g) and 30 (h), suggesting a negative correlationbetween pmc and population cycle period length. A positive correlation between theparameter and population cycle amplitudes is also apparent in these figures.

15

1.6 Predator trophic efficiency169

Summary170

The predator trophic efficiency parameter (pte) is used to determine the proportion of171

the eaten prey individual’s resources to be added to the resources of the predator in a172

predation event. In the simulations reported in this parameter sensitivity analysis, this173

parameter has a default value of 20.0%.174

With the default parameter set, values of 10 ≤ pte ≤ 40% result in population cy-175

cling and extinctions are observed when pte ≤ 16%. Mean populations of both species176

are negatively correlated with pte in this range of values, as illustrated by SM Figure 4a177

which graphs mean population levels and mean time step reached over 50 simulations178

at each parameter level.179

Eight individual executions of the model are illustrated in SM Figure 4b at eight dif-180

ferent parameter levels. These figures suggest no correlation between pte and population181

cycle period length and a negative correlation between the parameter and population cy-182

cle amplitudes.183

16

Predator trophic efficiency: Population levels, population persistence and range in184


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SM Figure 4a: Mean populations and mean number of time steps before an extinctiongraphed against predator trophic efficiency (pte). The default value for the simulationsreported here was 20.0%. The error bars represent one standard deviation. Extinctionswere observed when pte < 16% and population cycling was evident in the range 10(ap-prox.) to 40(approx.)% (bounded by the LH y-axis and the dotted vertical line).

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Predator trophic efficiency: Eight individual simulations at differing parameter186

levels187

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SM Figure 4b: Predator and prey populations per time step for eight executions of themodel using different values of the predator trophic efficiency (pte). The values of pteare 12 (a), 17 (b), 22 (c), 27 (d), 32 (e), 37 (f), 42 (g) and 47% (h). Note the predatorextinction at time step 260 in (a), the breakdown of population cycling at higher valuesof pte and the differing y-axis scales.The number of population peaks over 500 time steps, where they can be visually iden-tified, are 26 (b), 26 (c), 25 (d), 26 (e) and 25 (f). These figures suggest no correlationbetween pte and population cycle period length and a negative correlation between theparameter and population cycle amplitudes.

18

1.7 Predator chances of eating188

Summary189

The predator chances of eating parameter (pce) is used in the decision whether each190

predator will eat during each time step. Predators may consume a small number of191

prey per time step, the number calculated as the product of pce and the current prey192

population. A result of 2.3, for example, would mean that the predator will eat two prey193

and have a 30% chance of eating a third—if the current prey population is greater than194

the size of the prey refuge (bph). In the simulations reported in this parameter sensitivity195

analysis, this parameter has a default value of 0.03.196

With the default parameter set, values of 0.01 ≤ pce ≤ 0.06 result in population197

cycling and extinctions are observed when pce ≤ 0.02. Mean populations of both species198

are negatively correlated with pce in this range of values, as illustrated by SM Figure 5a199

which graphs mean population levels and mean time step reached over 50 simulations200

at each parameter level.201

Eight individual executions of the model are illustrated in SM Figure 5b at eight dif-202

ferent parameter levels. These figures suggest no correlation between pce and population203

cycle period length and a negative correlation between the parameter and population cy-204

cle amplitudes.205

19

Predator chances of eating: Population levels, population persistence and range in206


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SM Figure 5a: Mean populations and mean number of time steps before an extinctiongraphed against predator chances of eating (pce). The default value for the simula-tions reported here was 0.03. The error bars represent one standard deviation. Extinc-tions were observed when pce ≤ 0.02 and population cycling was evident in the range0.01(approx.) to 0.06(approx.) (bounded by the LH y-axis and the dotted vertical line).

20

Predator chances of eating: Eight individual simulations at differing parameter208

levels209

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SM Figure 5b: Predator and prey populations per time step for eight executions of themodel using different values of the predator chances of eating (pce). The values of pceare 0.01 (a), 0.02 (b), 0.03 (c), 0.04 (d), 0.05 (e), 0.06 (f), 0.07 (g) and 0.08 (h). Notethe predator extinction at time step 278 in (a), the breakdown of population cycling athigher values of pce and the differing y-axis scales.The number of population peaks over 500 time steps, where they can be visually identi-fied, are 26 (b), 26 (c), 25 (d) and 25 (e). These figures suggest no correlation betweenpce and population cycle period length and a negative correlation between the parameterand population cycle amplitudes.

21

1.8 Predator trapping rate210

Summary211

The predator trapping rate parameter (ptr) specifies a percentage of predators to be se-212

lected randomly and removed from the simulation each time step to simulate the effect213

of human trappers. In the simulations reported in this parameter sensitivity analysis,214

this parameter has a default value of 0%.215

With the default parameter set, values of 0 ≤ ptr ≤ 50% result in population cycling216

and extinctions are observed when ptr ≥ 6% and more commonly when ptr ≥ 25%.217

The mean prey population is positively correlated with ptr in this range of values as218

illustrated by SM Figure 6a, however no correlation is detectable between the predator219

population and the parameter by visual inspection of the figure which graphs mean220

population levels and mean time step reached over 50 simulations at each parameter221

level.222


different parameter levels. These figures suggest a negative correlation between ptr and224

population cycle period length and a positive correlation between the parameter and225


SM Figures 6c and 6d illustrate the effect of ptr on mean predator and prey pop-227

ulation peaks respectively. These figures indicate a positive correlation between the228

parameter and the population amplitudes of both species.229

22

Predator trapping rate: Population levels, population persistence and range in230


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SM Figure 6a: Mean populations and mean number of time steps before an extinctiongraphed against predator trapping rate (ptr). The default value for the simulations re-ported here was 0%. The error bars represent one standard deviation. Extinctions wereobserved when ptr ≥ 6% and became more common when ptr ≥ 25%. At ptr >= 50%extinctions occurred within 25 time steps in each simulation, the trapping rate over-whelming the predator population. Population cycling was evident in the range 0 to50% (bounded by the LH y-axis and the dotted vertical line). The steps in the data,especially from ptr = 24 to 25, are a result of interaction with other parameters and areconsistently observed, albiet at different parameter levels for different parameter sets.

23

Predator trapping rate: Eight individual simulations at differing parameter levels232

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SM Figure 6b: Predator and prey populations per time step for eight executions of themodel using different values of the predator trapping rate (ptr). The values of ptr are 0(a), 8 (b), 16 (c), 24 (d), 32 (e), 40 (f), 48 (g) and 56% (h). Note the predator extinctionsat time step 261 in (e), 458 in (f) and 19 in (h) and the differing y-axis scales.The number of population peaks over 500 time steps, where there is no extinction, are26 (a), 27 (b), 27 (c), 27 (d) and 30 (g), suggesting a negative correlation between ptrand population cycle period length. A positive correlation between the parameter andpopulation cycle amplitudes is also apparent in these figures.

24

Predator trapping rate: Predator population maxima [6]233

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SM Figure 6c: Mean predator population, mean predator population peaks and meannumber of time steps before an extinction graphed against predator trapping rate (ptr).The default value for the simulations reported here was 0%. The error bars representone standard deviation. Population cycling was evident between the LH y-axis and thedotted vertical line. Please see Figure 6a caption for further comments.

Please see Figure 6b for eight executions of the model using different values ofthe predator trapping rate.

25

Predator trapping rate: Prey population maxima [7]234

0

100

200

300

400

500

600

0 10 20 30 40 50 0

1000

2000

3000

4000

5000

6000

Me

an

pre

y p

opula

tion

Mean p

rey p

opula

tion m

axim

um

and

mea

n t

ime s

teps


Mean time stepsMean prey populationMean prey maximum

SM Figure 6d: Mean prey population, mean prey population peaks and mean numberof time steps before an extinction graphed against predator trapping rate (ptr). Thedefault value for the simulations reported here was 0%. The error bars represent onestandard deviation. Population cycling was evident between the LH y-axis and thedotted vertical line. Please see Figure 6a caption for further comments.

Please see Figure 6b for eight executions of the model using different values ofthe predator trapping rate.

26

1.9 Predator generalist rate235

Summary236

The predator generalist rate parameter (pgrate) specifies a percentage of predators, se-237

lected randomly, to be given a number of resources (the latter number specified by pgres)238

each time step to simulate the predators’ consumption of a second prey species. In the239


value of 0%.241

With the default parameter set, values of 0 ≤ pgrate ≤ 45% result in popula-242

tion cycling (albeit with reduced amplitudes) and no extinctions were observed when243

pgrate ≤ 80%. Mean populations of both species are negatively correlated with pgrate244

in this range of values, as illustrated by SM Figure 7a which graphs mean population245

levels and mean time step reached over 50 simulations at each parameter level.246


different parameter levels. These figures suggest a positive correlation between pgrate248

and population cycle period length and a negative correlation between the parameter249

and population cycle amplitudes.250

SM Figures 7c and 7d illustrate the effect of pgrate on mean predator and prey pop-251

ulation peaks respectively. These figures indicate a negative correlation between the252


The predator functional response is illustrated for eight values of pgrate in SM Fig-254

ure 7e and SM Table 2. The figure and table indicate that the intercepts and slopes of the255

regression lines may have negative and positive correlations respectively with pgrate—256

this was not formally tested but it appears that predation rates may rise slightly as the257

generalist rate rises.258

27

Predator generalist rate: Population levels, population persistence and range in259


0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Predator generalist rate (%)



SM Figure 7a: Mean populations and mean number of time steps before an extinctiongraphed against predator generalist rate (pgrate). The default value for the simulationsreported here was 0%. For all values of pgrate here 30.0 resource units were added tothe randomly selected predators each time step. The error bars represent one standarddeviation. No extinctions were observed and population cycling was evident in the range0 to 45(approx.)%, albeit with reduced amplitudes (bounded by the LH y-axis and thedotted vertical line).

28

Predator generalist rate: Eight individual simulations at differing parameter levels261

0

300

600

Po

pu

lation

(a

)

PredatorPrey

0

300

600

Popula

tion

(b)

PredatorPrey

0

300

600

Popula

tion

(c)

PredatorPrey

0

300

600

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

100

200

(e)

PredatorPrey

0

100

200

(f)

PredatorPrey

0

100

200

(g)

PredatorPrey

0

100

200

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 7b: Predator and prey populations per time step for eight executions of themodel using different values of the predator generalist rate (pgrate). The values of pgrateare 0 (a), 7 (b), 14 (c), 21 (d), 28 (e), 35 (f), 42 (g) and 49% (h). For all values of pgratehere 30.0 resource units were added to the randomly selected predators each time step.Note the breakdown of population cycling in (h) and the differing y-axis scales.The number of population peaks over 500 time steps, where they can be visually iden-tified, are 26 (a), 24 (b), 23 (c), 22 (d), 21 (e), 19 (f) and 18 (g), suggesting a positivecorrelation between pgrate and population cycle period length. A negative correlationbetween the parameter and population cycle amplitudes is also apparent in these fig-ures.

29

Predator generalist rate: Predator population maxima [8]262

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 0

200

400

600

800

1000

1200

1400

Me

an

pre

dato

r p

op

ula

tion a

nd

mean p

reda

tor

popula

tion m

axim

um

Mean tim

e s

teps



SM Figure 7c: Mean predator population, mean predator population peaks and meannumber of time steps before an extinction graphed against predator generalist rate(pgrate). The default value for the simulations reported here was 0%. The error barsrepresent one standard deviation. Population cycling was evident between the LHy-axis and the dotted vertical line. Please see Figure 7a caption for further comments.

Please see Figure 7b for eight executions of the model using different values ofthe predator generalist rate.

30

Predator generalist rate: Prey population maxima [9]263

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80 0

200

400

600

800

1000

1200

1400

Mean p

rey p

op

ula

tion a

nd

mean p

rey p

opula

tion m

axim

um

Mea

n t

ime s

teps



SM Figure 7d: Mean prey population, mean prey population peaks and mean numberof time steps before an extinction graphed against predator generalist rate (pgrate). Thedefault value for the simulations reported here was 0%. The error bars represent onestandard deviation. Population cycling was evident between the LH y-axis and thedotted vertical line. Please see Figure 7a caption for further comments.

Please see Figure 7b for eight executions of the model using different values ofthe predator generalist rate.

31

Predator generalist rate: Predator functional response264

0 100 200 300 400

02

46

8

Number of prey

Co

nsu

mp

tio

n r

ate

20 40 60 80 100 120 140

0.0

0.5

1.0

1.5

2.0

2.5

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Number of prey

Co

nsu

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tio

n r

ate

(a) (e)

0 100 200 300 400

02

46

8

Number of prey

Co

nsu

mp

tio

n r

ate

20 40 60 80 100 120

0.0

0.5

1.0

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2.0

2.5

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on

su

mp

tio

n r

ate

(b) (f)

50 100 150 200 250

01

23

45

6

Number of prey

Co

nsu

mp

tio

n r

ate

20 30 40 50 60 70 80

0.5

1.0

1.5

Number of prey

Co

nsu

mp

tio

n r

ate

(c) (g)

50 100 150 200

01

23

4

Number of prey

Co

nsu

mp

tio

n r

ate

20 30 40 50 60 70 80

0.5

1.0

1.5

Number of prey

Co

nsu

mp

tio

n r

ate

(d) (h)

SM Figure 7e: The predator per-capita consumption rate (y) plotted against the numberof prey (x) for each time step and for differing predator generalist rate (pgrate) values.The values of pgrate are 0 (a), 7 (b), 14 (c), 21 (d), 28 (e), 35 (f), 42 (g) and 49% (h).For all values of pgrate here 30.0 resource units were added to the randomly selectedpredators each time step. The data for each graph were collected from a single executionof the model of 1000 time steps. Please see SM Table 2 for the intercepts and slopes ofthe lines of best fit. Note the differing axis scales. Scatter plots and lines of best fit wereobtained using the R statistical environment (R Core Team, 2013).

32

Predator generalist rate: Predator functional response (continued)265

SM Table 2: Intercepts, slopes of lines of best fit and other descriptive statistics of thegraphs in SM Figure 7e.The intercepts and slopes may have negative and positive correlations respectively withpgrate, this was not formally tested. Descriptive statistics were obtained using the Rstatistical environment (R Core Team, 2013).

Prey populationpgrate Intercept Slope Min Median Max Mean SD R2 adj R2

0 -0.0453 0.0218 14.00 28.00 464.00 80.97 92.42 0.92 0.927 -0.0573 0.0220 15.00 25.00 403.00 68.01 75.42 0.93 0.93

14 -0.0749 0.0225 15.00 24.00 283.00 56.43 56.43 0.94 0.9421 -0.0837 0.0229 14.00 23.00 219.00 48.02 43.44 0.94 0.9428 -0.0915 0.0233 14.00 23.00 153.00 40.68 31.30 0.95 0.9535 -0.0804 0.0239 15.00 24.00 133.00 33.28 20.56 0.94 0.9442 -0.0857 0.0249 15.00 23.00 80.00 27.86 11.86 0.91 0.9149 -0.0995 0.0251 14.00 21.00 80.00 25.29 9.50 0.89 0.89

33

1.10 Predator generalist resources added266

Summary267

The predator generalist resources added per time step parameter (pgres) specifies the268

number of resources to be added to a percentage (pgrate) of randomly selected predators269

each time step to simulate the predators’ consumption of a second prey species. In the270


value of 0 resource units.272

With the default parameter set, values of 0 ≤ pgres ≤ 60 resource units result in pop-273

ulation cycling (albeit with reduced amplitudes) and no extinctions were observed when274

pgres ≤ 90 resource units. Mean populations of both species are negatively correlated275

with pgres in this range of values, as illustrated by SM Figure 8a which graphs mean276

population levels and mean time step reached over 50 simulations at each parameter277

level.278


different parameter levels. These figures suggest a positive correlation between pgres280

and population cycle period length and a negative correlation between the parameter281

and population cycle amplitudes.282

SM Figures 8c and 8d illustrate the effect of pgres on mean predator and prey pop-283

ulation peaks respectively. These figures indicate a negative correlation between the284


The predator functional response is illustrated for eight values of pgres in SM Fig-286

ure 8e and SM Table 3. These indicate that the intercepts and slopes of the regression287

lines may have negative and positive correlations respectively with pgres—this was not288

formally tested but it appears that predation rates may rise slightly as pgres rises.289

34

Predator generalist resources added: Population levels, population persistence and290

range in which population cycling is evident291

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Predator generalist resources added (resource units)



SM Figure 8a: Mean populations and mean number of time steps before an extinctiongraphed against predator generalist resources added per time step (pgres). The defaultvalue for the simulations reported here was 0 resource units. Resources were added to25% of the predators for all values of pgres here. The error bars represent one standarddeviation. No extinctions were observed and population cycling was evident in the range0 to 60 (approx.) resources, albeit with reduced amplitudes (bounded by the LH y-axisand the dotted vertical line).

35

Predator generalist resources added: Eight individual simulations at differing pa-292

rameter levels293

0

250

500

Po

pu

lation

(a

)

PredatorPrey

0

250

500

Popula

tion

(b)

PredatorPrey

0

250

500

Popula

tion

(c)

PredatorPrey

0

250

500

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

75

150

(e)

PredatorPrey

0

75

150

(f)

PredatorPrey

0

75

150

(g)

PredatorPrey

0

75

150

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 8b: Predator and prey populations per time step for eight executions of themodel using different values of the predator generalist resources added per time step(pgres). The values of pgres are 0 (a), 10 (b), 20 (c), 30 (d), 40 (e), 50 (f), 60 (g) and70 (h) resource units. Resources were added to 25% of the randomly selected predatorsper time step for all values of pgres here. Note the breakdown of population cycling in(g) and (h) and the differing y-axis scales.The number of population peaks over 500 time steps, where they can be visually identi-fied, are 26 (a), 24 (b), 22 (c), 21 (d), 20 (e) and 18 (f), suggesting a positive correlationbetween pgres and population cycle period length. A negative correlation between theparameter and population cycle amplitudes is also apparent in these figures.

36

Predator generalist resources added: Predator population maxima [10]294

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 0

200

400

600

800

1000

1200

1400

Me

an

pre

dato

r p

op

ula

tion a

nd

mean p

reda

tor

popula

tion m

axim

um

Mean tim

e s

teps



SM Figure 8c: Mean predator population, mean predator population peaks and meannumber of time steps before an extinction graphed against predator generalist resourcesadded per time step (pgres). The default value for the simulations reported here was 0resource units. The error bars represent one standard deviation. Population cycling wasevident between the LH y-axis and the dotted vertical line. Please see Figure 8a captionfor further comments.

Please see Figure 8b for eight executions of the model using different values ofthe predator generalist resources added.

37

Predator generalist resources added: Prey population maxima [11]295

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 0

200

400

600

800

1000

1200

Mean p

rey p

op

ula

tion a

nd

mean p

rey p

opula

tion m

axim

um

Mea

n t

ime s

teps



SM Figure 8d: Mean prey population, mean prey population peaks and mean numberof time steps before an extinction graphed against predator generalist resources addedper time step (pgres). The default value for the simulations reported here was 0 resourceunits. The error bars represent one standard deviation. Population cycling was evidentbetween the LH y-axis and the dotted vertical line. Please see Figure 8a caption forfurther comments.

Please see Figure 8b for eight executions of the model using different values ofthe predator generalist resources added.

38

Predator generalist resources added: Predator functional response296

0 100 200 300 400 500

02

46

81

0

Number of prey

Co

nsu

mp

tio

n r

ate

20 40 60 80 100 120 140

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Number of prey

Co

nsu

mp

tio

n r

ate

(a) (e)

0 100 200 300 400

02

46

8

Number of prey

Co

nsu

mp

tio

n r

ate

20 30 40 50 60 70 80

0.5

1.0

1.5

Number of preyC

on

su

mp

tio

n r

ate

(b) (f)

50 100 150 200 250

01

23

45

Number of prey

Co

nsu

mp

tio

n r

ate

20 30 40 50 60 70 80

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Number of prey

Co

nsu

mp

tio

n r

ate

(c) (g)

50 100 150 200

01

23

4

Number of prey

Co

nsu

mp

tio

n r

ate

20 30 40 50 60 70 80

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Number of prey

Co

nsu

mp

tio

n r

ate

(d) (h)

SM Figure 8e: The predator per-capita consumption rate (y) plotted against the numberof prey (x) for each time step and for differing predator generalist resources added(pgres) values. The values of pgres are 0 (a), 10 (b), 20 (c), 30 (d), 40 (e), 50 (f), 60 (g) and70 (h) resource units. Resources were added to 25% of the randomly selected predatorsper time step for all values of pgres here. The data for each graph were collected froma single execution of the model of 1000 time steps. Please see SM Table 3 for theintercepts and slopes of the lines of best fit. Note the differing axis scales. Scatter plotsand lines of best fit were obtained using the R statistical environment (R Core Team,2013).

39

Predator generalist resources added: Predator functional response (continued)297

SM Table 3: Intercepts, slopes of lines of best fit and other descriptive statistics of thegraphs in SM Figure 8e.The intercepts and slopes may have negative and positive correlations respectively withpgres, this was not formally tested. Descriptive statistics were obtained using the Rstatistical environment (R Core Team, 2013).

Prey populationpgres Intercept Slope Min Median Max Mean SD R2 adj R2

0 -0.0493 0.0217 15.00 28.00 535.00 83.45 96.72 0.92 0.9210 -0.0626 0.0221 14.00 25.00 424.00 65.98 71.13 0.93 0.9320 -0.0840 0.0228 14.00 24.00 241.00 51.74 48.15 0.94 0.9430 -0.0863 0.0231 15.00 24.00 199.00 42.85 34.30 0.95 0.9540 -0.0851 0.0240 14.00 24.00 136.00 33.92 20.37 0.94 0.9450 -0.0940 0.0246 14.00 23.00 80.00 28.39 12.22 0.92 0.9260 -0.1159 0.0260 15.00 22.00 80.00 24.03 7.28 0.85 0.8570 -0.1020 0.0254 15.00 19.00 80.00 20.75 4.67 0.75 0.75

40

1.11 Prey initial population298

Summary299

The initial population of prey (bn) is the size of the population used to start a simulation.300

In the simulations reported in this parameter sensitivity analysis, this parameter has a301

default value of 80 individuals—this value chosen because it is the mean prey population302

level which emerges over many time steps with this parameter set.303

With the default parameter set, values of bn ≥ 0 individuals result in population304

cycling and no extinctions were observed while adjusting this parameter. Higher values305

of the parameter do result in transient dynamics at the start of a simulation as the prey306

population falls to a sustainable level. SM Figure 9a graphs mean population levels and307

mean time step reached over 50 simulations at each parameter level.308


different parameter levels. These figures do not suggest any correlation between bn and310

population cycle period length or between the parameter and population cycle ampli-311

tudes.312

41

Prey initial population: Population levels, population persistence and range in313


0

20

40

60

80

100

120

0 100 200 300 400 500 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Prey initial population



SM Figure 9a: Mean populations and mean number of time steps before an extinctiongraphed against prey initial population (bn). To avoid any confounding effect of increas-ing the initial prey number, these data are from time steps 201–1000 only as transientdynamics at the start of a simulation very rarely persist for 200 time steps. The defaultvalue for the simulations reported here was 80 individuals. The error bars represent onestandard deviation. Very few extinctions were observed and population cycling was ev-ident in the range 1 to > 500 individuals. This graph indicates the lack of importance ofinitial population numbers—the level of the prey initial population may cause transientdymanics at the start of a simulation and in extreme cases may cause extinctions, but ifthe latter does not occur the population means, peaks and troughs settle to levels whichare dependent on the model parameters.

42

Prey initial population: Eight individual simulations at differing parameter levels315

0

300

600

Po

pu

lation

(a

)

PredatorPrey

0

300

600

Popula

tion

(b)

PredatorPrey

0

300

600

Popula

tion

(c)

PredatorPrey

0

300

600

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

300

600

(e)

PredatorPrey

0

300

600

(f)

PredatorPrey

0

300

600

(g)

PredatorPrey

0

300

600

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 9b: Predator and prey populations per time step for eight executions of themodel using different values of the prey initial population (bn). The values of bn are 10(a), 80 (b), 150 (c), 220 (d), 290 (e), 360 (f), 430 (g) and 500 (h) individuals.The number of population peaks over 500 time steps is 26 in each graph. These figuresdo not suggest any correlation between the parameter and population cycle period lengthor population cycle amplitudes.

43

1.12 Prey initial resources316

Summary317

The prey initial resources parameter (bir) represents the energy resources a prey indi-318

vidual is born with. At the start of a simulation all prey have this resource level and319

all individuals born during the simulation have the same resource level in their first320

time step. This parameter also specifies the cost of reproduction for a parent—it is the321

number of resources subtracted from a parent when it bears one offspring. In the simu-322

lations reported in this parameter sensitivity analysis, this parameter has a default value323

of 200.0 resource units.324

With the default parameter set, values of bir ≥ 60 resource units result in population325

cycling and extinctions are observed when bir ≤ 100 resource units. Mean populations326

of both species are negatively correlated with bir in this range of values, as illustrated by327

SM Figure 10a which graphs mean population levels and mean time step reached over328

50 simulations at each parameter level.329


different parameter levels. These figures suggest a positive correlation between bir and331

population cycle period length and a negative correlation between the parameter and332


44

Prey initial resources: Population levels, population persistence and range in which334

population cycling is evident335

0

500

1000

1500

2000

2500

50 100 150 200 250 300 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Prey initial resources (resource units)



SM Figure 10a: Mean populations and mean number of time steps before an extinc-tion graphed against prey initial resources (bir). The default value for the simulationsreported here was 200.0 resource units. The error bars represent one standard devi-ation. Extinctions were observed when bir < 100, becoming more common whenbir <= 60 and population cycling was evident in the range 60(approx.) to > 300resources (bounded by the dotted vertical line and the RH y-axis).

45

Prey initial resources: Eight individual simulations at differing parameter levels336

0

6000

12000

Po

pu

lation

(a

)

PredatorPrey

0

2000

4000

Popula

tion

(b)

PredatorPrey

0

600

1200

Popula

tion

(c)

PredatorPrey

0

600

1200

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

300

600

(e)

PredatorPrey

0

300

600

(f)

PredatorPrey

0

300

600

(g)

PredatorPrey

0

300

600

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 10b: Predator and prey populations per time step for eight executions of themodel using different values of the prey initial resources (bir). The values of bir are 60(a), 95 (b), 130 (c), 165 (d), 200 (e), 235 (f), 270 (g) and 305 (h) resource units. Notethe differing y-axis scales.The number of population peaks over 500 time steps are 32 (a), 30 (b), 27 (c), 26 (d), 26(e), 25 (f), 24 (g) and 24 (h), suggesting a positive correlation between bir and populationcycle period length. A negative correlation between the parameter and population cycleamplitudes is also suggested by these figures.

46

1.13 Prey metabolic cost per time step337

Summary338

The prey metabolic cost per time step parameter (bmc) represents the energy cost of339

metabolism in a living organism over time, this cost is subtracted from the resource340

total of each prey individual each time step. If after the subtraction the individual does341

not have enough resources to live another time step, it dies of starvation and is removed342

from the simulation. In the simulations reported in this parameter sensitivity analysis,343

this parameter has a default value of 25.0 resource units.344

With the default parameter set, values of 0 ≤ bmc ≤ 70 resource units result in345

population cycling and extinctions are observed when bmc ≥ 60 resource units. Mean346

populations of both species appear to be negatively correlated with bmc in this range of347

values, as illustrated by SM Figure 11a which graphs mean population levels and mean348

time step reached over 50 simulations at each parameter level.349


different parameter levels. These figures suggest a positive correlation between bmc and351



47

Prey metabolic cost per time step: Population levels, population persistence and354

range in which population cycling is evident355

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Prey metabolic cost per time step (resource units)



SM Figure 11a: Mean populations and mean number of time steps before an extinctiongraphed against prey metabolic cost per time step (bmc). The default value for the sim-ulations reported here was 25.0 resource units. The error bars represent one standarddeviation. Extinctions were observed when bmc >= 60 resource units and populationcycling was evident in the range 0 to 70(approx.) resources (bounded by the LH y-axisand the dotted vertical line).

48

Prey metabolic cost per time step: Eight individual simulations at differing param-356

eter levels357

0

300

600

Po

pu

lation

(a

)

PredatorPrey

0

300

600

Popula

tion

(b)

PredatorPrey

0

300

600

Popula

tion

(c)

PredatorPrey

0

300

600

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

300

600

(e)

PredatorPrey

0

300

600

(f)

PredatorPrey

0

300

600

(g)

PredatorPrey

0

300

600

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 11b: Predator and prey populations per time step for eight executions of themodel using different values of the prey metabolic cost per time step (bmc). The valuesof bmc are 5 (a), 15 (b), 25 (c), 35 (d), 45 (e), 55 (f), 65 (g) and 75 (h) resource units.The number of population peaks over 500 time steps are 27 (a), 26 (b), 26 (c), 25(d), 24 (e), 24 (f), 23 (g) and 21 (h), suggesting a positive correlation between bmc

and population cycle period length. A negative correlation between the parameter andpopulation cycle amplitudes is also suggested by these figures.

49

1.14 Prey resource consumption per time step358

Summary359

The prey minimum resources per time step (bminr) and prey maximum resources per360

time step (bmaxr) parameters are the lower and upper bounds respectively of a random361

number of resources added to each prey individual each time step. In the simulations362

reported in this parameter sensitivity analysis these parameters have default values of363

bminr = 125.0 and bmaxr = 175.0 resource units, an assumed mean over the course of a364

simulation of x = 150 resource units.365

With the default parameter set, values of 90 ≤ x ≤ 700 resource units result in366

population cycling and extinctions are observed when x ≤ 120 resource units. The367

mean predator population is positively correlated with the mean resource consumption368

per time step as illustrated in SM Figure 12a and the mean prey population appears369

to be negatively correlated with resource input, although this has not been formally370

analysed. The figure illustrates mean population levels and mean time step reached over371

50 simulations at each parameter level.372


different parameter levels. These figures suggest a negative correlation between prey374

resource consumption and population cycle period length and a negative correlation375

between the parameter and population cycle amplitudes.376

50

Prey resource consumption per time step: Population levels, population persistence377

and range in which population cycling is evident378

0

50

100

150

200

250

0 200 400 600 800 1000 1200 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Mean prey resource consumption per time step (resource units)



SM Figure 12a: Mean populations and mean number of time steps before an extinctiongraphed against mean prey resource consumption per time step. The default mean preyresource consumption per time step for the simulations reported here was 150.0 resourceunits (bminr = 125.0 resource units and bmaxr = 175.0 resource units). The error barsrepresent one standard deviation. Extinctions were observed when mean prey resourceconsumption per time step was below 120 resource units and population cycling wasevident in the range 90(approx.) to 700(approx.) resources (bounded by the dottedvertical lines).

51

Prey resource consumption per time step: Eight individual simulations at differing379

parameter levels380

0

300

600

Pop

ula

tion

(a)

PredatorPrey

0

300

600

Popula

tion

(b)

PredatorPrey

0

300

600

Popula

tion

(c)

PredatorPrey

0

300

600

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

150

300

(e)

PredatorPrey

0

150

300

(f)

PredatorPrey

0

150

300

(g)

PredatorPrey

0

150

300

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 12b: Predator and prey populations per time step for eight executions of themodel using different values of the prey minimum resources per time step (bminr) andprey maximum resources per time step (bmaxr). The values of bminr,bmaxr are 75,125 (a),175,225 (b), 275,325 (c), 375,425 (d), 475,525 (e), 575,625 (f), 675,725 (g) and 775,825(h) resource units. Note the predator extinction at time step 59 in (a), the breakdown ofpopulation cycling in (h) and the differing y-axis scales.The number of population peaks over 500 time steps, where they can be visually identi-fied, are 26 (b), 30 (c), 29 (d), 30 (e), 30 (f) and 31 (g), suggesting a negative correlationbetween prey resource consumption and population cycle period length. These figuresalso suggest a negative correlation between the parameter and population cycle ampli-tudes.

52

1.15 Prey hidden381

Summary382

The prey hidden parameter (bph) specifies the number of prey “hidden” from the preda-383

tors in simulated prey refuges. The hidden prey are not identified—prey refuges are384

modelled simply as a number: if the prey population is below that number then preda-385

tion will not occur regardless of the value of the chance of eating parameter (pce). In the386


value of 10 individuals.388

With the default parameter set, values of 5 ≤ bph ≤ 20 individuals result in popula-389

tion cycling and extinctions are observed when bph ≤ 6 individuals. Mean populations390

of both species are negatively correlated with bph in this range of values, as illustrated391

by SM Figure 13a which graphs mean population levels and mean time step reached392

over 50 simulations at each parameter level.393


different parameter levels. These figures suggest a positive correlation between bph and395



53

Prey hidden: Population levels, population persistence and range in which popu-398

lation cycling is evident399

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 0

200

400

600

800

1000

1200

Mean p

op

ula

tions

Mean tim

e s

teps

Hidden prey (individuals)



SM Figure 13a: Mean populations and mean number of time steps before an extinctiongraphed against prey hidden (bph). The default value for the simulations reported herewas 10 individuals. The error bars represent one standard deviation. Extinctions wereobserved when bph <= 6 individuals and population cycling was evident in the range5(approx.) to 20(approx.) individuals (bounded by the dotted vertical lines).

54

Prey hidden: Eight individual simulations at differing parameter levels400

0

750

1500

Po

pu

lation

(a

)

PredatorPrey

0

750

1500

Popula

tion

(b)

PredatorPrey

0

300

600

Popula

tion

(c)

PredatorPrey

0

300

600

0 100 200 300 400 500

Popula

tion

(d)

Time Step

PredatorPrey

0

150

300

(e)

PredatorPrey

0

150

300

(f)

PredatorPrey

0

150

300

(g)

PredatorPrey

0

150

300

0 100 200 300 400 500

(h)

Time Step

PredatorPrey

SM Figure 13b: Predator and prey populations per time step for eight executions of themodel using different values of the prey hidden (bph). The values of bph are 3 (a), 6 (b),9 (c), 12 (d), 15 (e), 18 (f), 21 (g) and 24 (h) individuals. Note the predator extinction attime step 52 in (a), the breakdown of population cycling at higher values of bph and thediffering y-axis scales.The number of population peaks over 500 time steps, where they can be visually identi-fied, are 26 (b), 26 (c), 25 (d), 25 (e), 23 (f) and 21 (g), suggesting a positive correlationbetween bph and population cycle period length. These figures also suggest a negativecorrelation between the parameter and population cycle amplitudes.

55

2 Predator functional response401

The linear per capita consumption rate graphed below indicates that the simulated preda-402

tors exhibit a Type I functional response.403

The data were collected over 1000 time steps of a single execution of the model404

using the default parameter set of this paper. They are typical of the behaviour of the405

model across a wide parameter space.406

0 100 200 300 400

02

46

8

Number of prey

Pre

da

tor

pe

r ca

pita

co

nsu

mp

tio

n r

ate

SM Figure 14: The predator per-capita consumption rate (y) plotted against the numberof prey (x) for each time step. These data were collected from a single execution ofthe model in which x ranged from 14–464 (median: 28, interquartile range: 18–119.2,mean: 80.97, SD: 92.42). The equation of the line of best fit is: x = −0.0453+0.0218yand explains 92% of the variation in y (R2 = 0.9201, adjusted R2 = 0.92). Scatter plot,line of best fit and descriptive statistics were obtained using the R statistical environment(R Core Team, 2013).

56

References407

Caron-Lormier G, Humphry RW, Bohan DA, Hawes C, Thorbek P. 2008. Asynchronous408

and synchronous updating in individual-based models. Ecol. Mod. 212: 522–527.409

Grimm V, Berger U, DeAngelis DL, Polhill JG, Giske J, Railsback SF. 2010. The ODD410

protocol: A review and first update. Ecol. Mod. 221: 2760–2768.411

Grimm V, Uchmanski J. 1994. Ecological systems are not dynamic systems: some con-412

sequences of individual variability. In Grasman J, van Straten G (eds.) Predictabil-413

ity and Nonlinear Modelling in Natural Sciences and Economics. Dordrecht, The414

Netherlands: Kluwer Academic Publishers, 248–259.415

Python Software Foundation. 2013. random — Generate pseudo-random numbers.416

Last accessed 20 June 2013.417

URL http://docs.python.org/2/library/random.html418

R Core Team. 2013. R: A language and environment for statistical computing. Last419

accessed 20 June 2013.420

URL http://www.R-project.org421

57

3 Appendix 1: Model description in pseudo-code422

The algorithm used in the ABM is described in this section using pseudo-code, a method423

of algorithm description intended for human reading.424

Programming control structures are written in upper case (for example FOR EACH),425

methods, functions or sub-programs which are further expanded in this model descrip-426

tion are written with parentheses as a suffix (for example process_predators()).427

3.1 Initialisation and main loop428

read initial conditions and parameter values429

create initial populations430

431

FOR EACH time step432

433

IF either population is extinct434

stop processing435

436

process_predators()437

process_prey()438

439

remove_starved_individuals()440

add newborn predator and prey objects to populations441

442

implement_trapping_rate()443

implement_generalist_predator()444

445

collect statistics446

Note: Referring to the Python implementation of the model included with this Sup-447

porting Information, the initial population sizes are read when the “Load” button is448

clicked—it can be clicked only once—and all parameter values are read each time the449

“Run” button is clicked.450

58

3.2 Method definitions451

process_predators()452

FOR EACH predator individual453

implement_predator_eating()454

apply_metabolic_cost()455

implement_reproduction()456

457

process_prey()458

FOR EACH prey individual459

add_prey_resources()460



463

implement_predator_eating()464

number_to_eat_this_time_step = current_number_of_prey * pred_chances_of_eating465

WHILE number_to_eat_this_time_step >= 1466

implement_predation_event()467

subtract 1 from number_to_eat_this_time_step468

determine_whether_predator_eats()469

COMMENT note that number_to_eat_this_time_step now < 1470

IF predator is to eat471


473

determine_whether_predator_eats()474

calculate random_number between 0 and 1475

IF number_to_eat_this_time_step > random_number476

predator is to eat this time step477

478


IF number of prey > number of hidden prey480

select prey at random481

add (resource total of selected prey * trophic efficiency) to pred total482

remove prey individual from population483

484

add_prey_resources()485

select random number between upper and lower prey resource intake parameters486

add this number to prey resource total487

488


subtract metabolic cost per time step from resource total490

IF new resource total < metabolic cost per time step491

flag individual for starvation492

493


IF NOT individual flagged for starvation495

WHILE resource total > (metabolic cost per time step + cost of reproduction)496

create new individual497

59

subtract cost of reproduction from resource total498

499

remove_starved_individuals()500

FOR EACH individual501

IF flagged for starvation502

remove from population503

504

implement_trapping_rate()505

FOR numberToRemove506

select random predator507

remove predator508

509

implement_generalist_predator()510

FOR numberOfGeneralists511

select random predator512

add resources to predator513

60

4 Appendix 2: The agent-based model implemented in514

the Python programming language515

The ABM code, written in the computer programming language Python, is reproduced516

following these instructions. This is the code used to generate all the data reported in517

this paper and Supporting Information.518

The Python source files (.py files) are available from the corresponding author.519

4.1 Using the model graphical interface520

Brief notes on installing Python and essential packages follow in the next sections. Once521

Python is installed and the model is started, the graphical interface contains additional522

notes. The populations should be loaded once before the ‘Run’ button is clicked. When523

the model completes the run, two graph windows will open—these can be closed before524

clicking the ‘Run’ button again.525

To see the six patterns discussed in this paper, the following sequence is suggested:526

• Click ‘Load’ then ‘Run’.527

• Close the two graph windows and set Trapping rate to 20. Click ‘Run’.528

• Close the two graph windows and set Trapping rate back to 0. Click ‘Run’.529

• Close the two graph windows and set Generalist rate to 25 and Generalist re-530

sources to 30. Click ‘Run’.531

• Close the two graph windows and set Generalist rate and Generalist resources532

back to 0. Click ‘Run’.533

61

The increased amplitudes associated with trapping rate and the decreased amplitudes534

associated with generalist predators should be evident.535

4.2 Python version and additional packages536

• This implementation of the ABM was written using Python 2.7.537

• The code uses the following Python packages:538

– Tkinter - for the user interface539

– numpy - for numerical computations540

– matplotlib - for graphs541

The Python language website, http://www.python.org, contains instructions on how542

to execute a Python program and could be consulted if the following notes are too brief.543

4.3 Running the ABM on Microsoft Windows544

These notes were tested on Windows version 7 (32bit).545

• Download the Windows installer from the Python site http://www.python.org.546

• Set the system PATH variable to include the Python directories:547

– Right-click ‘Computer’ and select ‘Properties’548

– In the dialogue box, select ‘Advanced System Settings’549

– In the next dialogue box, select ‘Environment Variables’550

– In the ‘User Variables’ section, add the following to the PATH statement:551

C:\Python27;C:\Python27\Lib\site-packages\;C:\Python27\Scripts\;552

62

• Download numpy from http://sourceforge.net/projects/numpy and install.553

• Download matplotlib from http://sourceforge.net/projects/matplotlib/ and install.554

When the above are installed and the code files created in an appropriate directory,555

the model can be executed from an integrated development environment such as Mi-556

crosoft Visual Studio or from the command line:557

python main.py558

4.4 Running the ABM on Linux or BSD559

Python is installed on most Linux distributions and on the BSD variants but you may560

need to install the additional packages listed above. When these packages are installed561

and the code files created in an appropriate directory, the model can be run from a562

terminal:563

python main.py564

4.5 Running the ABM on Apple OSX565

We suggest the use of a third party tool such as the Enthought Python Distribution,566

which is free of charge for academic purposes and is available at567

http://www.enthought.com/products/epd.php.568

63

4.6 The model code569

The model source code is written in in the following seven files:570

• main.py571

• gui.py572

• simulation.py573

• default_values.py574

• animal.py575

• predator.py576

• prey.py577

4.6.1 main.py578

#579

# Predator-prey individual-based model580

#581

# Dr William Chivers582

# Faculty of Science and Information Technology583

# University of Newcastle, PO Box 127, Ourimbah, NSW 2259, Australia584

# email: [email protected]

# alternative email: [email protected]

#587

# This file creates an instance of the graphical user interface to the model588

#589

590

from Tkinter import *591

from gui import *592

593

root = Tk()594

root.title("Predator-Prey ABM")595

596

app = gui(root)597

root.mainloop()598

64

4.6.2 gui.py599

#600


#602






#608

# This file defines the gui class. One instance of this class is created. The609

# resulting graphical interface allows users to change initial populations,610

# parameter values and other simulation settings.611

#612

613

# -------------------------------------614

# Naming convention615

#616

# Attributes: aAttributeName617

# Local variable: lVariableName618

# Parameters: pParameterName619

# Classes: ClassName620

# Objects: aObjectName621

# Methods: methodName()622

#623

# Button: aBButtonName624

# Text field: aTFTextFieldName625

# Label: aLLabelName626

# Check box: aCBCheckBoxName627

# Radio button: aRBButtonName628

# -------------------------------------629

630

from Tkinter import *631

from simulation import *632

from default_values import *633

634

class gui:635

""" Creates the graphical interface to the model """636

637

# Constructor method reads default values and creates GUI638

def __init__(self, master):639

640

# Create default_values object641

self.aDefValue = DefaultValues()642

643

# Read default values from aDefValue object644

self.aPredInitialNo = self.aDefValue.aPredInitialNo # Pred initial population645

self.aPredInitialRes = self.aDefValue.aPredInitialRes # Pred initial resources646

self.aPredMetTax = self.aDefValue.aPredMetTax # Pred metabolic cost per time step647

self.aPredTrophicEff = self.aDefValue.aPredTrophicEff # Pred trophic efficiency648

65

self.aPredChEat = self.aDefValue.aPredChEat # Pred chances of eating649

650

self.aPredTrappingRate = self.aDefValue.aPredTrappingRate # Pred trapping rate651

self.aPredGenRate = self.aDefValue.aPredGenRate # Pred generalist rate652

self.aPredGenResources = self.aDefValue.aPredGenResources # Pred generalist resources added653

654

self.aPreyInitialNo = self.aDefValue.aPreyInitialNo # Prey initial population655

self.aPreyInitialRes = self.aDefValue.aPreyInitialRes # Prey initial resources656

self.aPreyMetTax = self.aDefValue.aPreyMetTax # Prey metabolic cost per time step657

self.aPreyMinRes = self.aDefValue.aPreyMinRes # Prey min resource consumption per time step658

self.aPreyMaxRes = self.aDefValue.aPreyMaxRes # Prey max resource consumption per time step659

self.aPreyHidden = self.aDefValue.aPreyHidden # Prey hidden660

661

self.aTimeStepsThisRun = self.aDefValue.aTimeStepsThisRun # Number of time steps on click of Run button662

self.aMaxPopulationSize = self.aDefValue.aMaxPopulationSize # Maximum population size663

664

self.aXTermDisplay = self.aDefValue.aXTermDisplay # Display time step levels on xterm?665

self.aShowStatistics = self.aDefValue.aShowStatistics # Display run statistics on xterm?666

self.aPlotPopGraph = self.aDefValue.aPlotPopGraph # Plot the populations per time step?667

self.aPlotPhaseGraph = self.aDefValue.aPlotPhaseGraph # Plot population phase graph?668

669

670

# Create GUI frame671

lFrame = Frame(master)672

lFrame.pack()673

674

# add left vertical spacer675

self.aLVSpacer00 = Label(lFrame, text="", width=1)676

self.aLVSpacer00.grid( row=0, column=0, sticky=W)677

678

679

# Instructions680

self.aLParameters = Label(lFrame, text="Notes", fg="blue")681

self.aLParameters.grid(columnspan=2, row=1, column=1, sticky=W)682

# Note 1683

self.aLParameters = Label(lFrame, text="1. Click ’Load’ then ’Run’.")684


# Note 2686

self.aLParameters = Label(lFrame, text="2. The ’Load’ button can be used only once.")687


self.aLParameters = Label(lFrame, text=" Initial populations can be adjusted")689


self.aLParameters = Label(lFrame, text=" before clicking ’Load’.")691


# Note 3693

self.aLParameters = Label(lFrame, text="4. The ’Run’ button can be used indefinitely.")694


self.aLParameters = Label(lFrame, text=" All values other than initial populations")696


self.aLParameters = Label(lFrame, text=" can be changed between ’Run’ clicks.")698


66

# Note 4700

self.aLParameters = Label(lFrame, text="3. No input values are tested: non-numeric")701


self.aLParameters = Label(lFrame, text=" input and other errors will be dealt")703


self.aLParameters = Label(lFrame, text=" with by the Python exception sub-system.")705


# Note 5707

self.aLParameters = Label(lFrame, text="5. The default values indicate whether the")708


self.aLParameters = Label(lFrame, text=" code expects an integer or a real number.")710


self.aLParameters = Label(lFrame, text=" Integers can be typed into real text boxes.")712


# Note 6714

self.aLParameters = Label(lFrame, text="6. The simulation stops if a population exceeds")715


self.aLParameters = Label(lFrame, text=" the ’Max population’. This is included only ")717


self.aLParameters = Label(lFrame, text=" to allow some user control over simulation")719


self.aLParameters = Label(lFrame, text=" run time in the absence of a ’Stop’ button.")721


# Note 7723

self.aLParameters = Label(lFrame, text="7. The simulation stops on the extinction")724


self.aLParameters = Label(lFrame, text=" of either population.")726


728




732

# Initial populations733

self.aLParameters = Label(lFrame, text="Initial populations", fg="blue")734


736

# create initial populations labels737

self.aLPredInitialNo = Label(lFrame, text="Predators")738

self.aLPredInitialNo.grid( row=2, column=3, sticky=W)739

self.aLPreyInitialNo = Label(lFrame, text="Prey")740

self.aLPreyInitialNo.grid( row=2, column=6, sticky=W)741

742

# create initial populations text boxes743

self.aTFPredInitialNo = Entry(lFrame, width=8)744

self.aTFPredInitialNo.grid( row=2, column=4, sticky=W)745

self.aTFPredInitialNo.insert(0, self.aPredInitialNo)746

self.aTFPreyInitialNo = Entry(lFrame, width=8)747

self.aTFPreyInitialNo.grid( row=2, column=7, sticky=W)748

self.aTFPreyInitialNo.insert(0, self.aPreyInitialNo)749

750

67

# add horizontal spacer between pred prey settings settings and simulation settings751

self.aLHSpacer02 = Label(lFrame, text="")752

self.aLHSpacer02.grid(columnspan=6, row=3, column=3, sticky=W)753

754

# Parameters755

self.aLParameters = Label(lFrame, text="Parameters", fg="blue")756


758

# create predator labels759

self.aLPredators = Label(lFrame, text="Predators")760

self.aLPredators.grid(columnspan=1, row=5, column=3, sticky=W)761

self.aLPredInitialRes = Label(lFrame, text="Initial resources")762

self.aLPredInitialRes.grid( row=6, column=3, sticky=W)763

self.aLPredMetTax = Label(lFrame, text="Metabolic cost")764

self.aLPredMetTax.grid( row=7, column=3, sticky=W)765

self.aLPredTrophicEff = Label(lFrame, text="Trophic efficiency (%)")766

self.aLPredTrophicEff.grid( row=8, column=3, sticky=W)767

self.aLPredChEat = Label(lFrame, text="Chance of eating")768

self.aLPredChEat.grid( row=9, column=3, sticky=W)769

self.aLPredTrappingRate = Label(lFrame, text="Trapping rate (%)")770

self.aLPredTrappingRate.grid( row=10, column=3, sticky=W)771

self.aLPredGenRate = Label(lFrame, text="Generalist rate (%)")772

self.aLPredGenRate.grid( row=11, column=3, sticky=W)773

self.aLPredGenResources = Label(lFrame, text="Generalist resources")774

self.aLPredGenResources.grid( row=12, column=3, sticky=W)775

776

# create predator text boxes777

self.aTFPredInitialRes = Entry(lFrame, width=8)778

self.aTFPredInitialRes.grid( row=6, column=4, sticky=W)779

self.aTFPredInitialRes.insert(0, self.aPredInitialRes)780

self.aTFPredMetTax = Entry(lFrame, width=8)781

self.aTFPredMetTax.grid( row=7, column=4, sticky=W)782

self.aTFPredMetTax.insert(0, self.aPredMetTax)783

self.aTFPredTrophicEff = Entry(lFrame, width=8)784

self.aTFPredTrophicEff.grid( row=8, column=4, sticky=W)785

self.aTFPredTrophicEff.insert(0, self.aPredTrophicEff)786

self.aTFPredChEat = Entry(lFrame, width=8)787

self.aTFPredChEat.grid( row=9, column=4, sticky=W)788

self.aTFPredChEat.insert(0, self.aPredChEat)789

self.aTFPredTrappingRate = Entry(lFrame, width=8)790

self.aTFPredTrappingRate.grid( row=10, column=4, sticky=W)791

self.aTFPredTrappingRate.insert(0, self.aPredTrappingRate)792

self.aTFPredGenRate = Entry(lFrame, width=8)793

self.aTFPredGenRate.grid( row=11, column=4, sticky=W)794

self.aTFPredGenRate.insert(0, self.aPredGenRate)795

self.aTFPredGenResources = Entry(lFrame, width=8)796

self.aTFPredGenResources.grid( row=12, column=4, sticky=W)797

self.aTFPredGenResources.insert(0, self.aPredGenResources)798

799

# add vertical spacer between predator and prey settings800


68


803

# create prey labels804

self.aLPrey = Label(lFrame, text="Prey")805

self.aLPrey.grid(columnspan=1, row=5, column=6, sticky=W)806

self.aLPreyInitialRes = Label(lFrame, text="Initial resources")807

self.aLPreyInitialRes.grid( row=6, column=6, sticky=W)808

self.aLPreyMetTax = Label(lFrame, text="Metabolic cost")809

self.aLPreyMetTax.grid( row=7, column=6, sticky=W)810

self.aLPreyMinRes = Label(lFrame, text="Min. resources")811

self.aLPreyMinRes.grid( row=8, column=6, sticky=W)812

self.aLPreyMaxRes = Label(lFrame, text="Max. resources")813

self.aLPreyMaxRes.grid( row=9, column=6, sticky=W)814

self.aLPreyHidden = Label(lFrame, text="Number hidden")815

self.aLPreyHidden.grid( row=10, column=6, sticky=W)816

817

# create prey text boxes818

self.aTFPreyInitialRes = Entry(lFrame, width=8)819

self.aTFPreyInitialRes.grid( row=6, column=7, sticky=W)820

self.aTFPreyInitialRes.insert(0, self.aPreyInitialRes)821

self.aTFPreyMetTax = Entry(lFrame, width=8)822

self.aTFPreyMetTax.grid( row=7, column=7, sticky=W)823

self.aTFPreyMetTax.insert(0, self.aPreyMetTax)824

self.aTFPreyMinRes = Entry(lFrame, width=8)825

self.aTFPreyMinRes.grid( row=8, column=7, sticky=W)826

self.aTFPreyMinRes.insert(0, self.aPreyMinRes)827

self.aTFPreyMaxRes = Entry(lFrame, width=8)828

self.aTFPreyMaxRes.grid( row=9, column=7, sticky=W)829

self.aTFPreyMaxRes.insert(0, self.aPreyMaxRes)830

self.aTFPreyHidden = Entry(lFrame, width=8)831

self.aTFPreyHidden.grid( row=10, column=7, sticky=W)832

self.aTFPreyHidden.insert(0, self.aPreyHidden)833

834

# add horizontal spacer between pred prey settings settings and simulation settings835



838

# create simulation control labels839

self.aLSimulation = Label(lFrame, text="Simulation Settings", fg="blue")840

self.aLSimulation.grid(columnspan=2, row=14, column=3, sticky=W)841

self.aLTimeStepsThisRun = Label(lFrame, text="Time steps")842

self.aLTimeStepsThisRun.grid( row=15, column=3, sticky=W)843

844

self.aLMaxPopulationSize = Label(lFrame, text="Max. population")845

self.aLMaxPopulationSize.grid( row=16, column=3, sticky=W)846

847

# create simulation controls848

self.aTFTimeStepsThisRun = Entry(lFrame, width=9)849

self.aTFTimeStepsThisRun.grid( row=15, column=4, sticky=W)850

self.aTFTimeStepsThisRun.insert(0, self.aTimeStepsThisRun)851

852

69

self.aTFMaxPopulationSize = Entry(lFrame, width=9)853

self.aTFMaxPopulationSize.grid( row=16, column=4, sticky=W)854

self.aTFMaxPopulationSize.insert(0, self.aMaxPopulationSize)855

856

# output settings857

self.aLSimulation = Label(lFrame, text="Output Settings", fg="blue")858

self.aLSimulation.grid(columnspan=2, row=14, column=6, sticky=W)859

860

self.aXTermDisplayIV = IntVar() # Integer variable associated with check box861

self.aCBXTermDisplay = Checkbutton(lFrame, text="Time step levels on terminal?",862

variable=self.aXTermDisplayIV, onvalue=1, offvalue=0)863

self.aCBXTermDisplay.grid(columnspan=2, row=15, column=6, sticky=W)864

self.aXTermDisplayIV.set(self.aXTermDisplay)865

866

self.aShowStatisticsIV = IntVar() # Integer variable associated with check box867

self.aCBShowStatistics = Checkbutton(lFrame, text="Overall means on terminal?",868

variable=self.aShowStatisticsIV, onvalue=1, offvalue=0)869

self.aCBShowStatistics.grid(columnspan=2, row=16, column=6, sticky=W)870

self.aShowStatisticsIV.set(self.aShowStatistics)871

872

self.aPlotPopGraphIV = IntVar() # Integer variable associated with check box873

self.aCBPlotPopGraph = Checkbutton(lFrame, text="Plot populations per time step?",874

variable=self.aPlotPopGraphIV, onvalue=1, offvalue=0)875

self.aCBPlotPopGraph.grid(columnspan=2, row=17, column=6, sticky=W)876

self.aPlotPopGraphIV.set(self.aPlotPopGraph)877

878

self.aPlotPhaseGraphIV = IntVar() # Integer variable associated with check box879

self.aCBPlotPhaseGraph = Checkbutton(lFrame, text="Plot population phase graph?",880

variable=self.aPlotPhaseGraphIV, onvalue=1, offvalue=0)881

self.aCBPlotPhaseGraph.grid(columnspan=2, row=18, column=6, sticky=W)882

self.aPlotPhaseGraphIV.set(self.aPlotPhaseGraph)883

884

# add horizontal spacers between simulation settings and control buttons885





890

# Button: load populations - executed only once891

self.aBLoad = Button(lFrame, text="Load", command=self.createInitialPopulations)892

self.aBLoad.grid( row=21, column=3, sticky=W)893

# Button: run simulation - executed indefinitely894

self.aBRun = Button(lFrame, text="Run", command=self.runSimulation)895

self.aBRun.grid( row=21, column=4, sticky=W)896

self.aBRun[’state’] = DISABLED # initially disable Run button897

# Button: close GUI898

self.aBClose = Button(lFrame, text="Close", command=lFrame.quit)899

self.aBClose.grid( row=21, column=7, sticky=W)900

901

# add horizontal spacer between control buttons and bottom of window902


70


905




# end constructor909

910

911

# implementor methods912

913

# create initial populations914

def createInitialPopulations(self):915

""" Create initial populations - executed only once on first click of Run button """916

917

# create simulation control object918

self.aSimulation = Simulation()919

920

# create predator list921

self.aSimulation.initPredators(int(self.aTFPredInitialNo.get()), # Pred initial population922

float(self.aTFPredInitialRes.get())) # Pred initial resources923

924

# create prey list925

self.aSimulation.initPrey(int(self.aTFPreyInitialNo.get()), # Prey initial population926

float(self.aTFPreyInitialRes.get())) # Prey initial resources927

928

# disable Load button and initial population text fields929

self.aTFPredInitialNo[’state’] = DISABLED930

self.aTFPreyInitialNo[’state’] = DISABLED931

self.aBLoad[’state’] = DISABLED932

# enable Run button933

self.aBRun[’state’] = NORMAL934

935

# end createInitialPopulations()936

937

# run simulation938

def runSimulation(self):939

""" Run simulation - executed any number of times """940

941

# run the simulation942

self.aSimulation.runSimulation(int(self.aTFPredInitialNo.get()), # Pred initial population943

float(self.aTFPredInitialRes.get()), # Pred initial resources944

float(self.aTFPredMetTax.get()), # Pred metabolic cost per time step945

float(self.aTFPredTrophicEff.get()), # Pred trophic efficiency946

float(self.aTFPredChEat.get()), # Pred chances of eating947

948

float(self.aTFPredTrappingRate.get()), # Pred trapping rate949

float(self.aTFPredGenRate.get()), # Pred generalist rate950

float(self.aTFPredGenResources.get()), # Pred generalist resources added951

952

int(self.aTFPreyInitialNo.get()), # Prey initial population953

float(self.aTFPreyInitialRes.get()), # Prey initial resources954

71

float(self.aTFPreyMetTax.get()), # Prey metabolic cost per time step955

float(self.aTFPreyMinRes.get()), # Prey min res cons per time step956

float(self.aTFPreyMaxRes.get()), # Prey max res cons per time step957

int(self.aTFPreyHidden.get()), # Prey hidden958

959

int(self.aTFTimeStepsThisRun.get()), # Number of ts on click of Run button960

int(self.aTFMaxPopulationSize.get()), # Maximum population size961

962

int(self.aXTermDisplayIV.get()), # Display time step levels on xterm?963

int(self.aShowStatisticsIV.get()), # Display run statistics on xterm?964

int(self.aPlotPopGraphIV.get()), # Plot the populations per time step?965

int(self.aPlotPhaseGraphIV.get()) # Plot population phase graph?966

)967

# end runSimulation()968

72

4.6.3 simulation.py969

#970


#972






#978

# This file defines the simulation class. One instance of this class is created by the gui object.979

# The Simulation class has methods to create initial predator and prey populations and to execute980

# the model algorithm each time step. It also collects and displays statistics and creates the981

# graphs.982

#983

984

import sys985

import tkMessageBox986

import random987

import numpy988

import matplotlib.pyplot as aPlot989

990

from prey import *991

from predator import *992

993

994

class Simulation:995

""" Creates initial populations, runs the model, collects and displays statistics996

and creates graphs """997

998

# instance attributes - values read from gui in the methods below999

aPredInitialNo = 0 # Pred initial population1000

aPredInitialRes = 0.0 # Pred initial resources1001

aPredMetTax = 0.0 # Pred metabolic cost per time step1002

aPredTrophicEff = 0.0 # Pred trophic efficiency1003

aPredChEat = 0.0 # Pred chances of eating1004

1005

aPredTrappingRate = 0.0 # Pred trapping rate1006

aPredGenRate = 0.0 # Pred generalist rate1007

aPredGenResources = 0.0 # Pred generalist resources added1008

1009

aPreyInitialNo = 0 # Prey initial population1010

aPreyInitialRes = 0.0 # Prey initial resources1011

aPreyMetTax = 0.0 # Prey metabolic cost per time step1012

aPreyMinRes = 0.0 # Prey min resource consumption per time step1013

aPreyMaxRes = 0.0 # Prey max resource consumption per time step1014

aPreyHidden = 0 # Prey hidden1015

1016

aTimeStepsThisRun = 0 # Number of time steps on click of Run button1017

aMaxPopulationSize = 0 # Maximum population size1018

73

1019

aXTermDisplay = 0 # Display time step levels on xterm?1020

aShowStatistics = 0 # Display run statistics on xterm?1021

aPlotPopGraph = 0 # Plot the populations per time step?1022

aPlotPhaseGraph = 0 # Plot population phase graph?1023

1024

# instance attributes - other1025

aTotalTimeSteps = 0 # Total time steps including previous Run button clicks1026

1027

aPred = [] # Predator list1028

aPredNewBorn = [] # Pred list - newborn this time step1029

aPredPopPerTimeStep = [] # Predator population per time step1030

aNextPredSNo = 0 # The next predator serial number to be used1031

1032

aPrey = [] # Prey list1033

aPreyNewBorn = [] # Prey list - newborn this time step1034

aPreyPopPerTimeStep = [] # Prey population per time step1035

aNextPreySNo = 0 # The next prey serial number to be used1036

1037

aPredMin = sys.maxint # Minimum predator population over one simulation1038

aPredMax = 0 # Maximum predator population over one simulation1039

aPreyMin = sys.maxint # Minimum prey population over one simulation1040

aPreyMax = 0 # Maximum prey population over one simulation1041

1042

1043

# create predator list1044

def initPredators(self,1045

pPredInitialNo, # Pred initial population1046

pPredInitialRes): # Pred initial resources1047

""" Creates initial number of predators with initial resource totals """1048

1049

# create new predator list on first and only execution of Run button1050

self.createNewPredList(pPredInitialNo, # Pred initial population1051

pPredInitialRes) # Pred initial resources1052

# end initPredators()1053

1054

1055

# create prey list1056

def initPrey(self,1057

pPreyInitialNo, # Prey initial population1058

pPreyInitialRes): # Prey initial resources1059

""" Creates initial number of prey with initial resource totals """1060

1061

# create new prey list on first and only execution of Run button1062

self.createNewPreyList(pPreyInitialNo, # Prey initial population1063

pPreyInitialRes) # Prey initial resources1064

# end initPrey()1065

1066

1067

# run the simulation1068

def runSimulation(self,1069

74


pPredInitialRes, # Pred initial resources1071

pPredMetTax, # Pred metabolic cost per time step1072

pPredTrophicEff, # Pred trophic efficiency1073

pPredChEat, # Pred chances of eating1074

1075

pPredTrappingRate, # Pred trapping rate1076

pPredGenRate, # Pred generalist rate1077

pPredGenResources, # Pred generalist resources added1078

1079


pPreyInitialRes, # Prey initial resources1081

pPreyMetTax, # Prey metabolic cost per time step1082

pPreyMinRes, # Prey min resource consumption per time step1083

pPreyMaxRes, # Prey max resource consumption per time step1084

pPreyHidden, # Prey hidden1085

1086

pTimeStepsThisRun, # Number of time steps on click of Run button1087

pMaxPopulationSize, # Maximum population size1088

1089

pXTermDisplay, # Display time step levels on xterm?1090

pShowStatistics, # Display run statistics on xterm?1091

pPlotPopGraph, # Plot the populations per time step?1092

pPlotPhaseGraph): # Plot population phase graph?1093

1094

1095

""" Runs the simulation a given number of time steps. The gui class passes current parameter values. """1096

1097

# read parameter values into instance attributes1098

self.aPredInitialNo = pPredInitialNo # Pred initial population1099

self.aPredInitialRes = pPredInitialRes # Pred initial resources1100

self.aPredMetTax = pPredMetTax # Pred metabolic cost per time step1101

self.aPredTrophicEff = pPredTrophicEff # Pred trophic efficiency1102

self.aPredChEat = pPredChEat # Pred chances of eating1103

1104

self.aPredTrappingRate = pPredTrappingRate # Pred trapping rate1105

self.aPredGenRate = pPredGenRate # Pred generalist rate1106

self.aPredGenResources = pPredGenResources # Pred generalist resources added1107

1108

self.aPreyInitialNo = pPreyInitialNo # Prey initial population1109

self.aPreyInitialRes = pPreyInitialRes # Prey initial resources1110

self.aPreyMetTax = pPreyMetTax # Prey metabolic cost per time step1111

self.aPreyMinRes = pPreyMinRes # Prey min resource consumption per time step1112

self.aPreyMaxRes = pPreyMaxRes # Prey max resource consumption per time step1113

self.aPreyHidden = pPreyHidden # Prey hidden1114

1115

self.aTimeStepsThisRun = pTimeStepsThisRun # Number of time steps on click of Run button1116

self.aMaxPopulationSize = pMaxPopulationSize # Maximum population size1117

1118

self.aXTermDisplay = pXTermDisplay # Display time step levels on xterm?1119

self.aShowStatistics = pShowStatistics # Display run statistics on xterm?1120

75

self.aPlotPopGraph = pPlotPopGraph # Plot the populations per time step?1121

self.aPlotPhaseGraph = pPlotPhaseGraph # Plot population phase graph?1122

1123

1124

# main simulation loop (aTimeStepsThisRun) on each execution of Run button1125

for i in range(self.aTimeStepsThisRun):1126

1127

# stop simulation if predators are extinct1128

if len(self.aPred) < 1:1129

print "Predator extinction at time step", self.aTotalTimeSteps1130

tkMessageBox.showwarning("Simulation stopped",1131

"Predator extinction at time step %d" % self.aTotalTimeSteps)1132

break1133

1134

# stop simulation if prey are extinct1135

if len(self.aPrey) < 1:1136

print "Prey extinction at time step", self.aTotalTimeSteps1137


"Prey extinction at time step %d" % self.aTotalTimeSteps)1139

break1140

1141

# stop simulation if predator population exceeds aMaxPopulationSize1142

if len(self.aPred) > self.aMaxPopulationSize:1143

print "Predator population exceeded max. size at time step", self.aTotalTimeSteps1144


"Predator population exceeded max. size at time step %d" % self.aTotalTimeSteps)1146

break1147

1148

# stop simulation if prey population exceeds aMaxPopulationSize1149

if len(self.aPrey) > self.aMaxPopulationSize:1150

print "Prey population exceeded max. size at time step", self.aTotalTimeSteps1151


"Prey population exceeded max. size at time step %d" % self.aTotalTimeSteps)1153

break1154

1155

1156

# display levels per time step on xterm?1157

if self.aXTermDisplay:1158

# output has the following columns:1159

print self.aTotalTimeSteps, # 1. time step1160

print len(self.aPred), # 2. pred population1161

print len(self.aPrey) # 3. prey population1162

1163

1164

# Increment aTotalTimeSteps - total time steps including previous Run button clicks1165

self.aTotalTimeSteps += 11166

1167

# process predators1168

for j in range(len(self.aPred)):1169

1170

# implement predator eating1171

76

1172

# Determine chance of eating or number of prey to eat this time step by this predator1173

lNumOfPreyToEat = len(self.aPrey) * self.aPredChEat # current number of prey1174

# * pred chances of eating1175

1176

# The random.random() method returns a pseudorandom1177

# number between 0.0000000000000 and 0.99999999999991178

lRandomNum = random.random()1179

1180

# If lNumOfPreyToEat >= 1 the predator eats one or more1181

# prey objects (if prey population > number hidden)1182

while lNumOfPreyToEat >= 1:1183

if(len(self.aPrey) > self.aPreyHidden):1184

self.eatPrey(self.aPred[j])1185

lNumOfPreyToEat -= 11186

1187

# If lNumOfPreyToEat < 1 the predators might eat a1188

# prey object - note lNumOfPreyToEat is now < 11189

if lNumOfPreyToEat > lRandomNum:1190

if(len(self.aPrey) > self.aPreyHidden):1191

self.eatPrey(self.aPred[j])1192

1193

1194

# apply metabolic cost1195

1196

self.aPred[j].applyMetTax(self.aPredMetTax) # Predator metabolic cost per time step1197

1198

1199

# implement reproduction1200

1201

# set/reset counter1202

lNumOfPredToAdd = 0 # Count the number of offspring this time step for this predator1203

1204

if (not self.aPred[j].getDiedThisTimeStep()):1205

while (self.aPred[j].getResourceTotal() >= (self.aPredInitialRes + self.aPredMetTax)):1206

1207

# add new predator object to new predators list1208

lNumOfPredToAdd += 1 # Number of predators to add this time step1209

1210

# subtract current aPredInitialRes from resource total1211

self.aPred[j].setResourceTotal(self.aPred[j].getResourceTotal() - self.aPredInitialRes)1212

1213

# create the new born predators1214

self.createNewBornPred(lNumOfPredToAdd)1215

1216

1217

# process prey1218

for j in range(len(self.aPrey)):1219

1220

# add resources to prey objects1221

1222

77

self.aPrey[j].addResources(self.aPreyMinRes, # Prey min resource consumption per time step1223

self.aPreyMaxRes) # Prey max resource consumption per time step1224

1225

# apply metabolic cost1226

1227

self.aPrey[j].applyMetTax(self.aPreyMetTax) # Prey metabolic cost per time step1228

1229

# implement reproduction1230

1231

# set/reset counter1232

lNumOfPreyToAdd = 0 # Count the number of offspring this time step for this prey1233

1234

if (not self.aPrey[j].getDiedThisTimeStep()):1235

while (self.aPrey[j].getResourceTotal() >= (self.aPreyInitialRes + self.aPreyMetTax)):1236

1237

# add new prey object to new prey linked list1238

lNumOfPreyToAdd += 1 # Number of prey to add this time step1239

1240

# subtract current aPreyInitialRes from resource total1241

self.aPrey[j].setResourceTotal(self.aPrey[j].getResourceTotal() - self.aPreyInitialRes)1242

1243

# create the new born prey1244

self.createNewBornPrey(lNumOfPreyToAdd)1245

1246

1247

# remove predator and prey objects which have starved1248

self.removeDeadPredators()1249

self.removeDeadPrey()1250

1251

# add newborn predator and prey objects to lists1252

self.aPred.extend(self.aPredNewBorn) # add new predators to main list, to be processed next time step1253

del self.aPredNewBorn[:] # empty new predators list1254

self.aPrey.extend(self.aPreyNewBorn) # add new prey to main list, to be processed next time step1255

del self.aPreyNewBorn[:] # empty new prey list1256

1257

# simulate trapping by removing a percentage of the predator population1258

self.implementTrappingRate()1259

1260

# simulate generalist predator by adding resources1261

self.implementGeneralistPredator()1262

1263

# update population levels1264

self.aPredPopPerTimeStep.append(len(self.aPred)) # collect predator population each time step1265

self.aPreyPopPerTimeStep.append(len(self.aPrey)) # collect prey population each time step1266

1267

# update maxima and minima1268

if self.aPredMin > len(self.aPred): # Minimum predator population over one simulation1269

self.aPredMin = len(self.aPred)1270

if self.aPredMax < len(self.aPred): # Maximum predator population over one simulation1271

self.aPredMax = len(self.aPred)1272

if self.aPreyMin > len(self.aPrey): # Minimum prey population over one simulation1273

78

self.aPreyMin = len(self.aPrey)1274

if self.aPreyMax < len(self.aPrey): # Maximum prey population over one simulation1275

self.aPreyMax = len(self.aPrey)1276

1277

1278

# end main simulation loop (aTimeStepsThisRun) on each execution of Run button1279

1280

# print run statistics?1281

if self.aShowStatistics:1282

self.showStats()1283

1284

# plot the populations per time step and/or the phase graph1285

self.plotGraphs()1286

1287

# end runSimulation()1288

1289

1290

# display simulation statistics1291

def showStats(self):1292

""" Displays mean predator and prey populations for all time steps completed """1293

1294

print ""1295

print "Pred mean", numpy.mean(self.aPredPopPerTimeStep),1296

print "SD", numpy.std(self.aPredPopPerTimeStep, ddof=0), # ddof: degrees of freedom1297

print "range", self.aPredMin, "to", self.aPredMax # Min to max predator population1298

1299

print "Prey mean", numpy.mean(self.aPreyPopPerTimeStep),1300

print "SD", numpy.std(self.aPreyPopPerTimeStep, ddof=0), # ddof: degrees of freedom1301

print "range", self.aPreyMin, "to", self.aPreyMax # Min to max prey population1302

1303

# end showStats()1304

1305

1306

# createNewPredList1307

def createNewPredList(self,1308


pPredInitialRes): # Pred initial resources1310

""" Creates a new predator list at the start of the simulation """1311

1312

for i in range(pPredInitialNo):1313

lPred = {}1314

# create predator object1315

lPred[i] = Pred(i)1316

# set resource total to aPredInitialRes1317

lPred[i].setResourceTotal(pPredInitialRes)1318

# add predator object to main predator linked list1319

self.aPred.append(lPred[i])1320

1321

self.aNextPredSNo = pPredInitialNo # the next predator serial number to be used1322

# end createNewPredList()1323

1324

79

1325

# createNewPreyList1326

def createNewPreyList(self,1327


pPreyInitialRes): # Prey initial resources1329

""" Creates a new prey list at the start of the simulation """1330

1331

for i in range(pPreyInitialNo):1332

lPrey = {}1333

# create prey object1334

lPrey[i] = Prey(i)1335

# set resource total to aPreyInitialRes1336

lPrey[i].setResourceTotal(pPreyInitialRes)1337

# add prey object to main prey linked list1338

self.aPrey.append(lPrey[i])1339

1340

self.aNextPreySNo = pPreyInitialNo # the next prey serial number to be used1341

# end createNewPreyList()1342

1343

1344

# createNewBornPred1345

def createNewBornPred(self,1346

pNumberToAdd): # number of predators to add1347

""" Creates individual predator objects during execution of the simulation """1348

1349

for i in range(pNumberToAdd):1350

lNewPred = {}1351

# create predator object1352

lNewPred[i] = Pred(self.aNextPredSNo)1353

# set resource total to aPredInitialRes1354

lNewPred[i].setResourceTotal(self.aPredInitialRes)1355

# add predator object to temporary newborn linked list1356

self.aPredNewBorn.append(lNewPred[i])1357

# increment the next predator serial number to be used1358

self.aNextPredSNo += 11359

# end createNewBornPred()1360

1361

1362

# createNewBornPrey1363

def createNewBornPrey(self,1364

pNumberToAdd): # number of prey to add1365

""" Creates individual prey objects during execution of the simulation """1366

1367

for i in range(pNumberToAdd):1368

lNewPrey = {}1369

# create prey object1370

lNewPrey[i] = Prey(self.aNextPreySNo)1371

# set resource total to aPreyInitialRes1372

lNewPrey[i].setResourceTotal(self.aPreyInitialRes)1373

# add prey object to temporary newborn linked list1374

self.aPreyNewBorn.append(lNewPrey[i])1375

80

# increment the next prey serial number to be used1376

self.aNextPreySNo += 11377

# end createNewBornPrey()1378

1379

1380

# implement predator eating1381

def eatPrey(self,1382

lPred): # current predator object1383

1384

# select random prey:1385

# The random.randint() method returns a pseudorandom integer1386

# between the lower and upper parameters inclusively1387

lPreyToBeEaten = random.randint(0, len(self.aPrey)-1)1388

1389

# aquire resources of prey object1390

lPred.eatPrey(self.aPrey[lPreyToBeEaten].getResourceTotal(), # resource total of prey1391

self.aPredTrophicEff) # Pred trophic efficiency1392

1393

# remove prey object1394

del self.aPrey[lPreyToBeEaten]1395

1396

1397

# remove predator objects which have starved1398

def removeDeadPredators(self):1399

""" Removes individual predator objects during execution of the simulation """1400

1401

lLivingPred = []1402

for i in range(len(self.aPred)):1403

if not (self.aPred[i].getDiedThisTimeStep()):1404

lLivingPred.append(self.aPred[i])1405

self.aPred = lLivingPred1406

# end removeDeadPredators()1407

1408

1409

# remove prey objects which have starved1410

def removeDeadPrey(self):1411

""" Removes individual prey objects during execution of the simulation """1412

1413

lLivingPrey = []1414

for i in range(len(self.aPrey)):1415

if not (self.aPrey[i].getDiedThisTimeStep()):1416

lLivingPrey.append(self.aPrey[i])1417

self.aPrey = lLivingPrey1418

# end removeDeadPrey()1419

1420

# simulate trapping by removing a percentage of the predator population1421

def implementTrappingRate(self):1422

""" Remove a percentage of the predator population. Called each time step. """1423

1424

lNumberToRemove = int( round( len(self.aPred) * (self.aPredTrappingRate / 100) ) )1425

1426

81

for i in range(lNumberToRemove):1427

# select random predator1428



lPredToBeEaten = random.randint(0, len(self.aPred)-1)1431

1432

# remove predator object1433

del self.aPred[lPredToBeEaten]1434

# end implementTrappingRate()1435

1436

# simulate generalist predator by adding resources1437

def implementGeneralistPredator(self):1438

""" Add resources to a percentage of the predator population. Called each time step. """1439

1440

lNumberOfGeneralists = int(round(len(self.aPred) * (self.aPredGenRate / 100)))1441

1442

for i in range(lNumberOfGeneralists):1443

# select random predator1444



lPredToBeGeneralist = random.randint(0, len(self.aPred)-1)1447

1448

# add resources to predator1449

self.aPred[lPredToBeGeneralist].setResourceTotal(self.aPred[lPredToBeGeneralist].getResourceTotal()1450

+ self.aPredGenResources)1451

# end implementGeneralistPredator()1452

1453

# plot the populations per time step and/or the phase graph1454

def plotGraphs(self):1455

""" Plot population and phase graphs after the specified number of time steps. """1456

1457

# plot population phase graph?1458

if self.aPlotPhaseGraph:1459

lPlot2 = aPlot.figure()1460

self.plotPhaseGraph()1461

1462

# plot the populations per time step?1463

if self.aPlotPopGraph:1464

lPlot1 = aPlot.figure()1465

self.plotPredPreyInteraction()1466

1467

aPlot.show()1468

1469

def plotPhaseGraph(self):1470

aPlot.plot(self.aPreyPopPerTimeStep, self.aPredPopPerTimeStep, ’b’)1471

aPlot.grid()1472

# set label names1473

aPlot.ylabel(’Predators’)1474

aPlot.xlabel(’Prey’)1475

1476

def plotPredPreyInteraction(self):1477

82

aPlot.plot(self.aPreyPopPerTimeStep, ’b’, self.aPredPopPerTimeStep, ’r’)1478

aPlot.legend(["Prey", "Predators"])1479

aPlot.grid()1480

# set label names1481

aPlot.ylabel(’Population’)1482

aPlot.xlabel(’Time step’)1483

1484

# end plot the populations per time step and/or the phase graph1485

# end class Simulation1486

83

4.6.4 default_values.py1487

#1488


#1490






#1496

# This file lists the default values for initial populations, parameters and other simulation settings1497

#1498

1499

class DefaultValues:1500

""" Default values for initial populations, parameters and other simulation settings """1501

1502

# constructor method1503

def __init__(self):1504

1505

self.aPredInitialNo = 35 # Pred initial population1506

self.aPredInitialRes = 220.0 # Pred initial resources1507

self.aPredMetTax = 30.0 # Pred metabolic cost per time step1508

self.aPredTrophicEff = 20.0 # Pred trophic efficiency1509

self.aPredChEat = 0.03 # Pred chances of eating1510

1511

self.aPredTrappingRate = 0.0 # Pred trapping rate1512

self.aPredGenRate = 0.0 # Pred generalist rate1513

self.aPredGenResources = 0.0 # Pred generalist resources added1514

1515

self.aPreyInitialNo = 80 # Prey initial population1516

self.aPreyInitialRes = 200.0 # Prey initial resources1517

self.aPreyMetTax = 25.0 # Prey metabolic cost per time step1518

self.aPreyMinRes = 125.0 # Prey min resource consumption per time step1519

self.aPreyMaxRes = 175.0 # Prey max resource consumption per time step1520

self.aPreyHidden = 10 # Prey hidden1521

1522

self.aTimeStepsThisRun = 200 # Number of time steps on click of Run button1523

self.aMaxPopulationSize = 10000 # Maximum population size1524

1525

self.aXTermDisplay = 1 # Display time step levels on xterm?1526

self.aShowStatistics = 1 # Display run statistics on xterm?1527

self.aPlotPopGraph = 1 # Plot the populations per time step?1528

self.aPlotPhaseGraph = 1 # Plot population phase graph?1529

1530


84

4.6.5 animal.py1532

#1533


#1535






#1541

# This file defines the Animal class which is used as an abstract class from which the1542

# Pred and Prey classes inherit the attributes and methods below.1543

#1544

1545

class Animal():1546

""" Represents a generic animal """1547

1548

# instance attributes1549

aSNo = 0 # Serial number1550

aResourceTotal = 0.0 # Resource total of individual1551

aDiedThisTimeStep = 0 # Flags the individual for removal1552

1553

1554


def __init__(self,1556

pSNo): # Serial number1557

self.aSNo = pSNo # Serial number1558


1560

1561

# getter methods1562

def getSNo(self):1563

return self.aSNo1564

1565

def getResourceTotal(self):1566

return self.aResourceTotal1567

1568

def getDiedThisTimeStep(self):1569

if self.aDiedThisTimeStep == 0:1570

return False1571

else:1572

return True1573

1574

1575

# setter methods1576

def setResourceTotal(self,1577

pResourceTotal): # Resource total of individual1578

self.aResourceTotal = pResourceTotal1579

1580

def setDiedThisTimeStep(self):1581

85

self.aDiedThisTimeStep = 11582

1583

1584


1586

# apply metabolic tax1587

def applyMetTax(self,1588

pMetTax): # metabolic cost per time step1589

""" Subtract the metabolic cost per time step from the object’s resource total and1590

set the Boolean aDiedThisTimeStep if the subsequent resource total is now1591

below the metabolic cost. """1592

1593

self.setResourceTotal(self.getResourceTotal() - pMetTax)1594

1595

if (self.getResourceTotal() < pMetTax):1596

self.setDiedThisTimeStep()1597

# end applyMetTax()1598

86

4.6.6 predator.py1599

#1600


#1602






#1608

# This file defines the Pred (predator) class. It inherits attributes and1609

# methods from the Animal class.1610

#1611

1612

import random1613

from animal import *1614

1615

class Pred(Animal):1616

""" Defines the predator class. Inherits from Animal """1617

1618




Animal.__init__(self,1622

pSNo) # Serial number1623


1625

1626


1628

# aquire resources of prey object1629

def eatPrey(self,1630

pResourceTotal, # resource total of prey object to be eaten1631

pPredTrophicEff): # Pred trophic efficiency1632

""" Uses resource total of the selected prey object and the ’trophic efficiency’ parameter1633

to add resources to predator object """1634

1635

lNewResourceTotal = self.getResourceTotal() + (pResourceTotal * (float(pPredTrophicEff) / 100))1636

self.setResourceTotal(lNewResourceTotal)1637

# end eatPrey()1638

87

4.6.7 prey.py1639

#1640


#1642






#1648

# This file defines the Prey class. It inherits attributes and1649

# methods from the Animal class.1650

#1651

1652

import random1653

from animal import *1654

1655

class Prey(Animal):1656

""" Defines the prey class. Inherits from Animal """1657

1658




Animal.__init__(self,1662

pSNo) # Serial number1663


1665

1666


1668

# add resources1669

def addResources(self,1670

pPreyMinRes, # Prey min resource consumption per time step1671

pPreyMaxRes): # Prey max resource consumption per time step1672

""" Selects a random number between the two parameters and adds this to resource total """1673

1674

# The random.randint() method returns a pseudorandom integer between1675

# the lower and upper parameters inclusively1676

lNewResources = random.randint(pPreyMinRes, pPreyMaxRes)1677

self.setResourceTotal(self.getResourceTotal() + lNewResources)1678

# end addResources()1679

88

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