Individual-Based Model for the Dispersal of the South African Wild Dog Population in the Kwazulu-Natal Province

INDIVIDUAL-BASED MODEL FOR THE DISPERSAL OF THE SOUTH AFRICAN WILD DOG POPULATION IN THE KWAZULU-NATAL PROVINCE

HUMBOLDT STATE UNIVERSITY

Elizabeth Grace Arnold

A Thesis

Presented to

The Faculty of Humboldt State University

In Partial Fulﬁllment

Of the Requirements for the Degree

Master of Science

In Environmental Systems: Mathematical Modeling

October, 2010 INDIVIDUAL-BASED MODEL FOR THE DISPERSAL OF THE SOUTH AFRICAN WILD DOG POPULATION IN THE KWAZULU-NATAL PROVINCE

HUMBOLDT STATE UNIVERSITY

Elizabeth Grace Arnold

Approved by the Master’s Thesis Committee:

Dr. Diane Johnson, Major Professor Date

Dr. Sharon Brown, Committee Member Date

Dr. Micaela Szykman Gunther, Committee Member Date

Dr. Steve Railsback, Committee Member Date

Dr. Christopher Dugaw, Graduate Coordinator Date

Dr. Jena´ Burges, Vice Provost Date ABSTRACT

INDIVIDUAL-BASED MODEL FOR THE DISPERSAL OF THE SOUTH AFRICAN WILD DOG POPULATION IN THE KWAZULU-NATAL PROVINCE

Elizabeth Grace Arnold

The African wild dog (Lycaon pictus) is facing a high risk of extinction with fewer than 5,000 individuals living in fragmented landscapes. After an absence of nearly 50 years, several sub-populations of wild dogs have been reintroduced into isolated, fenced game reserves in the province of KwaZulu-Natal (KZN), South Africa. To better understand the effect of natural dispersal on the African wild dog population in KZN, we developed a spatially explicit individual-based model employing the software NetLogo. Wild dogs reintroduced into Phinda Munyawan Conservancy, Greater St. Lucia Wetland Park and Zu- luland Rhino Reserve had the greatest dispersal success while wild dogs reintroduced into Ithala Game Reserve, Ndumo Game Reserve and Tembe Elephant Park displayed the least successful dispersal and persistence. This information will aid researchers and wildlife managers in determining effective, cost-efﬁcient management plans for the KZN wild dog population and can be further extended to all of South Africa.

iii ACKNOWLEDGEMENTS

First and foremost, I have to give many, many thanks to my committee members: Dr. Diane Johnson, Dr. Micaela Szykman Gunther, Dr. Steve Railsback and Dr. Sharon Brown. Without all of their help, knowledge, support and undying patience, I would not have completed this project! Diane, thank you so much for stepping in and supporting me over the years. You have helped me with both my undergraduate and graduate degrees and I greatly appreciate all of the time you have spent meeting with me and helping me with my writing! Micaela, thank you for all of your help and inspiring me to study the African wild dogs. You have so much passion for the wild dogs that I can not help but get excited when we discuss them! Steve, thank you so much for your support with NetLogo. At times I needed to distract myself and play Frogger on NetLogo but I have really enjoyed learning about individual-based models and NetLogo! Finally, Sharon, you have been a great teacher, ad- visor, mentor and friend throughout all of this. Thank you so much for sticking with me! I can not express how much I appreciate all of your help and guidance throughout the years and through the distance. I know I have procrastinated long enough on my thesis but it is ﬁnally done! Thank you so very much to all of my committee members! I am also grateful for my fellow graduate students, friends and the Mathematics De- partment. I would also like to thank Bori and Chris for being great teachers and I enjoyed taking your classes in graduate school. To Jason Barnes and the GIS club, thank you very much for helping me with the GIS layers used in my model. Finally, I have to thank my parents for all of their help. They have supported me in so many ways throughout my collegiate career at HSU. Thanks for the car, Dad!

iv TABLE OF CONTENTS

ABSTRACT ...... iii

ACKNOWLEDGEMENTS ...... iv

TABLE OF CONTENTS ...... v

LIST OF FIGURES ...... vi

LIST OF TABLES ...... viii

INTRODUCTION ...... 1 Causes of African Wild Dog Population Decline ...... 3 Conservation Efforts ...... 7 Appearance of the African Wild Dog ...... 12 Sociality and Group Structure ...... 13 Dispersal ...... 14

MODEL ...... 17 Individual-Based Model ...... 18 ODD Protocol ...... 19 Model Validation ...... 47 Sensitivity Analysis ...... 52 Experiments ...... 55

RESULTS ...... 57

DISCUSSION ...... 69 Future African Wild Dog Studies ...... 73

Literature Cited ...... 76

APPENDIX A ...... 79

APPENDIX B ...... 83

APPENDIX C ...... 87

v LIST OF FIGURES

Figure Page

1 Location of KwaZulu-Natal, South Africa (WWF, 2010)...... 2

2 Past and current distributions of the African wild dog population (Woodroffe et al., 2004)...... 4

3 NetLogo display of the KZN environment. Game reserves are the green patches, rivers are the blue lines, roads are the brown lines, red circles are the villages and the KZN boundary lines are yellow lines...... 10

4 The African wild dog, Lycaon pictus (Photo c M. Szykman Gunther). . . . 12

5 Flow chart describing the disperser groups’ processes...... 23

6 Flow chart describing the packs’ processes...... 24

7 Percentage of disperser groups that joined an existing game reserve pack when the parameter ‘game-reserve-pack-radius’ was set to 1.25, 1.50 and 1.75 (Note: y-axis begins at 23.5 to emphasize the slight variation in the percentages)...... 33

8 Percentage of disperser groups that formed a new pack with another disperser group when the parameter ‘dispersergroup-radius’ was set to 1.00, 1.125 and 1.25 (Note: y-axis begins at 25 to emphasize the slight variation in the percentages)...... 33

9 Percentage of wild dogs dying due to diseases when the parameter ‘village- radius’ was set to 0.33, 0.50, 0.75 and 1.00...... 34

10 General example of a gamma probability density function with a mean of 30. α = 1.91 and β = 15.73...... 36

11 Graphs of a disperser group’s ﬁtness level traced for one year. a.) ‘movement- loss-percent’ = 8%. b.) ‘movement-loss-percent’ = 10%. c.) ‘movement- loss-percent’ = 15%. d.) ‘movement-loss-percent’ = 25%...... 38

12 Average percentage of total wild dog pack formations tested at different values of the parameter ‘join-game-reserve-pack.’ ...... 41

vi 13 Average percentage of wild dogs dying due to dehydration tested at different values of the parameter ‘chance-of-water.’ ...... 42

14 Average percentage of disperser groups that formed a new pack when ‘join- game-reserve-pack’ was varied from 1% to 5%. a.) ‘join-game-reserve- pack’ = 1%. b.) ‘join-game-reserve-pack’ = 2%. c.) ‘join-game-reserve- pack’ = 3%. d.) ‘join-game-reserve-pack’ = 4%. e.) ‘join-game-reserve- pack’ = 5%...... 58

15 Average percentage of disperser groups that joined an existing game reserve pack when ‘join-game-reserve-pack’ was varied from 1% to 5%. a.) ‘join- game-reserve-pack’ = 1%. b.) ‘join-game-reserve-pack’ = 2%. c.) ‘join- game-reserve-pack’ = 3%. d.) ‘join-game-reserve-pack’ = 4%. e.) ‘join- game-reserve-pack’ = 5%...... 59

16 Average percentage of total wild dog pack formations (solid) versus the average percentage of wild dogs that died (open)...... 60

17 Average percentage of single disperser groups at the end of each model run. 61

18 Total combined average a.) time in days and b.) distance in km a disperser group traveled to form a new pack...... 62

19 Total combined average a.) time in days and b.) distance in km a disperser group traveled to join an existing game reserve pack...... 66

20 Dispersal success of only the reintroduced wild dogs...... 68

vii LIST OF TABLES

Table Page

1 Game reserve name, size, public or private ownership and the number of packs living in each game reserve in 2009...... 11

2 State variables and their descriptions for the entity disperser groups. . . . . 20

3 State variables and their descriptions for entity packs...... 21

4 State variables and their descriptions for the entity game reserve packs. . . . 21

5 State variables and their descriptions for the entity KZN environment. . . . 22

6 Model Parameter Name and Value(s)...... 30

7 Fitness levels and the corresponding probabilities of traveling 60 km or more. 37

8 Fitness levels and the corresponding probabilities of catching prey once a day...... 45

9 Sensitivity of parameters...... 54

10 Frequency of where new packs were formed...... 63

11 Game reserve origins of the disperser groups that formed a new pack. . . . 64

12 Percentage of the time new packs reached given game reserve...... 65

13 Game reserve origins of the disperser groups that joined an existing game reserve pack...... 67

viii INTRODUCTION

The African wild dog Lycaon pictus, often called the painted wolf, is among the most endangered large carnivores in Africa. There are fewer than 5,000 individuals remaining. Populations have rapidly declined over the last century and this decline has accelerated in the last 30 years (Woodroffe et al., 1997, 2004; Creel and Creel, 2002). The primary causes of this decline are increasingly fragmented landscapes combined with infectious diseases and diminishing prey populations (Woodroffe et al., 1997, 2004). Most of the 600 - 1,000 remaining packs of wild dogs have populations no longer sustainable. Currently the South African wild dog population has been limited to a single viable population in Kruger National Park, located in northeast South Africa (Woodroffe et al., 1997, 2004). The ongoing decline in the number of mature individuals resulting from decreasing populations has caused African wild dogs to be categorized as Endangered on the Inter- national Union for Conservation of Nature (IUCN) Red List (IUCN, 2010). The IUCN Species Survival Commission Canid Specialist Group has also designated African wild dogs as a high priority species for wildlife conservation. “African wild dogs are the only extant representatives of a distinct lineage of wolf-like canids and as a result of this phy- logenetic distinctiveness, they have a high conservation value” (Woodroffe et al., 1997). Furthermore, wild dogs are among Africa’s most efﬁcient predators and have a crucial impact on the structure and function of ecosystems in Africa. Conservationists predict the imminent extinction of this species unless immediate action is taken (Woodroffe et al., 1997, 2004). With South Africa described as the place that “holds wild dogs’ best hope for the future” (Woodroffe et al., 1997), researchers at the Smithsonian Conservation Biology Institute (SCBI) have been collaborating with South African scientists and wildlife managers to

1 2 conserve the South African wild dog population. A plan has been implemented in the KwaZulu-Natal (KZN) Province of South Africa (Figure 1) to manually translocate and reintroduce several sub-populations of wild dogs into geographically isolated provincial and private game reserves.

Figure 1: Location of KwaZulu-Natal, South Africa (WWF, 2010).

IUCN (2010) defines reintroductions as “an attempt to establish a species in an area which was once part of its historical range, but from which it has been extirpated or become extinct.” Translocation is defined as a “deliberate and mediated movement of wild individuals or populations from one part of their range to another.” Periodic manual reintroductions and translocations mimicking natural dispersal are necessary to maintain genetic diversity within the South African wild dog population (Spiering et al., 2010). Small populations of wild dogs located in game reserves throughout KZN as well as the long distances between 3 these game reserves are the major contributing factors for these interventions. However, these periodic manual reintroductions and translocations are time consuming, costly and add undue stress to wild dogs. To better understand the possibilities of a more natural dispersal, we modeled the natural dispersal of the South African wild dog population in KZN by developing a spatially explicit individual-based model employing the software NetLogo. This modeling and analysis of the natural dispersal dynamics will aid researchers and wildlife managers in determining whether manual translocations are required or whether natural dispersal may be possible and successful. This information will also assist in determining the most effective, cost-efficient management plans for the wild dog population in KZN, South Africa.

Causes of African Wild Dog Population Decline

Population decline appears to have resulted from an increased mortality rate coupled with a lowered rate of successful reproduction. African wild dogs have a high annual mortality rate ranging from 20% to 57% (Creel and Creel, 2002; Woodroffe et al., 2004, 2007). This is a consequence of both human interactions and natural causes. The expanding human population has fragmented the wild dogs’ home ranges thereby reducing population sizes. Additional causes of wild dog mortality include death due to roads and human persecution. Natural causes such as diseases have also contributed to an increase in the wild dogs’ annual mortality rate.

Habitat Loss and Fragmentation

Conﬂict with human beings is the single most important conservation problem for African wild dogs (Creel and Creel, 2002; Woodroffe et al., 2004). Once widely distributed through- 4 out much of sub-Saharan Africa, in the last 30 years wild dogs have disappeared from 65% of the land they once occupied (Fanshawe et al., 1991; Woodroffe et al., 1997, 2004; Creel and Creel, 2002; Szykman, 2006b). They have been virtually eradicated from West Africa and there are signiﬁcantly lower numbers in central and north-eastern Africa. Wild dogs are now primarily found in scattered populations on fragmented landscapes of southern and eastern Africa (Figure 2; Woodroffe et al., 2004).

Figure 2: Past and current distributions of the African wild dog population (Woodroffe et al., 2004).

Few of these scattered wild dog populations are known to contain more than 100 individuals (Fanshawe et al., 1991). The largest populations remain in southern Africa - namely northern Botswana, western Zimbabwe, north-eastern Namibia, Kruger National Park and northern Mozambique (Woodroffe et al., 1997; Creel and Creel, 2002). In recent years critical habitat has been disrupted by the development of new villages, buildings and roads (Woodroffe et al., 2004). Land has also been converted for livestock grazing, cultivation and agriculture. This fragments the wild dogs’ home ranges and de- 5 pletes their prey population (Creel and Creel, 2002; Lindsey et al., 2004). Currently, most wild dogs are conﬁned to protected game reserves and their surroundings. Wild dogs require large home ranges with the average pack requiring about 379 km2 (Creel and Creel, 2002). Wild dog packs occasionally inhabit as much as 1,000 km2, making their ranges among the largest recorded for carnivores (Creel and Creel, 2002; Lindsey et al., 2004). As a result, only the largest game reserves are capable of providing adequate space and the necessary protection. However, insufﬁcient prey and suitable mates inside these game reserves force the wild dogs to frequently travel outside the boundaries of game reserve where they are legally protected. In doing so, wild dogs risk the dangers of coming in contact with the human population.

Direct Mortality Due to Humans

As human populations expand and fragment wild dogs’ home ranges, wild dogs become more at risk. Human contact accounts for approximately 73% of adult mortality (Woodroffe et al., 1997, 2004, 2007). One major factor is the growing system of roads, especially those that transect or border game reserves. High speed roads can be particularly deadly for the African wild dogs. Wild dogs will characteristically rest along roads and are seemingly unafraid of cars (Woodroffe et al., 2004). Consequently, road trafﬁc accidents account for approximately 16% of total adult wild dog deaths (Woodroffe et al., 2004, 2007). Although such accidents may occur inside game reserves, they occur much more frequently outside game reserves when wild dogs are dispersing (Woodroffe et al., 1997). Human persecution has historically been the single largest reason for the wild dog population decline causing an average of approximately 57% of recorded adult mortality. Wild 6 dogs are killed by being shot, snared or poisoned (Woodroffe et al., 2004, 2007). They have obtained a poor reputation as being cruel, merciless killers whose cursorial hunting disrupts ungulate populations and livestock (Creel and Creel, 2002). In an attempt to help ungulate populations increase their numbers, even game reserve managers and staff have been known to shoot or poison wild dogs (Creel and Creel, 2002). African wild dogs have been shown little or no sympathy and were actively persecuted throughout much of the 20th century (Creel and Creel, 2002). However by the end of the 20th century wild dogs were legally protected throughout Africa (Gusset et al., 2008a). As humans became progressively more educated about the wild dogs’ ecology and behavior, the number of wild dogs being directly persecuted by humans decreased. However, human persecution has not been eliminated as it was discovered that many members of the local communities ignored the legal protection of wild dogs (Gusset et al., 2008a). Snares targeted and set for game species and wild ungulates have unintentionally captured and killed many wild dogs. Snares contribute to approximately 30% of adult wild dog mortality (Woodroffe et al., 2004, 2007). Wild dogs living in protected game reserves typically come across snare lines as they travel in and out of the game reserves in KZN (Szykman Gunther, Pers. Comm.). Although there has been a decrease in the percentage of wild dogs dying due to human persecution, it still currently remains the largest contributor of their moratlity rates (Woodroffe et al., 2004, 2007).

Diseases

Wild dogs not only require large home ranges, they typically live at low population densities (Creel and Creel, 2002). Kruger National Park contains the only viable population of wild dogs in South Africa. It is 18,989 km2 in size and in 2009 Kruger National Park contained 7 approximately 140 wild dogs (Szykman Gunther, Pers. Comm.). Most other game reserves are much smaller and contain considerably fewer wild dogs. These smaller populations are exposed to diseases and are at a higher risk of extinction than similar larger populations. Wild dogs are highly vulnerable to diseases (Fanshawe et al., 1991). Due to the increased presence and contact with domestic dogs, diseases are often transmitted to the wild dogs. Although domestic dogs are not allowed in the game reserves, wild dogs frequently come into contact with them. For example, poachers occasionally bring their domestic dogs into the game reserves. In addition, on the boundaries of game reserves wild dogs come into contact with domestic dogs (Szykman Gunther, Pers. Comm.). Rabies, canine distemper virus, canine parvovirus and anthrax are a few of the diseases transmitted to wild dogs. Since wild dogs live at low population densities and have numerous daily social interactions, they are particularly threatened by diseases transmitted through saliva or feces. Social behaviors that affect the likelihood of disease transmission include greeting one another by licking each other’s mouths, puppies licking the mouths of returning hunters to obtain regurgitated meat and healthy wild dogs caring for those sick and/or injured. Consequently, if one member of a group of wild dogs becomes infected, all members experience a high risk of being infected.

Conservation Efforts

Many conservation efforts have been implemented in the last 30 years on behalf of the endangered African wild dog population. These include radio-collaring, genetics studies, fencing game reserve boundaries, using non-invasive fecal sample analysis, studying the effects of lions (Panthera leo) and spotted hyenas (Crocuta crocuta) on wild dog population dynamics and communicating with the local communities (Woodroffe et al., 1997, 2004; 8

Mills et al., 1998; Vucetich and Creel, 1999; Creel and Creel, 2002; Szykman, 2006b; Gusset et al., 2008a; Spiering et al., 2009; Spiering et al., 2010). In addition, to help promote genetic variability among the local wild dog populations in KZN and increase their population sizes, wild dogs have been reintroduced and translocated within protected game reserves.

Past Conservation Efforts

In 1980, after an absence of nearly 50 years, 22 captive and wild-caught African wild dogs were reintroduced into one of South Africa’s oldest and largest game reserves, Hluhluwe- iMfolozi Park (HiP) (Woodroffe et al., 1997; Maddock, 1999). Twenty of these 22 wild dogs were raised in captivity. The wild dogs raised in captivity had difficulty hunting and evading predators and as a result, they were struggling to survive (Szykman, 2006a). Despite the captive wild dogs’ difficulty in hunting, it was observed that wild dogs (captive and wild-caught) were able to cooperate, bond and form a pack. Thus, this conservation effort was classified as a moderate success (Woodroffe et al., 1997; Maddock, 1999; Gusset et al., 2008a). Seventeen years later, after determining further need for action, members of the IUCN Species Survival Commission Canid Specialists Group developed a Population and Habitat Viability Assessment which resulted in a conservation action plan for the South African wild dogs (Woodroffe et al., 1997, 2004). This plan focused on protecting and enlarging game reserves that contained wild dogs. HiP and KZN were identified as appropriate areas in which to establish new wild dog populations (Woodroffe et al., 1997). After the initial reintroduction to HiP in 1980, a series of more successful reintroductions took place between 1997 and 2003 (Woodroffe et al., 9

1997; Szykman, 2006b). Not only did HiP’s wild dog population increase signiﬁcantly but natural dispersal was also taking place (Szykman, 2006a, 2006b). A record breaking number of ﬁve breeding packs containing more than 45 adults and yearlings resulted from these effects. Currently that number has doubled and HiP is home to more than 90 adults and yearlings (Szykman Gunther, Pers. Comm.).

Current Conservation Efforts

The current management plan includes reintroducing wild dogs into various game reserves inside KZN. In addition, wild dogs are periodically translocated to other game reserves to mimic natural dispersal (Gusset et al., 2008b; Spiering et al., 2010). KZN contains several public and private game reserves that were considered in the model. The names of these game reserves include: HiP, uMkhuze, Thanda, Ithala Game Reserve, Coastal, Ndumo Game Reserve, Pongola Game Park, Mkuze Falls Private Game Reserve, Zululand Rhino Reserve, Tembe Elephant Park, Greater St. Lucia Wetland Park and Phinda Munyawana Conservancy (Figure 3, Table 1). Coastal, uMkhuze and Greater St. Lucia Wetland Park are all different areas located in iSimangaliso Wetland Park but we considered them as separate game reserves in the model. Few of these game reserves are inhabited by wild dogs, although several are sufﬁciently large to accommodate them (Table 1). Currently, researchers and wildlife managers have been translocating, reintroducing and monitoring wild dogs into three game reserves: HiP, uMkhuze and Thanda. Most of the game reserves in KZN contain boundary fencing with a great diversity of habitat and size. Habitat ranges from densely vegetated valleys, high- lying grassland plateaus, wetlands, savannah, woodlands, waterways, forests to mountain- ous landscapes. These game reserves serve as wildlife refuges that provide legal protection 10

Figure 3: NetLogo display of the KZN environment. Game reserves are the green patches, rivers are the blue lines, roads are the brown lines, red circles are the villages and the KZN boundary lines are yellow lines. and habitat for African wild dogs. Fences around the game reserves serve as a form of protection from intruders and also decrease the chances of the wild dogs coming in contact with the human population. Following the reintroductions and translocations of wild dogs, studies of the wild dogs’ survival rates, behavior and physiology were carried out (Woodroffe et al., 1997, 2004; Szykman, 2006b). Fecal material was analyzed to determine the wild dogs’ hormone and stress levels. “Excessive stress can increase wild dogs’ vulnerability to disease and reduce their reproductive success” (Szykman, 2006a), adversely affecting their persistence as a species. During 1997 and 2001, an estimated $378,887 was spent on wild dog conservation 11

Table 1: Game reserve name, size, public or private ownership and the number of packs living in each game reserve in 2009. Game Reserve Size Public/Private Number of Packs Hluhluwe-iMfolozi Park 960 km2 Public 8

uMkhuze 400 km2 Public 1

Thanda 60 km2 Private 1

Ithala Game Reserve 300 km2 Public 0

Coastal 274 km2 Public 0

Ndumo Game Reserve 101 km2 Public 0

Pongola Game Park 224 km2 Public 0

Mkuze Falls Private Game Reserve 305 km2 Private 0

Zululand Rhino Reserve 230 km2 Public 0

Tembe Elephant Park 300 km2 Public 0

Greater St. Lucia Wetland Park 499 km2 Public 0

Phinda Munyawana Conservancy 175 km2 Private 0

efforts in the South African game reserves (Lindsey et al., 2005). If wild dogs were able to successfully disperse without human intervention, money could be spent elsewhere such as building fences around each game reserve, analyzing the effect lions and hyenas have on the wild dog population, controlling the number of wild dogs dying from human persecution, conserving wild dog populations outside of KZN and educating local communities about the importance of this endangered species. 12

Improving public relations and educating local communities is very important to ensure the survival of this endangered species. Researchers and managers have developed outreach programs to educate members of the local communities about the ecology of the African wild dogs. A conservation education program was conducted from 1999 to 2000 which addressed the negative reputation of wild dogs. Through questionnaires and surveys it was found that wild dogs are a top attraction for tourists (Gusset et al., 2008a). Wild dogs can therefore be used proﬁtably for ecotourism, which further increases their conservation value.

Appearance of the African Wild Dog

The scientiﬁc name Lycaon pictus literally means “painted wolf,” referring to the wild dogs’ fur which appears to be painted with brown, red, black, yellow and white areas (Figure 4). Each wild dog can be visually identiﬁed by its extremely variable coat patterns (Creel and

Figure 4: The African wild dog, Lycaon pictus (Photo c M. Szykman Gunther).

Creel, 2002; Szykman Gunther, Pers. Comm.). This allows researchers to collect speciﬁc 13 data on individuals. Typically ranging from 18 to 29 kilograms in weight and standing 65 to 75 centimeters at the shoulder, the African wild dog is lean and tall with outsized saucer-shaped ears (Creel and Creel, 2002; Szykman, 2006a).

Sociality and Group Structure

Wild dogs are extremely social animals that spend most of their time in proximity to one another. Individual wild dogs are classiﬁed as adults (two years and older), yearlings (one to two years old) or pups (less than one year old). Living together in packs ranging from 2 to 27 individuals, wild dogs survive by acting as one cohesive unit. The basic pack structure is comprised of a group of related females together with a group of related males. Wild dogs also appear to have a strong inbreeding avoidance behavior (Woodroffe et al., 1997; Spiering et al., 2010). Wild dogs therefore need to disperse and leave their natal pack when they reach maturity. A disperser group is comprised of a group of related females or males that travel in search of mates. Disperser groups typically consist of yearlings and/or adults. New packs form when disperser groups join similar, unrelated opposite-sex disperser groups. Alterna- tively, a dispersing group of wild dogs may join an existing pack of wild dogs previously established in one of the game reserves. Obligate cooperative hunting, reproduction, defending against kleptoparasitism by spotted hyenas and continually caring for one another occurs within most disperser groups and packs of wild dogs. Wild dogs depend on one another and work cooperatively as a group. Researchers consider disperser groups and packs as the basic unit of a population rather than thinking of an individual wild dog as the basic unit structure. By hunting together, wild dogs are able to track and capture prey much larger than 14 themselves, including impalas (Aepyceros melampus) and wildebeests (Connochaetes tau- rinus). Although the alpha female and male are the primary individuals to reproduce, the remainder of the pack members are involved in caring for the pups. Wild dogs are capable of giving birth to large litters once a year ranging from 2 to 15 pups. As a result, additional pack members are needed to successfully raise and care for these pups. It becomes increasingly difﬁcult for the pack to care for the pups with a reduced number of pack members (Courchamp and Macdonald, 2001; Courchamp et al., 2002). This implies that efforts to increase the survival of reproductive adults and subordinate members of packs of wild dogs will positively affect the survival of the species.

Dispersal

Natural dispersal has great consequences not only for an individual’s fitness but also for population genetics and dynamics (McNutt, 1996). Given that the African wild dog population is very small, wild dogs successfully dispersing has a profound impact on the wild dog population such as ensuring a larger and more genetically diverse population. Both sexes of African wild dogs disperse equally all year round dispersing in groups of one to four same sex individuals (Creel and Creel, 2002). Wild dogs are more likely to leave their natal pack during their first year of sexual maturity. On the average, a wild dog will leave its pack between the age of one and a half and three and a half years. Wild dogs are known to be great roamers. Moving as an interconnected unit, wild dogs tend to travel alongside rivers and roads (Woodroffe et al., 1997, 2004; Creel and Creel, 2002). In some cases wild dogs have been observed to travel up to 250 kilometers (km) in one day. However, they usually average 30 km per day (Creel and Creel, 2002). Dispersing groups of wild dogs are believed to travel until they find another group of compatible wild 15 dogs to form a pack. Wild dogs show considerable interest in the scent-marks of other packs and will track the scent trails for kilometers (Creel and Creel, 2002). In some cases, wild dogs temporarily return to their original pack but eventually leave again (Creel and Creel, 2002). Even though disperser groups are continually looking for other wild dogs, when two unrelated, opposite sex groups of wild dogs meet, they do not always bond and combine as one pack (Creel and Creel, 2002). It has been estimated that two disperser groups have a 64% chance of bonding and forming a new pack (Gusset et al., 2009). Furthermore, when two same sex disperser groups meet, a fight may arise causing injuries and possible death to some of the wild dogs (Creel and Creel, 2002). While dispersal affords wild dogs the advantages of finding mates, avoiding inbreeding and finding food, there is a high mortality risk associated with dispersal (Creel and Creel, 2002; Woodroffe et al., 2004, 2007). The dangers dispersing wild dogs face include preda- tion, persecution, snaring, starvation and being unable to encounter or bond with another group of wild dogs. The size of a dispersal group determines various advantages and disadvantages. For example, more members in a group results in better protection from predators and an easier time capturing more and larger prey. Wild dogs require energy and resources such as water and food to survive. They need an average of approximately 3 kilograms (kg) of food as well as water every day (Creel and Creel, 2002). Wild dogs have a high hunting success rate with 43% to 70% of their hunts resulting in a kill (Creel and Creel, 2002). Having more members in a group also requires less energy expended from each wild dog to catch prey. However, if there are more wild dogs in a group, additional food is needed to sufficiently feed all group members. This requires more overall expenditure of energy from each individual in capturing prey (Courchamp and Macdonald, 2001). 16

Although some wild dogs have been observed dispersing throughout KZN, there are a minimal number of habitats containing other packs or disperser groups to join (Szykman Gunther, Pers. Comm.). Some dispersing groups of wild dogs reach other game reserves only to ﬁnd that there are no wild dogs to form a pack with. These “empty” game reserves in KZN currently have no management plans. Modeling the possibility of having packs and disperser groups in these empty game reserves along with analyzing the effect they will have on the KZN population will allow scientists, researchers and managers to explore the possibilities of managing wild dog populations in more game reserves throughout KZN. MODEL

The canid species has been a focus of wildlife management for much of the last century (Pitt et al., 2003). The species’ complex biology and ecological interactions must be considered in effective wildlife management plans (Pitt et al., 2001). Moreover, territorial and social behaviors are important factors in the development of canid population models as canids are generally highly social (Pitt et al., 2001, 2003). Individual-based models are better suited for populations living at low densities such as the African wild dogs. Wild dogs interact with one another locally, rather than glob- ally, and this can not be modeled accurately using analytical models. That is, wild dogs in KZN interact with each other and not other wild dogs in western Zimbabwe, for example. In addition, analytical models are not suited to include the individual characteristics that are critical to the management of the wild dog population (Grimm, 1999; Pitt et al., 2001, 2003) such as the decisions wild dogs use when dispersing and forming new packs. More- over, since there are relatively few wild dogs in KZN, to best model this specific population of wild dogs we had to consider incorporating each “collective” into our model, where collectives are aggregations of specific individuals. The three aggregations in the model were disperser groups, packs (newly formed packs) and game reserve packs. We can analyze these collectives and see any patterns that emerged from their modeled behavior that will aid in making predictions about the entire population of wild dogs in KZN. Vucetich and Creel (1999) developed an individual-based model in which they mim- icked the ecological and social interactions of wild dog populations to assess their extinction risk, primarily focusing on intraspecific competition with lions. Dispersal was found to influence the probability of a wild dog population persisting 50 years. The spatial arrange- ment of wild dogs dispersing across KZN is essential in both understanding the species’

17 18 ecology and in creating effective management plans (King and With, 2002). Spatially explicit population models are very beneﬁcial in wildlife management because managers are able to visualize the effects of different management plans (Turner et al., 1995). Thus, we developed a spatially explicit individual-based model to mimic the wild dogs’ dispersal movements. The programming for this model can be found in Appendix C.

Individual-Based Model

Individual-based models (IBM) are simulations consisting of an environment and some number of individuals where these individuals can be a collective. IBMs consider the properties and interactions between individuals and their surrounding environment (Grimm and Railsback, 2005). IBMs “describe the changes in numbers of individuals rather than in population density” (Uchmanski` and Grimm, 1996). Using a “bottom-up” approach, which starts with the individuals of a population and works its way up to explain the overall population dynamics, IBMs track each individual through time to predict the resulting population’s properties and dynamics that emerged from the individual behavior (Grimm, 1999; Grimm et al., 2006). In the model, we deﬁned “rules” for how individuals interacted with the spatial environment and one another. We modeled resource dynamics explicitly in NetLogo (Wilensky, 1999) to mimic natural dispersal. One of the leading platforms used to implement IBMs, NetLogo is a programmable modeling environment used for simulating emergent behaviors of populations. IBMs are likely to be more complex in structure than standard analytical mathematical models and the resulting computer simulations from IBMs tend to have no standard language or protocol for communication (Grimm and Railsback, 2005). A recent standard 19 protocol for describing IBMs has been introduced in hopes of increasing communication. This new protocol consists of three main blocks comprised of seven elements. Referred to as the ODD protocol the three main blocks include ‘Overview’, ‘Design Concepts’ and ‘Details’ (Grimm et al., 2006). Using the descriptions from these three blocks, one should be able to completely re-implement the model and run the baseline simulations (Grimm et al., 2006). Our model is described using the following ODD protocol.

ODD Protocol

1. Overview

a.) Purpose:

The purpose of the model was to analyze the success rate of African wild dogs naturally dispersing to and between protected game reserves in KZN. We aimed to answer the following questions: What management scenarios (i.e., to which game reserve(s) should a pack of wild dogs be reintroduced or translocated) lead to the highest percentage of pack formations? How does the location of the reintroduced pack affect the dispersal success rate? Which game reserve will ultimately be the best location to start reintroducing or translocating packs of wild dogs?

b.) Entities, State Variables and Scales:

The model had four kinds of entities: disperser groups, packs, game reserve packs and the KZN environment. These entities were characterized by the corresponding state variables (Tables 2 - 5). 20

Table 2: State variables and their descriptions for the entity disperser groups. State Variable Name Description Sex Two types: male or female.

Natal Pack Membership The disperser group’s natal pack name.

Pack Membership? Whether or not a disperser group has formed a new pack or joined an existing game reserve pack.

Game Reserve Home Game reserve origins of the disperser groups.

Spatial Location The grid cell the disperser group occupies.

Fitness Level The “strength” of a disperser group represented by a number between 0 and 100 where 100 represents the “healthiest.”

Days Without Food The number of consecutive days a disperser group has gone without food.

Days Without Water The number of consecutive days a disperser group has gone without water.

Days on the Road The number of consecutive days a disperser group has traveled on a road.

Total Distance Traveled The total distance traveled by a disperser group, measured in kilometers, since day 1. 21

Table 3: State variables and their descriptions for entity packs. State Variable Name Description Spatial Location The grid cell the pack occupies.

Fitness Level The “strength” of a pack represented by a number between 0 and 100 where 100 represents the “healthiest.”

Days Without Food The number of consecutive days a pack has gone without food.

Days Without Water The number of consecutive days a pack has gone without water.

Days on the Road The number of consecutive days a pack has traveled on a road.

Total Distance Traveled The total distance traveled by a pack, measured in kilometers, since the formation of this new pack.

Table 4: State variables and their descriptions for the entity game reserve packs. State Variable Name Description Natal Pack Membership The game reserve pack’s name.

Game Reserve Home Game reserve origins of the game reserve packs.

Spatial Location The grid cell the game reserve pack occupies.

Fitness Level The “strength” of a game reserve pack represented by a number between 0 and 100 where 100 represents the “healthiest.”

The spatially explicit model environment was constructed with the use of vector based GIS (Geographic Information Systems) data layers set to resemble the northern section of the KZN Province. The GIS layers used in the model included game reserves, rivers, roads, villages and boundary lines. These ﬁve GIS layers were used directly by the wild dogs in the model. However, for the user to visually see these layers in NetLogo, patches were 22

Table 5: State variables and their descriptions for the entity KZN environment. State Variable Name Description Game Reserves The game reserves inside the KZN Province.

Rivers The rivers inside the KZN Province.

Roads The major freeways and roads inside the KZN Province.

Villages The villages inside the KZN Province.

Boundary Lines The boundary lines of the KZN Province.

colored accordingly (Figure 3). The KZN environment was imported on a 47×47 square grid where one grid cells represented nine square kilometers. The location of each collective in the model was tracked discretely by which grid cell they occupied. One time step represented one day and model runs were executed for 365 days (1 year). c.) Process Overview and Scheduling:

Disperser groups and packs completed several processes that were simulated every time step in a specific order (Figures 5 - 6). Each time step, disperser groups were the first entity to run through their processes sequentially followed by packs running through all of their processes sequentially. That is, all of the disperser groups in the model finished one process before they were all able to move onto the next process. Once all of the disperser groups completed each of their processes, every pack then completed all of their processes. The order in which individual disperser groups (then packs) completed their processes was a default random shuffle via NetLogo’s command “ask.” In addition, the state variables were updated asynchronous (i.e., state variables were immediately updated as soon as that value 23 was calculated by a process).

Gather Disperser Groups * Adjust Fitness Level Form a * Change Pack Membership? New Pack Y Y Y Move Unrelated? Opposite Sex? Bond? Y N N N N Do Not Form Fight? a New Pack N Y Find Disperser Decrease Group? Fitness Level

N Y Y Y Join Game Find Game Unrelated? Bond? Reserve Reserve Pack? N Pack N Do Not Join Game Reserve * Set Fitness Level to 100 N Pack * Change Pack Membership?

Y On a Y Look for Water Drink River? * Set Number of Days Without N Y Water to 0 Other Source * Increase Fitness Level of Water? N

Increase Number of Days Without Water by 1 Day

* Set Number of Days Without Look for Food Y Catch Y Food to 0 Prey? Eat * Increase Fitness Level N

Increase Number of Days Without Food by 1 Day

Check Survivorship

Figure 5: Flow chart describing the disperser groups’ processes. 24

Gather Newly Formed Packs

Record Game On a Game Y Stop Traveling Reserve? Reserve Name

Move

Y On a Y Look for Water Drink River? N Y * Set Number of Days Without Other Source Water to 0 of Water? * Increase Fitness Level N

Increase Number of Days Without Water by 1 Day

Look for Food Y Catch Y Eat Prey? * Set Number of Days Without N Food to 0 * Increase Fitness Level

Increase Number of Days Without Food by 1 Day

Check Survivorship

Figure 6: Flow chart describing the packs’ processes. 25

2. Design Concepts

a.) Emergence:

The spatial distribution of disperser groups and newly formed packs emerged from the adaptive behavior and traits they used to make decisions while traveling. That is, this spatial distribution varied depending on the initial location of wild dogs.

b.) Adaptation:

Wild dogs adapted their movement behavior according to their fitness level, surrounding environment and proximity to other wild dogs. The direction they moved was modeled via a prioritized list of decision rules that were based on the desires of disperser groups and packs. However, the distance wild dogs traveled in one day was a direct consequence of their fitness level and empirical rules. Disperser groups desired to find other wild dogs first and foremost and then increase their survival rate. Thus, disperser groups used the following prioritization list: (1) look for other disperser groups, (2) look for game reserve packs, (3) look for rivers, (4) look for roads, and (5) look for villages. Newly formed packs no longer desired to find other wild dogs and consequently their movement behavior was based on increasing their survival rate. Thus, packs used the following prioritization list: (1) look for rivers, (2) look for roads, and (3) look for villages.

c.) Objectives:

The objective of disperser groups was to ﬁnd other wild dogs. Once disperser groups found other wild dogs, they had a given probability of bonding with them. If disperser groups bonded and joined other wild dogs, they were considered to have a successful dispersal. 26

d.) Learning:

Wild dogs learning from their experience(s) was not considered in the model.

e.) Prediction:

Predicting future conditions was also not considered in the model.

f.) Sensing:

Disperser groups were assumed to know their sex, natal pack membership, pack membership?, game reserve home and fitness level. Disperser groups were able to “look ahead” within a given radius and sense other disperser groups, game reserve packs, rivers, roads, villages and boundary lines. Newly formed packs were assumed to know their fitness level and the name of the game reserve occupied. These packs were able to “look ahead” within a given radius and sense rivers, roads, villages and boundary lines. Existing game reserve packs were assumed to know their natal pack membership, game reserve home and fitness level. These game reserve packs were considered to have perma- nently made a home in one of the game reserves and consequently remained stationary throughout the model runs. Therefore game reserve packs were not “looking ahead” for anything.

g.) Interaction:

Three types of interactions were modeled: (1) disperser groups forming a new pack was dependent upon encountering and bonding with an opposite sex disperser group originating from a different, unrelated pack, (2) disperser groups being accepted into an existing 27 game reserve pack was dependent upon encountering and bonding with an unrelated game reserve pack, and (3) disperser groups ﬁghting with another disperser group was dependent upon the encounter of a same sex disperser group originating from an unrelated pack. h.) Stochasticity:

Stochasticity was used to represent the behavioral and environmental parameters and processes in the model. Disperser group and pack behavior such as movement, pack formations, ﬁghting, obtaining water, catching prey and dying were all modeled stochastically. These behaviors were modeled stochastically due to the fact that we considered many assumptions when modeling them. Since our model was largely stochastic, numerous model runs occurred to make more meaningful predictions about the wild dog population in KZN. Model runs were executed 990 times, each running for 365 days. However, a consequence of having a largely stochastic model was that the model’s results will be uncertain when the behavioral and environmental parameters and processes are different from the stochastic ones used in the model.

i.) Collectives:

Disperser groups, packs and game reserve packs were the three collectives in the model.

j.) Observation:

The model outputted the following results: the number of single disperser groups, the number of wild dogs that died, the number of disperser groups that formed a new pack, the spatial location of where new packs formed, the game reserve origins of each disperser group in the newly formed pack, the time and distance traveled by each disperser group 28 until they formed a new pack, the name of the game reserve in which new packs traveled, the number of disperser groups that joined an existing game reserve pack, the game reserve origins of the disperser groups that joined an existing game reserve pack, and the time and distance a disperser group traveled until it joined a game reserve pack.

3. Details

a.) Initialization:

The KZN environment was initialized at the beginning of each model run. The GIS layers that made up the KZN environment were imported from a file containing the GIS vector data. Game reserve packs and disperser groups were also initialized at the start of each model run. The number of game reserves initialized in HiP (8), Thanda (1) and uMkhuze (1) remained constant in each model scenario. Together, these three initializations made up the “Original” scenario used in the model. There were nine other scenarios which involved initializing one more additional game reserve pack into the corresponding game reserve. The natal pack membership of each initialized game reserve pack was set to the name of the game reserve they occupied. In addition, these game reserve packs were considered to have an established territory and be completely healthy. For these reasons, they were assigned a constant fitness level of 100 (the maximum fitness level). Wild dogs are highly territorial carnivores (Creel and Creel, 2002) and thus, game reserve packs were initialized at least nine kilometers apart from one another. This distance allowed the possibility of initializing more than eight game reserves packs inside HiP. In addition, the initial location of each game reserve pack was randomly selected to a location inside their game reserve. Finally, each initialized game reserve pack contained both one female and male disperser 29 group. Assuming all disperser groups were moderately healthy at the start of each model, the fitness level of each disperser group was set to a uniform random number between 50 and 100. At the start of each model run, disperser groups had yet to form a new pack or join an existing game reserve pack and thus, their state variable ‘Pack Membership?’ was set to “single.” Additionally, disperser groups’ state variables ‘Days Without Food’, ‘Days With- out Water’, ‘Days on the Road’ and ‘Total Distance Traveled’ were all initialized to zero. b.) Input:

The model did not contain processes that changed over time, so there was no input data.

c.) Submodels:

Twenty one parameter values were used in the model (Table 6). These parameters are dis- cussed and explained in further detail with their corresponding submodels. The processes and their possible outcomes both disperser groups and packs had to complete at each time step (Figures 5 - 6) are described in the following seven submodels. 30

Table 6: Model Parameter Name and Value(s). Parameter Value Name Value dispersergroup-fight 41% chance-of-water 96% chance-of-disease 93% close-enough? 0.50 (1.5 km) close-enough-to-village? 1.00 (3 km) snare-death 0.06 dispersergroup-radius 1.00 (3 km) game-reserve-pack-radius 1.25 (3.75 km) fight-with-dispersergroup 8 daily-fitness-loss 1 road-mortality 0.155 other-death-in-park 0.08 other-death-out-park 0.04 river-radius 0.50 (1.5 km) road-radius 0.50 (1.5 km) village-radius 0.75 (2.25 km) movement-loss-percent 8% fitness-from-water 4 fitness-from-impala 12 join-pack 64% join-game-reserve-pack 1%, 2%, 3%, 4%, 5% 31

The Submodel MOVE (disperser groups and packs)

To begin with, a command used to move individuals in NetLogo is “fd 1.” This moves the individuals forward one step. In the model, 1.00 (one step) represented 3 km. Wild dogs lose some fitness points each day regardless of what they do. This accounts for wild dogs aging and exerting any energy that was not described in the model. Before individuals moved, a ‘daily-fitness-loss’ was deducted from their overall fitness level. Not knowing how much energy wild dogs exerted on a daily basis, it seemed appropriate to set the parameter value ‘daily-fitness-loss’ to one. Setting ‘daily-fitness-loss’ to one affected the wild dogs’ overall fitness level minimally which allowed us to focus more on other aspects affecting wild dogs such as movement and mortality. Both disperser groups and newly formed packs followed the same movement rules. At the beginning of each time step, both of these entities chose a direction to face based on a prioritized list pertaining to them. Wild dogs were able to “look ahead” and sense what was around them. Wild dog disperser groups’ main purpose was to find other groups of wild dogs and thus disperser groups’ prioritization listed included “looking ahead” for: (1) other disperser groups, (2) game reserve packs, (3) rivers, (4) roads, and (5) villages. If disperser groups sensed another disperser group they would face and move directly towards them. Otherwise, they would continue down their prioritization list and look for game reserve packs, rivers, roads and villages. Additionally, disperser groups moved directly towards all items in their prioritization list except for villages. Wild dogs tend to stay away from villages in order to minimize human contact (Creel and Creel, 2002). As a result, if wild dogs “look ahead” and sense a village, they would face the opposite direction and then move. New packs no longer needed to look for other wild dogs, thus newly formed packs were looking for resources to ensure survival. Packs used the following prioritized list 32 when “looking ahead”: (1) rivers, (2) roads, and (3) villages. Again, packs would move directly towards rivers and roads but turn away from villages. The parameter ‘disperser-group-radius’ was the distance a disperser group could sense (smell) another disperser group and the parameter ‘game-reserve-pack-radius’ was the distance a disperser group could sense a game reserve pack. These two parameter values will affect the percentage of disperser groups forming a new pack and joining a game reserve pack respectively. Wild dogs are able to track the scent of other wild dogs for kilometers (Creel and Creel, 2002). However, there was no information stating exactly how many kilometers wild dogs were able to track other wild dogs so we assumed that it was at least 3 km. The percentages of wild dogs that joined an existing game reserve pack varied less than 0.20% when the parameter ‘game-reserve-pack-radius’ was adjusted from 3.75 km to 5.25 km (Figure 7). Since there was such a slight difference between the percentages, we chose the smallest distance to represent the distance wild dogs were able to sense a game reserve pack. Thus, we set the parameter ‘game-reserve-pack-radius’ to 1.25 which represented 3.75 km. Game reserve packs will contain, on average, more wild dogs than disperser groups (Creel and Creel, 2002). Hence, game reserve packs will have a stronger scent than disperser groups. This allowed wild dogs to sense game reserve packs at a further distance than disperser groups. Thus, the parameter value for ‘dispersergroup-radius’ will have to be smaller than the parameter value ‘game-reserve-pack-radius’. There was such a small difference (0.22%) in the percentage of disperser groups forming a new pack as the parameter ‘dispersergroup-radius’ was varied (Figure 8). Based on the assumptions we made, we need to choose a distance at least 3 km but less than 3.75 km for the parameter ‘dispersergroup-radius.’ Since there was little variation in the percent- 33

23.75

23.7

23.65

Percent 23.6

23.55

23.5 1.25 1.50 1.75 H3.75 kmL H4.50 kmL H5.25 kmL 'game-reserve-pack-radius' parameter value Hdistance in kmL

Figure 7: Percentage of disperser groups that joined an existing game reserve pack when the parameter ‘game-reserve-pack-radius’ was set to 1.25, 1.50 and 1.75 (Note: y-axis begins at 23.5 to emphasize the slight variation in the percentages).

ages, we assumed 3 km would best represent the parameter value ‘dispersergroup-radius.’ Thus, ‘dispersergroup-radius’ was set to 1.00 in the model.

25.2

25.15

25.1 Percent

25.05

25 1.00 1.125 1.25 H3.00 kmL H3.375 kmL H3.75 kmL 'disersergroup-radius' parameter value Hdistance in kmL

Figure 8: Percentage of disperser groups that formed a new pack with another disperser group when the parameter ‘dispersergroup-radius’ was set to 1.00, 1.125 and 1.25 (Note: y-axis begins at 25 to emphasize the slight variation in the percentages). 34

Disperser groups and packs would also “look ahead” for villages, rivers and roads. The parameter ‘village-radius’ was the distance a wild dog could sense a village. There was a small difference (0.24%) in the average percent of wild dogs that died due to diseases as ‘village-radius’ was varied (Figure 9). Domestic dogs have been known to be in villages implying that wild dogs may sense villages at a distance close to the distance they can sense other disperser groups (3 km). Thus we chose 2.25 km to represent the distance wild dogs could sense villages.

2.5

1.5 Percent 1

0.5

0 0.33 0.50 0.75 1.00 H1.00 kmL H1.50 kmL H2.25 kmL H3.00 kmL 'village-radius' parameter values Hdistance in kmL

Figure 9: Percentage of wild dogs dying due to diseases when the parameter ‘village- radius’ was set to 0.33, 0.50, 0.75 and 1.00.

Wild dogs travel near rivers and roads (Creel and Creel, 2002) and we assumed they would be able to sense both rivers and roads from the same distance. Domestic dogs will not be traveling on roads and rivers and there may not be as many wild dogs on roads and rivers as there were in disperser groups and game reserve packs. For these reasons, we assumed roads and rivers were not sensed as far as villages, disperser groups and game reserve packs were. Thus, the distance a wild dog was able to sense a road (‘road-radius’) and river (‘river-radius’) must be smaller than 2.25 km (the distance a wild dog was able to 35 sense a village). In addition, ‘road-radius’ and ‘river-radius’ should be greater than 1 km because Creel and Creel (2002) state that wild dogs are able to sense other wild dogs for “kilometers” and there may be a few wild dogs on the rivers and roads. We assumed wild dogs would be able to sense a river or a road from a distance of 1.5 km in the model. Thus, we set the parameter values ‘river-radius’ and ‘road-radius’ to 0.50 which represented 1.5 km. In summary, disperser groups would “look ahead” with a radius of 3 km for other disperser groups and 3.75 km for game reserve packs. Disperser groups and packs would “look ahead” with a radius 2.25 km for villages, and 1.5 km for both roads and rivers. Once wild dogs “looked ahead” and determined the direction they would face, they would move accordingly. The daily distance a disperser group and pack traveled was positively associated with their corresponding fitness level; the higher the fitness level, the greater the chance of traveling longer distances in one day. Given that the mean distance traveled by African wild dogs is 30 km (Creel and Creel, 2002), we made the assumption that disperser groups and packs would have a small chance of traveling 60 km (double the mean) or more. However, wild dogs are capable of traveling up to 250 km in one day (Creel and Creel, 2002). To represent the distance traveled by wild dogs in one day, we created a probabilistic density function (pdf) with a mean of 30. This pdf needed to be heavily skewed to the right to represent the small chance wild dogs had of moving 60 km or more in one day. One type of pdf heavily skewed to the right that could be implemented in NetLogo was the gamma distribution. The gamma pdf is defined by the equation

1 f(y) = yα−1e−y/β, Γ(α)βα 36 with the gamma function deﬁned as

Z ∞ Γ(α) = yα−1e−y dy. 0

The general silhouette of the gamma pdf depends on α (the shape parameter) and β (the scale parameter). These two parameters work together to give the appropriate skewness and shape of the gamma pdf (Figure 10). 0.04 0.03 0.02 0.01 0.00

0 20 40 60 80 100

distance (km)

Figure 10: General example of a gamma probability density function with a mean of 30. α = 1.91 and β = 15.73.

The fitness level of a disperser group and pack ranged from 0 to 100 and we separated this range into 10 equal intervals with a corresponding probability of traveling 60 km or more in one day (Table 7). Assuming healthier wild dogs had a higher probability of traveling longer distances, wild dogs with a fitness level higher than 90 were given a probability of 0.095 of traveling 60 km or more each time step. Each subsequent fitness level interval 37 had the probability of traveling 60 km or more decreased by 0.01. Ten different gamma pdfs with a mean of 30 were created to represent the probabilities of traveling 60 km or more. The values of α and β used in these 10 gamma pdfs along with the code used to find them can be found in Appendix A. To determine the distance a wild dog would travel, at each time step a number was randomly selected from the appropriate gamma pdf.

Table 7: Fitness levels and the corresponding probabilities of traveling 60 km or more. Fitness Level Probability of Traveling 60 km or More

(0,10] 0.005 (10,20] 0.015 (20,30] 0.025 (30,40] 0.035 (40,50] 0.045 (50,60] 0.055 (60,70] 0.065 (70,80] 0.075 (80,90] 0.085 (90,100] 0.095

When wild dogs travel, they expend energy (fitness). The parameter ‘movement-loss- percent’ was the percentage of the total distance traveled in one day that was deducted from the wild dogs’ fitness level. The farther a wild dog traveled, the more energy they used and thus, more fitness points were deducted from their overall fitness level. To determine the effect ‘movement-loss-percent’ had on the wild dogs’ fitness level, we analyzed the variation in a disperser group’s fitness level traced throughout one year (Figure 11). 38

a.L b.L

100 100

80 80

60 60 level level

40 40 Fitness Fitness

20 20

0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time HDayL Time HDayL

c.L d.L

100 100

80 80

60 60 level level

40 40 Fitness Fitness

20 20

0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time HDayL Time HDayL

Figure 11: Graphs of a disperser group’s ﬁtness level traced for one year. a.) ‘movement- loss-percent’ = 8%. b.) ‘movement-loss-percent’ = 10%. c.) ‘movement-loss-percent’ = 15%. d.) ‘movement-loss-percent’ = 25%.

Since wild dogs are highly active, we expect that the fluctuation in their fitness level should be minimal when they travel. When ‘movement-loss-percent’ was set to 8%, the wild dog’s fitness level exhibited fluctuations that varied by four fitness points throughout the year. It was observed that when ‘movement-loss-percent’ was set below 8%, the wild dog’s fitness level either remained constant or fluctuated by only one fitness point throughout the year providing too insignificant of a change to be considered in the model. Thus, ‘movement-loss-percent’ was set to a minimum of 8%. 39

The Submodel FIND DISPERSER GROUP? (disperser groups only)

Two disperser groups will not always bond and form a new pack. The chance that these wild dogs bond and form a new pack was represented by the parameter ‘join-pack.’ To have a chance of bonding, disperser groups must be “close enough” to another disperser group. The parameter ‘close-enough’ defined the maximum distance disperser groups need to be to other disperser groups in order to determine whether or not they will bond. The distance disperser groups can sense other disperser groups (‘dispersergroup-radius’) was set to 3 km. We assumed that disperser groups should be at least half this distance when determining whether or not they will bond with another disperser group. Thus, the parameter ‘close-enough’ was set to 1.5 km. Moreover, once disperser groups were “close enough” they had a 64% chance of forming a new pack (Gusset et al., 2009). When a new pack was formed, the unit became a larger and stronger group of wild dogs. Thus, the fitness level of this new pack was adjusted and was dependent upon the fitness levels of the two disperser groups that formed this new pack. The maximum fitness level of an individual was set at 100. There were two possibilities that could happen to the fitness level of this newly formed pack. A formally weak disperser group would have become stronger with the addition of more members. Similarly a formally strong disperser group may have had to slow down and take care of its new members decreasing its fitness level. Thus, newly formed packs had their fitness level set to a ratio of the sum of the two disperser groups’ fitness level. We assumed that the ratio would be bigger than one-half but smaller than one. Thus, we set the ratio as the midpoint of those

two numbers, three-quarters. Letting f1 and f2 be the ﬁtness level of disperser group 1 and disperser group 2 respectively, the ﬁtness level of the newly formed pack was calculated as

3 3 follows. If 4 (f1 + f2) < 100, the new pack’s fitness level was set to 4 (f1 + f2). Otherwise 40 the new pack’s fitness level was set to 100. Wild dogs may defend their territory from other wild dogs by fighting (Creel and Creel, 2002). In the model, disperser groups may have fought with unrelated, same sex disperser groups. The parameter ‘fight-with-dispersergroup’ was the amount of fitness points deducted from their fitness levels when disperser groups fought. Fighting primarily to scare off other wild dogs, these fights may lead to a wild dog’s death (Creel and Creel, 2002). Setting ‘fight-with-dispersergroup’ to 8 allowed a small percentage of wild dogs to die from fighting. However, wild dogs may not always get in a fight. The parameter ‘dispersergroup-fight’ was defined as the chance disperser groups had of getting into a fight with other disperser groups that were “close enough.” Four percent of wild dog deaths are due to other wild dogs (Woodroffe et al., 2004). Thus, if disperser groups lost 8 fitness points each time they were in a fight, we must set ‘dispersergroup-fight’ to 41% to get the desired average death rate of 4%.

The Submodel FIND GAME RESERVE PACK? (disperser groups only)

Disperser groups may also join an existing, unrelated game reserve pack and this pack formation depended on whether or not these two groups bonded. Disperser groups had to be “close enough” to the game reserve pack to determine whether or not they bonded. The disperser group decides whether or not to join the game reserve pack via a probability set by the parameter ‘join-game-reserve-pack.’ Disperser groups joining a game reserve pack does not happen as often as when they form a new pack (Woodroffe et al., 2004). Thus, ‘join-game-reserve-pack’ had to be smaller than ‘join-pack’ (64%). Both of these parameters ultimately determined the total percentage of pack formations. 41

When ‘join-game-reserve-pack’ was set to 5% the total percentage of pack formations was approximately 50% (Figure 12). We assumed that realistically there would be no more than 50% of the total wild dog population forming a new pack and joining an existing game reserve pack. Since, we had an exact value for ‘join-pack’, we decided to vary the parameter ‘join-game-reserve-pack’ from 1% to 5% in increments of 1% to analyze the effect this parameter value had on the results.

50 45 40 35 30 25

Percent 20 15 10 5 0 2% 3% 4% 5%

'join-game-reserve-pack' parameter values

Figure 12: Average percentage of total wild dog pack formations tested at different values of the parameter ‘join-game-reserve-pack.’

The Submodel LOOK FOR WATER (disperser groups and packs)

Wild dogs need water to survive (Creel and Creel, 2002). Wild dogs obtained water in one of two ways: (1) coming in direct contact with a river or (2) drinking water from other sources of water such as a stream, lake or puddle. The model’s spatially explicit environment contained only the main rivers in KZN and thus we incorporated a probabilistic event of obtaining water from sources other than rivers. If a wild dog came in contact with a river, they automatically drank water. Otherwise, wild dogs had a chance of ﬁnding water from another source (‘chance-of-water’ parameter). There is no information available stating exactly how successful wild dogs are at obtaining 42 water from other sources. Additionally, there is no data suggesting how many wild dogs die due to dehydration. Since wild dogs are highly mobile, we assumed they should have a high chance of obtaining water from other sources. When ‘chance-of-water’ was set to 95% approximately 8% of wild dogs were dying due to dehydration (Figure 13). This mortality rate appeared to be too high so we set the parameter ‘chance-of-water’ to 96%. This produced a mortality rate less than 6% which seems more reasonable for this population.

40 Percent

0 75% 80% 85% 90% 95% 'chance-of-water' parameter values

Figure 13: Average percentage of wild dogs dying due to dehydration tested at different values of the parameter ‘chance-of-water.’

When wild dogs drank water, their state variable ‘Days Without Water’ was set to 0. If they failed to drink any water, ‘Days Without Water’ was updated by 1 day. The wild dogs’ fitness levels should increase when they drink water because they are obtaining a source of energy. The parameter ‘fitness-from-water’ was defined as the number of fitness points a wild dog received once they drank water. Again, we had no information on how much a wild dog’s fitness level was affected when they drank water. Thus, we made the assumption that four points would be added to their fitness level each time they drank 43 water. If adding four points to their total fitness level resulted in a value greater than 100, the wild dog’s fitness level was set to the maximum, 100.

The Submodel LOOK FOR FOOD (disperser groups and packs)

To address the wild dogs’ foraging behavior without including another collective (prey) in the model, we represented hunting, catching and eating prey as a probabilistic event. Wild dogs hunt once or twice a day and the success rate of a wild dog hunt averages between 43% and 70% or conversely, 30% to 57% of not getting food each hunt (Creel and Creel, 2002). Each attempt at capturing prey was assumed an independent event. This implied that wild dogs had 30% to 57% chance of not getting any food the ﬁrst time they hunted in a day and 30% to 57% chance of not getting food the second time they hunted in a day. Letting

P (A) = probability of not getting food both times

P (B) = probability of not getting food the ﬁrst time

P (C) = probability of not getting food the second time

we calculated the possible range of values for not getting any food at all. Starting with a 57% chance of not getting food, we had

P (A) = P (B)P (C)

= (0.57)(0.57)

= 0.3249

which concluded that the complement, 67.51%, was the smallest chance wild dogs had of 44 getting food at least once a day. Now using a 30% chance of not getting food, we had

P (A) = P (B)P (C)

= (0.3)(0.3)

= 0.09 which concluded that the complement was 91%. This was the highest chance wild dogs had of getting food at least once a day. Thus, the chance of wild dogs catching and eating prey at least once a day ranged from 67.51% to 91%. In the model, hunting success was also dependent upon the wild dog’s fitness level. Larger, healthier groups of wild dogs that contained higher fitness levels were able to hunt larger prey much easier than the smaller, weaker groups of wild dogs that contained lower fitness levels. Thus, we separated the fitness level into 10 different intervals and assigned a probability of obtaining food at least once a day (Table 8). For simplicity, when a group of wild dogs acquired food, we made the assumption that all members of that group would eat enough. The parameter ‘fitness-from-impala’ was the number of fitness points added to the fitness level. Food has a higher calorie intake than water but we did not have the necessary information to state exactly how food affected the fitness levels. Thus, we assumed wild dogs would get three times the energy from eating than they did from drinking water. Consequently, each daily intake of food resulted in increasing the fitness level by 12 points. If adding 12 fitness points resulted in a fitness value greater than 100, the fitness level was set to the maximum value. Additionally if wild dogs ate food, the state variable ‘Number of Days Without Food’ was set to zero. Otherwise ‘Number of Days Without Food’ increased by one day. 45

Table 8: Fitness levels and the corresponding probabilities of catching prey once a day. Fitness Level Probability of Catching Prey

(0,10] 0.675 (10,20] 0.701 (20,30] 0.727 (30,40] 0.753 (40,50] 0.779 (50,60] 0.805 (60,70] 0.831 (70,80] 0.857 (80,90] 0.883 (90,100] 0.91

The Submodel CHECK SURVIVORSHIP (disperser groups and packs)

At the end of each time step, the program checked if any individuals were still alive. There were seven different ways individuals could die: (1) low ﬁtness level, (2) starvation, (3) dehydration, (4) road mortality, (5) snare mortality, (6) disease, and (7) other. When the individual’s ﬁtness level was less than or equal to one, they were considered too unhealthy to survive and died. Individuals were also assumed to die from starvation after 12 consecutive days without food and die from dehydration after 3 consecutive days without water. The percentage of wild dog deaths due to road mortality was approximately 16% (Woodroffe et al., 2004, 2007). The parameter ‘road-mortality’ was the probability an individual was killed when they were on a road. Setting ‘road-mortality’ to 0.155 resulted in desired road mortality rate. 46

The parameter ‘snare-death’ was the probability an individual died from a snare. Snares accounted for approximately 30% of adult wild dog mortality (Woodroffe et al., 2004, 2007). Setting the parameter ‘snare-death’ to 0.06 resulted in the desired mortality rate. Diseases were another source of wild dog mortality and accounted for approximately 5% of African wild dog deaths (Woodroffe et al., 2004, 2007). Dying from a disease was dependent upon individuals coming in contact with a village as well as having a certain chance of catching a disease. Individuals needed to be “close enough to a village” to have a chance of catching a disease. The parameter ‘chance-of-disease’ was defined as the chance wild dogs had of catching a disease. The parameter ‘close-enough-to-village’ was the maximum distance wild dogs had to be to a village to catch a disease. Recall, wild dogs tend to avoid villages and human contact (Creel and Creel, 2002) and were able to sense villages from a distance of 2.25 km. If they sensed a village, they would face the opposite direction and move. Thus, to catch a disease the distance ‘close-enough- to-village’ must be a further distance than their capabilities of sensing a village. Otherwise, individuals would always turn around and never be able to catch a disease. Since villages contained domestic dogs who are also mobile we assumed that 3 km would represent an adequate distance needed to catch a disease. Since ‘close-enough-to-village’ was set to 2.25km, ‘chance-of-disease’ had to be set to 93% to get the desired mortality rate of wild dogs dying due to diseases. Once wild dogs are close enough to a village, they will have a specific chance of catching a disease. To get the desired mortality rate due to diseases of 5%, we must set the parameter ‘chance-of-disease’ to 93%. Thus, if wild dogs are within 3 km of a village, they have a 93% chance of catching and dying from a disease in the model. Finally, 41.5% of wild dog deaths were classified into other categories such as death caused by predators, being shot or poisoned or dying due to unknown causes (Woodroffe 47 et al., 2004, 2007). We used the parameters ‘other-death-in-park’ and ‘other-death-out- park’ to represent the other death categories. The parameter ‘other-death-in-park’ was the probability a wild dog had of dying inside a game reserve due to other causes and the parameter ‘other-death-out-park’ was the probability a wild dog had of dying outside of a game reserve due to other causes. Most of these other causes of death occurred inside protected game reserves (Woodroffe et al., 2007) requiring us to choose a larger value for ‘other-death-in-park’ than ‘other- death-out-park.’ Setting ‘other-death-in-park’ to 0.08 and ‘other-death-out-park’ to 0.04 resulted in desired mortality rate of 41.5%.

The Submodel ON A GAME RESERVE? (packs only)

When packs reached a game reserve they stop moving. Moreover, the name of the game reserve the pack traveled to was reported.

Model Validation

NetLogo contains “Agent Monitors” which displayed the values of each state variable for a particular individual. These Agent Monitors were very helpful when testing the model code for accuracy. Moreover, each of the seven submodels were individually tested and validated, one at a time.

1. Validation of Submodel ‘MOVE’

The distance wild dogs moved in one day was dependent upon their fitness level and a gamma pdf. To test the accuracy of these two attributes, a disperser group and pack were assigned a specific fitness level. The distance assigned to them from the gamma pdf was 48 reported and checked to make sure the wild dogs were traveling that distance. Additionally, the wild dogs’ ability to travel more than 60 km in one day was tested. For example, a disperser group’s fitness level was set to a constant 10 implying that this disperser group had a probability of 0.005 of traveling 60 km or more in one day (Table 7). Each time step, the distance this disperser group traveled was reported. This was simulated for 365 days and the daily distance traveled was analyzed to ensure a distance of 60 km or more was reported infrequently. Agent Monitors were used to ensure ‘movement-loss-percent’ was implemented correctly. A disperser group was assigned a constant fitness level and a specific distance to travel in one day. The amount of fitness points to be deducted was manually calculated and this deduction was verified by observing the fitness level reported in the disperser group’s Agent Monitor. Each portion in the “look ahead” code was tested individually, one at a time, for accuracy. For example, when testing whether or not a wild dog within 1.5 km of a river would face and travel towards the river, a wild dog was first placed very close to a river. The wild dog was then examined over and over again to make sure it would face and travel towards the river. Similar tests were done ensuring wild dogs would face and travel appropriately when they were within the range of a road, village, disperser group and game reserve pack. Once each portion of the “look ahead” code was validated, we tested the disperser group’s and pack’s prioritization lists by creating pseudo-environment. A disperser group and pack were placed next to various habitats and wild dogs. Then their prioritization lists were analyzed for accuracy. For example, a disperser group was placed in range of a game reserve pack and a road. It was observed that the disperser group headed towards the game reserve pack rather than the road. Similar experiments were done to test each portion of the prioritization lists pertaining to disperser groups and packs. 49

2. Validation of Submodel ‘FIND DISPERSER GROUP?’

Testing the submodel ‘FIND DISPERSER GROUP?’ involved confirming that only unrelated, opposite sex disperser groups were able to form new packs. To guarantee that only opposite sex disperser groups were able to form a new pack, only female disperser groups (then only male disperser groups) were placed in the NetLogo environment. After numerous model runs, it was observed that no packs were formed. Finally, a related male and female disperser group were placed in the model and it was verified that it was impossible for these two related disperser groups to form a new pack. Recall that when two disperser groups formed a pack, this new pack’s fitness level was set to three-fourths of the sum of the two disperser groups’ fitness levels. A constant fitness level of 50 was given to these disperser groups. Thus, when they formed a new pack, the pack’s fitness level should have been 75. Agent Monitors verified that the pack’s fitness level was being calculated correctly. When unrelated, same sex disperser groups met, there was a chance a fight would occur. When disperser groups fought, their color would change to white and the user message “Fight!” would appear. These two attributes were helpful to visually see when disperser groups fought. Related, same sex disperser groups were placed in the model to make sure no fight occurred. Then unrelated, same sex disperser groups were placed in the model and ‘dispersergroup-fight’ was adjusted from 0% to 100% to test whether or not a fight occurred. Finally, when disperser groups were in a fight, Agent Monitors verified that each disperser group lost the correct amount of fitness points. 50

3. Validation of Submodel ‘FIND GAME RESERVE PACK?’

When a disperser group joined an existing game reserve pack, the color of the game reserve pack would change in NetLogo enabling the user to verify that a pack formation occurred. A disperser group may only join an unrelated game reserve pack and this was tested by placing a disperser group and its related game reserve pack in the environment and ensuring that the disperser group would not join this game reserve pack. Agent Monitors veriﬁed that the ﬁtness level of a disperser group was reset to 100 once it joined a game reserve pack.

4. Validation of Submodel ‘LOOK FOR WATER’

To test the submodel ‘LOOK FOR WATER’ user messages were placed in the code. If a wild dog was on a river, the user message “On Water” appeared. If a wild dog was not on a river but still able to drink water, “Got Water” appeared. Similarly, if a wild dog did not drink water, the user message “No Water” appeared. These three user messages were tested for accuracy by placing wild dogs on and off rivers and adjusting the wild dog’s daily chance of drinking water. Agent Monitors were used to verify that the correct number of fitness points were being added to the wild dogs’ fitness level each time they drank water. Additionally, when wild dogs did not drink any water, their state variable ‘Days Without Water’ was increased by one day and this was confirmed via Agent Monitors.

5. Validation of Submodel ‘LOOK FOR FOOD’

Wild dogs obtaining food depended upon their fitness level and the corresponding probability of obtaining food (Table 8). Initially, the probability of obtaining food was set to zero 51 and the user message “No Food” appeared each time. Conversely, when the probability of catching prey was set to one, the user message “No Food” did not appear once. To test the fitness intervals and corresponding probabilities of obtaining food, a disperser group was given a set fitness level of 100, meaning that it had a 91% chance of catching prey each day. Through numerous model runs, it was determined that the wild dog was obtaining food about 91% of the time. Similar experiments were done for each fitness interval. Agent Monitors were used to ensure the correct number of fitness points were being added when the wild dogs ate food and that their state variable ‘Number of Days Without Food’ was updating correctly.

6. Validation of Submodel ‘CHECK SURVIVORSHIP’

Each of the death classifications were tested individually, one at a time. To ensure individuals died when their fitness level was less than or equal to one, a disperser group was assigned a low fitness level. This disperser group was observed dying as soon as its fitness level reached one or below. When testing death due to starvation and dehydration, both the chance of getting food and water were set to zero, one at a time. This meant that at each time step the number of days without food and water would have increased by one day. To ensure an individual had no chance of drinking water, the individual was specifically placed far away from any rivers when testing death due to dehydration. Agent Monitors were were used to examine the state variables ‘Days Without Food’ and ‘Days Without Water.’ It was found that the individual died from starvation after 12 consecutive days without food and after 3 consecutive days without water. The probability of dying from a snare was set to 1.00 and an individual was monitored 52 to see if it would die accordingly. Similarly, death due to roads was tested by placing an individual on a road and setting the road mortality rate to 1.00 and monitoring the results. An individual should not die due to road mortality when they were away from a road. This was tested by placing an individual away from a road and verifying that they did not die from road mortality. Death due to disease was tested by adjusting ‘chance-of-disease’ and ‘close-enough- to-village’ and then monitoring the individuals. When individuals were far away from a village, they did not die from a disease. Similarly, ‘chance-of-disease’ was set to 100% and it was observed that all individuals that were close enough to a village were dying from diseases. Finally, deaths classified as other were tested individually by varying the values of the parameters ‘other-death-in-park’ and ‘other-death-out-park.’ An individual was monitored to see whether or not it would die in the appropriate location.

7. Validation of Submodel ‘ON A GAME RESERVE?’

To test the submodel ‘ON A GAME RESERVE?,’ I visually inspected whether or not a new pack would stop moving once it reached a game reserve. Once the pack reached a game reserve, the name of the game reserve was reported correctly.

Sensitivity Analysis

A sensitivity analysis is a test used to determine how sensitive a model is to changes in the model’s parameters. Many of the parameter values used in our model represented quantities that were often difficult to measure in the real world and consequently were based on stochastic probabilities or assumptions. The purpose of a sensitivity analysis is to set 53 different values for each parameter and examine how a change in the parameter value will affect a certain dynamic behavior of the model. In our case, we examined how a change in a parameter value affected the total percentage of disperser groups that formed a new pack or joined an existing game reserve pack. The sensitivity analysis gave us insight as to which parameters contributed more to successful dispersal. This will give us an insight as to which parameters were important biologically, to dispersal success as well as point out the important assumptions used in the model. Moreover, a sensitivity analysis helps build confidence in the model. It validates that the model is behaving as expected. For example, if the chance of joining a game reserve pack increased, we would expect that the number of total pack formations increased as well. A simplified, local sensitivity analysis was conducted by varying each parameter over a small range of four values and recording the resulting percentages of pack formations (i.e., the percentage of disperser groups that formed a new pack and joined a game reserve pack). Each such parameter value was re-scaled by dividing its value by the “standard” parameter value (Table 6) used in the model. Re-scaling each parameter was necessary to compare the different parameters which have varying magnitude and unit measurements. A regression analysis was performed on each parameter to estimate the rate of change of pack formations with respect to the parameter. The sensitivity of each parameter was defined as the magnitude of its corresponding regression slope (Table 9). The regression figures for each parameter value can be found in Appendix B. The parameter ‘chance-of-water’ displayed the most sensitivity to the model. The fourth most sensitive parameter value was ‘join-game-reserve-pack’ and we examined the effect this parameter had by varying it in the model experiments. Additionally the sensitivity of the parameters ‘other-death-out-park’, ‘snare-death’,‘other-death-in-park’ and ‘road-mortality’ were ranked in the top nine. However, the values of these parameters were 54 specifically chosen so they would give rise to the mortality rates found in actual data.

Table 9: Sensitivity of parameters. Parameter Magnitude of the corresponding slope

chance-of-water 44.81 other-death-out-park 2.16 snare-death 2.08 join-game-reserve-pack 1.75 game-reserve-pack-radius 1.51 close-enough-to-village? 1.49 chance-of-disease 1.41 other-death-in-park 1.39 road-mortality 1.21 dispersergroup-fight 1.19 dispersergroup-radius 1.12 village-radius 0.99 close-enough? 0.86 fitness-from-water 0.64 daily-fitness-loss 0.59 river-radius 0.55 fitness-from-impala 0.48 movement-loss-percent 0.46 fight-with-dispersergroup 0.42 road-radius 0.08 55

Experiments

The aim of this model was to analyze the natural dispersal dynamics of the African wild dog population in KZN. To do this, we first analyzed the natural dispersal dynamics of the “Original” wild dog population. Recall that the “Original” population/scenario of wild dogs consisted of 8 game reserve packs in HiP, 1 game reserve pack in Thanda and 1 game reserve pack in uMkhuze. Then, we analyzed the changes in natural dispersal that occurred when a game reserve pack was reintroduced, one at a time, into a different game reserve. Thus, we had a total of ten scenarios to analyze. Along with the Original scenario, the nine other scenarios were named: Coastal, Ithala, Mkuze Falls, Ndumo, Phinda (Phinda Munyawana Conservancy), Phongola, St. Lucia (Greater St. Lucia Wetland Park), Tembe (Tembe Elephant Park) and Zuluand RR (Zul- uland Rhino Reserve). For example, the scenario Ithala implied that there were 8 game reserve packs in HiP, 1 game reserve pack in Thanda, 1 game reserve pack in uMkhuze and 1 game reserve pack in Ithala at the beginning of the model run. Each of the 10 scenarios were executed through five different experiments each. These experiments included setting ‘join-pack’ to 64% and varying the parameter ‘join-game- reserve-pack’ from 1% to 5% in increments of 1%. Each experiment was executed 990 times, each running for 365 days. The model was largely stochastic containing many parameters that were based on random events and probabilities. Due to this stochasticity in the model, we applied the Central Limit Theorem (CLT) to analyze the results. The CLT states that when a sample is large (30 and over), the sampling distribution will be approximately normal (Wackerly et al., 2002) which allowed us to make more meaningful and realistic predictions from our results. Thus, we first separated the 990 simulations into 33 groups of 30. Each of these 33 56 groups were analyzed separately and then all of results from these 33 groups were averaged to give us the results that are presented in the next section. RESULTS

We were interested in determining the game reserve(s) into which wild dogs could be reintroduced that would lead to the highest percentage of pack formations. Pack formations occurred when disperser groups formed a new pack and when disperser groups joined an existing game reserve pack. At the end of each model run, we analyzed the total percentage of disperser groups that formed a new pack (Figure 14). As the parameter ‘join-game-reserve-pack’ varied from 1% to 5%, the average percentage of new packs formed ranged from 24.4% to 32.6%. In the 990 simulations, the scenarios Phinda, St. Lucia and Zululand RR typically displayed the highest percentages of new packs formed. Conversely, the lowest percentages of new packs formed occurred when wild dogs were reintroduced into Ithala, Ndumo and Tembe. We also analyzed the percentage of disperser groups that joined an existing game reserve pack (Figure 15). In this case, as the parameter ‘join-game-reserve-pack’ was varied there was a greater range ([8.1%, 51.6%]) of success. After 990 simulations, we found that when wild dogs were reintroduced into Phinda, St. Lucia, Zululand RR and Mkuze Falls, a slightly higher percentage of disperser groups joined an existing game reserve pack. Alternatively, the scenarios involving Ithala, Ndumo and Tembe displayed the lowest percentages of disperser groups that joined an existing game reserve pack. Reintroducing wild dogs into game reserves that led to the highest percentages of all pack formations would be futile if the majority of these wild dogs perished while dispersing. There was a narrow range in the percentage of total pack formations ([44.5%, 47.2%]) and the percentage of wild dogs that died ([24.1%, 25.3%]) throughout the scenarios. We found that scenarios displayed an inverse relationship with the percentage of pack formations and the percentage of wild dog deaths (Figure 16). Throughout the sim-

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Figure 14: Average percentage of disperser groups that formed a new pack when ‘join- game-reserve-pack’ was varied from 1% to 5%. a.) ‘join-game-reserve-pack’ = 1%. b.) ‘join-game-reserve-pack’ = 2%. c.) ‘join-game-reserve-pack’ = 3%. d.) ‘join-game- reserve-pack’ = 4%. e.) ‘join-game-reserve-pack’ = 5%. 59

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Figure 15: Average percentage of disperser groups that joined an existing game reserve pack when ‘join-game-reserve-pack’ was varied from 1% to 5%. a.) ‘join-game-reserve- pack’ = 1%. b.) ‘join-game-reserve-pack’ = 2%. c.) ‘join-game-reserve-pack’ = 3%. d.) ‘join-game-reserve-pack’ = 4%. e.) ‘join-game-reserve-pack’ = 5%. 60 ulations, scenarios such as Phinda, St. Lucia and Zululand RR that resulted in the highest percentages of pack formations also displayed the lowest percentages of wild dog deaths. Alternatively, the scenarios Ithala, Ndumo and Coastal which had the lowest percentages of pack formations also displayed the highest percentages of wild dogs that perished.

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RR Falls Ithala Lucia Coastal Ndumo Phinda . Tembe Original Pongola St

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Figure 16: Average percentage of total wild dog pack formations (solid) versus the average percentage of wild dogs that died (open).

When a disperser group did not form a new pack or join an existing game reserve pack, this disperser group was considered “single.” We found another inverse relationship between the percentage of pack formations and the percentage of single disperser groups at the end of each model run. In the 990 simulations, the scenarios Ithala, Ndumo and Tembe displayed the lowest percentages of pack formations, but on average, they contained the highest percentages of single disperser groups (Figure 17). Alternatively, the scenarios that led to some of the highest pack formations percentages (Phinda, St. Lucia and Zululand RR) contained the lowest percentages of single disperser groups. Overall, there was a narrow range ([28.7%, 30.2%]) in the average percentage of single disperser groups at the end of each model run. 61

16 Percent 12

RR Falls Ithala Lucia Coastal Ndumo Phinda . Tembe Original Pongola St

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Figure 17: Average percentage of single disperser groups at the end of each model run.

The model predicted that the average percent of disperser groups able to successfully disperse (i.e., form a new pack or join an existing game reserve pack) was 45.7%. Addi- tionally, we found an average of 29.6% of disperser groups still alive and looking for other wild dogs at the end of the model runs. Finally, the model predicted 24.7% of the wild dog population died while dispersing. In addition to predicting the percentage of wild dogs able to successfully disperse, it is useful for management to know the time required and distance disperser groups traveled until they met. This information is beneﬁcial in determining the best game reserves to reintroduce wild dogs. We analyzed the time and distance traveled by disperser groups who met, bonded and formed a new pack with another disperser group (Figure 18). The total average time taken for disperser groups to form a new pack correlated with the total average distance traveled by these disperser groups. On average, the number of days it took disperser groups to form a new pack was between 73.7 to 81.5 days whereas the average distance traveled ranged 62 between 2211.6 to 2441.8 km. These distances and days traveled implied that disperser groups were averaging approximately 27 km/day to 33 km/day before they found another disperser group. Over the total number of simulations, the longest time and furthest distance traveled by disperser groups who formed a new pack occurred in the scenario Ithala, which also displayed one of the lowest percentages of new packs formed. Phinda, St. Lu- cia and Zululand RR, all of which had the highest percentages of new pack formations, also displayed the shortest times and smallest distances traveled by disperser groups who formed a new pack.

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Mkuze Zululand Mkuze Zululand Scenario Scenario

Figure 18: Total combined average a.) time in days and b.) distance in km a disperser group traveled to form a new pack.

Not only were we interested in the distances and times traveled by disperser groups who formed new packs, we were also interested in examining the origins of these disperser groups and the destination of the new packs. After the 990 simulations, the model predicted wild dogs were more likely to encounter other wild dogs while dispersing outside of the game reserves (Table 10). HiP was the next most likely location where new packs were formed, followed by St. Lucia, Thanda, 63 uMkhuze, Phinda and Zululand RR. New packs were formed in the other six game reserves for a combined frequency of only 2%. This is attributed to the fact that these six game reserves (Phongola, Mkuze Falls, Coastal, Tembe, Ithala and Ndumo) were the furthest away from the original population of wild dogs living in HiP, uMkhuze and Thanda.

Table 10: Frequency of where new packs were formed. Location Percentage of new packs formed

Outside a Game Reserve 59.8% HiP 25.5% St. Lucia 5.8% Thanda 2.2% uMkhuze 1.9% Phinda 1.5% Zululand RR 1.1% Phongola 0.6% Mkuze Falls 0.5% Coastal 0.3% Tembe 0.3% Ithala 0.2% Ndumo 0.1%

We saw that there was only a 2.7% difference in the total percentages of pack formations for each scenario (Figure 16). This may be due to the fact that in each scenario, except for Original, there were the same number of packs and disperser groups at the beginning of each model run. Additionally, each scenario always had disperser groups from HiP, Thanda and uMkhuze. In each scenario, there were no considerable differences in the percentages 64 of disperser groups originating from HiP (76.4% to 80.3%), Thanda (8.3% to 8.7%) and uMkhuze (6.6% to 7.9%). Instead of examining all of disperser groups in each scenario, we only focused on the disperser groups originating from the speciﬁc game reserve in which wild dogs were introduced. We sought to determine the game reserves from which the successfully dispersing wild dogs originated (Table 11).

Table 11: Game reserve origins of the disperser groups that formed a new pack. Game Reserve Percentage of disperser groups that originated from given game reserve

Phinda 8.2% St. Lucia 8.2% Zululand RR 7.7% Phongola 6.6% Mkuze Falls 5.9% Coastal 5.7% Ndumo 5.3% Tembe 5.2% Ithala 4.7%

In the 990 simulations, when new packs were formed, the disperser groups were originating more frequently from Phinda, St. Lucia and Zululand RR. Wild dogs from Ithala, Tembe and Ndumo had the lowest percentages of dispersal success but these game reserves were also the furthest from HiP and were among the most isolated game reserves used in the model. In the model, when disperser groups formed a new pack, that new pack would continue to travel until they reached a game reserve. Thus, we examined how often a new pack traveled to a speciﬁc game reserve (Table 12). 65

Table 12: Percentage of the time new packs reached given game reserve. Game Reserve Percentage of new packs that reached this game reserve

Mkuze Falls 37.5% HiP 36.4% Zululand RR 10.3% Thanda 7.4% Phongola 3.3% uMkhuze 3.2% Phinda 0.8% St. Lucia 0.7% Ithala 0.5% Coastal 0.05% Tembe 0.04% Ndumo 0.0%

Throughout the total number of simulations, most of the new packs traveled to Mkuze Falls, followed closely by HiP. On the other hand, less than 1% of newly formed packs traveled to Phinda. Moreover, not only did reintroducing wild dogs into Zululand RR lead to one of the highest percentages of pack formations, a good percentage of new packs reached Zululand RR. Recall, wild dogs joined existing game reserve packs as well. We looked at the average time (ranging from 78.4 to 83.6 days) and distance (ranging from 2349.6 to 2505.3 km) disperser groups traveled until they joined an existing game reserve pack (Figure 19). These data implied that dispersing groups of wild dogs traveled approximately 28 km/day to 31 km/day before they found an acceptable game reserve pack in which to join. In the 990 66 simulations, the fewest days and shortest distances traveled to reach a game reserve pack occurred in the scenarios Phinda, St. Lucia and Zululand RR whereas the most days and longest distances traveled occurred in the scenarios Ithala, Tembe and Coastal.

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L 2000 60 L km days H H 50 1500 time 40 distance 1000 30 Average

20 Average 500 10 0 0

RR RR Falls Falls Ithala Lucia Ithala Lucia Coastal Ndumo Phinda . Tembe Coastal Ndumo Phinda . Tembe Original Pongola Original Pongola St St

Mkuze Zululand Mkuze Zululand Scenario Scenario

Figure 19: Total combined average a.) time in days and b.) distance in km a disperser group traveled to join an existing game reserve pack.

Again, we saw that each scenario varied slightly in the percentage of disperser groups that joined an existing game reserve pack (Figure 15). Thus, we are interested in where these disperser groups originated from. We determined that disperser groups who joined an existing game reserve pack originated from HiP (78.6% to 83.4% of the time), Thanda (7.2% to 8.1% of the time) and uMkhuze (5.7% to 6.7% of the time). However, HiP, Thanda and uMkhuze always contained wild dogs at the beginning of each model run. Thus, we are interested in examining from what additional game reserves the disperser groups who joined an existing game reserve pack originated (Table 13). After the total number of simulations we found that disperser groups who joined an existing game reserve pack were mostly originating from Phinda, St. Lucia and Zululand RR. Few of these disperser groups originated from Ndumo, Ithala and Tembe. 67

Table 13: Game reserve origins of the disperser groups that joined an existing game reserve pack.

Game Reserve Percentage of disperser groups that originated from given game reserve Phinda 7.4%

St. Lucia 6.7%

Zululand RR 6.6%

Phongola 4.8%

Mkuze Falls 4.3%

Coastal 3.6%

Ndumo 3.3%

Ithala 3.2%

Tembe 3.1%

Finally, there was less than a 3% difference in total percentage of all pack formations for each of the scenarios (Figure 16). Thus, instead of looking at the dispersal success of the entire population of wild dogs in each model run, we examined the dispersal success of only the reintroduced wild dogs. Wild dogs were reintroduced into Coastal, Ithala, Mkuze Falls, Ndumo, Phinda, Pongola, St. Lucia, Tembe and Zululand RR and consequently, we only focused on wild dogs originating from these game reserves. There was a considerably larger range in the dispersal success of only the reintroduced wild dogs ([20.1%, 41.1%]) than the range in the dispersal success of the entire wild dog population in each scenario ([44.5%, 47.2%]). Among the reintroduced game reserve packs, wild dogs from Phinda, St. Lucia and Zululand RR had the greatest dispersal 68 success throughout the 990 simulations whereas wild dogs from Ithala, Ndumo and Tembe had the worst dispersal success (Figure 20).

50 45 40 35 30 25

Percent 20 15 10 5 0

RR Falls Ithala Lucia Coastal Ndumo Phinda . Tembe Pongola St

Mkuze Zululand Origin of reintroduced wild dogs

Figure 20: Dispersal success of only the reintroduced wild dogs. DISCUSSION

We have simulated natural dispersal of the Africa wild dog population in the province of KZN, South Africa. We believe that our model captured the essential behaviors of wild dogs dispersing and made plausible predictions for the best game reserves in which to reintroduce and translocate them. The model showed that wild dogs were capable of dispersing successfully after being reintroduced into various game reserves. On average, the model predicted 45.7% of the total dispersing wild dog population being able to meet and bond with another group of wild dogs. Determining optimal game reserves in which to reintroduce and translocate wild dogs is very beneﬁcial to researchers and wildlife managers. Recall, pack formations occurred when disperser groups formed a new pack or when they joined an existing game reserve pack. The total average percentage of pack formations varied less than 3% throughout each of the scenarios executed in the model (Figure 16). The overall wild dog population had higher dispersal success when wild dogs were reintroduced in Phinda, St. Lucia and Zululand RR. Alternatively, the total population of wild dogs were the least successful while dispersing when wild dogs were reintroduced into Ndumo, Tembe and Ithala. This slight variation in the percentage of total pack formations may have been due to the fact that each scenario, excluding Original, was initialized to contain the same number of game reserve packs (11) and disperser groups (22). The Original scenario contained 10 game reserve packs and 20 disperser groups. Instead of analyzing the entire population of wild dogs, we focused on the dispersal success of only the reintroduced wild dogs. For these wild dogs, we found a more signiﬁcant range in the percentage of pack formations (Figure 20). We were able to conclude that wild dogs reintroduced in Phinda, St. Lucia and

69 70

Zululand RR were the most successful when dispersing. The combined average percentage of wild dogs successfully dispersing from these three game reserves was approximately 40%. Dispersal for wild dogs reintroduced in Ithala, Ndumo and Tembe was the least successful, leading to a combined average percentage of approximately 21%. Dispersal success correlated with the time and distance disperser groups had to travel until they met another group of wild dogs (Figures 18 and 19). In each scenario, there were always wild dogs initialized in HiP, uMkhuze and Thanda. As a result, wild dogs reintroduced in the game reserves that were closest to HiP, uMkhuze and Thanda displayed the highest percentage of pack formations. Conversely, wild dogs reintroduced in the game reserves that were furthest from HiP, uMkhuze and Thanda had the lowest percentage of pack formations. Thus, successful dispersal was dependent upon where wild dogs were reintroduced and their proximity to other wild dogs. The closest game reserves to the Original population of wild dogs were Phinda, St. Lucia and Zululand RR. As these wild dogs did not have to travel as far they required fewer days to find other wild dogs and their mortality rates were lower. The game reserves furthest from HiP, uMkhuze and Thanda were Ithala, Ndumo and Tembe. In addition, these three game reserves were among the most isolated in KZN. Consequently, wild dogs in the scenarios Ithala, Ndumo and Tembe had to travel longer distances to find other wild dogs and were not as successful when dispersing. Our sensitivity analysis (Table 9) found that the parameters corresponding to the mortality rates were among the top ten most sensitive in the model. Wild dogs face more risks when they travel outside of the game reserves. Consequently, when wild dogs spend more time dispersing their mortality rate increases. The model predicted that an average of 24.7% of the wild dog population died while dispersing. Fewer wild dogs in the scenarios Phinda, Zululand RR and St. Lucia died while dispersing whereas mortality rates were higher in 71 the scenarios including Ndumo, Tembe and Ithala (Figure 16). Disperser groups were meeting and forming new packs most frequently outside of the protected game reserves (Table 10). Approximately 60% of the new packs were formed outside game reserves. Given that this meeting location adds undue risks such as deaths due to snares and roads, managers may want to focus on protecting the wild dogs outside game reserves and ensuring their safe passage. Developing corridors to and from the game reserves may aid in this effort. We also analyzed the travel patterns of new packs (Table 12). When new packs were formed, the game reserve they traveled to the most frequently was Mkuze Falls followed very closely by HiP. In fact, 37.5% of the newly formed packs traveled to Mkuze Falls. Thus, managers may consider focusing on facilitating wild dogs’ travel to Mkuze Falls rather than reintroducing or translocating wild dogs there. On the other hand, when new packs were formed, their final destination was rarely Phinda. Less than 1% of the newly formed packs traveled there. Moreover, new packs were being formed in Phinda only 1.6% of the time. We suggest that management focus primarily on reintroducing wild dogs into Phinda and aid disperser groups leaving there rather than focusing on making Phinda a final destination. All of the results in the model were based on the fact that wild dogs were already in HiP, uMkhuze and Thanda. If these wild dogs were not currently in KZN, there would not have been as many pack formations reported. The Original scenario generally displayed good results and contained one of the highest percentages of pack formations, indicating that the original population of wild dogs was able to disperse and find other wild dogs. However, at the conclusion of our simulations approximately 30% of the original population of wild dogs were single and still looking for other wild dogs. This implies that if additional wild dogs were placed in other game reserves, the wild dog population could increase. 72

Although there was not a huge variation in the percentages within most of the results, the game reserves that displayed the best and worst results were consistent throughout the 990 simulations. However, these variations may not be statistically significant. Phinda, St. Lucia and Zululand RR consistently displayed the most favorable results. These scenarios led to the highest percentages of pack formations, the highest dispersal success among the reintroduced packs only, the lowest percentages of wild dogs that died and the smallest times and distances traveled to find other wild dogs. Alternatively, Ithala, Ndumo and Tembe consistently displayed the least favorable results. Wild dogs reintroduced in these game reserves had to travel the furthest to find other wild dogs, had the least successful dispersal and displayed the highest percentage of wild dog deaths. Not only was dispersing from Ithala, Ndumo and Tembe not as successful, wild dogs from other game reserves rarely traveled to these game reserves. The combined percentage of packs formed in these three game reserves was less than 0.7% and the newly formed packs reached one of these game reserves less than 0.6% of the time. Therefore, when focusing on the KZN population of wild dogs, it is inadvisable to expend time and money on encouraging wild dogs reintroductions in Ithala, Ndumo and Tembe. However, Ndumo and Tembe are just south of Kruger National Park and further models incorporating this game reserve may provide important information. It appears advisable to have the wild dogs currently in HiP, Thanda and uMkhuze remain in their prospective game reserves. Since the results predicted that the wild dogs closest to these game reserves had the highest dispersal success, we suggest keeping wild dogs in proximity to one another. This will allow researchers to reduce the potential distances wild dogs need to travel to find other wild dogs and increase their survival rate. Thus, initially reintroducing wild dogs in the closest game reserves would be the most beneficial. We have concluded that initially wild dogs should be reintroduced in Phinda, St. Lucia 73 and Zululand RR. Once additional populations of wild dogs are established in KZN, we recommend reintroducing additional wild dogs in the other game reserves such as Pongola and Coastal.

Future African Wild Dog Studies

Few individual-based models involving African wild dogs have been developed. The dispersal movement of African wild dogs is a complex behavior to model and there are many different influences that affect dispersal. We provided a base model for the dispersal movement of the wild dog population in KZN, South Africa. This model can be further expanded upon to provide additional information about the wild dog population. In our extensive model, we provided detailed considerations for the factors that influ- enced the directions and distances wild dogs traveled each day. Other behaviors such as some of the mortality risks involved while dispersing, bonding with other disperser groups and game reserve packs, eating, as well as drinking and fighting were modeled stochastically. Wild dogs were able to “look ahead” for other wild dogs and habitats within a set radius. The values for the parameters ‘dispersergroup-radius’, ‘game-reserve-pack-radius’, ‘river- radius’, ‘road-radius’ and ‘village-radius’ were based on educated assumptions. Dispersal movement may be more accurately modeled if better information was available regarding these attributes. In our model, once a wild dog had a direction to face, it would move. The model predicted disperser groups traveled up to 2505 kilometers to find other wild dogs, an enor- mous distance. A mean dispersal distance of 30 km/day was used in the model. However, wild dogs may not consistently travel 30 km/day every day they are dispersing. Lowering 74 the mean distance traveled in the model may provide more accurate representations of the distances they need to travel to find other wild dogs. In the model, some of the death rates were a fixed constant throughout the KZN environment. For example, we set a constant probability of dying from a snare. However, realistically snares are a greater risk near some of the game reserves than others (Szykman Gunther, Pers. Comm.). Overall, different parts of KZN are more dangerous than other and so future studies may more accurately code this variability. Approximately 30% of the disperser groups were still alive and looking for other wild dogs after 365 days. Therefore, future studies may include longer simulations to better predict dispersal success. In addition, the GIS data layers used to import the KZN environment contained only one city. Recall that wild dogs tend to avoid contact with humans and villages as it is potentially hazardous for them. A consequence of having a single city included in our model was that the parameter ‘chance-of-disease’ was set very high (96%). This ensured the desired 4% mortality rate due to diseases. GIS data containing more of the villages in KZN could be imported in the model in a future study. We also assumed that prey was available for the wild dogs over each time step which may not always be the case. The amount of prey available is much lower outside of the game reserves versus inside the game reserves (Szykman Gunther, Pers. Comm.). Intro- ducing another entity, prey, and incorporating the prey’s movement behavior could more accurately model the wild dog’s own movement and success in hunting. In addition, other entities that affect the wild dog population such as lions and hyenas could be incorporated. Wild dogs often compete with lions and hyenas for the same prey. In addition, lions and hyenas are predators of wild dogs accounting for approximately 12% of their deaths (Woodroffe et al., 2004, 2007). Since wild dogs are highly territorial, the size of each game reserve could be incorpo- 75 rated in the model. For example, Thanda could not contain as many packs of wild dogs as HiP. Modeling this aspect may change management’s decisions as to where to reintroduce wild dogs. Fencing surrounding the game reserves in KZN was not considered in the model. One could include fences in the model which may affect the wild dog’s ability to travel in and out of the game reserves. This will affect the percentage of pack formations along with the spatial location of where packs are formed. We also made the assumption that each game reserve pack contained both one male and one female disperser group. This is not always the case and one could model the population with different original numbers of female and male disperser groups. Moreover, we made both disperser groups leave at the same time (day one). It would be interesting to see how dispersal dynamics change when disperser groups leave their natal packs at different times. Moreover, one could even model the effects of seasons in the time scale. During different months of the year there is variation in wild dog dispersal rates and in the amount of water available. As the model was the most sensitive to the parameter ‘chance-of-water’ (Table 9), to give an even more accurate presentation of wild dog dispersal one could more accurately model the seasonal availability of water. Finally, we only reintroduced a group of wild dogs one at a time. Higher dispersal success occurred when wild dogs were in proximity to one another. It would be interesting to see the effects of reintroducing more than one group of wild dogs at once. The African wild dogs are in danger of becoming extinct and natural dispersal is oc- curring and can be helpful in creating more viable populations of wild dogs. The model presented in this thesis provides the ground work for future understanding of the dispersal dynamics of the KZN wild dog population and may ultimately benefit the understanding and management of wild dog populations throughout all of Africa. Literature Cited

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WWF. 2010. World Wildlife Fund. http://assets.panda.org/img/original/kwazulu map 1.jpg. APPENDIX A

The scale and shape parameter values used to create the 10 gamma pdfs that determined the distance a wild dog traveled in one day is shown below. In addition, the following codes written in R were used to obtain the values of α (the shape parameter) and β (the scale parameter) belonging to each gamma probability density function (pdf) used in the model. These gamma pdfs were used to model the distance wild dogs dispersed at each time step.

Fitness Level Shape (α) Scale (β) (0,10] 9.99 3.00 (10,20] 6.85 4.38 (20,30] 5.43 5.52 (30,40] 4.51 6.65 (40,50] 3.84 7.81 (50,60] 3.31 9.06 (60,70] 2.88 10.43 (70,80] 2.51 11.96 (80,90] 2.19 13.71 (90,100] 1.91 15.73

R code used to obtain α and β for the ﬁtness interval (0, 10] f=function(x) pgamma(60,shape=x,scale=30/x)-0.995 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(8,10)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y)

R code used to obtain α and β for the ﬁtness interval (10, 20] f=function(x) pgamma(60,shape=x,scale=30/x)-0.985 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(6,8))

79 80 a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y) R code used to obtain α and β for the fitness interval (20, 30] f=function(x) pgamma(60,shape=x,scale=30/x)-0.975 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(4,6)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y) R code used to obtain α and β for the fitness interval (30, 40] f=function(x) pgamma(60,shape=x,scale=30/x)-0.965 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(4,6)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y) R code used to obtain α and β for the fitness interval (40, 50] f=function(x) pgamma(60,shape=x,scale=30/x)-0.955 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(2,4)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y) 81

R code used to obtain α and β for the ﬁtness interval (50, 60] f=function(x) pgamma(60,shape=x,scale=30/x)-0.945 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(2,4)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y)

R code used to obtain α and β for the ﬁtness interval (60, 70] f=function(x) pgamma(60,shape=x,scale=30/x)-0.935 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(1,3)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y)

R code used to obtain α and β for the ﬁtness interval (70, 80] f=function(x) pgamma(60,shape=x,scale=30/x)-0.925 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(1,3)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y)

R code used to obtain α and β for the ﬁtness interval (80, 90] f=function(x) pgamma(60,shape=x,scale=30/x)-0.915 x=seq(0,10,length=1000) 82 y=f(x) plot(x,y,type="l") ans=uniroot(f,c(1,3)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y)

R code used to obtain α and β for the ﬁtness interval (90, 100] f=function(x) pgamma(60,shape=x,scale=30/x)-0.905 x=seq(0,10,length=1000) y=f(x) plot(x,y,type="l") ans=uniroot(f,c(1,3)) a=ans$root s=30/a x=seq(0,100,length=1000) y=dgamma(x,shape=a,scale=s) plot(x,y) APPENDIX B

Twenty one parameter values were used in the model (Table 6). To analyze the effect each parameter had on dispersal success, a sensitivity analysis was performed. The sensitivities of each parameter were the magnitudes of the slopes of the regression lines shown below.

60 60 y = 44.81x + 4.14 r = 0.977

40 40 y = −1.39x + 48.01 r = −0.953

20 20

0 0 Percentage of Pack Formations 0 0.5 1 1.5 Percentage of Pack Formations 0 1 2 3 Scaled chance−of−water Parameter Value Scaled other−death−out−park Parameter Value

60 60

40 y = −2.08x + 52.67 40 r = −0.999 y = 1.75x + 39.81 r = 0.999 20 20

0 0 Percentage of Pack Formations 0 1 2 3 4 5 Percentage of Pack Formations 0 2 4 6 Scaled snare−death Parameter Value Scaled join−game−reserve−pack Parameter Value

83 84

60 60

y = 2.10x + 47.75 y = −0.87x + 50.61 40 y = 1.51x + 47.47 40 r = 0.933 r = −1.00 r = 0.999

20 20

Avg. Magnitude of Slopes = 1.49 0 0 Percentage of Pack Formations 0 0.5 1 1.5 Percentage of Pack Formations −0.5 0 0.5 1 1.5 2 2.5 Scaled game−reserve−pack−radius Parameter Value Scaled close−enough−to−village? Parameter Value

60 60

40 y = −1.41x + 49.81 40 y = −2.16x + 48.97 r = −0.793 r = −0.981

20 20

0 0 Percentage of Pack Formations 0 0.2 0.4 0.6 0.8 1 Percentage of Pack Formations 0 0.5 1 1.5 2 Scaled chance−of−disease Parameter Value Scaled other−death−in−park Parameter Value

60 60

40 40 y = 1.19x + 48.54 y = −1.21x + 52.88 r = 0.999 r = −0.997 20 20

0 0 Percentage of Pack Formations 0 2 4 6 Percentage of Pack Formations 0 0.2 0.4 0.6 0.8 1 Scaled road−mortality Parameter Value Scaled dispersergroup−fight Parameter Value 85

60 60

40 y = 1.12x + 47.77 40 y = 0.99x + 47.88 r = 0.916 r = 0.984

20 20

0 0 Percentage of Pack Formations 0 0.5 1 1.5 2 Percentage of Pack Formations 0 0.5 1 1.5 2 Scaled dispersergroup−radius Parameter Value Scaled village−radius Parameter Value

60 60

40 y = 0.79x + 48.52 y = −0.92x + 50.40 40 y = 0.64x + 48.30 r = 0.57 r = −1.00 r = 0.975

20 20

Avg. Magnitude of Slopes = 0.86 0 0 Percentage of Pack Formations −2 0 2 4 Percentage of Pack Formations 0 0.5 1 1.5 2 2.5 Scaled close−enough? Parameter Value Scaled fitness−from−water Parameter Value

60 60

40 40 y = −0.55x + 49.87 y = −0.59x + 49.43 r = −0.917 r = −0.974 20 20

0 0 Percentage of Pack Formations 0 2 4 6 Percentage of Pack Formations 0 0.5 1 1.5 2 Scaled daily−fitness−loss Parameter Value Scaled river−radius Parameter Value 86

60 60

40 y = −0.48x + 49.86 40 y = 0.40x + 49.13 y = −0.52x + 49.72 r = −0.856 r = 1.00 r = −0.60

20 20

Avg. Magnitude of Slopes = 0.46 0 0 Percentage of Pack Formations 0 0.5 1 1.5 Percentage of Pack Formations −2 0 2 4 Scaled fitness−from−impala Parameter Value Scaled movement−loss−percent Parameter Value

60 60

40 y = −0.42x + 49.52 40 y = −0.08x + 49.15 r = −0.695 r = −0.676

20 20

0 0 Percentage of Pack Formations 0 0.5 1 1.5 2 Percentage of Pack Formations 0 0.5 1 1.5 2 Scaled fight−with−dispersergroup Parameter Value Scaled road−radius Parameter Value APPENDIX C

NetLogo code used to model the dispersal movement of the wild dog population in KZN, South Africa. extensions [ gis ] globals [ cities-dataset rivers-dataset all_roads_clip-dataset boundary-dataset parks-dataset

ijklmnopqrst ] breed [ cities-labels city-label ] breed [ river-labels river-label ] breed [ parks-labels parks-label ] breed [ boundary-labels boundary-label ] breed [ all_roads_clip-labels all_roads_clip-label ] breed [ packs pack ] breed [ dispersergroups dispersergroup ] breed [ game-reserve-packs game-reserve-pack ] turtles-own [ fitness distancetraveled ] packs-own [ my-pack my-pack-name my-home-pack-number my-home-pack-name food day-on-road water ] dispersergroups-own [ food day-on-road water my-pack my-home-pack-name my-home-pack-number my-list ] game-reserve-packs-own [ my-pack my-home-pack-number my-home-pack-name my-list ] patches-own [ has-a-park has-a-city has-a-river has-a-road has-a-boundary parklabel ]

; PART 1 ; ******************************************************************************************************************* ; ******************************************************************************************************************* ; The following code sets everything up. The game reserve packs, disperser groups, impalas, "parks", "cities",

87 88

; "rivers", and "roads" are all created. The game reserve names and the fitness of the wild dogs are displayed.

; ------to setup------to setup clear-all

gis:load-coordinate-system (word "wild_dogs_7_17_09/data_3/" projection ".prj")

set cities-dataset gis:load-dataset "wild_dogs_7_17_09/data_3/cities.shp" set parks-dataset gis:load-dataset "wild_dogs_7_17_09/data_3/kznw_pa_2008_cut.shp" set rivers-dataset gis:load-dataset "wild_dogs_7_17_09/data_3/rivers.shp" set all_roads_clip-dataset gis:load-dataset "wild_dogs_7_17_09/data_3/nat_pri_roads_new.shp" set boundary-dataset gis:load-dataset "wild_dogs_7_17_09/data_3/boundary.shp"

gis:set-world-envelope (gis:envelope-union-of (gis:envelope-of cities-dataset) (gis:envelope-of parks-dataset) (gis:envelope-of rivers-dataset) (gis:envelope-of all_roads_clip-dataset) (gis:envelope-of boundary-dataset) )

display-cities display-parks display-roads display-rivers display-boundaries

make-game-reserve-packs make-packs if label-parks [ foreach gis:feature-list-of parks-dataset [ let centroid gis:location-of gis:centroid-of ? ; centroid will be an empty list if it lies outside the bounds ; of the current NetLogo world, as defined by our current GIS ; coordinate transformation if not empty? centroid [ create-parks-labels 1 [ set xcor item 0 centroid set ycor item 1 centroid set size 0 set label gis:property-value ? "PROC_NAME" ] ] ] ] end to display-cities ask cities-labels [ die ] gis:set-drawing-color red gis:draw cities-dataset 2

foreach gis:feature-list-of cities-dataset [ ask patches with [ gis:intersects? self ? ] [ set has-a-city true ] ] end to display-parks ask parks-labels [ die ] gis:set-drawing-color green gis:draw parks-dataset 1 gis:fill parks-dataset 1

foreach gis:feature-list-of parks-dataset [ ask patches with [ gis:intersects? self ? ] [ set has-a-park true set parklabel gis:property-value ? "PROC_NAME" ] ] end to display-rivers ask river-labels [ die ] gis:set-drawing-color blue gis:draw rivers-dataset 1 89

foreach gis:feature-list-of rivers-dataset [ ask patches with [ gis:intersects? self ? ] [ set has-a-river true ] ] end to display-roads ask all_roads_clip-labels [ die ] gis:set-drawing-color brown gis:draw all_roads_clip-dataset 1

foreach gis:feature-list-of all_roads_clip-dataset [ ask patches with [ gis:intersects? self ? ] [ set has-a-road true ] ] end to display-boundaries ask boundary-labels [ die ] gis:set-drawing-color yellow gis:draw boundary-dataset 1

foreach gis:feature-list-of boundary-dataset [ ask patches with [ gis:intersects? self ? ] [ set has-a-boundary true ] ]

ask patches with [ pxcor >= -47 and pxcor <= 0 and pycor = -46 ] [ set has-a-boundary true ]

ask patches with [ pxcor = -47 and pycor >= -45 and pycor <= 20 ] [ set has-a-boundary true ]

ask patches with [ pxcor = 0 and pycor = -45 ] [ set has-a-boundary true ] end

; ------game-reserve-packs------to make-game-reserve-packs set-default-shape dispersergroups "wolf 2"

set-default-shape game-reserve-packs "wolf 2"

; ------game-reserve-packs in HiP------; ------

set i initial-number-game-reserve-packs-HiP

while [ i > 0 ] [ let z i create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Hluhluwe Game Reserve" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 2.5 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-HiP [ 90

set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-HiP [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set i (i - 1) ] ]

; ------game-reserve-packs in uMkhuze------; ------

set j initial-number-game-reserve-packs-uMkhuze

while [ j > 0 ] [ let z j create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "uMkhuze" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-uMkhuze [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-uMkhuze [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set j (j - 1) ] ]

; ------game-reserve-packs in Ithala------; ------

set k initial-number-game-reserve-packs-Ithala

while [ k > 0 ] [ let z k create-game-reserve-packs 1 91

[ set size 2 set color yellow move-to one-of patches with [ parklabel = "Ithala Game Reserve" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Ithala [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Ithala [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set k (k - 1) ] ]

; ------game-reserve-packs in Thanda------; ------

set l initial-number-game-reserve-packs-Thanda

while [ l > 0 ] [ let z l create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Thanda" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Thanda [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Thanda [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set l (l - 1) ] 92

]

; ------game-reserve-packs in Tembe------; ------

set m initial-number-game-reserve-packs-Tembe

while [ m > 0 ] [ let z m create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Tembe Elephant Park" and has-a-boundary != true and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Tembe [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Tembe [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set m (m - 1) ] ]

; ------Stay-home-packs in Phongola------; ------

set n initial-number-game-reserve-packs-Phongola

while [ n > 0 ] [ let z n create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Phongola Nature Reserve" and has-a-boundary != true and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Phongola [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] 93

hatch-dispersergroups initial-number-male-dispersergroups-Phongola [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set n (n - 1) ] ]

; ------game-reserve-packs in Ndumo------; ------

set o initial-number-game-reserve-packs-Ndumo

while [ o > 0 ] [ let z o create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Ndumo Game Reserve" and has-a-boundary != true and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 2 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Ndumo [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Ndumo [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set o (o - 1) ] ]

; ------game-reserve-packs in St Lucia------; ------

set p initial-number-game-reserve-packs-StLucia

while [ p > 0 ] [ let z p create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Greater St Lucia Wetland Park" and has-a-boundary != true and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel 94

set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-StLucia [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-StLucia [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set p (p - 1) ] ]

; ------game-reserve-packs in Zululand------; ------

set q initial-number-game-reserve-packs-Zululand

while [ q > 0 ] [ let z q create-stay-home-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Zululand Rhino Reserve" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Zululand [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Zululand [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set q (q - 1) ] ]

; ------game-reserve-packs in Phinda------95

; ------

set r initial-number-game-reserve-packs-Phinda

while [ r > 0 ] [ let z r create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Phinda" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Phinda [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Phinda [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set r (r - 1) ] ]

; ------game-reserve-packs in Coastal------; ------

set s initial-number-game-reserve-packs-Coastal

while [ s > 0 ] [ let z s create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Coastal" and has-a-boundary != true and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-Coastal [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-Coastal [ set size 2 96

set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set s (s - 1) ] ]

; ------game-reserve-packs in Mkuze Falls------; ------

set t initial-number-game-reserve-packs-MkuzeFalls

while [ t > 0 ] [ let z t create-game-reserve-packs 1 [ set size 2 set color yellow move-to one-of patches with [ parklabel = "Mkuze Falls" and ( not any? game-reserve-packs-here ) and ( not any? game-reserve-packs in-radius 3 ) ] set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set fitness max-fitness

hatch-dispersergroups initial-number-female-dispersergroups-MkuzeFalls [ set size 2 set color pink set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ]

hatch-dispersergroups initial-number-male-dispersergroups-MkuzeFalls [ set size 2 set color blue set fitness ( 100 - random 50 ) set my-pack nobody set my-home-pack-name parklabel set my-home-pack-number z set my-list list parklabel z set distancetraveled 0 ] set t (t - 1) ] ] show-fitness end

; ------make packs------to make-packs set-default-shape packs "wolf 2"

show-fitness end

; ------show fitness------to show-fitness ifelse show-fitness? [ ask turtles [ set label fitness ] ] 97

[ ask turtles [ set label "" ] ] end

;; PART 2 ;; ******************************************************************************************************** ;; ******************************************************************************************************** to go tick

; Program will stop if ticks > simulation-time [ stop ]

; Every day a wild dog loses 1 fitness level point if ticks mod 1 = 0 [ ask dispersergroups [ set fitness fitness - 1 ]

ask packs [ set fitness fitness - 1 ] ]

; Processes disperser groups and packs do each time step. Disperser groups first, then packs.

; Disperser Groups Processes

; 1. - move ask dispersergroups [ move ]

; 2. - look for dispersergroups ask dispersergroups [ check-for-dispersergroups-to-join-pack ]

; 3. - look for game-reserve-packs ask dispersergroups [ check-for-game-reserve-packs ]

; 4. - get water ask dispersergroups [ get-water ]

; 5. - get food ask dispersergroups [ get-food ]

; 6. - check death ask dispersergroups [ check-death ]

; Packs Processes

; 1. - move ask packs [ move-packs ]

; 2. - get water ask packs [ get-pack-water ]

; 3. - get food ask packs [ get-pack-food ]

; 4. - check death ask packs [ check-death ] show-fitness end

;;*****************************DISPERSER GROUP STUFF****************************************

;------to move------to move 98

; Disperser groups movement is based on their current fitness level

; (0,10] interval - 0.5\% chance of 60 km or more ifelse fitness > 0 and fitness <= 10 [ let stepsize1 random-gamma 9.99735 0.333245 let stepdist1 round stepsize1 let step1 round ( stepsize1 / step-size )

repeat step1 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist1 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize1 ) ]

[ ; (10,20] interval - 1.5\% chance of 60 km or more ifelse fitness > 10 and fitness <= 20 [ let stepsize2 random-gamma 6.851243 0.2283748 let stepdist2 round stepsize2 let step2 round ( stepsize2 / step-size )

repeat step2 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist2 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize2 ) ]

[ ; (20,30] interval - 2.5\% chance of 60 km or more ifelse fitness > 20 and fitness <= 30 [ let stepsize3 random-gamma 5.430152 0.1810051 let stepdist3 round stepsize3 let step3 round ( stepsize3 / step-size )

repeat step3 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist3 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize3 ) ]

[ ; (30,40] interval - 3.5\% chance of 60 km or more ifelse fitness > 30 and fitness <= 40 [ let stepsize4 random-gamma 4.513349 0.150445 let stepdist4 round stepsize4 let step4 round ( stepsize4 / step-size )

repeat step4 99

[ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist4 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize4 ) ]

[ ; (40,50] interval - 4.5\% chance of 60 km or more ifelse fitness > 40 and fitness <= 50 [ let stepsize5 random-gamma 3.840341 0.1280114 let stepdist5 round stepsize5 let step5 round ( stepsize5 / step-size )

repeat step5 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist5 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize5 ) ]

[ ; (50,60] interval - 5.5\% chance of 60 km or more ifelse fitness > 50 and fitness <= 60 [ let stepsize6 random-gamma 3.311061 0.1103687 let stepdist6 round stepsize6 let step6 round ( stepsize6 / step-size )

repeat step6 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist6 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize6 ) ]

[ ; (60,70] interval - 6.5\% chance of 60 km or more ifelse fitness > 60 and fitness <= 70 [ let stepsize7 random-gamma 2.876247 0.0958749 let stepdist7 round stepsize7 let step7 round ( stepsize7 / step-size )

repeat step7 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] 100

set distancetraveled distancetraveled + stepdist7 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize7 ) ]

[ ; (70,80] interval - 7.5\% chance of 60 km or more ifelse fitness > 70 and fitness <= 80 [ let stepsize8 random-gamma 2.508021 0.0836007 let stepdist8 round stepsize8 let step8 round ( stepsize8 / step-size )

repeat step8 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist8 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize8 ) ]

[ ; (80,90] interval - 8.5\% chance of 60 km or more ifelse fitness > 80 and fitness <= 90 [ let stepsize9 random-gamma 2.188929 0.0729643 let stepdist9 round stepsize9 let step9 round ( stepsize9 / step-size )

repeat step9 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist9 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize9 ) ]

[

; (90,100] interval - 9.5\% chance of 60 km or more if fitness > 90 and fitness <= 100 [ let stepsize10 random-gamma 1.907243 0.0635748 let stepdist10 round stepsize10 let step10 round ( stepsize10 / step-size )

repeat step10 [ look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist10 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize10 ) ] ] ] ] ] ] ] ] 101

] ] end

; ------look-ahead------to look-ahead ifelse any? dispersergroups-on patches in-radius dispersergroup-radius [ face min-one-of patches in-radius dispersergroup-radius with [ self != [patch-here] of myself][distance myself] ] [ ifelse any? game-reserve-packs-on patches in-radius game-reserve-pack-radius [ face min-one-of patches in-radius game-reserve-pack-radius with [ self != [patch-here] of myself][distance myself] ] [ ifelse any? patches in-radius river-radius with [ has-a-river = true and self != [patch-here] of myself ] [ face min-one-of patches in-radius river-radius with [ has-a-river = true and self != [patch-here] of myself][distance myself] ] [ ifelse any? patches in-radius road-radius with [ has-a-road = true and self != [patch-here] of myself ] [ face min-one-of patches in-radius road-radius with [ has-a-road = true and self != [patch-here] of myself][distance myself] ] [ ifelse any? patches in-radius village-radius with [has-a-city = true and self != [patch-here] of myself] [ face min-one-of patches in-radius village-radius with [ has-a-city = true and self != [patch-here] of myself][distance myself] rt 180 ] [ facexy random-xcor random-ycor ] ] ] ] ] end

;------Check for game reserve packs------to check-for-game-reserve-packs let singles dispersergroups with [ my-pack = nobody ] ask singles [ if (random-float 100 < join-game-reserve-pack) and (any? other game-reserve-packs in-radius close-enough? with [ my-list != [my-list] of myself ] ) [ set color violet let two [fitness] of self ; fitness energy of single dispersergroup set my-pack one-of other game-reserve-packs in-radius close-enough? with [my-list != [my-list] of myself] ask my-pack [ let one [fitness] of self ; fitness energy of game-reserve-pack

set my-pack [my-home-pack-name] of self set my-home-pack-number [my-home-pack-number] of self

set color violet hatch-stay-home-packs 1 [ set fitness max-fitness ] ]

ask my-pack [ die ] die 102

] ] end

; ------check for dispersergroups------to check-for-dispersergroups-to-join-pack let singles dispersergroups with [my-pack = nobody] ask singles [ if (random 100 < join-pack) and (any? other singles with [color != [color] of myself] in-radius close-enough? with [my-list != [my-list] of myself] ) [ set color red

let two [fitness] of self ; fitness energy of single dispersergroup set my-pack one-of other singles in-radius close-enough? with [my-list != [my-list] of myself and color != [color] of myself]

ask my-pack [ let one [fitness] of self ;fitness energy of partner

set my-pack [my-home-pack-name] of self set color red

hatch-packs 1 [ set distancetraveled 0

ifelse ( 0.75 * (two + one) ) < max-fitness [ set fitness ( 0.75 * (two + one) ) ]

[ set fitness max-fitness ] ] ] ask my-pack [ die ] die ] ] ask singles [ if (random 100 < dispersergroup-fight) and (any? other singles with [color = [color] of myself] in-radius close-enough? with [my-list != [my-list] of myself]) [ ;user-message "Fight!" ;set color white

set fitness ( fitness - fight-with-dispersergroup ) ]

] end

; ------FOOD------to get-food ; Wild dogs hunt twice a day - success rate is between 43 - 70% ; Need on average 3.5 kg/day ; Assuming if a dog gets a kill, all members get enough food to eat ; Broken down into 10 intervals like the movement ; 67.51 - 91\% chance of getting food at least once a day ; Every days, dogs either get food = 0, or no food = food + 1

ifelse fitness > 0 and fitness <= 10 [ ifelse random-float 100 < 67.5 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ 103

set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 10 and fitness <= 20 [ ifelse random-float 100 < 70.1 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 20 and fitness <= 30 [ ifelse random-float 100 < 72.7 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 30 and fitness <= 40 [ ifelse random-float 100 < 75.3 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 40 and fitness <= 50 [ 104

ifelse random-float 100 < 77.9 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 50 and fitness <= 60 [ ifelse random-float 100 < 80.5 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 60 and fitness <= 70 [ ifelse random-float 100 < 83.1 [ set food 0 ifelse (( fitness + fitness-from-impala ) < max-fitness) [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 70 and fitness <= 80 [ ifelse random-float 100 < 85.7 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] 105

]

[ ifelse fitness > 80 and fitness <= 90 [ ifelse random-float 100 < 88.3 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ if fitness > 90 and fitness <= 100 [ ifelse random-float 100 < 91 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ] ] ] ] ] ] ] ] ] ] end

; ------WATER------

; Wild dogs can get water two different ways - direct contact with a river or they have ; a certain chance of drinking from a different source. to get-water if ticks mod 1 = 0 [ ifelse has-a-river = true [ set water 0 ;user-message "ON WATER" ifelse ( fitness + fitness-from-water ) < max-fitness [ set fitness ( fitness + fitness-from-water ) ]

[ set fitness max-fitness ] ]

[ ifelse random 100 < chance-of-water [ set water 0 106

;user-message "GOT WATER" ifelse ( fitness + fitness-from-water ) < max-fitness [ set fitness ( fitness + fitness-from-water ) ]

[ set fitness max-fitness ] ]

[ set water water + 1 ;user-message "NO WATER" ] ] ] end

;;*****************************PACK STUFF****************************************************

;; ------move packs------to move-packs

ifelse has-a-park = true [ stop ]

; movement - same as for disperser groups [ ; (0,10] interval - 0.5\% chance of 60 km or more ifelse fitness > 0 and fitness <= 10 [ let stepsize1 random-gamma 9.99735 0.333245 let stepdist1 round stepsize1 let step1 round ( stepsize1 / step-size )

repeat step1 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist1 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize1 ) ]

repeat step2 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist2 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize2 ) ]

[ ; (20,30] interval - 2.5\% chance of 60 km or more 107

ifelse fitness > 20 and fitness <= 30 [ let stepsize3 random-gamma 5.430152 0.1810051 let stepdist3 round stepsize3 let step3 round ( stepsize3 / step-size )

repeat step3 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist3 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize3 ) ]

repeat step4 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist4 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize4 ) ]

repeat step5 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist5 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize5 ) ]

repeat step6 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ 108

rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist6 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize6 ) ]

repeat step7 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist7 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize7 ) ]

repeat step8 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist8 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize8 ) ]

repeat step9 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist9 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize9 ) ] 109

[ ; (90,100] interval - 9.5\% chance of 60 km or more if fitness > 90 [ let stepsize10 random-gamma 1.907243 0.0635748 let stepdist10 round stepsize10 let step10 round ( stepsize10 / step-size )

repeat step10 [ pack-look-ahead ifelse [has-a-boundary] of patch-ahead 1 = true [ rt 180 fd 1 ] [ fd 1 ] ] set distancetraveled distancetraveled + stepdist10 set fitness fitness - round ( ( (movement-loss-percent) / 100 ) * stepsize10 ) ] ] ] ] ] ] ] ] ] ] ] end

; ------pack-look-ahead------to pack-look-ahead

ifelse any? patches in-radius river-radius with [ has-a-river = true and self != [patch-here] of myself ] [ face min-one-of patches in-radius river-radius with [ has-a-river = true and self != [patch-here] of myself][distance myself] ] [ ifelse any? patches in-radius road-radius with [has-a-road = true and self != [patch-here] of myself] [ face min-one-of patches in-radius road-radius with [ has-a-road = true and self != [patch-here] of myself][distance myself] ] [ ifelse any? patches in-radius village-radius with [has-a-city = true and self != [patch-here] of myself] [ face min-one-of patches in-radius village-radius with [ has-a-city = true and self != [patch-here] of myself][distance myself] rt 180 ] [ facexy random-xcor random-ycor ] ] ] end

; ------FOOD------to get-pack-food ; same as disperser group getting food

ifelse fitness > 0 and fitness <= 10 [ ifelse random-float 100 < 67.5 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] 110

]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 10 and fitness <= 20 [ ifelse random-float 100 < 70.1 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 20 and fitness <= 30 [ ifelse random-float 100 < 72.7 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 30 and fitness <= 40 [ ifelse random-float 100 < 75.3 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 40 and fitness <= 50 [ ifelse random-float 100 < 77.9 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) 111

]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 50 and fitness <= 60 [ ifelse random-float 100 < 80.5 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 60 and fitness <= 70 [ ifelse random-float 100 < 83.1 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 70 and fitness <= 80 [ ifelse random-float 100 < 85.7 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ ifelse fitness > 80 and fitness <= 90 [ ifelse random-float 100 < 88.3 112

[ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ]

[ if fitness > 90 [ ifelse random-float 100 < 91 [ set food 0 ifelse ( fitness + fitness-from-impala ) < max-fitness [ set fitness ( fitness + fitness-from-impala ) ]

[ set fitness max-fitness ] ]

[ set food food + 1 ;user-message "NO FOOD" ] ] ] ] ] ] ] ] ] ] ] end

; ------WATER------to get-pack-water if ticks mod 1 = 0 [ ifelse has-a-river = true [ set water 0 ;user-message "ON WATER" ifelse ( fitness + fitness-from-water ) < max-fitness [ set fitness ( fitness + fitness-from-water ) ]

[ set fitness max-fitness ] ]

[ ifelse random 100 < chance-of-water [ set water 0 ;user-message "GOT WATER" ifelse ( fitness + fitness-from-water ) < max-fitness [ set fitness ( fitness + fitness-from-water ) ]

[ set fitness max-fitness ] 113

]

[ set water water + 1 ;user-message "NO WATER" ] ] ] end

; ***************************CHECKING DEATH - Dispersergroups and packs**********************************

; ------DEATH------to check-death

; fitness LEVEL ; if fitness <= 0, the dogs will die

if fitness <= 1 [ die ]

; snare death

if has-a-park != true [ if random-float 100 < snare-death [ die ] ]

; FOOD LEVEL ; After 12 days without food, the dogs will die

if food = 12 [ die ]

; WATER LEVEL ; After 3 days without water, the dogs will die

if water = 3 [ die ]

; CONTACT VILLAGE ; If the dogs come in contact with a village they have a chance of dying

if any? patches in-radius close-enough-to-village? with [ has-a-city = true ] and random 100 < chance-of-village-death [ die ]

; ROAD DEATH ; If the dogs are on a road, they have a chance of dying

ifelse has-a-road = true [ set day-on-road day-on-road + 1 if random-float 100 < road-mortality [ die ] ;user-message "On-Road" ] [ set day-on-road 0 ]

; OTHER DEATHS

ifelse has-a-park = true 114

[ if random-float 100 < other-death-in-park [ die ] ]

[ if random-float 100 < other-death-out-park [ die ] ] end