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Developing an artificial ecology for use as a strategic management tool: A case study of ibex hunting in the North Tien Shan

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Abstract

We develop an artificial ecology that simulates the interaction between hunter decisions and prey behaviour, using ibex hunting in the North Tien Shan Mountains as a case study. The aim is to model hunter and prey behaviour at a low enough level that overall population dynamics and hunter costs are emergent properties of the system rather than being assumed, as is usually the case. A genetic algorithm linked to artificial neural networks is used to evolve hunter decisions about where to hunt. We demonstrate the importance of the number of people hunting, which is determined by the profitability of hunting, as a key driver of system dynamics. A fundamental difference emerges between outcomes on approach to equilibrium, and after stochastic equilibrium had been reached, with extinction being common on approach and virtually non-existent thereafter. This probably reflects naive ibex behaviour on commencement of hunting. The framework developed here is flexible and transferable, and is particularly useful for the strategic testing of management strategies.

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... Agent-based models have been applied to the related problem of sustainable hunting in both recreational and subsistence contexts. Ling & Milner-Gulland [69] investigated an Asiatic ibex (Capra sibirica) hunting system by coupling models of ibex ecology and the behaviour of human hunters, and found a complex set of dynamics in which the likelihood of sustainable equilibrium depended both on ibex behaviour (specifically the selection of relatively inaccessible locations) and the costs experienced by hunters. In a model of human settlement expansion in Amazonian Guyana, Iwamura et al. [70] simulated interactions between social and ecological systems driven by human nutritional requirements and resource availability in the environment. ...
... At the system level, prey population dynamics, the response of patrols to changes in hunter behaviour, and setting the scenario in a spatially explicit context, would all be important steps towards realism. Patrol responses would require a second set of agents in the ABM, as per Ling & Milner-Gulland [69,77], while prey dynamics could also be modelled as part of a spatially explicit ABM (cf. [50]). ...
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We examine factors regulating numbers of domestic livestock and saiga antelopes during the major periods of Kazakhstan's history. In the pre-Soviet period livestock migrations were relatively unrestricted and covered huge distances. Little winter feed or veterinary care was provided for domestic livestock and numbers were regulated largely by winter snow or ice cover. Drought affected fecundity but did not cause large-scale mortality. During the Soviet period the provision of winter feed shielded domestic livestock from winter mortality while hunting controls allowed saiga numbers to recover from overhunting. Livestock and saiga numbers during this period were high and there is evidence that productivity was affected. However, there were no crashes in livestock numbers linked to high densities, probably because rainfall variability is relatively low and catastrophic droughts are rare. Today livestock numbers in Kazakhstan have crashed because of the withdrawal of state support and the use of animals as currency. The collapse of the state also meant the end of hunting controls and increased poverty, which has lead to widespread saiga poaching and dramatic population declines.
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Longitudinal studies of survival are valuable because age-specific survival affects population dynamics and the evolution of several life history traits. We used capture-mark-recapture models to assess the relationship between survival and sex, age, population, year of study, disease, winter weather, and population density in two populations of bighorn sheep (Ovis canadensis) in Alberta, Canada. The Ram Mountain population, monitored for 20 yr, more than doubled in density; the Sheep River population, monitored for 13 yr, experienced a pneumonia epizootic. Yearling survival varied among years and was lower than that of older sheep of the same sex, except for yearling males at Ram Mountain. Yearling females at Ram Mountain were the only sex-age class exhibiting density dependence in survival. Senescence was evident for both sexes in both populations. Female survival from age 2 to age 7 was very high in both populations, but males aged 2 and 3 yr enjoyed better survival than males aged 4-6 yr. Our data support the suggestion that where hunters remove many males older than 5 yr of age, the natural mortality of males increases at 3-5 yr, possibly because young males suffer a mortality cost of participating in rutting activity. The decline in survival for sheep older than 7 yr was greater for males than for females. Survival was lower for males than for females, both among prime-aged sheep (0.896 vs. 0.939 at Sheep River; 0.837 vs. 0.945 at Ram Mountain) and among older sheep (0.777 vs. 0.859 at Sheep River; 0.624 vs. 0.850 at Ram Mountain), but not among yearlings. Survival of sheep aged 2-7 yr was not significantly different between the two populations. Winter weather did not affect survival. Survival of sheep 2 yr of age and older did not vary significantly between years, except at Sheep River where survival of prime-aged sheep of both sexes was lower in the year of the pneumonia epizootic. Studies of survival of mountain sheep based upon skull collections may have overestimated survival of young rams. Our results underline the need for accurate information on age-specific survival.
Article
The adult survival of three Alpine ibex (Capra ibex ibex) populations, in the Vanoise National Park, was studied by capture-mark-recapture. These populations differ by geographical location and history. The Maurienne population is the less recent one and the only one constituted from native individuals. The Prariond-Sassiere population has been constituted from the natural colonization of animals coming from the Gran Paradiso National Park (Italy). The Champagny-Peisey population has been created by the re-establishment of a few individuals. Many caught and tagged sessions have resulted in the identification of 96 males and 36 females, which have been then observed for a few months to 10 years, according to the individuals. Several survival models have been tested according to time-, age- or sex-dependence (this last criterion has been only studied in the Maurienne). The recapture probability has also been estimated. The selection of the model with the best fit to the data has been made on the basis of the Akaike Information Criterion. In the Maurienne, females had constant and high survival rate (S = 0.94; standard-error = 0.024) and a recapture probability varying according to years. Males had a survival rate decreasing according to age while recapture probability remained constant (P = 0.96; standard-error = 0.015). In the Champagny-Peisey population, males had a survival rate varying according to age and a recapture probability free of time-effect (P = 0.86; standard-error = 0.038). In the Prariond-Sassiere population, the survival rate also varied according to male age. The recapture probability remained constant all over the years (P = 0.86; standard-error = 0.039). Ibex is a highly dimorphic species which shows a strong sexual segregation. Its survival appears to depend on the connexion of several factors, linked to sex and animals age but also to extrinsic parameters (climatology, epidemiology,...).
Article
A wide variety of modelling approaches have been developed over the past few decades to provide quantitative advice to fishery managers about the potential consequences of proposed alternative management actions and to improve the design of fishery- management systems. This article surveys these approaches to identify the main differences among them in their application of decision theory, particularly in the methods used to account for uncertainty, and to identify model structures that need to be considered. Six interlinked model structures are identified: population dynamics, data collection, data analysis and stock assessment, setting harvest controls, the harvest decision process, and imperfect implementation. Their inclusion and design will depend on the institutional arrangements for fishery management. For example, some evaluations have included the last two structures to account for the flexibility of fishery managers in their making of annual harvest decisions and limitations on their ability to implement management policy precisely. Other evaluations have excluded them because they have evaluated “management procedures” whereby all participants would be bound to strictly follow a preset protocol for data collection, data analysis, and a harvest decision rule. In addition, this article identifies some trade-offs that are often made when modelling methods are formulated that can strongly affect model results and the advice given. Partly as a result of these trade-offs, analysts have recently been combining some of the originally divergent aspects of different modelling approaches. Examples of this include combining the use of Bayesian statistical methods with the use of alternative operating models (rather than only one) to account for both parameter and model uncertainty.
Article
We correlated two group size measures and the proportion of isolated males during spring, with total size of a french Alpine ibex (Capra ibex ibex) population. Mean group size (TM), typical group size (TGT) and the proportion of isolated individuals were highly correlated with the Belledonne-7 Laux population size (with respectively 83 %, 74 % and 86 % of the variability of these measures explained by population size variations). The link between TM or TGT and population size was logarithmic. This shows a threshold beyond which group size incresased only slightly. Proportion of isolated individuals decreased exponentially with population size. When using group size as a biological indicator, one has to be aware of not inducing confounding factors : in the case of species with sexual segregation outside the rutting period, we have to use observations made on one sex only. In this study, contrary to population size, ecological constraints such as food availability, social group composition and habitat structure seemed to have only little influence on group size.
Article
Ecosystem objectives in fisheries management usually flow from high-level national policies or strategies and international agreements. Consequently they are often broadly stated and hence are difficult to incorporate directly in management plans. Predicting the results of any management action is very uncertain because the dynamics of ecosystems are complex and poorly understood. Methods to design and evaluate operational management strategies have advanced considerably in the past decade. These management-strategy-evaluation (MSE) methods rely on simulation testing of the whole management process using performance measures derived from operational objectives. The MSE approach involves selecting (operational) management objectives, specifying performance measures, specifying alternative management strategies, and evaluating these using simulation. The MSE framework emphasizes the identification and modelling of uncertainties, and propagates these through to their effects on the performance measures. The framework is outlined and illustrated by three ecosystem-related applications: management of benthic habitats and broad fish community composition; by-catch of species of high conservation value; and food-chain interactions and dependencies. Challenges to be overcome before broader ecosystem-related objectives can be fully handled are discussed briefly.
Article
The evaluation of stock-assessment methods, monitoring programmes and harvest strategies for the South East Fishery using the Management Strategy Evaluation approach requires the development of a set of operating models. A generic framework for the development of operating models that includes the possibility of technical interactions among species is outlined. The operating model allows for discarding due to fish size, due to lack of quota and because of mismatches in the Total Allowable Catches (TACs) set independently for the species considered. The importance of technical interactions, mismatches in TACs, and the limits placed by constraints on landed catches and fishing effort is demonstrated by a set of illustrative simulations.
Article
The MSE approach provides a simulation-based framework within which harvest strategies, stock assessment methods, performance indicators and research programmes can be compared. This approach has been used in the Australian South East Fishery (SEF) to assess harvest strategies for the over-exploited eastern gemfish resource and to compare different levels of discard monitoring for blue grenadier. The main challenges to use of the MSE approach in the SEF are poorly specified management objectives and the lack of quantitative stock assessments on which to build operating models for many of the species.
Article
The interaction of large-scale fire, vegetation, and ungulates is an important management issue in Yellowstone National Park. A spatially explicit individual-based simulation model was developed to explore the effects of fire scale and pattern on the winter foraging dynamics and survival of free-ranging elk (Cervus elaphus) and bison (Bison bison) in northern Yellowstone National Park. The Northern Yellowstone Park (NOYELP) model simulates the search, movement, and foraging activities of individuals or small groups of elk and bison. The 77 020-ha landscape is represented as a gridded irregular polygon with a spatial resolution of 1 ha. Forage intake is a function of an animal's initial body mass, the absolute amount of forage available on a site, and the depth and density of snow. When the energy expenditures of an animal exceed the energy gained during a day, the animal's endogenous reserves are reduced to offset the deficits. Simulations are conducted with a 1-d time step for a duration of 180 d, [approximately]1 November through the end of April. Simulated elk survival for three winters (1987-1988; 1988-1989; 1990-1991) agreed with observed data.
Article
We used logistic regression to develop habitat models from observation of mountain goats (Oreamnos americanus) in alpine habitats near Mt. Evans, Colorado. Mountain goats used areas near escape terrain, on moderate slopes, at midelevations, and on southerly exposures more than expected. Habitat models for summer, winter, or all-seasons correctly classified 81—83% of observations and incorrectly classified 12—13% of locations not used by mountain goats. A model based only on distance to escape terrain correctly classified 87% of observations and classified 38% of the study area as suitable habitat. Our models provide a way to use readily available data and simple techniques to quickly identify suitable habitat over large geographical areas.
Article
Biological invasions create serious conservation problems at local to global scales, and decisions about their management require evaluation of the likely environmental consequences of an expanding population. An expanding population of exotic mountain goats (Oreamnos americanus) occupy an area near Rocky Mountain National Park, Colorado, USA (RMNP), an area managed for preservation of natural communities and processes. If mountain goats colonized RMNP, they could have detrimental impacts on native bighorn sheep (Ovis canadensis) in the Park. A simulation model was used to evaluate population-level interactions of these species. Simulated mountain goats and bighorn sheep each attained total population sizes of about 950 in the absence of disease or competition. Disease and competition resulted in bighorn sheep populations that were an average of 31% (moderate competition) and 47% (strong competition) smaller than populations without these influences, while competition reduced mountain goat populations by an average of 9%. Competition was responsible for most (>75%) of the reduction in average size of bighorn sheep populations, but disease increased variation in population size by a factor of 5. The combined population-level effects of competition (reduced average size) and disease (increased variance) represent a substantial risk to native bighorn sheep populations in RMNP.
Article
Evaluating the sustainability of hunting is key to the conservation of species exploited for bushmeat. Researchers are often hampered by a lack of basic biological data, the usual response to which is to develop sustainability indices based on highly simplified population models. However, the standard indices in the bushmeat literature do not perform well under realistic conditions of uncertainty, bias in parameter estimation, and habitat loss. Another possible approach to estimating the sustainability of hunting under uncertainty is to use Bayesian statistics, but this is mathematically demanding. Red listing of threatened species has to be carried out in extremely data-poor situations: uncertainty has been incorporated into this process in a relatively simple and intuitive way using fuzzy numbers. The current methods for estimating sustainability of bushmeat hunting also do not incorporate spatial heterogeneity. No-take areas are one management tool that can address uncertainty in a spatially explicit way.
Article
Using recent developments in capture – recapture modeling, we analyzed the adult survival pattern of an Alpine ibex (Capra ibex ibex) population recently established in the northern Alps of France. Survival rates varied little over time and did not differ between the sexes. The survival rate was 0.97 (SE = 0.011). Recapture probabilities were stable over time but differed according to sex: 0.71 (SE = 0.035) for males versus 0.88 (SE = 0.033) for females. The absence of a between-sex difference in survival was not expected for a highly sexually dimorphic species. Environmental conditions, such as a low population density and a low pressure of limiting factors on population dynamics, could explain this absence of a survival cost of sexual selection for males. The high and rather constant survival rate of ibex over time is consistent with the idea that, in large mammals, individuals should be selected for maximizing their own adult survivorship.
Article
Synchrony of activities is usually high in foraging groups, possibly to maintain group cohesion. Individuals with different levels of activity budgets, however, may have a hard time synchronizing their behavior to each other without incurring a cost. We predicted that the age and sex structure of a group would affect synchronization levels within a group because of differing individual activity budgets. Individuals in same-sex-age groups were hypothesized to show higher levels of activity synchrony than individuals in mixed sex-age groups. We investigated activity synchrony in adult male, adult female, subadult, and mixed sex-age groups of Alpine ibex - one of the most sexually dimorphic ruminant species. Activity budgets and movement rates were measured to calculate synchrony of activities between group members in June and July 1999. Adult males were more synchronized with group peers than either females or subadults of both sexes. However, while adult males were synchronized in 81% when in bachelor (adult male) groups, they were only synchronized in 65% of the time when in mixed sex-age groups. Adult females were synchronized 61% of their time when in mixed sex-age groups and 69% when in female groups. Individual subadult males displayed higher synchrony when in bachelor or female groups than when in mixed sex-age or subadult mixed-sex groups. Subadult groups and mixed sex-age groups showed the lowest degree of synchrony of all group types. In general, animals in groups of same body-sized individuals were more synchronized with their group members than animals in mixed body-size groups. Two and three year-old males did not adjust their time spent lying to the group but their time spent walking. They also tended to change their time spent grazing and standing according to group type. Among subadults, females spent more time foraging than males but less time lying and standing. There was no difference in time spent walking. Bachelor and subadult groups had the greatest movement rates while female groups were relatively sedentary within escape terrain. Individuals in escape terrain did only marginally synchronize their behavior to each other likely because groups did not move much and synchrony was presumably less important. We conclude that habitat type, group movement rates, and a group's sex-age composition may affect the extent to which an individual will synchronize its activities to the other group members.
Article
Translocation of bighorn sheep (Ovis canadensis) is time, labor, and cost intensive and, therefore, high levels of success are desirable. We tested a widely used habitat suitability model against translocation success and then modified it to include additional factors which improved its usefulness in predicting appropriate translocation sites. The modified Smith habitat suitability model for bighorn sheep was 64% accurate in predicting success or failure of 32 translocations of bighorn sheep into the Rocky Mountains, Colorado Plateau desert, and prairie-badlands of six states. We had sheep location data for 13 populations, and the modified habitat model predicted the areas used by bighorn sheep with greater than 90% accuracy in eight populations, greater than 55% accuracy in four populations, and less than 55% accuracy in one population. Translocations were more successful when sheep were placed into discrete habitat patches containing a high proportion of lambing period habitat (>10% of suitable habitat, p = 0.05), where animals had a migratory tendency ( p = 0.02), no contact with domestic sheep ( p = 0.02), or greater distance to domestic sheep (>23 km, p = 0.02). Rate of population growth was best predicted by area of lambing period habitat, potential area of winter range, and distance to domestic sheep. We retested the model using these refined criteria and the refined model then predicted success or failure of these 32 translocated populations with 82% accuracy.
Article
Individual bighorn ewes (Ovis canadensis) at 4-14 years of age were 1.5% heavier preceding years when they weaned a lamb than preceding years when their lamb died before weaning. Intra-individual differences in mass between years of successful and unsuccessful reproduction appeared independent of a ewe's multiyear average mass. Relative mass loss both in the winter before and in the winter after a given reproductive episode increased with reproductive success. Long-term monitoring of individual mass and reproductive success is a promising technique to study life histories in capital breeders, because it allows to partially account for differences in reproductive potential
Article
With females weighing about half-as much as males, ibex are one of the most sexually dimorphic ungulate species. Time budgets and bite rates of different age, sex, and reproductive condition classes as well as of animals in different reproductive condition were compared to evaluate how sexual differences in body size and differences in energetic needs of lactating and non-lactating. females affects these measures. Adult males spent more time lying, standing and walking and less time grazing than adult females. Non-lactating females spent more time lying and walking and less time grazing than lactating females. Lactating females took the most bites per minute and adult males the fewest, while non-lactating females showed intermediate bite rates. Lactating. females fed less on bushes and more on graminoids than non-lactating females or. males. While the mean lengths of activity bouts did not differ between lactating-and non-lactating females, males grazed on average for a shorter period of time, stood an
Article
We describe a new learning procedure, back-propagation, for networks of neurone-like units. The procedure repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector. As a result of the weight adjustments, internal 'hidden' units which are not part of the input or output come to represent important features of the task domain, and the regularities in the task are captured by the interactions of these units. The ability to create useful new features distinguishes back-propagation from earlier, simpler methods such as the perceptron-convergence procedure.
Article
1. It has been hypothesized that a balanced adult sex ratio is necessary for the full participation of ungulate females in reproduction and therefore high productivity. We tested this general hypothesis by combining two complementary approaches. 2. First, using telemetry (n = 60) and annual aerial censuses between 1995 and 1998, we compared two moose Alces alces populations in Quebec, Canada, one non-harvested and the other subject to intensive sport harvesting from the end of September to mid-October. We tested the following predictions for the harvested population: (i) females increase movements and home ranges during the mating period; (ii) the mating system is modified, with the appearance of groups of one male and many females; (iii) subadult males participate in reproduction; (iv) the mating period extends over two to three oestrus cycles; (v) the calving period extends over several months; and (vi) productivity declines. 3. Daily movements and home range sizes during the mating period did not differ between harvested and non-harvested populations. Most groups observed were male–female pairs. Subadult males (1·5–2·5 years old) were only observed with females in the harvested population. Mating and calving periods did not differ between populations. The proportion of females that gave birth and the number of calves produced were also comparable in the two populations. 4. Secondly, we also assessed the existence of a relationship between population productivity and percentage of males in various management units of the province of Quebec that were characterized by a wide range in sex ratios. Contrary to prediction (vi), the number of calves per 100 adult females was not related to the percentage of adult males in the population. 5. The participation of young adult males (subadults) in reproduction in our harvested population may have compensated for the lower percentage of adult males, and thus productivity was unaffected. We therefore reject the hypothesis that intensive harvesting, at least at the level we observed, affects reproduction and population productivity. 6. As there are some uncertainties regarding the long-term effects of high hunting pressure, however, managers should favour sex ratios close to levels observed in non-harvested populations.
Article
In the Ram Mountain bighorn sheep (Ovis canadensis) population, ewes differing by more than 30% in body mass weaned lambs with an average mass difference of only 3%. Variability in adult body mass was partly due to additive genetic effects, but inheritance of weaning mass was weak. Maternal effects could obscure genetic effects in the phenotypic expression of weaning mass, particularly if they reflected strategies of maternal expenditure that varied according to ewe mass. We performed a quantitative genetic analysis to assess genetic and environmental influences on ewe mass and on maternal expenditure. We used the mean daughters/mother regression method and Derivative Free Restricted Maximum Likelihood models to estimate heritability (h2) of ewe mass and indices of maternal expenditure. We found additive genetic effects on phenotypic variation in maternal mass, in lamb mass at weaning (absolute maternal expenditure) and in weaning mass relative to maternal mass at weaning (relative maternal expenditure). Heritability suggests that maternal expenditure has the potential to evolve. The genetic correlation of ewe mass and absolute maternal expenditure was weak, while ewe mass and relative maternal expenditure were strongly negatively correlated. These results suggest additive genetic effects on mass-dependent reproductive strategies in bighorn ewes. Mass-dependent reproductive strategies could affect lamb survival and phenotypic variation in adult mass. As population density increased and reproduction became costlier, small females reduced maternal expenditure more than large females. Constraints on reproductive strategy imposed by variations in resource availability are therefore likely to differ according to ewe mass. A general trend for a decrease in maternal expenditure relative to maternal size in mammals suggests that size-dependent negative maternal effects may be common.
Article
In addition to sexual segregation, many social ungulates show varying degrees of age segregation, especially among males. We investigated factors affecting group choice by subadult male bighorn sheep, using census data collected between 1982 and 1998 in a marked population. We examined whether group composition varied with population size and structure. Changes in total population size were correlated with the number of yearling males and yearling females, but not with the size of other sex-age classes. In years of high population size, female groups were larger than in years of low population size, while mixed sex-age and subadult groups showed a nonsignificant trend in the same direction. Typical group sizes of bachelor groups and the occurrence of mixed or bachelor groups were not affected by population size. When there were few subadult males in the population, groups of subadult males were less frequent than in years with many subadult males in the population, but the typical group size did not change. Subadult males were rarely seen in peer groups, and switched from female groups in spring to bachelor groups in autumn. An individual’s choice of group type is affected by its body mass, but also by the availability of enough potential group mates to provide sufficient predator-detection efficiency.
Article
We tested the idea that ruminants allocate their feeding time to habitat patches in relation to foraging efficiency. We used five tame red deer (Cervus elaphus) in an enclosure planted with four treatment of timothy grass (Phleum pratense) differing in their stage of growth. Older swards offered higher biomass but lower nutritional quality than younger swards. We observed time spent feeding in each treatment during each of seven trials. We measured goodness-of-fit between observed times and predictions from two alternative hypotheses differing in optimization strategy (maximizing versus matching), and a third, null hypothesis. We tested the hypotheses using two alternative currecies: digestible protein, and digestible dry matter or energy. Although digestible protein concentration and dry-matter digestibility were highly correlated (r=0.763, PR infPred sup2 =0.899) across all animals and trials. The other hypotheses were rejected. The results have important ecological implications in showing the underlying role of food in the selection of habitat by ruminants, and that simple, mechanistic models of forage intake and digestion can be scaled up to the level of animal behavioural choices.
Article
Three Beauties of the Gobi National Conservation Park was established in south central Mongolia in 1994. We performed a biological assessment of the parks wildlife and other biological/ecological resources from 1995-to assist in conservation management initiatives. Ground and aerial surveys collected data on 130 vertebrate species, several of which are listed as threatened or endangered globally or in Mongolia. We analyzed group structures and estimated population sizes for goitred gazelle (Gazella subgutturosa), Mongolian gazelle (Procapra gutturosa), ibex (Capra sibirica), and argali (Ovis ammon). We report on 20 species previously not reported in the park, including 17 birds, 2 mammals, and 1 reptile. The park is rich in diversity and abundance of raptors, and we observed 29 species of raptors. Several vertebrates appear to be faring better in the park than in other regions of Mongolia or the world. Under a new protected areas law (1994), the Mongolian Protected Areas Bureau is required to establish management zones within the park. Data from this study should be used to facilitate this process.
Article
A model system, HOOFS (Hierarchical Object Orientated Foraging Simulator), has been developed to study foraging by animals in a complex environment. The model is implemented using an individual-based object-orientated structure. Different species of animals inherit their general properties from a generic animal object which inherits from the basic dynamic object class. Each dynamic object is a separate program thread under the control of a central scheduler. The environment is described as a map of small hexagonal patches, each with their own level of resources and a patch-specific rate of resource replenishment. Each group of seven patches (0th order) is grouped into a 1st order super-patch with seven nth order super-patches making up a n+1th order super-patch for n up to a specified value. At any time each animal is associated with a single patch. Patch choice is made by combining the information on the resources available within different order patches and super-patches along with information on the spatial location of other animals. The degree of sociality of an animal is defined in terms of optimal spacing from other animals and by the weighting of patch choice based on social factors relative to that based on food availability. Information, available to each animal, about patch resources diminishes with distance from that patch. The model has been used to demonstrate that social interactions can constrain patch choice and result in a short-term reduction of intake and a greater degree of variability in the level of resources in patches. We used the model to show that the effect of this variability on the animal’s intake depends on the pattern of patch replenishment.