Predicting local population distributions around a central shelter based on a predation risk-growth trade-off

Animals face trade-offs between predation risk and foraging success depending on their location in the landscape; for example, individuals that remain near a common shelter may be safe from predation but incur stronger competition for resources. Despite a long tradition of theoretical exploration of the relationships among foraging success, conspecific competition, predation risk, and population distribution in a heterogeneous environment, the scenario we describe here has not been explored theoretically. We construct a model of habitat use rules to predict the distribution of a local population (prey sharing a common shelter and foraging across surrounding habitats). Our model describes realized habitat quality as a ratio of density- and location-dependent mortality to density-dependent growth. We explore how the prey distribution around a shelter is expected to change as the parameters governing the strength of density dependence, landscape characteristics, and local abundance vary. Within the range of parameters where prey spend some time away from shelter but remain site-attached, the prey density decreases away from shelter. As the distance at which prey react to predators increases, the population range generally increases. At intermediate reaction distances, however, increases in the reaction distance lead to decreases in the maximum foraging distance because of increased evenness in the population distribution. As total abundance increases, the population range increases, average population density increases, and realized quality decreases. The magnitude of these changes differs in, for example, ‘high-’ and ‘low-visibility’ landscapes where prey can detect predators at different distances.