A mechanistic home range model for optimal use of spatially distributed resources

Home ranges of animals are associated with the spatial distribution of limiting resources on a landscape, yet no mechanistic models representing this relationship exist. We present models of how animals might choose patches for their home ranges in ways that are optimal with respect to spatially distributed resources. The models assume that animals choose patches for their home ranges based on resource benefits discounted for travel costs. Animals might select patches to maximize resources within their home ranges over random use of the landscape (resource maximization), or to satisfy a minimum resource threshold needed for survival or reproduction (area minimization). We evaluated how landscape configuration structures home ranges of animals by performing individual-based, spatially explicit computer simulations using each model on simulated landscapes that differed only in the spatial continuity of resources among patches (from over-dispersed to clumped). The most important factor determining quality, efficiency, resource content, and spatial distribution of home ranges was the extent to which resources were clumped on a landscape. Characteristics of resource-maximizing home ranges were determined only by the distribution of resources, and differed from those of area-minimizing home ranges depending upon the magnitude of the resource threshold required. An increase in resource threshold increased area and total resource content for area-minimizing home ranges, but did not change their quality or efficiency. Because animals can consume or protect resources within their home ranges, they can depress the value of resources available to other animals and hence how those animals will choose their home ranges. Depression of resource values on a landscape by animals should result in different configuration and spatial distribution of home ranges on a landscape than would be predicted in its absence. We modified the two home range models to depress the value of resources available to other animals within patches selected for each home range. We generated home ranges with the new models on the simulated landscapes and evaluated how home ranges with resource depression varied with landscape configuration and with the number of home ranges on the landscape. We compared characteristics and spatial distribution of home ranges with resource depression to those of home ranges that do not. For the number of simulations we performed, resource depression resulted in home ranges that differed little in configuration and landscape interactions from those without, except that they were distributed more evenly on the landscapes and overlapped each other less. As the number of home ranges on a landscape increased, resource distributions declined in quality and heterogeneity, and home ranges became larger, less efficient, and of lower quality. Our results suggest that, in addition to landscape configuration, the extent to which animals depress resources included in their home ranges should determine the evenness of spatial dispersion, overlap, and home range structure, especially where animals select home ranges to satisfy a specific resource threshold and the density of animals is high. Because resource depression sets a limit on the number of home ranges a landscape with fixed resource levels can support, our models provide a means of assessing carrying capacity of a landscape.