Foraging on spatially distributed resources with sub-optimal movement, imperfect information, and travelling costs: departures from the ideal free distribution

Abstract

Ideal free distribution (IFD) theory off ers an important baseline for predicting the distribution of foragers across resource patches. Yet it is well known that IFD theory relies on several over-simplifying assumptions that are unlikely to be met in reality. Here we relax three of the most critical assumptions: (1) optimal foraging moves among patches, (2) omniscience about the utility of resource patches, and (3) cost-free travelling between patches. Based on these generalizations, we investigate the distributions of a constant number of foragers in models with explicit resource dynamics of logistic type. We fi nd that, fi rst, when foragers do not always move to the patch off ering maximum intake rate (optimal foraging), but instead move probabilistically according to diff erences in resource intake rates between patches (sub-optimal foraging), the distribution of foragers becomes less skewed than the IFD, so that high-quality patches attract fewer foragers. Second, this homogenization is strengthened when foragers have less than perfect knowledge about the utility of resource patches. Th ird, and perhaps most surprisingly, the introduction of travelling costs causes departures in the opposite direction: the distribution of sub-optimal foragers approaches the IFD as travelling costs increase. We demonstrate that these three fi ndings are robust when considering patches that diff er in the resource’s carrying capacity or intrinsic growth rate, and when considering simple two-patch and more complex multiple-patch models. By overcoming three major over-simplifi cations of IFD theory, our analyses contribute to the systematic investigation of ecological factors infl uencing the spatial distribution of foragers, and thus help in deriving new hypotheses that are testable in empirical systems. A confl uence of theoretical and empirical studies that go beyond classical IFD theory is essential for improving insights into how animal distributions across resource patches are determined in nature.