Area-restricted Search and the Scale Dependence of Path Quality Discrimination

This paper considers how the spatial distribution of resource patches can influence resource quality discrimination when search behavior is conditioned on patch quality. Two models of animal dispersal between patches are presented, a random walk simulation and a simple analytical treatment. These models are used to examine whether a patch-based version of “area-restricted search” can produce scale dependence in the level of patch quality discrimination. Simulations of the random walk model suggest that when animals condition search behavior on patch quality: (i) equilibrium levels of patch quality discrimination will be scale dependent, and (ii) patch quality discrimination may be minimal at small and large interpatch distances. The analytical model suggests that scale dependence in patch quality discrimination should be expected not just in random dispersal systems, but whenever dispersal behavior meets two simple conditions: (i) the probability of a trip reaching a given displacement from the home patch decrease with increasing displacement, (ii) trip displacement is conditioned on patch quality. Since these conditions seem likely to be broadly applicable, scale dependence in patch quality discrimination should be common. Scale dependence develops in these models because they explicitly represent the interaction between trip length distribution and the distance between patches. This suggests that both optimal foraging models and the metapopulation models currently popular in conservation biology may need to explicitly represent how patch quality dependent search behavior interacts with interpatch distance in producing interpatch migration rates.