Spatial Patterns of Depletion Imposed by Foraging Vertebrates: Theory, Review and Meta-Analysis

Abstract

1. A simulation model is used to examine the spatial pattern of resource depletion imposed by vertebrates foraging in a heterogeneous environment; this may have important consequences for the dynamics of resource populations. It is assumed that consumers distribute themselves to maximize intake rates, that mutual interference occurs between competing consumers, and that the coefficient of interference, m, is less than one. 2. Where individuals are equal in their susceptibility to interference, depletion is density-dependent and variation in resource density is reduced towards zero. However, individuals often differ in their susceptibility to interference and incorporating such individual variation modifies the expected pattern of depletion. Spatial variation in resource density is no longer reduced to zero. After consumption of a given proportion of the total resource, spatial variation in the density of that remaining is greater when there is stronger interference, greater individual variation in susceptibility to interference, or a larger consumer population. With large individual variation and a large consumer population, domed or inversely density-dependent patterns of depletion are predicted, even where the coefficient of interference, m, is less than 1. 3. Field studies that quantify depletion of resource patches within the sampling range of a vertebrate population are reviewed and related to patterns predicted by the simulation model. The correlation between depletion and intial resource density is positive in 22 of 24 cases and significantly density-dependent (P < 0.05) in 11 of these, while only one correlation is significantly inversely density-dependent. The mean correlation in meta-analysis of vertebrate predators of invertebrate prey (22 cases) is significantly positive, showing that these groups tend to impose spatially density-dependent depletion. In contrast, reviews of invertebrate parasitoids find that inverse and positive density dependence are equally common. This difference may result partly from greater mobility of vertebrates, allowing them to sample the environment and distribute themselves closer to a rate-maximizing optimum. It is also possible that studies of vertebrates measure depletion at scales appropriate to the aggregative response of the consumers more frequently than studies of invertebrates.