Transit Time and Density-Dependent Predation on a Patchily Distributed Prey

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Abstract
When prey are distributed in spatially separated patches, predators must spend time traveling from patch to patch that would otherwise be spent searching for prey. Since proportionately less time might be spent in transit when patches contain many prey than when they contain few, it seems likely that transit time will be a source of hunting inefficiency that will decline as prey become more abundant. As a result, it could be a mechanism by which predators stabilize their prey, by eating a larger fraction of the prey population per unit time when prey are abundant. The details depend on how the average search time and average number of prey eaten, per patch visit by a predator, vary with the average number of prey per patch. Several examples are given, and the effects of varying some of the parameters is described. In almost all cases, an increase in the transit time leads to an increase in the range of prey densities over which predation is density dependent. In about half of these cases, the increase leads to an increase in an alternative measure of the stabilizing tendency of predation, the predation rate at the maximum prey density at which predation is density dependent. A high prey densities the inversely density-dependent effect of handling time swamps all other effects. The analysis does not take account of variation of prey numbers from patch to patch (clumping), optimal foraging strategies, or predator interference, which are suggested as areas for future study.

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