Random Prey Detection with Pause-Travel Search

We develop a mechanistic approach to the relationship between prey density and predator-prey encounter rate, incorporating perceptual constraints, search costs, and search tactics. We find that encounter rate should be density-dependent and the functional response sigmoid whenever the effects of (1) density on distance to prey and of (2) distance on instantaneous rate of detection do not cancel perfectly. We can predict how search tactics should change with prey density and detectability given the various constraints. If search movements are relatively cheap in both time and energy, then pause-travel search tactics can reduce the density dependence toward linearity, approximating a Type II functional response. If we ignore mechanistic details like search tactics that vary over several orders of magnitude, we can describe very accurately the encounter rates generated by this process with the simple traditional form aDb. We show how the critical exponent b relates to various constraints. The analysis leads to counterintuitive expectations about frequency dependence when prey types are intermixed.

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