Sources of variation in predation rates at high prey densities: an analytic model and a mite example

Abstract

Some mathematical techniques for the analysis of satiation-based predation models previously developed by the first author are applied in the present paper to a model by the second author for predation by the predatory miteMetaseiulus occidentalis (Nesbitt). It turns out that for this predator the predation rate should keep increasing at high prey densities as the square root of the prey density,x. This particular shape of the functional response is shown to occur if and only if the upper satiation threshold for prey capture coincides with the maximum gut capacity. The functional response predicted by the model, moreover, is in fair quantitative agreement with predation rates observed by the third author in artificial arenas.

A further analysis of the model shows that the variance of the catch should also increase as the square root ofx. This prediction is consistent in a qualitative manner with the continued increase in the variance of the catch. However, quantitatively, the observed variances are even too large to be compatible with any model in which the feeding rate is subject to regulation by a negative feedback. Therefore, the difference between predicted and observed variances is hypothesized to be due to nonhomogeneities in the experimental material. The inferred additional variance component proportional tox accords fairly well with the trend apparent in the data.