A model of the functional response of a predator to prey density involving the hunger effect

Abstract

A mathematical model of the functional response to prey density involving the hunger effect was constructed in this paper. In that model, the amount of prey captured by predators, y, is assumed to be proportional to the product of the prey density, x, and the degree of hunger. The range of prey density is divided into the following three areas along the x-axis, according to the maximum rate of ingestion and the maximum rate of capture: (i) the area in which the value of y increases convexly with increasing x, (ii) the area in which the value of y increases proportionally to x and (iii) the area in which y reaches the maximum. It is shown that these equations are a generalization of Ivlev's equation, and Holling's disc epuation, that is, both equations hold in special cases in only the first area of x. These equations were applied to several experimental results obtained by using two kinds of wolf spiders and some values of parameters were estimated.