A mathematical model of predation based upon the theory of nutrition kinetics 2. A nutrition structure of the predator population and its functional response to the prey

Abstract

The paper presents a predation model with two structures and n + 1 satiated states based on the theory of nutrition kinetics. The functional response of the predator population to the prey can be expressed as follows: B = x(1+x) n−1 + RrX(1+X) n−1 (1+X) n + R(1+rX) n It is a general form of many other models which were obtained by other authors. In particular, it has included the three types of functional response of the famous Holling model. The problem of nutrition structure of population has rarely been discussed before. In this paper, nutrition structure is defined as the frequency distribution of predators corresponding with their predation efficiency and the degree of hunger or satiation. The relative number of normal, un-normal and different satiated- of hungry-state predators will vary with abundance of prey in the system. This kind of nutrition structure can express the qualitative behaviour of the predators; therefore, it may be important in nutrient-growth kinetics.