Discrete Growth Models for Interacting Populations

Abstract

Here we consider two interacting species, each with non-overlapping generations, which affect each others population dynamics. As in the continuous growth models, there are the same main types of interaction namely predator-prey, competition and mutualism. In a predator-prey situation the growth rate of one is enhanced at the expense of the other whereas in competition the growth rates of both are decreased while in mutualism they are both increased. These topics have been widely studied but nowhere near to the same extent as for continuous models for which, in the case of two species, there is a complete mathematical treatment of the equations. The book by Hassel (1978) deals with predator-prey models. Beddington et al. (1975) present some results on the dynamic complexity of coupled predator-prey systems. The book by Gumowski and Mira (1980) is more mathematical, dealing generally with the mathematics of coupled systems but also including some interesting numerically computed results: see also the introductory article by Lauwerier (1986). The review article by May (1986) is apposite to the material here and that in the previous chapters, the central issue of which is how populations regulate. He also discusses, for example, the problems associated with unpredictable environmental factors superimposed on deterministic models and various practical aspects of resource management.