Populations of Two Interacting Species

Abstract

A single species never exists in isolation. It may draw sustenance from others or may share resources with others. There may be collaborations between species in their daily activities. Indeed a typical species interacts with a very large number of others in an ecosystem. Such interactions of course affect the growth or decline of that species. The task of modeling complex interactions among the multitude of species in an ecosystem is clearly a formidable one. Therefore following the usual strategy, only one small step is taken towards increasing realism in models. Here we shall discuss models describing interactions between two species. These models try to account for the fact that populations are affected by intraspecific and interspecific interactions simultaneously. The standard group of models for this purpose is the Lotka — Volterra system. Two mathematicians A. J. Lotka, an American and V. Volterra an Italian, developed the system independently at the same time. For a very readable history of this and related work, see Kingsland (1985). Of the intraspecific and interspecific interactions, the latter are generally classified into three types, namely, competition, symbiosis or mutualism and predation or parasitism. We shall begin with the discussion of competition.