Selective strategies in food webs

Abstract

Since the time of Lotka and Volterra, interactions among populations and more generally evolution of ecological systems have been modelled by differential or difference equations. Since various strategies may influence the interactions among different populations and thus the fate of the whole system, complex systems cannot be described by coupling many one-prey-one-predator differential equations. These strategies are both internal (e.g. due to selective feeding) and external (e.g. due to interactions of the environment with the system). In the literature, man-made strategies (i.e. controls) were considered especially in connection with the management of renewable resources (see Clark, 1976). Internal strategies were studied in connection with switching (Legovic, 1989; Murdoch et al., 1975; Oaten & Murdoch, 1975; Pulliam, 1981; Roughgarden, 1979). Several factors may determine feeding preferences for predators. For example, in the case of Acanthaster planci feeding on different coral species (Moran, 1986), these factors comprise abundance of corals, accessibility of corals, nutritional value of corals, etc. In g~neral, it is often believed that predators forage so as to maximize their short-term rate of resource intake. In this paper we consider systems of interacting populations, each of which may utilize several resources and at the same time be a resource for others. Therefore different populations may adopt different strategies. The main questions are: what is a strategy and which strategies will be adopted? .Or, in other words, according to which criteria should be strategies be chosen? It seems reasonable to postulate that any population optimizes some given quantity. This leads us to adopt the following procedure. We assume that the various populations choose strategies so that some given quantities are optimized at any time. In other words, at any instant the system 281