LOGISTIC THEORY OF FOOD-WEB DYNAMICS

Classical food-web theory arises from Lotka-Volterra models. As an alternative, we develop a model from the logistic concept of demand and supply. We first extend the logistic to an arbitrary species in a trophic chain or stack by developing a simple equation for any population X(i): [GRAPHICS] which includes the effects of intra-specific competition for fixed resources (the term b(i)X(i), intra-specific competition for renewable resources in the lower trophic level (the term X(i)/c(i)X(i-1)), and consumers in the upper trophic level (the term d(i)X(i+1)/X(i)). This equation emerges from the basic logistic concept of demand and supply, as captured by the consumer/resource ratios, and fulfills all the requirements for a plausible food-chain equation. We then generalize the equation to any population in a food web of arbitrary complexity [GRAPHICS] where F-j(r(i)) is the fraction of population X(j) that is a resource for i, and F-k(c(i)) is the fraction of population X(k) that consumes i. This equation meets all the requirements for a general food web model. Some properties of the model are discussed.