Bifurcation Phenomena in Population Models

Abstract

Biological systems tend to be considerably more complex than those studied in physics or chemistry. In analyzing models, one is frequently presented with two alternatives: either resorting to brute force computer simulation or to reducing the model further via such drastic approximations as to render it biologically uninteresting. Neither alternative is attractive. Indeed, the former alternative is hardly viable for most situations in ecology since sufficient data is rarely available to quantitatively validate a model. This contrasts starkly with the physical sciences where small differences can often discriminate between competing theories. The situation is such that many ecologists seriously question whether mathematics can play any useful role in biology. Some claim that there has not yet been a single fundamental advance in biology attributable to mathematical theory.* Where complex systems are concerned, they assert that the appropriate language is English, not mathematical. A typical attitude among biologists is that models are useful only insofar as they explain the unknown or suggest new experiments. Such models are hard to come by.