An Evolutionary Game Theory for Differential Equation Models with Reference to Ecosystem Management

Abstract

Either through exploitation or conservation, man is constantly tinkering with ecosystems. On the one hand, we cultivate and harvest a selected few species in man-controlled environments, and on the other hand we recognize the importance of preserves, hoping that still other “wild” species will continue to exist in their “natural” environments (Albeit, in most cases the preserves are still subject to direct control and/or harvesting by man). Do we have any idea of the long-term evolutionary consequences of what our exploitation or conservation activities will be? We present here some new results from evolutionary game theory which, when used with appropriate differential equation models, has the capacity to predict the evolutionary response of biological systems subject to human inputs. These inputs include physiographic changes, harvesting, and the introduction or removal of new species. Some previous results are discussed in terms of ecosystem management and a new example is presented to demonstrate potential use of the theory in the treatment of cancer by chemotherapy.