Modeling and managing the evolutionary component of biological systems

While differential equations have been commonly used to model the population dynamics of biological systems, it is uncommon for such models to include the evolutionary potential of the species being modeled. As a consequence, the focus of such models has generally been directed toward ecological stability rather than on evolutionary stability. Here, an evolutionary game approach to modeling is presented that allows for a very clear distinction between ecological and evolutionary stability. Necessary conditions are given for each type of stability so that they may be studied separately. In order to include evolution into management models, we are faced with two fundamental questions: what is evolving, and where is it evolving to? In the evolutionary game theory presented here, the ‘what’ are parameters in the differential game model associated with characteristics of the species that are clearly adaptive (such as sunlight conversion efficiency for plants or body length in animals), which we call strategies. The ‘where’ is the evolutionarily stable strategies (ESS) to which these parameters can evolve. These strategies can be determined using the ESS maximum principle presented here. The ESS maximum principle when used with appropriate models, has the capacity to predict the evolutionary response of biological systems subject to a wide range of inputs, including physiographic changes, harvesting, and the introduction or removal of new species and/or resources. Applications are discussed in terms of some typical managed ecosystems. A detailed example, illustrating use of the theory, is given in which the treatment of cancer with drugs is ‘simulated’.