Grant: Discovery Grants Program - Individual

The static analysis of ""non-cooperative"" games has long been used by economic game theorists to predict a player's rational choice in human conflict situations. It has also become the accepted method to predict long term individual behaviors in an evolving biological population through the game-theoretic solution of an evolutionarily stable strategy (ESS). My research proposal is to analyze the dynamics of evolutionary games relevant for biological systems, paying particular attention to the dynamic stability of equilibria found in the above static analysis. This is an active area of research with many applied mathematicians as well as theoretical biologists involved. There are several specific areas of evolutionary game theory that I will concentrate on. One area is coevolutionary models in ecology. Coevolution here includes changing population sizes of several species in the ecosystem as well as changing patterns of individual behavior within each species. For instance, when there are several habitats, game-theoretic intuition suggests a species will distribute itself among these habitats according to the Ideal Free Distribution (IFD) whereby all individuals have the same ""fitness"". My research examines if this IFD is an ESS and/or dynamically stable; otherwise one does not expect to observe this equilibrium state in nature. An application of such models is to predator-prey systems when prey face a tradeoff between accessing a refuge with limited food supply versus habitats where they are not safe from predation. Another application involves the use of ""extensive form games"" that describe the sequential decision making resulting from ongoing interactions among the same individuals. For example, prey may have a choice of habitat followed by different possible behaviors depending on where they and their predators live. A more technical area of proposed research involves continuous trait spaces and adaptive dynamics, a current area of much research. The goal here is again to predict the outcome of evolution as populations adapt to their changing environment and to the changing populations around them.