Population Games

Abstract

The three main avenues of research in ecology focus onВ  animal behavior, population dynamics, and evolution of traits. Historically, differences between these three research programs are the underlying time scales: fast changes in animal behavior, intermediate fast changes in animal numbers, andВ  slow changes in traits. Following these time scalesВ  various mathematical methodologies were applied to develop corresponding mathematical models. While changes in population abundance are often described by differential/difference equations, models of animal behavior or evolution often rely on methods of optimization and evolutionary game theory. It is clear that an ``ideal'' mathematical model should integrate all these three time scales, but such models would be difficult if not impossible to analyze. Recently some new approachesВ  integrating processes operating on different time scales have been developed.В  In my talk I will discussВ  the so calledВ  ``population games''В  showing thatВ  the new insights they lead toВ  are not only of mathematical interest, but are also important toolsВ  for better understanding mechanisms regulatingВ  biodiversity.I will start with the classical Lotka--Volterra predator-prey model that describes changes in predator and prey numbers. This model assumes a homogeneous environment where predators and prey are well mixed. I will focus on an extension of this model to a heterogeneous environment consisting of two patchesВ  ...