Comparing theory and data on multi-species interactions using evolutionary game theory

Abstract

Mathematical models with fixed parameters have a long history of use in describing the dynamics of populations in ecological interactions. However, in many instances, evolutionary changes in species characteristics can have a significant influence on these dynamics. Using evolutionary game theory, we incorporate evolution into population dynamic models and apply the resulting “Darwinian dynamic” models to study the effects that evolutionary changes can have on populations in several ecological scenarios. We start with a single species (Chapter 2), then add a competitor (Chapter 3), and a predator (Chapter 4). In Chapter 2, a rigorous mathematical analysis of the Darwinian logistic model for a single species shows that stable equilibria occur at strategies that maximize population size rather than growth rate. We apply this model to the data obtained from an experimental study on genetically perturbed populations of the flour beetle Tribolium castaneum. In Chapter 3, we apply a Darwinian dynamic modification of the Lotka-Volterra model to investigate circumstances under which evolution will change expected competitive outcomes. We compare the results of our Darwinian Lotka-Volterra model to studies in which unusual observations were made in studies of the flour beetles T. castaneum and T. confusum, including a reversal in the “winner” of competitive exclusion, and evolution from exclusion to coexistence. Chapters 2 and 3 provide one of the few examples in which evolutionary game theory has been successfully applied to empirical data. From a foundation provided by the Darwinian logistic equation, we build Darwinian dynamic models with two and three trophic levels to study effects of evolution on some basic ecological interactions in Chapter 4. We show how a consumer can cause a resource (producer) species to evolve to a mean strategy that increases its growth rate rather than its population size. We also briefly study how predation on the consumer species can affect equilibrium strategies of species lower in the food chain. Our results show how evolutionary game theoretic methods can be useful for studying both theoretical and applied problems that arise due to evolutionary processes, even when they occur on a ecological time scale. They provide a foundation for the future study of evolutionary effects in larger complex networks of interacting species.