Information Theory applied to Models of Ecological Systems

There are several "classic" models of ecological phenomenon, including the logistic population growth model and the Lotka-Volterra predator-prey model. While these classic models provide a solid foundation for ecological modeling, the dynamic regime of these canonical ODEs is limited. The dynamics of these models can be expanded in a number of different ways and quantified using information theoretic measures like excess entropy and entropy rate. In the case of both the logistic model and the predator-prey model quantitatively new dynamic regimes, including chaos, can be obtained simply by simulating the model in discrete time. Alternatively, chaotic regimes also arise by simulating the continuous time models in a spatial context using reaction diffusion equations. In contrast to the deterministic discrete and continuous time models, the dynamic regime of the stochastic versions of these models has been (we think) relatively less explored. Stochastic simulations qualitatively appear to better reflect real world dynamics but it is unclear whether they are quantitatively any different than deterministic continuous time models. The goal of our project is to examine the dynamic regime of a stochastic simulation of the predator-prey model using the same information theoretic measures, both independent of and within a spatial context. Secondarily, we are interested in exploring the flow of information between the prey and predator populations using the mutual information metric both in space and time.