COMB, University of Maryland
In collaboration with Simon A. Levin.
It has been shown that individual-based predator-prey systems can display at an intermediate spatial scale of aggregation, a dynamic regime in which oscillations differ from random fluctuations around a global average. This intermediate scale has been proposed as a natural size at which to aggregate individuals into densities. It can be identified with an approach based on a determinism test from nonlinear data analysis. I illustrate some of these ideas with an individual-based predator-prey model that is spatial, stochastic, and nonlinear. I then move to the open problem of deriving an appropiate approximation for the dynamics of densities at the selected intermediate scale. I show that the two simplest candidate models-the mean-field system with a limit cycle attractor and an extension of it that adds demographic noise-fail to provide a good approximation. Thus, space is nonnegligible. I end with a conjecture (and hopefully by the time of this talk, some evidence) on the type of model needed to approximate the aperiodic dynamics of densities.