Lattice-based models

The assumptions of, say, a logistic growth model or the Lotka-Volterra equations are clearly broken as soon as we step away from the chalkboard; organisms aren't uniformly distributed in space. One would like to understand this spatial heterogeneity. What are its sources? What are its consequences?

I investigate these questions in the context of a simple birth-death model in which time is continuous but space is discretized. Organisms die at rate mu, and give birth at rate beta. A birth event is long-distance with probability p, and is local with probability 1-p. I'm particularly interested in how this sliding parameter p affects the spatial structure of the population, and the way the population responds to disturbance.

All of this will be explained in a pair of papers I'm working on, although you're free to ask me for a preprint. In the meantime, you're welcome to play with the models and draw your own conclusions.