In this seminar, I analyse a simple two-dimensional stochastic lattice model. This model is based on a model for wave patterns in fir forests adopted by Satake, Kubo and Iwasa. It is a Markov chain model with interaction of neighboring sites based on their age. The model can explain the scale of the patterns observed in nature while still offering some of the formal simplicity of the Ising model which itself is not an adequate model.
This study is a work in progress. I will present simulation results that illustrate the main properties of the model (parameter dependence, scaling properties, etc.), and I will discuss the relation to other lattice models that have recently been applied to similar situations in ecology.