Spontaneous emergence of spatial patterns in a predator-prey model.

We present studies for an individual based model of three interacting populations whose individuals are mobile in a two-dimensional lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations' time series. Our model displays both traveling wave solutions, clustering and uniform distributions, both related to the parameter values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plant, regulated the presence of predators, as well as the type of spatial configuration. This result corroborates the theory that the enrichment of prey can stabilize the predator-prey dynamic in more realistic models.