Spontaneous natural selection in a model for spatially distributed interacting populations

We present an individual-based model for two interacting populations diffusing on lattices in which a strong natural selection develops spontaneously. The models combine traditional local predator-prey dynamics with random walks. Individual's mobility is considered as an inherited trait. Small variations upon inheritance, mimicking mutations, provide variability on which natural selection may act. Although the dynamic rules defining the models do not explicitly favor any mobility values, we found that the average mobility of both populations tend to be maximized in various situations. In some situations there is evidence of polymorphism, indicated by an adaptive landscape with many local maxima. We provide evidence relating selective pressure for high mobility with pattern formation.