Extinctions in a spatial model of fossil communities subject to correlated environmental disturbance

We present a spatial model to study the behaviour of species communities subjected to environmental stress in the form of coloured noise, focusing on long-time changes of time scales larger than 1 ka. The sensitivity to environmental change is introduced by assigning each species with an optimal value of a certain environmental variable like e.g., the temperature, and with a fitness function having the form of a Gaussian. Each species is represented by a point on a surface and competes with neighbours. Species can evolve to new species with a different optimal value, or they can migrate to regions with better environmental conditions. We find that coloured noise can prompt sudden extinctions in similarity with the fossil record. The model also reproduces the well-known fact that that eurytopic species (generalists) are favoured during environmental stresses, and shows that a strong environmental gradient may ameliorate the species performance.