Sympatric Speciation Through Assortative Mating in a Long-Range Cellular Automaton

A probabilistic cellular automaton is developed to study the combined effect of competition and assortativity on the speciation process in the absence of geographical barriers. The model is studied in the case of long-range coupling. A simulated annealing technique was used in order to find the stationary distribution in reasonably short simulation times. Two components of fitness are considered: a static one that describes adaptation to environmental factors not related to the population itself, and a dynamic one that accounts for interactions between organisms such as competition. The simulations show that both in the case of flat and steep static fitness landscape, competition and assortativity do exert a synergistic effect on speciation. We also show that competition acts as a stabilizing force preventing the random sampling effects to drive one of the newborn populations to extinction. Finally, the variance of the frequency distribution is plotted as a function of competition and assortativity, obtaining a surface that shows a sharp transition from a very low (single species state) to a very high (multiple species state) level, therefore featuring as a phase transition diagram. Examination of the contour plots of the phase diagram graphycally highlights the synergetic effect.