  A microscopic model is developed, within the frame of the theory of
quantitative traits, to study both numerically and analytically the combined
effect of competition and assortativity on the sympatric speciation process,
i.e. speciation in the absence of geographical barriers. 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, e.g. competition. The effects of finiteness
of population size on survival of coexisting species are also accounted for.
The simulations show that both in the case of flat and ripid static fitness
landscapes, competition and assortativity do exert a synergistic effect on
speciation. We also show that competition acts as a stabilizing force against
extinction due to random sampling in a finite population. Finally, evidence is
shown that speciation can be seen as a phase transition.
