Geographic speciation in the Derrida-Higgs model of species formation

We consider the Derrida-Higgs (DH) statistical model of species formation in the case where the population is geographically distributed in discrete locations, and mating only takes place within one location. Keeping the rate of migration between neighbouring locations at a fixed value, we change the mutation rate, changing therefore the average overlap between genotypes. When the overlap between individuals living in different locations falls below a fecundity threshold, speciation occurs. When more species coexist, the genetic structure of the population (as described by the overlap distribution $P(q)$) fluctuates. However, the average overlap, both within one location and among neighbouring locations, appears to vary according to the same laws as in the absence of speciation. The model provides a reasonable estimate of the parameter values necessary to observe geographic speciation, which is found to be much more likely than the sympatric speciation of the original DH model. Applications to the case of circular invasion, where the concept of biological species appears to run into difficulties, are sketched.