Speciation in the Derrida-Higgs model with finite genomes and spatial populations

The speciation model proposed by Derrida and Higgs demonstrated that a sexually reproducing population can split into different species in the absence of natural selection or any type of geographic isolation, provided that mating is assortative and the number of genes involved in the process is infinite. Here we revisit this model and simulate it for finite genomes, focusing on the question of how many genes it actually takes to trigger neutral sympatric speciation. We find that, for typical parameters used in the original model, it takes of the order of $10^5$ genes. We compare the results with a similar spatially explicit model where about 100 genes suffice for speciation. We show that when the number of genes is small the species that emerge are strongly segregated in space. For larger number of genes, on the other hand, the spatial structure of the population is less important and the species distribution overlap considerably.