Percolation, Phase Transitions and Speciation on a Neutral Landscape
The problem of speciation and species aggregation on a neutral landscape, subject to random mutational fluctuations without selective drive, has been a focus of research since the seminal work of Kimura on genetic drift. This problem, which has received increased attention due to the recent development of a neutral ecological theory by Hubbell, bears comparison with mathematical problems such as percolation and branching and coalescing random walks. I will discuss an agent-based computational model in which clustering (speciation) occurs on a neutral phenotype landscape. This model corresponds to sympatric speciation: organisms cluster phenotypically, but are not spatially separated. Moreover, clustering occurs not only in the case of assortative mating, but also in the case of asexual fission (bacterial splitting). In contrast, clusters fail to form in a control case where organisms mate randomly. The population size and the number of clusters (species) undergo a critical phase transition, most likely of the directed percolation universality class, as the maximum mutation size is varied, and cluster size appears to undergo a percolation transition.