Clustering and phase transitions on a neutral landscape

¹ Department of Physics and Astronomy and Center for Neurodynamics, University of Missouri at St. Louis St. Louis MO, 63121, USA
² Department of Mathematics and Computer Science, University of Missouri at St. Louis - St. Louis MO, 63121, USA

^(a) bahars@umsl.edu

Received: 2 April 2013
Accepted: 6 June 2013

Abstract

Recent computational studies have shown that speciation can occur under neutral conditions, i.e., when the simulated organisms all have identical fitness. These works bear comparison with mathematical studies of clustering on neutral landscapes in the context of branching and coalescing random walks. Here, we show that sympatric clustering/speciation can occur on a neutral landscape whose dimensions specify only the simulated organisms’ phenotypes. We demonstrate that clustering occurs not only in the case of assortative mating, but also in the case of asexual fission; it is not observed in the control case of random mating. We find that the population size and the number of clusters undergo a second-order non-equilibrium phase transition as the maximum mutation size is varied.