Clustering and phase transitions on a neutral landscape

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.

Multiple phase transitions in an agent-based evolutionary model with neutral fitness

“…This result is also consistent with the body of literature above showing that, in order for emergent clustering to appear, the dynamics must be governed by a local dispersion process and global death [9,12,24–30]. …”

“…Clustering patterns have been demonstrated in evolutionary, agent-based models with distinctly different dynamical rules [9,12,24–30]. For example, Young et al .…”

Diploid versus haploid models of neutral speciation

“…Ring species are interesting examples of such, where geography plays a crucial role in physically shaping the ring but does not block dispersal or gene flow along the ring [22][23][24][25]. A recent study of cluster formation with similar interactions was performed by Scott et al (2013) using a sympatric model [26]. In this model, phenotypes are represented by two continuous traits and the initial population is assumed to be uniformly distributed in the phenotypic space, i.e., to have high diversity.…”

Extinction phase transitions in a model of ecological and evolutionary dynamics

“…For a competition radius of κ = 0.25, this allows populations of up to 42 million organisms to exist without competition-caused death. These systems are at least three orders of magnitude larger than those used in earlier simulations [18,19,20].…”

“…The model was originally conceived [18,19] as a model of evolutionary dynamics in phenotype space but it can be interpreted as a model for population dynamics in real space as well. Organisms reside in a continuous twodimensional space of size L × L. In the evolutionary interpretation, the two coordinates correspond to two independent phenotype characteristics (in arbitrary units) while they simply represent the real space position of the organism for population dynamics.…”