Speciation dynamics of an agent-based evolution model in phenotype space

This dissertation is an exploration of phase transition behavior and clustering of populations of organisms in an agent-based model of evolutionary dynamics. The agents in the model are organisms, described as branching-coalescing random walkers, which are characterized by their coordinates in a two-dimensional phenotype space. Neutral evolutionary conditions are assumed, such that no organism has a fitness advantage regardless of its phenotype location. Lineages of organisms evolve by limiting the maximum possible offspring distance from their parent(s) (mutability, which is the only heritable trait) along each coordinate in phenotype space. As mutability is varied, a non-equilibrium phase transition is shown to occur for populations reproducing by assortative mating and asexual fission. Furthermore, mutability is also shown to change the clustering behavior of populations. Random mating is shown to destroy both phase transition behavior and clustering. The phase transition behavior is characterized in the asexual fission case. By demonstrating that the populations near criticality collapse to universal scaling functions with appropriate critical exponents, this case is shown to belong to the directed percolation universality class. Finally, lineage behavior is explored for both organisms and clusters. The lineage lifetimes of the initial population of organisms are found to have a power-law probability density which scales with the correlation length exponent near critical mutability. The cluster centroid step-sizes obey a probability density function that is bimodal for all mutability values, and the average displays a linear dependence upon mutability in the supercritical range. Cluster lineage tree structures are shown to have Kingman's coalescent universal tree structure at the directed percolation phase transition despite more complicated lineage structures.