Universality in a Neutral Evolution Model

Agent-based models are ideal for investigating the complex problems of biodiversity and speciation because they allow for complex interactions between individuals and between individuals and the environment. Presented here is a ``null'' model that investigates three mating types -- assortative, bacterial, and random -- in phenotype space, as a function of the percentage of random death $\delta $. Previous work has shown phase transition behavior in an assortative mating model with variable fitness landscapes as the maximum mutation size ($\mu )$ was varied (Dees and Bahar, 2010). Similarly, this behavior was recently presented in the work of Scott et al. (submitted), on a completely neutral landscape, for bacterial-like fission as well as for assortative mating. Here, in order to achieve an appropriate ``null'' hypothesis, the random death process was changed so each individual, in each generation, has the same probability of death. Results show a continuous nonequilibrium phase transition for the order parameters of the population size and the number of clusters (analogue of species) as $\delta$ is varied for three different mutation sizes of the system. The system shows increasing robustness as $\mu $ increases. Universality classes and percolation properties of this system are also explored.