Document Type

Thesis

Degree

Master of Science

Major

Physics

Date of Defense

6-14-2012

Graduate Advisor

Sonya Bahar, PhD

Committee

Maric, Nevena

Flores, Ricardo

Abstract

Amongst the scientific community, there is consensus that evolution has occurred; however, there is much disagreement about how evolution happens. In particular, how do we explain biodiversity and the speciation process? Computational models aid in this study, for they allow us to observe a speciation process within time scales we would not otherwise be able to observe in our lifetime. Previous work has shown phase transition behavior in an assortative mating model as the control parameter of maximum mutation size (µ) is varied. This behavior has been shown to exist on landscapes with variable fitness (Dees and Bahar, 2010), and is 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 I investigate another dimension of the phase transition. In order to achieve an appropriate ‘null’ hypothesis and make the model mathematically tractable, the random death process was changed so each individual has the same probability of death in each generation. Thus both the birth and death processes in each simulation are now ‘neutral’: every organism has not only the same number of offspring, but also the same probability of being randomly killed. Results show a continuous nonequilibrium phase transition for the order parameters of the population size and the number of clusters (analogue of species) as the random death control parameter δ is varied for three different mutation sizes of the system. For small values of µ, the transition to the active state of survival happens at a small critical value of δ; in contrast, for larger µ, the transition happens later – suggesting a robustness of the system with increased mutation ability.

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