# Diffusive growth and noisy replication : models at the interface of statistical physics and biological evolution

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- eScholarship - University of California
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## Abstract

The bulk of this dissertation consists of three separate research projects. Each of them involves models of multi- locus evolution in the context of finite population size, genetic linkage, and both beneficial and deleterious mutations. Each project employs stochastic computer simulations and numerical solutions to equations which approximate a full stochastic model. The first project, presented in chapter two, was conceived as a problem in the field of non-equilibrium statistical physics known as "front propagation'' and was published in Physical Review E. The connection to biological evolution is due to my advisor, Herbert Levine, and his colleagues who pointed out an analogy between diffusive fronts propagating through physical space and a mutating population evolving through fitness space. The second project, presented in chapter three and published in Genetics, is more biologically oriented than the first project. It concerns the evolutionary pressures acting on the rate at which organisms produce spontaneous mutation. Our results agree with experimental data and also make testable predictions. The mathematical methods used are familiar from non- equilibrium statistical physics, but are quite distinct from those used in the first project. The third project, presented in chapter four, is currently being prepared for publication. It concerns the evolutionary advantage of "competence'' for genetic transformation in bacteria, which is conceptually similar to sex. Thus, issues related to the evolution of sex have bearing on this project, and vice versa. A puzzling feature of competence in many species is that normal, vegetatively growing cells stochastically switch in and out of the competence phenotype. We believe that this project provides a novel explanation for this puzzling "mixed strategy.'' A common theme in this dissertation is the drastic effect of having a finite population size N. In each project, the system behaves qualitatively differently in the infinite N limit than for any finite N. Thus, although "mean field theory'' provides helpful approximations in many areas of physics and stochastic processes, it should be used cautiously in evolutionary problems or those with a similar mathematical structure