Divergence and diversity in rapidly evolving populations

Abstract

Models in theoretical population genetics and evolutionary dynamics seek to connect the underlying forces of mutation, selection and genetic drift to observable patterns of phenotypic and/or genotypic variation. To do so, the bulk of classical work proceeds by making one of two assumptions: that the selective effects of mutations are predominantly neutral, or that the different loci in the genome can be considered independently of one another. Mounting empirical evidence has demonstrated that both of these assumptions are violated in many populations of biological relevance, particularly in microbial and viral populations. In these populations, several selected mutations are often simultaneously present, and their evolutionary dynamics must be considered in tandem. The focus of this thesis is on modeling the fitness variation in these rapidly evolving populations---which is maintained as a steady-state traveling wave by a balance between selection and new mutations---and on using knowledge of this fitness variation to analyze statistics of genetic divergence between populations and genetic diversity within populations.

We begin in Chapter 1 with a streamlined review of classical population genetics, reviewing key quantities describing both genetic divergence and genetic diversity. In Chapter 2, we present a novel theoretical approach to analyze the same quantities in rapidly evolving populations, when interference among mutations simultaneously present is widespread. Our approach extends previous work to apply when mutations confer fitness effects on a broad range of scales---both weak and/or strong, and both beneficial and/or deleterious. We analyze how mutations of different selective effects contribute to statistics of genetic divergence and genetic diversity including fixation probabilities and the site frequency spectrum, and discuss related implications for inferences of population genetic parameters in natural populations. In Chapter 3, using the same approach we consider the fate of a population at long evolutionary times, and the extent to which natural selection can act as an optimization process. We demonstrate that our approach enables a simple partitioning of the parameter space between the region in which a population will adapt, and the region in which natural selection is overwhelmed by the mutation pressure of deleterious mutations, leading to overall fitness decline of a population. This can be used, together with a pattern of how the evolutionary parameters vary with fitness, to identify whether a long-term evolutionarily stable state exists, and if so, where in the parameter space the population will end up at long times.