Asexual Evolution Waves: Fluctuations and Universality
Daniel S. Fisher
(Submitted on 23 Oct 2012)
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is still not fully understood, fundamentally because the effects of fluctuations due to the small numbers of the fittest individuals are large even in enormous populations. In this paper, branching processes and various asymptotic methods for analyzing the stochastic dynamics are further developed and used to obtain information on fluctuations, time dependence, and the distributions of sizes of subpopulations, jumps in the mean fitness, and other properties. The focus is on the behavior of a broad class of models: those with a distribution of selective advantages of available beneficial mutations that falls off more rapidly than exponentially. For such distributions, many aspects of the dynamics are universal – quantitatively so for extremely large populations. On the most important time scale that controls coalescent properties and fluctuations of the speed, the dynamics is reduced to a simple stochastic model that couples the peak and the high-fitness “nose” of the fitness distribution. Extensions to other models and distributions of available mutations are discussed briefly.
Genealogies of rapidly adapting populations
Richard A. Neher, Oskar Hallatschek
(Submitted on 15 Aug 2012)
The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Toward this goal, we explore the properties of genealogies that emerge from models of continual adaptation. We show that lineages trace back to a small pool of highly fit ancestors, in which simultaneous coalescence of more than two lineages frequently occurs. While such multiple mergers are unlikely under the neutral coalescent, they create a unique genetic footprint in adapting populations. The site frequency spectrum of derived neutral alleles, for example, is non-monotonic and has a peak at high frequencies, whereas Tajima’s D becomes more and more negative with increasing sample size. Since multiple merger coalescents emerge in various evolutionary scenarios characterized by sustained selection pressures, we argue that they should be considered as null-models for adapting populations.
Genetic Diversity and the Structure of Genealogies in Rapidly Adapting Populations.
Michael M. Desai, Aleksandra M. Walczak, Daniel S. Fisher
(Submitted on 16 Aug 2012)
Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a single genetic locus. However, in linked regions of rapidly adapting genomes, multiple beneficial mutations at different loci can segregate simultaneously within the population, an effect known as clonal interference. This leads to a subtle interplay between hitchhiking and interference effects, which leads to a unique signature of rapid adaptation on genetic variation both at the selected sites and at linked neutral loci. Here, we introduce an effective coalescent theory (a “fitness-class coalescent”) that describes how positive selection at many perfectly linked sites alters the structure of genealogies. We use this theory to calculate several simple statistics describing genetic variation within a rapidly adapting population, and to implement efficient backwards-time coalescent simulations which can be used to predict how clonal interference alters the expected patterns of molecular evolution.