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Analytical Description of Mutational Effects in Competing Asexual Populations

The adaptation of a population to a new environment is a result of selection operating on a suite of stochastically occurring mutations. This article presents an analytical approach to understanding the population dynamics during adaptation, specifically addressing a system in which periods of growth are separated by selection in bottlenecks. The analysis derives simple expressions for the average properties of the evolving population, including a quantitative description of progressive narrowing of the range of selection coefficients of the predominant mutant cells and of the proportion of mutant cells as a function of time. A complete statistical description of the bottlenecks is also presented, leading to a description of the stochastic behavior of the population in terms of effective mutation times. The effective mutation times are related to the actual mutation times by calculable probability distributions, similar to the selection coefficients being highly restricted in their probable values. This analytical approach is used to model recently published experimental data from a bacterial coculture experiment, and the results are compared to those of a numerical model published in conjunction with the data. Finally, experimental designs that may improve measurements of fitness distributions are suggested.