Originally published as Genetics Published Articles Ahead of Print on October 18, 2007.

Genetics, Vol. 177, 2135-2149, December 2007, Copyright © 2007
doi:10.1534/genetics.107.075697

Analytical Description of Mutational Effects in Competing Asexual Populations

Daniel Pinkel1

Comprehensive Cancer Center and Department of Laboratory Medicine, University of California, San Francisco, California 94143

1 Address for correspondence: University of California, Box 0808, San Francisco, CA 94143.
E-mail: pinkel{at}cc.ucsf.edu

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.