The stochastic edge in adaptive evolution

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  • 24 July 2007
Abstract
In a recent article, Desai and Fisher (2007) proposed a new method to calculate the speed of adaptation in asexual populations. The main idea behind their method is that the speed of adaptation is determined by the dynamics of the stochastic edge of the population, that is, by the emergence and subsequent establishment of rare mutants that exceed the fitness of all sequences currently present in the population. They perform an elaborate stochastic calculation of the mean time until a new class of mutants has been established, which leads them to a prediction of the speed at which the population adapts. Their result, however, is at variance with previous work on the same model (Rouzine et al. 2003 and its recent upgrade Rouzine et al. 2007), which is based on the same main idea but uses a rather different approach to predict the adaptation speed. Here, we substantially extend Desai and Fisher's analysis of the dynamics at the stochastic edge. First, we rederive their result more carefully using the same basic approach, and point out the approximations made. Then, we argue that some of these approximations are too coarse, for example the method of back-extrapolation of the best-fit class's dynamics. We suggest alternative assumptions, which lead us to a different result compatible with the findings of Rouzine et al. (2003, 2007). Finally, we compare the accuracy of both results with numerical simulations.

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