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Genetics, Vol. 179, 603-620, May 2008, Copyright © 2008
doi:10.1534/genetics.107.079319
The Stochastic Edge in Adaptive Evolution
Éric Brunet*,
Igor M. Rouzine
and
Claus O. Wilke
,1
* Laboratoire de Physique Statistique, École Normale Supérieure, 75230 Paris Cedex 05, France, Department of Molecular Biology and Microbiology, Tufts University, Boston, Massachusetts 02111 and Section of Integrative Biology, Institute for Cell and Molecular Biology, and Center for Computational Biology and Bioinformatics, University of Texas, Austin, Texas 78712
1 Corresponding author: Integrative Biology, #1 University Station—C0930, University of Texas, Austin, TX 78712.
E-mail: cwilke{at}mail.utexas.edu
In a recent article, Desai and Fisher proposed that the speed of adaptation in an asexual population 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. Desai and Fisher perform an elaborate stochastic calculation of the mean time 
until a new class of mutants has been established and interpret 1/ as the speed of adaptation. As they note, however, their calculations are valid only for moderate speeds. This limitation arises from their method to determine : Desai and Fisher back extrapolate the value of from the best-fit class's exponential growth at infinite time. This approach is not valid when the population adapts rapidly, because in this case the best-fit class grows nonexponentially during the relevant time interval. Here, we substantially extend Desai and Fisher's analysis of the stochastic edge. We show that we can apply Desai and Fisher's method to high speeds by either exponentially back extrapolating from finite time or using a nonexponential back extrapolation. Our results are compatible with predictions made using a different analytical approach (Rouzine et al.) and agree well with numerical simulations.