arXiv,
Genetics,
pdf.
In a recent article, Desai and Fisher (2007) 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
τ until a new class of
mutants has been established, and interpret 1/
τ 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
τ: Desai and Fisher back-extrapolate the value of
τ
from the best-fit class' exponential growth at infinite time. This approach is
not valid when the population adapts rapidly, because in this case the best-fit
class grows non-exponentially 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 non-exponential
back-extrapolation. Our results are compatible with predictions made using a
different analytical approach (Rouzine et al. 2003, 2007), and agree well with
numerical simulations.