Abstract
The common forces shaping the evolution of biological
organisms on earth are mutation, selection, and genetic drift arising from
sampling noise in the reproduction process. A decent theory of
evolution should incorporate all three features. In addition,
the possible effects of recombination must be taken into account.
If there is no recombination, as in asexually reproducing
organisms such as bacteria or viruses, beneficial mutations
which appear almost at the same time compete against each other
for fixation, which is not the case in organisms with
recombination. This phenomenon is referred to as clonal
interference (CI). The theory of CI developed
by Gerrish and Lenski (GL) in a seminal paper 1 is based on two crucial
assumptions - the absence of multiple mutations and the independence
of genetic drift and CI - which are both expected to become invalid
in very large populations. To assess the range of validity of the GL
theory, we studied the Wright-Fisher model of non-overlapping discrete
generations with multiplicative fitnesses numerically for
finite populations, and analytically in the deterministic
limit of infinite population size.
We found that when the population size is very large, the GL theory
deviates significantly from the simulation results.
In particular, the prediction of Gerrish 2 for the reduction of the
index of dispersion (the ratio of the variance to the mean) of
the number of fixed mutations in the CI regime
is not compatible with our findings. We show that, for large populations,
a distinction has to be made between the number of substitution events
and the number of fixed mutations, and we predict the limiting values of
the index of dispersion for these two quantities.
Moreover, our simulations partly explain why the GL theory,
despite it shortcomings, has provided a reasonable interpretation of
microbial evolution experiments.
1) P.J. Gerrish and R.E. Lenski, Genetica 102/103, 127 (1998).\\
2) P.J. Gerrish, Nature 413, 299 (2001).
Links and resources
Tags