Speed of evolution in large asexual populations with diminishing returns
Résumé
The adaptive evolution of large asexual populations is generally
characterized by competition between clones carrying different beneficial
mutations. Interference slows down the adaptation speed and makes the
theoretical description of the dynamics more complex with respect to the
successional occurrence and fixation of beneficial mutations typical of
small populations. A simplified modeling framework considering multiple
beneficial mutations with equal and constant fitness advantage is known to
capture some of the essential features of laboratory evolution
experiments. However, in these experiments the relative advantage of a
beneficial mutation is generally dependent on the genetic background. In
particular, the general pattern is that, as mutations in different loci
accumulate, the relative advantage of new mutations decreases, a trend
often referred to as “diminishing return” epistasis. Here, we propose a
phenomenological model that generalizes the fixed-advantage framework to
include this negative epistasis in a simple way. We evaluate analytically
as well as with direct simulations the quantitative consequences of
diminishing returns on the evolutionary dynamics. The speed of adaptation
decreases in time and reaches a limit value corresponding to neutral
evolution in the long time limit. This corresponds to an increase of the
diversity in terms of “classes of mutation” in the population. Finally, we
show how the model can be compared with dynamic data on fitness and number
of beneficial mutations from laboratory evolution experiments.