In evolutionary dynamics, a key measure of a mutant trait's success is its fixation probability---the probability that it takes over the population given some initial mutant-appearance distribution. This fixation probability is difficult to compute in general, as it depends on the mutation's effect on URLanism as well as the population's spatial structure, mating patterns, and other factors. Here we consider weak selection, meaning the mutation's effect on URLanism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which spatial structure is arbitrary , but fixed . The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We apply method to obtain new results for well-studied models of evolutionary dynamics on graphs.
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on URLanism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on URLanism is small. We obtain a weak-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed) . The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.
R
its fixation probability---the
the
R
fixation probability
"fixation probability"
R
Here
In this study,
R
meaning
which means that
R
spatial structure is arbitrary , but fixed
the size and spatial structure are arbitrary (but fixed)
R
apply method
conclude by applying these methods
D
well-studied models of