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. Under weak selection, meaning a small perturbation of the neutral model, we give a general first-order expansion of a mutant's fixation probability for an arbitrary initial configuration of mutant and resident types. This result reduces the problem of whether weak selection favors a trait from exponential to polynomial complexity in the population size . We conclude with applications to evolutionary games in structured populations .
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 .
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the
its fixation probability---the
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Under
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
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a small perturbation of the neutral model, we give a general first-order
the mutation's effect on URLanism is small. We obtain a weak-selection perturbation
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for
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This result reduces the
Our results apply to a broad class of stochastic evolutionary models, in which spatial structure is arbitrary, but fixed. The
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weak
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trait
given trait is thereby reduced
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. We conclude with applications to evolutionary games in structured populations
, when selection is weak. We apply method to obtain new results for well-studied models of evolutionary dynamics on graphs