Fixation probabilities in evolutionary dynamics under weak selection

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