On inferring evolutionary stability in finite populations using infinite population models

Abstract Models of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations selected against always go extinct, whereas in finite they can persist and even reach fixation. Nevertheless, for arbitrarily small phenotypic effect , it is widely believed sufficiently large if opposes invasion mutants, then also their Here, we identify circumstances under which infinite-population models do or not accurately predict evolutionary outcomes large, populations. We show there no size above considering only generally suffices: any size, situations effect, but favours This an unlikely limiting case; occur when fitness a smooth function evolving trait, process biologically sensible. opposition does imply fixation: fact, $$n$$ n -player snowdrift game (a common model cooperation) sufficient conditions mutants precludes fixation—in populations— . find which—no matter how population—the trait fixes depends on important because particular approximation reality.