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Abstract

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in
game outcomes translate into small fitness differences. Many results have been derived using weak selection
approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results
derived under weak selection are also qualitatively valid for intermediate and strong selection. By ‘‘qualitatively valid’’ we
mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection
increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to
higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous
examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In
particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant
for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even
when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate
intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player
games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number
of strategies n. In particular, rank changes are almost certain for n§8, which jeopardizes the predictive power of results
derived for weak selection.