Survival of the weakest inn-person duels and the maintenance of variation under constant selection

The persistence of extensive variation in nature seems to stand against the most general principle of evolution by natural selection: in antagonistic interactions, the stronger type is expected to replace the weaker. Game theory shows that, however, in contrast to this intuitive expectation for interactions between two players, strategic considerations on fitness maximization in repeated pairwise interactions between three players (truels) or more (N-person duels) lead to what can be dubbed "survival of the weakest": the weakest individual can have the highest fitness. A paradox arises: competitive skills cannot be improved by natural selection, unless we assume mutations with strong effects or unless we assume that interactions are exclusively between two individuals. The paradox disappears, however, with more realistic assumptions (a mixture of duels and truels; the attacked individual backfires; the contest can end without a winner; defensive and offensive skills are correlated; players not directly involved in the contest suffer collateral damage). An unexpected new result emerges: the weaker types can persist in a population in the absence of recurrent mutations, migration, and fluctuating selection. Game theory and the analysis ofN-person duels, therefore, help understand one of the most enduring puzzles in evolutionary biology: the maintenance of variation under constant selection.