N-person games and the evolution of co-operation: a model based on predator inspection in fish

Two N-person game theoretical models examining the evolution of co-operation during predator inspection in fish are presented. Predator inspection occurs in small shoals of fish, in which one to a few individuals, the "inspectors" (co-operators) break away from the shoal and cautiously approach a predator to obtain information on this potential danger. In the models presented here, remaining with the shoal and not inspecting is considered an act of defection. Both model I and II produce a stable internal polymorphism of inspectors and noninspectors. While the equilibrial frequency of inspectors can be low (i.e. less than 10%) at large shoal size, the proportion of shoals containing any inspectors--and therefore exhibiting the inspection behavior--is much greater. Both models presented here, and N-person games in general are equivalent to intrademic group selection models of evolution in structured populations, in which shoals are trait groups and co-operation evolves by between-shoal selection. While the results are cast in terms of predator inspection, the model itself is general and applies to any multi-group scenario where co-operators benefit entire groups at their own expense. The results presented here add to the mounting theoretical and empirical evidence that co-operation is frequently not a pure evolutionarily stable strategy, and that many metapopulations should be polymorphic for both co-operators and defectors.