Drastic growth effect may explain sympatric cannibalistic polymorphism

Cannibalistic polyphenism is observed in many fishes and amphibians. In the case of amphibian larvae, cannibal morph and typical morph coexist. Benefits and costs of the cannibal morph have been studied empirically but the mechanism of the maintenance of polymorphism is not well known. Here, we construct a game model of typical and cannibal morph strategies to obtain the condition of stable coexistence. Generally, once an individual succeeds in cannibalism, it grows very quickly, which facilitates the next cannibalism. In a model without this 'drastic growth effect', stable coexistence cannot occur. To represent drastic growth effect, it is assumed that cannibal/typical morph stage is followed by giant/normal stage. A cannibal morph that performs cannibalism in the first stage can become a 'giant' in the next stage. This model allows stable coexistence of cannibal and typical morphs. The condition for coexistence is that payoff of a giant is two times larger than normal individuals. As long as direct consumption of victim's body is considered as reward for successful cannibalism, coexistence cannot be explained. When the reward is considered as social standing of being outstanding size in a population, sympatric cannibalistic polymorphism is possible, without regard to the initial size variation or resource shortage.