Unusual predator-prey dynamics under reciprocal phenotypic plasticity.

Recent theories and experiments have shown that plasticity, such as an inducible defense or an inducible offense in predator-prey interactions, strongly influences the stability of the population dynamics. However, such plastic adaptation has not been expected to cause unusual dynamics such as antiphase cycles, which occur in experimental predator-prey systems with evolutionary adaptation in the defensive trait of prey. Here I show that antiphase cycles and cryptic cycles (a large population fluctuation in one species with almost no change in the population of the other species) can occur in a predator-prey system when both member species can change their phenotypes through adaptive plasticity (inducible defenses and offenses). I consider a familiar type of predator-prey system in which both species can change their morphology or behavior through phenotypic plasticity. The plasticity, that is, the ability to change between distinct phenotypes, is assumed to occur so as to maximize their fitness. I examined how the reciprocal adaptive plasticity influences the population dynamics. The results show that unusual dynamics such as antiphase population cycles and cryptic cycles can occur when both species show inducible plasticity. The unusual dynamics are particularly likely to occur when the carrying capacity of the prey is small (the density dependence of the prey's growth is strong). The unusual predator-prey dynamics may be induced by phenotypic plasticity as long as the phenotypic change occurs to maximize fitness.