Unique coevolutionary dynamics in a predator–prey system

In this paper, we study the predator–prey coevolutionary dynamics when a prey's defense and a predator's offense change in an adaptive manner, either by genetic evolution or phenotypic plasticity, or by behavioral choice. Results are: (1) The coevolutionary dynamics are more likely to be stable if the predator adapts faster than the prey. (2) The prey population size can be nearly constant but the predator population can show very large amplitude fluctuations. (3) Both populations may oscillate in antiphase. All of these are not observed when the handling time is short and the prey's density dependence is weak. (4) The population dynamics and the trait dynamics show resonance: the amplitude of the population fluctuation is the largest when the speed of adaptation is intermediate. These results may explain experimental studies with microorganisms.