Eco-Evolutionary Oscillations in Predators and Prey System

We investigate the coevolutionary dynamics in a predator–prey system with Holling-III functional response. By using the theory of adaptive dynamics, we first classify coevolutionary singular coalitions and then prove the existence of cyclic coevolution. Coupling this cyclic trait evolution with oscillatory population dynamics generates multi-timescale oscillations in population size. These oscillations arise from the interplay of fast ecological and slow evolutionary processes, producing distinct patterns such as frequency-modulated and bursting oscillations. Our results demonstrate that complex oscillations in population size emerge intrinsically from eco-evolutionary feedback loops.