A comparison of ecological and eco-evolutionary system with rapid predator evolution

Evolution takes place in ecological system which involves interactions with other species. To describe such evolution, the modeling of predator-prey system is essential with simultaneous evolution of interacting species. In this paper, a predator-prey system with rapid predator evolution is proposed and studied. Rapid evolution is considered to affect the outcomes of simultaneous ecological change of dieting. The change of such diet is fast compared to the timescale of ecological system. We introduce a timescale difference parameter between the dynamics of a predator trait and the ecological system. The model is analyzed in terms of theoretical as well as numerical point of view. The comparisons are shown in between ecological and evolutionary dynamics. Simulated results illustrate that evolution causes chaotic dynamics and it will be controlled to periodic orbits, and stable steady state by increasing parameter values. On the other hand, the ecological system has only limit cycle and steady state dynamics with the variation of parameters. Therefore, the evolution makes the predator-prey dynamics to more complex. The proposed model is applicable in large population size, short generation times, and well-changed environment system. More preciously, the system has the suitable applicability in plankton system.