Predator-prey coevolution: Interactions across different timescales

Using a simple predator-prey model we studied the consequences of interlocking processes that occur on ecological and evolutionary timescales. Various evolutionary attractors are shown, one of which is a system of two prey and two predator quasi-species packed in an alternating pattern. This pattern, which proves to be very robust, is studied in more detail to investigate the interaction between evolutionary and population dynamics. The evolutionary and the population dynamics both show complex periodic behaviour, with the same two dominant periods. The two prey quasi-species as well as the two predator 'quasi-species' oscillate synchronously, albeit out of phase. It is this temporal pattern in the population dynamics which drives the evolutionary dynamics and evolutionary dynamics which force the population dynamics to periodic behaviour with much shorter periods than if there were no evolution. This mutual influencing of the periodic behaviour is an interesting consequence of the interaction across different timescales. It is further shown that the evolutionary dynamics are essential for the maintenance of different species in the system.