Self-reinforcing spatial patterns enslave evolution in a host-parasitoid system.

Spatially structured models of host-parasitoid interactions exhibit self-structuring into spatial patterns such as spiral waves and turbulence. We discuss the consequences of these patterns in an eco-evolutionary model of host-parasitoid interactions with evolution of the parasitoids' ability to disperse towards dense populations of hosts (termed the aggregation strength). It turns out that the direction of, and the time-scale over which the evolutionary selection pressure acts depends on the type of spatial pattern a parasitoid finds itself in. Evolution tends to reinforce the existence of the prevalent local pattern. Moreover, there is also competition between the patterns that ultimately determines the eco-evolutionary attractor. It is the interaction between multiple processes across spatial and temporal scales that leads to the rich meso-scale behaviour. Predicting the evolutionary outcome from statistical measures and subprocesses is shown to give incorrect and conflicting answers. Comparison with the behaviours of the complex Ginzburg-Landau equation shows striking similarities on which we comment.