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 parasitoidsʹ 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.