Evolution of hunting efficiency of predator and hiding efficiency of prey in a stage-structured prey-predator model

The predator-prey interaction is likely the most studied relationship in ecology. Predator consumption rate is modulated by more efficient hunting of prey by predators or, conversely, by more efficient hiding from predators by prey. Here, we study predator and prey adaptations in these traits using a common modeling framework, consisting of juvenile prey, adult prey, and an unstructured predator. What distinguishes the cases with predator and prey adaptations is the trade-offs. While more efficient predator hunting is assumed to be negatively correlated to its mortality rate (hunting trade-off), more efficient prey hiding is assumed to reduce prey reproduction (hiding trade-off). Natural selection benefits predators with high hunting efficiency if the hunting trade-off is strongly concave. For prey hiding efficiency, concave trade-offs give rise to a continuously stable strategy, whereas evolutionary branching is observed for convex trade-offs. In the latter case, the distance separating two branches on the evolutionary tree grows with increasing prey maturation rate; one branch eventually develops toward maximal hiding efficiency and minimal reproduction rate, while the other branch evolves towards minimal hiding efficiency and maximal reproduction rate. The concave trade-off thus serves a dual function in prey and predator evolution. For prey-hiding evolution, it increases prey protection. For predator-hunting evolution, it decreases hunting efficiency and thus promotes prey protection, too. Thus, the trade-off form proves to be a crucial determinant of evolutionary outcomes.