Adaptive evolution of aposematism of a prey species subject to Shepherd’s recruitment function

We develop and analyze a prey–predator interaction model with aposematic prey. Prey’s per-capita growth is subjected to Shepherd’s recruitment function, while predators have a Holling type-II functional response. Ecological dynamics is investigated in presence of a trade-off between prey’s aposematic behavior and resource searching efficiency; significance of the searching efficiency and the saturation constant in the coexistence of prey and predators are explored. Adaptive dynamics is employed to explore the evolution of aposematic behavior of prey species. To assess the evolutionary process, invasion fitness is constructed, and the corresponding evolutionary singular strategies are identified in pairwise invasibility plot (PIP). We discover that the prey strategy evolution is incapable of facilitating evolutionary branching and thus prey species stay monomorphic throughout its evolutionary history. Evolutionary bistability arises when the aposematism function is regarded as normal distribution. Furthermore, predator behavior determines the extent of the feasible evolution set, which in turn dictates the occurrence of bifurcation. For concave–convex–concave form of aposematism function, unique evolutionary attractor is identified. The prey’s aposematic behavior in this situation increases and finally saturates as the prey’s searching efficiency and saturation constant increase.