Effects of size refuge specificity on a predator-prey model

Predation is a major cause of early-stage mortality for prey individuals, which are often forced to use refuges in order to reduce the risk of being consumed. The ability of certain genotypes in a prey population to reach a size refuge from predation may contribute significantly to the preservation of community diversity. We investigate how the specificity of this behavior affects the evolution of a given population by using a modified Lotka-Volterra model, in which the proportion of each genotype available for predation consists of two components: an intrinsic part and a combination from all genotypes present in the population. The trade-off of these components is characterized by a specificity parameter. From the viewpoint of population dynamics, we observe that the ability of the mutant to invade the resident population strongly depends on the values of this parameter. Finally, we describe the possible evolutionary outcomes, analytically and numerically.