Evolution of signalling through pursuit deterrence in a two-prey model using game theory

Abstract

We model the evolution of a pursuit-deterrent signal of ‘perception advertisement’ for the case in which a predator can travel among many patches, each of which contain two prey. We consider a signal that is difficult for prey to fake, such as approaching the predator, and assume that the signal also alerts other prey in the patch, thereby reducing the overall value of that patch to the predator. We analyse the model using evolutionary game theory and adaptive dynamics on prey and predator fitness-generating functions to determine convergent stable equilibrium solutions for the behaviour of prey and predator. We consider the effects on equilibria of the probability of predator detection, signalling cost, predator travel time and the chance of killing the prey. Depending on the parameter values, we find stable equilibria at pure signalling, nonsignalling and mixed evolutionarily stable strategies (ESSs). For example, prey are more likely to signal when they have a low probability of detecting the predator, and when the predator's missed opportunity costs are higher. We also find that there are two basins of attraction such that the system evolves towards one of them depending on the initial strategy values. This is the first two-prey pursuit-deterrent signalling game we are aware of, providing a novel theoretical basis for the evolution of signalling in group-living prey.