Modelling the sequential behaviours of simultaneous predator and prey patch use

Abstract

Models investigating predator–prey games often fix one player's behaviour while allowing the other to make patch use choices. Here, we use adaptive dynamics to model changes in behavioural rates of a predator and prey, while explicitly allowing both to make decisions simultaneously. Our model focuses on a two-patch situation. The prey can move between an open patch, allowing for energy intake but also predation risk, and a refuge with no possibility of energy intake or predation risk. The predator can move between that patch, where it can attack prey, and an alternative patch that provides a fixed rate of energy intake, and consequently imposes a missed opportunity cost (MOC) of using the focal patch. The model predicts how the rates of movement by the players are influenced by specific parameters, including the predator's lethality and MOC, as well as the information available to the players. For example, our model predicts that the time a prey takes to emerge from its refuge and the time a predator waits for the prey to emerge depend on the sequence of events leading to the prey entering the refuge. For instance, the predator would leave the patch more quickly and the prey would emerge from the refuge more quickly if the prey entered the refuge after a failed attack rather than as part of its time allocation. • We use adaptive dynamics to model behavioural changes in predator–prey patch use. • We model a two-patch choice: open vs environment (predator); open vs refuge (prey). • Players can make decisions simultaneously and use information from recent encounters. • Specific parameters (risk, opportunity) affect each player's rate of movements. • Adaptive movement rules depend on predator lethality and missed opportunity costs.