Stochastic rules for predator and prey hunting and escape behavior in a lattice-based model

Abstract

Understanding of ecosystem resilience and stability requires comprehending predator–prey dynamics because ecosystems consist of dynamically interacting subsystems that include predator–prey relationships. This relationship is closely related to the hunting–escaping strategies employed by the predator and prey. Therefore, understanding the effects of hunting and escaping strategies on ecosystems will lead to a better understanding of these systems. As an approach for describing the predator–prey interaction, lattice-based models have been adopted because this approach has strong advantages for simulating various dynamical processes of individual–individual interaction. In the models, each lattice cell is either considered as an attractive/repulsive cell, or an individual cell, or else it is empty. The attractive (or repulsive cell) can be interpreted as the prey (or predator) of the individual. These states allow us to incorporate the ecological processes of local antagonistic interactions, namely the spread of disturbances (by the predator) and regrowth or recovery (by the prey). These processes are directly related to the strategic behavior of individuals, such as hunting and escaping. In this study, we suggest a simple and effective mapping formula as a stochastic rule to describe the hunting and escaping behavior. This formula could be widely used not only in the behavior but also in competitive and cooperative relationships.