Intra-seasonal Strategies Based on Energy Budgets in a Dynamic Predator-Prey Game

We propose a game-theoretical model to describe intra-seasonal predator-prey interactions between predatory mites (Acari: Phytoseiidae) and prey mites (also called fruit-tree red spider mites) (Acari: Tetranychidae) that feed on leaves of apple trees. Its parameters have been instantiated based on laboratory and field studies. The continuous-time dynamical model comprises predator and prey densities, along with corresponding energy levels, over the length of a season. It also includes time-dependent decision variables for the predator and the prey, representing the current portions of the predator and prey populations that are active, as opposed to diapausing (a state of physiological rest). Our aim is to find the optimal active/diapausing ratio during a season of interaction between predatory
mites and prey mites: this is achieved by solving a dynamic game between predator and prey. We hereby extend our previous work that focused solely on the optimal strategy for the prey. Firstly, we analyze the optimal behavior of the prey. Secondly, we show that the optimal strategy for the predator is to stay active for the entire season. This result corresponds to biological observations.