Joining or opting out of a Lotka-Volterra game between predators and prey: does the best strategy depend on modelling energy lost and gained?

Apart from interacting, prey and predators may also avoid each other by moving into refuges where they lack food, yet survive by switching to an energy-saving physiological state. Lotka-Volterra models of predator-prey interactions ignore this option. Therefore, we have modelled this game of 'joining versus opting out' by extending Lotka-Volterra models to include portions of populations not in interaction and with different energy dynamics. Given this setting, the prey's decisions to join or to opt out influence those of the predator and vice versa, causing the set of possible strategies to be complex and large. However, using game theory, we analysed and published two models showing (i) which strategies are best for the prey population given the predator's strategy, and (ii) which are best for prey and predator populations simultaneously. The predicted best strategies appear to match empirical observations on plant-inhabiting predator and prey mites. Here, we consider a plausible third model that does not take energy dynamics into account, but appears to yield contrasting predictions. This supports our assumption to extend Lotka-Volterra models with 'interaction-dependent' energy dynamics, but more work is required to prove that it is essential and that what is best for the population is also best for the individual.