Top predators constrain the habitat selection games played by intermediate predators and their prey

Effects of predators on prey habitat selection, and reciprocal effects of prey on predator habitat selection, have been analyzed using game theory. In the absence of predators, models predict that prey (e.g., herbivores) will aggregate strongly in habitats where their resources (e.g., plants) are abundant. However, game theoretic models predict that in the presence of predators, prey use of resource-rich habitats declines. Paradoxically, it is instead predators that are predicted to be mostly strongly aggregated in areas where the prey's resources (plants) are abundant, even though the predators themselves do not utilize these resources. This striking result has been dubbed the leapfrog effect by Sih (1998, 2004). Here I explore the possibility that predictions for predator and prey habitat selection are sensitive to the assumption that predators forage free from any predation risk of their own. I contrast the predictions of a 3-trophic level model with those of a 4-trophic level model, and show that incorporating the constraint imposed on intermediate predator foraging behavior by the risk of attack from top predators can produce substantial changes in model predictions. Most importantly, the leapfrog effect is largely eliminated. Top predators impose important constraints on foraging decisions made by intermediate predators, opening up new solutions for herbivores.