The effects of opportunistic and intentional predators on the herding behavior of prey

In this article, we study how predator behavior influences the aggregation of prey into herds. Game-theoretic models of herd formation are developed based on different survival probabilities of solitary prey and prey that join the herd and on the predator's preference of what type of prey to search for. For an intentional predator that will only pursue its preferred type of prey, a single herd with no solitaries cannot emerge unless the herd acts as a prey refuge. If neither prey choice provides a refuge, it is shown that an equilibrium always exists where there are both types of prey and the predator does not always search for the same type of prey (i.e., a mixed equilibrium exists). On the other hand, if the predator is opportunistic in that it sometimes shifts to pursue the type of prey that is observed first, there may be a single herd equilibrium that does not act as a prey refuge when there is a high level of opportunistic behavior. For low opportunistic levels, a mixed equilibrium is again the only outcome. The evolutionary stability of each equilibrium is tested to see if it predicts the eventual herding behavior of prey in its corresponding model. Our analysis confirms that both predator and prey preferences (for herd or solitary) have strong effects on why prey aggregate. In particular, in our models, only the opportunistic predator can maintain all prey in a single herd that is under predation risk.