You can run--or you can hide: optimal strategies for cryptic prey against pursuit predators

We consider the optimal behavior of a cryptic prey individualas it is approached by a predator searching for prey. Althoughthe predator has not yet discovered the prey, it has an increasinglikelihood of doing so as it gets closer to the prey. Further,the closer the predator is to the prey when it discovers it,the more likely the predator will be to capture the prey. Thesearguments suggest that the prey should flee before the predatordiscovers it. However, the act of fleeing will alert the predatorto the presence of the prey and trigger an attack that mightnot have occurred otherwise. We capture these conflicting outcomesin a mathematical model, which we then use to predict the optimalbehavior of the prey and predator. We argue that the optimalstrategy for the prey is either to run as soon as they detecta predator approaching or to only flee in response to havingbeen detected by the predator. Running as soon as the predatoris detected is associated with low predator search speeds, alow nonpredation cost to running, a large advantage to the preyin initiating chases rather than reacting, limited ability tospot the predator at distance, a high ability to spot prey bythe predator, and a high probability that chases will be successful.The optimal strategy for the predator depends on whether itscurrent trajectory is taking it closer to or further from theprey. In the latter case, the predator should attack immediatelyon discovering the prey; in the former case, it should delayits attack until it reaches the point on its current trajectorywhere distance to the prey is minimized.