Interactions Between Searching Predators and Hidden Prey - Search Theory: A Game Theoretic Perspective - page 222

attacked by a hawk [ 7 ]. However, there are also important situations where this is not
the case. The classic case is on open plains where predators are very often present
and where both prey and predators can be clearly visible to each other. To flee on all
occasions would disrupt foraging to an unsustainable extent. Rather the prey must
decide when the level of risk is sufficiently high to make fleeing the best strategy,
and when to continue foraging [ 12 ]. A second scenario is when a prey individual
has not yet been observed by the predator, for example an ungulate calf hiding in
long grass. To run will alert the predator to its presence, so it may be best to remain
still if there is sufficient chance that the predator will not discover the individual.
Thus the key decision for the prey here again, is when to run and when not to [ 2 ].
These two important cases are related, and we shall look at existing models of both,
although the central focus of this chapter is on the second case. In particular we
shall then introduce a new model of an interesting variant of the second case where
the predator also has key strategic decisions to make.
15.2 Interactions Between Visible Prey and Predators
Avoiding and fleeing from predators is one of the central activities of many animals.
It has been postulated that this task is so important in comparison to foraging (the
threat of death versus an incremental gain in resources) that when there is a predator
threat this always takes precedence over foraging, see for example [ 9 ]. Thus when
an approaching predator is detected by a prey individual this should lead to some
immediate anti-predator response, such as flight. Ydenberg and Dill [ 14 ] suggested
that this view was incorrect and that detection and response were often not so di-
rectly associated. They introduced an “economic” model, with benefits and costs
associated with fleeing from predators or continuing to forage (with the potential
for later flight).