Interactions Between Searching Predators and Hidden Prey - Search Theory: A Game Theoretic Perspective - page 223

15.2.1 The Model of Ydenberg and Dill

The argument of [ 14 ] is as follows. Suppose that a prey individual has seen a
predator approaching it. Thus both are aware of each other's location. If the prey
continues foraging the predator will continue its approach and an attack will occur.
If the prey flees it will lose some foraging time. The earlier it flees, the more foraging
time will be lost. The earlier the prey flees, the more chance it will have of escaping
the predator. There is thus a benefit from fleeing B which decreases with predator
distance, and a cost C which increases with predator distance. They contend that at
every point the prey chooses to flee if the benefit of doing so outweights the cost,
i.e. B C decreases with distance, and so increases with time (the distance

decreases with time as the predator approaches), and so the prey should flee at the
critical point when B

> C . B −

C .
It should also be noted that instead of just not fleeing, prey often give responses
short of flight when detecting a predator. This includes lifted tails in squirrels, stand-
ing posture in hares, primate alarm calls and stotting by gazelles. Stotting is where
the gazelle jumps high into the air when faced by a potential predator, and is be-
lieved to be a signal to the predator that the prey is healthy and so should not be
chased, see [ 4 ]. These can be signals to the predator that it has been detected, and
that it consequently has low success probability, and so should not waste its time
and energy in an attack.
The model of [ 14 ] makes clear predictions which match real observations well,
and consequently has been very influential. The key predictions of the model are as
follows:

=

(i) Flight distance should increase with the risk of capture.

(ii) Flight distance should decrease with increased cost of fleeing.

(iii) Flight distance changes with the effectiveness of alternative defence
tactics such as crypsis. If a prey is cryptic then perhaps an approaching
predator has not seen it and the level of crypsis may affect flight distance
(see the model of [ 2 ] described in Sect. 15.3 ).

(iv) Flight distance varies with the fitness benefit associated with group mem-
bership. Larger group size may reduce predation risk (but also possibly
foraging efficiency) and so may reduce flight distance.