Interactions Between Searching Predators and Hidden Prey - Search Theory: A Game Theoretic Perspective - page 225

Cooper and Frederick [ 3 ] developed a more realistic model, which nevertheless
agreed with the main predictions of the model of [ 14 ]. The extra flexibility of their
model meant that they were also able to make new predictions based upon the differ-
ent parameters that they introduced, that we see in ( 15.4 ). For instance flight distance
should increase with initial fitness F 0 , as the fitter the individual initially, the more it
has to lose and the costs associated with predator attack increase, whereas the gain
associated with extra forgaging is unchanged. Conversely if the benefit of foraging
B ∗ increases, then the gain associated with remaining increases, but the cost is un-
changed, and so the optimal flight distance is reduced. For each parameter there was
a clear prediction of the effect that altering its size would have on the flight distance.
We should note also that it is of course easy to replace the functions used with al-
ternative ones if they represent a particular scenario better, but that effectively the
same qualitative behaviour is likely to result from most plausible functions.

15.3 Interactions Between Cryptic Prey and a Mobile
Visible Predator

Broom and Ruxton [ 2 ] consider prey that are initially stationary and to some extent
cryptic in their environment, such that predators cannot detect them at a distance.
Examples include ungulate calves hiding in long grass, many cryptically coloured
ground-nesting birds and flat fish lying on the sea bottom.

15.3.1 The Predator-Prey Interaction

In their model, a predator-prey encounter begins when the prey detects an approach-
ing predator. Since the predator has yet to detect the prey when the interaction
begins, there is no reason to expect that its trajectory will be taking it directly to-
wards the prey. The closer the predator gets to the prey, the more likely it is to detect
it. The closer the predator is when the prey is detected, the more likely it is that
the ensuing attack by the predator will be successful. Fleeing from the predator will
in most cases alert the predator to the presence of the prey individual. Hence, there
may be a countervailing pressure for the prey to sit tight, rely on its crypsis, and only
flee if it perceives that the predator has detected it, and is attacking. A key difference
between this model and that of [ 14 ] is in the cost to the prey associated with fleeing
early; in the model of [ 14 ] this cost is the opportunity cost associated with reduced
time spent feeding.
The predator starts at a distance r from the prey, initially at an angle

θ to the

prey (so 0 means it is heading straight for the prey). The predator is assumed

to move in an undeviating straight line at a constant speed, unless it detects the prey
individual. Thus, as in Sect. 15.2.2 , there is a deterministic relationship between
time and the position of the predator, and we again focus on the predator position.

θ =