Interactions Between Searching Predators and Hidden Prey - Search Theory: A Game Theoretic Perspective - page 230

crevice in a rock). In the second procedure, the experimenter proceeded as above,
but after stopping ran towards the lizard, simulating an attack. The lizard then fled
to a refuge, after which the experimenter stayed in the local area until the lizard next
left its refuge. When the lizard left, the first procedure was again followed. In each
case the human predators did not discontinue their search until the prey had fled.
Thus in the experiments, two levels of predator threat were displayed. A lower
level threat where the predator had just arrived in the area, was clearly searching but
had not discovered the lizard, and a higher level one where the prey was hiding as a
direct result of a chase, so it was clear that the predator knew it was in the vicinity.
Martin et al. [ 8 ] found that the lizards fled after some time, typically of the order
of 3 min or less. This time depended upon the level of danger that they were in. In
the high risk case the time was significantly shorter than in the low risk case. There
were differences between males and females, with males generally fleeing earlier
(males are more brightly coloured so that crypsis is a less reliable defence).

15.4.2 A Model of the Interaction Between a Stationary
Searching Predator and a Hidden Prey

Here we describe a model of this predator prey interaction. A predator arrives at
a location with cover that may conceal hidden prey, and a good vantage point for
searching. The predator begins to search the cover area for prey. It may be that at
some point during the search a hidden prey individual flees. We shall assume that
the cover area does not contain more than one prey individual. It is possible that
there are no prey present. Eventually, if it does not find prey, the predator will give
up and try a new location. The predator must decide when to give up searching if no
prey is found.
A prey individual is in cover when it observes a predator arrive. The prey knows
that there are no other prey nearby, and that the predator is not aware of its presence.
It also knows that the predator is there to hunt and is searching to find prey, and that
eventually if the predator finds nothing it will give up and move elsewhere. The prey
must decide how long to stay in hiding and when to run, if ever.
When the predator arrives, the probability that there is a prey individual present
is 0 < α < 1. If the predator finds the prey it will attack it, the prey surviving with

probability . If the prey runs before the predator sees it, it will alert the predator to

its presence, but have an increased chance of survival

γ

1. The
rate that the predator spots a prey individual (conditional on it being there) is given
by g

β ,where0 ≤ γ < β <

which depends upon how long the predator has been searching, and so the
probability that the prey has been seen by time t is

( t )

t

G ( t )= g ( s ) ds . (15.16)

0