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that the value of U which maximises the predator's payoff P
0. Thus
the predator should always wait until the closest position, and the prey should either
flee immediately if R
(
N
,
U
)
is U
=
(
1
,
0
) >
R
(
N
,
0
)
, or never flee otherwise.
15.3.4 Summary
The optimal strategy for the prey is thus either to run immediately or never to initi-
ate a chase. This is true whether the predator attacks immediately on discovering the
prey or whether the predator delays its attack until it has closed the distance to the
prey. We note that in our different models either the predator had no choice, or there
was a clear predator optimal strategy, regardless of whether the prey runs immedi-
ately or never. This reduces the prey's strategy to a simple optimisation problem,
and thus effectively rules out a mixed strategy. The strategy of immediate flight is
associated with slow predator search speed, a low non-predation cost to running, a
large advantage to the prey in initiating chases, limited ability to spot the predator
at distance, a high ability to spot prey by the predator, and a high probability that
chases will be successful. Note that it was assumed that searching predators never
spontaneously change direction, or do so sufficiently rarely that this situation can
be ignored. If many such directional changes are made, this will affect optimal prey
and predator strategy.
15.4 Interactions Between Cryptic Prey and a Stationary
Visible Predator
In this section we consider a model of a related scenario to the above, where an
ambush predator appears close to a concealed prey individual. The predator does
not move, but begins to scan the environment for hidden prey. An example is a bird
of prey such as an eagle settled at a high vantage point. The prey must choose when
(if at all) to run. This model was developed following experiments by Martin et al.
[ 8 ] which we describe below.
15.4.1 Experiments with Hidden Rock Lizards
Martin et al. [ 8 ] conducted experiments in central Spain with hidden rock lizards in
their natural habitat, and humans as simulated predators. The experimenter walked
around the study area until a lizard was spotted. Then the experimenter carried out
one of two procedures. In the first case they approached the lizard slowly without
obviously looking at it, and stopped at a short distance from the lizard. The ex-
perimenter then timed how long it took for the lizard to flee to a refuge (usually a
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