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many predators it is likely that on a grassy cell, for which the rabbit is looking,
thereisalsoawolf.Ourrabbitsarenotintelligentanddonotdistinguishbetween
a deadly cell (grass and wolf) and a friendly one (grass only).
We have also investigated the role played by the concentration of cover -
the rabbit-holes. For the wolves the rabbit-holes are no good at all. Therefore
if there is relatively less cover (
C
h
= 0.1) in the system, the three strategies
ESC,NO
and
R
are the best for the wolves and give them approximately the
same chance of survival. However when the number of rabbit-holes increases, it
is better for the wolves if the rabbits follow the
ESC
or
R
strategy. The chances
of survival are then improved by a factor of at least two with respect to the
NO
strategy, which directs often the rabbits into cover, where they are inaccessible
to the wolves. The gain is even larger if the initial concentration of predators is
lower. For higher concentration of shelters,
C
h
= 0.3, the wolves have no chance
at all to survive under the passive
NO
strategy. Their survival chances raise to
27% under the
ESC
strategy and to 41% under the
R
one. This is the result of
rabbits looking primarily for food, thus avoiding the rabbit-holes. For the same
reason the optimal strategy for the rabbits changes, from
ESC
and
R
at lower
concentrations of shelter, into
NO
at higher concentrations. The
NO
strategy
is the best for the rabbits (it gives them 100% survival chances) for the density
of shelters
C
h
= 0.3. Then the wolves become extinct pretty fast and the rabbit
population lives without danger.
We may conclude that the comparison of the four active and one passive
strategies (escape for rabbits, food for rabbits, food for wolves, food for wolves
and rabbits and finally no strategy at all) shows that
-
for both species the worse strategies are
W
and
RW
,
-
the advantage of one or another of the remaining three strategies depends
on the concentration of rabbit-holes, initial concentrations of wolves and
rabbits,
-
when the number of predators is low, the choice of the strategy is not im-
portant. In the extreme conditions the survival of the species may strongly
depend on the strategy adopted by the prey,
-
wolves are more vulnerable to the choice of the strategy.
The above findings are in good, qualitative of course, agreement with the known
biological data and models (see e.g [13]).
3 Model B
3.1 Definition
We consider a population composed at time
t
of
N
(
t
) individuals. The individ-
uals live in a habitat which has the form of a square lattice of dimensions
L
x
along the
X
-axis and
L
y
along the
Y
-axis. The lattice is divided into three equal
parts (denoted regions I, II and III afterwards), perpendicular to the
X
-axis. A
site could be either empty or occupied by only one individual.
