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5. Escape for rabbits (
ESC
). A rabbit prefers a move into a cell without a
wolf. It does not matter whether there is a rabbit-hole or not. Wolves move
randomly.
The model has the following parameters - linear size of the lattice
L
, initial
densities of rabbits
C
r
(0), wolves
C
w
(0), concentration of rabbit-holes
C
h
, maxi-
mum period of time (MCS)
k
an animal may survive without eating, the amount
of food,
k
min
, needed to be fit for breeding, the amount of food,
k
of
, received
at birth, and finally
M
, the physiological birth rate. The role of the most of
the parameters has been estimated in [6], hence we have decided on fixing the
parameters at the following values:
L
= 50,
k
=6,
k
min
=2,
k
of
= 2 and
M
=
4. We shall be interested in the role played by initial concentrations of predators
and prey and the density of shelter.
Typically we have averaged over 100 independent runs, although as a check
in some cases we averaged over 300 runs.
2.2 Properties of Model A
A detailed description of the properties of model A can be found in [11].
Accordingly, we shall only give here a summary of the results.
We have found three asymptotic states for the evolution - regardless of the
adopted strategy. In the first one the predator and prey coexist, and their con-
centrations fluctuate mildly around some stationary values. In the second one
the predators vanished and the concentration of prey reached a value higher
than in the coexisting case, but below the carrying capacity of the system. In
the third one the predators ate away the prey and the final state is the empty
one.
The effect of the different strategies, was measured as a probability that a
population will reach a stationary state.
It turns out that there are two, nearly equivalent, strategies which give a
better chance to survive for the wolves population. Both concern the behavior
of the rabbits only - escape (
ESC
) and food for rabbits (
R
). When the initial
concentration of predators is relatively high (
C
w
(0) = 0.4), the remaining strate-
gies give no chance for survival for the wolves. Lowering the initial number of
predators permits them to survive also under other strategies, although they
are always inferior to
ESC
and
R
. Only with very low initial concentration of
predators all strategies are equivalent and all lead always to the coexisting state.
With initial concentration of predators at the level
C
w
(0) = 0.5, neither strategy
is good and the wolves face extinction almost always.
The fate of the prey (rabbits) population is more bright. At
C
w
(0) = 0.2 all
strategies guarantee survival in the coexisting state; at
C
w
(0) = 0.3 there are
threegoodstrategies(
NO,ESC,R
)andtwobadones(
W, RW
).Withincreasing
the initial concentration of wolves, the group of three splits into better ones
(
NO,ESC
) and a worse (
R
). For still higher
C
w
(0), the preference of the two
becomesmoreandmorepronounced.Thisisunderstandablesincewhenthereare
