Libro de Resúmenes / Book of Abstracts (Español/English)

Resumenes 67
There exists wide evidence that P. darwini presents changes in
behavior as antipredator response [6] that tend to diminish its exposure to
predation. These behavioral responses refer mainly to a greater use of
physical refuge, that AIDS a lower presence in open areas.
In this way, we assumed that the vulnerability V = V(P) of P darwini
(probability of being killed by predator) diminishes as an effect of the
behavioral changes in the presence of predators.
One way to express vulnerability is through the function:
V
P
=
( 1−
V )
P
+ V
P + PV
=
α u
u α
( )
α
,
P + Pu
P + Pu
where P = P(t) is the predator population size, Pu is the amount of
predators that provokes an antipredatory behaviour and V α is the minimum
value of vulnerability. This function depends on the predator density and is
monotonically decreasing; that is to say, when there are more predators,
rodents assume the antipredatory behaviour diminishing vulnerability (there
is lesser probability of death).
We assume that the growth function in the rodent population is of a
logistic type which includes density-dependence as principal form of
population self-regulation and that they have a food resource without
restrictions. The extraction of prey by predators (functional response) is of a
Beddington-DeAngelis type which incorporates the hyperbolic response with
interference among predators.
On the other hand, the equation that describes the predator
population growth is also of a logistic type where the predator's carrying
capacity is directly proportional to the prey density [5]. Then the proposed
model is of a Leslie type [5] and is described by the differential equations
system:
X
µ
⎧dN
⎛ N ⎞ qN
⎪ = r⎜1−
⎟N
−
P
⎪ dt ⎝ K ⎠ V ( P)
N + bP + a
⎪
: ⎨
⎪
⎪dP
⎛ P ⎞
= s
⎪ ⎜
⎜1−
⎟ P
⎩ dt ⎝ n g(
N,
P)
⎠
7
where µ = ( r,
K,
q,
b,
a,
s,
n)
∈ℜ
+ and the parameters have different biological
meanings. Moreover, the function g(N, P) indicates the amount of prey
needed by each predator to sustain the permanence of predator population,
that is,
φ N
g(
N,
P)
=
V ( P)
N + bP + c
we show that (0,0) is a non-hyperbolic attractor point, then this model
predicts that both populations go to extinction.
Referencias