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

Resumenes 93
punto de equilibrio y oscilaciones de población amortiguadas, analizando un
modelo de depredación tiempo continuo descrito por el sistema:
⎧ dx x
⎪ = r(
1−
) x − q ( x − xr
) y
dt K
X µ : ⎨
⎪ dy
= ( p ( x − x − c)
y
⎪
r )
⎩ dt
y considerando las siguientes hipótesis acerca del refugio de las presas: el
número de presas protegidas xr es ya sea una fracción constante del total,
un número fijo [9], o proporcional a la abundancia de depredadores [11].
Nuestros resultados indican que el refugio puede preservar la estabilidad del
punto de equilibrio positivo del sistema.
Dynamics of simple predator-prey models with prey refuge
use. A small review and new findings
Within the field of population dynamics, the so-called predator
functional response to prey density refers to the density of prey attacked
per unit time per predator as a function of prey density [5]. In most
predator-prey models considered in the literature, the functional response is
assumed to be monotonically increasing, the inherent assumption being
that the more prey in the environment, the better off the predator.
To incorporate biological realism into the basic formal framework
developed in the first half of the XX century by Volterra and others, densitydependent
effects on the endogenous dynamic of predators and prey, and
non-linear functions for consumption of prey by predators were included [3,
7]. More recently, the behavior of prey and its consequences at the
population level has been incorporated into the predation theory [13]. In
this context, one of the more relevant behavioral traits affecting the
dynamics of predator-prey systems is the use of spatial refuges by the prey.
Here we consider a refuge as a physical location in which prey either live or
temporarily hide [9], where predators have little or no chance to kill prey.
According to Taylor [15] the different kinds of refuges can be
arranged into three types:
a) those which provides permanent spatial protection for a small
subset of the prey population,
b) those which provide temporary spatial protection, and
c) those which provide a temporal refuge in numbers, i.e. decrease
the risk of predation by increasing the abundance of vulnerable prey.
From a theoretical point of view, different forms of mathematical
representations of refuge use in a population context have been presented.
These models, mostly invoking either environment heterogeneity or some
type of phenotypic structure in the prey, relies on different basic
assumptions and therefore their results are hardly comparable.
Different forms of mathematical representations of refuge have been
used in a population context; some invoke environment heterogeneity while
others some type of phenotypic structure in the prey. However, because
they rely on different basic assumptions their results are hardly comparable.
By analyzing a continuous time predator-prey model described by the
system: