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

Conferencias 11
Sin embargo pocos artículos se han centrado en la dinámica
poblacional o en la discusión de los efectos estabilizantes o
desestabilizantes del efecto Allee en sistemas de depredación [3, 6, 11, 14].
Nuestra atención es centrada en modelos deterministas tiempo continuo
describiendo la interacción depredador-presa, porque modelos
matemáticamente simples pueden revelar mucho acerca de las dinámicas e
implicaciones importantes de este fenómeno [7].
Mostramos que las marcadas diferencias entre el crecimiento logístico
y el crecimiento sujeto al efecto Allee tienen profundas influencias en la
interacción depredador-presa, pero resultados distintos pueden ser
obtenidos cuando son consideradas formas diferentes de este fenómenos
[21].
Stability and persistence on predator-prey models
considering Allee effect on prey
A positive relationship between population density and the
individual’s fitness is often known as the Allee effects [7, 15, 16], named
after the pioneering work of W.C. Allee [1, 2], and arise as a result of the
benefits of conspecific presence, and manifest as reductions in individual
fitness as populations become smaller and these benefits are lost. Also is
termed depensation [4, 5, 8, 9, 12], or Negative competition effect [20] .
This effect can be caused by difficulties in, for example, mate finding,
food exploitation (e.g. host resistance can only be overcome by sufficient
numbers of consumers) and predator avoidance or defense [7, 13, 15, 16].
Naturally occurring aggregated distributions of organisms over the available
resources may indicate the presence of an Allee effect, because the Allee
effect might select for aggregation behavior [15, 16]. Such behavior can,
for example, be induced by individuals excreting substances to attract
conspecifics.
The implications of the Allee effect are potentially very important in
most areas of ecology and evolution since social species, particularly those
that are obligate cooperators, might greatly increases the likelihood of local
and global extinction, a phenomenon that has received considerable
attention from ecologists [8, 9, 13].
The population growth rate shows an Allee effect if an increase in the
per capita growth rate occurs over certain ranges of density and this
phenomenon can have two form strong Allee effect [15,16] or critical
depensation [4, 5] and the weak Allee effect or noncritical depensation.
When the Allee effect is sufficiently strong, there is a critical threshold below
which the population experiences extinction [3, 10, 20]. In contrast, a
population with a weak Allee effect does not have a threshold the population
must surpass to grow [20].
Different mathematical ways there exist for formalize the Allee effect
in continuous time models. Resting a term in the logistic equation is
presented in [15, 16, 17, 19]. A more known form is presented in [4, 5, 7,
18] using a factor that modify the logistic equation; in [7] it show that by
one extra parameter m, the lower unstable equilibrium point, it is possible
to introduce inverse density dependence at low population sizes. The effect
of this is to produce a relationship between per capita growth rate and
population size, where negative density dependence at an upper threshold