TY - JOUR

T1 - Allee effects in an iteroparous host population nd in host-parasitoid interactions

AU - Jang, Sophia R.J.

PY - 2011/1

Y1 - 2011/1

N2 - We investigate a stage-structured model of an iteroparous popu-lation with two age classes. The population is assumed to exhibit Allee effects hrough reproduction. The asymptotic dynamics of the model depend on the aximal reproductive number of the population. The population may per-sist if the maximal reproductive number is greater than one. There exists a pulation threshold in terms of the unstable interior equilibrium. The host opulation will become extinct if its initial distribution lies below the threshold nd the host population can persist indefinitely if its initial distribution lies bove the threshold. In addition, if the unstable equilibrium is a saddle point nd the system has no 2-cycles, then the stable manifold of the saddle point rovides the Allee threshold for the host. Based on this host population sys-em, we construct a host-parasitoid model to study the impact of Allee effects pon the population interaction. The parasitoid population may drive the host o below the Allee threshold so that both populations become extinct. On the ther hand, under some conditions on the parameters, the host-parasitoid sys-tem may possess an interior equilibrium and the populations may coexist as n interior equilibrium.

AB - We investigate a stage-structured model of an iteroparous popu-lation with two age classes. The population is assumed to exhibit Allee effects hrough reproduction. The asymptotic dynamics of the model depend on the aximal reproductive number of the population. The population may per-sist if the maximal reproductive number is greater than one. There exists a pulation threshold in terms of the unstable interior equilibrium. The host opulation will become extinct if its initial distribution lies below the threshold nd the host population can persist indefinitely if its initial distribution lies bove the threshold. In addition, if the unstable equilibrium is a saddle point nd the system has no 2-cycles, then the stable manifold of the saddle point rovides the Allee threshold for the host. Based on this host population sys-em, we construct a host-parasitoid model to study the impact of Allee effects pon the population interaction. The parasitoid population may drive the host o below the Allee threshold so that both populations become extinct. On the ther hand, under some conditions on the parameters, the host-parasitoid sys-tem may possess an interior equilibrium and the populations may coexist as n interior equilibrium.

KW - Allee effects

KW - Monotone map

KW - Population threshold

KW - Stable manifold

UR - http://www.scopus.com/inward/record.url?scp=78651258912&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2011.15.113

DO - 10.3934/dcdsb.2011.15.113

M3 - Article

AN - SCOPUS:78651258912

SN - 1531-3492

VL - 15

SP - 113

EP - 135

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 1

ER -