TY - JOUR
T1 - Discrete-time host-parasitoid models with Allee effects
T2 - Density dependence versus parasitism
AU - Jang, Sophia R.J.
N1 - Funding Information:
This work was carried out at the University of Cologne and Sandia National Laboratories (SNL), with United States Department of Energy, Office of Basic Energy Sciences funding. SNL is a multiprogram laboratory operated by the Sandia Corporation, a Lockhead Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000. Additional support for Michael Commer was provided by a short-term scholarship granted by the German Academic Exchange Service (DAAD), for G. A. Newman through a Mercator Fellowship granted by the Deutsche Forschungsgemein-schaft (DFG). We express our gratitude to Tilman Hanstein for providing the analytical results for the permeable layered model and to Vladimir Druskin and Leonid Knizhnerman for permission to use their SLDM code. We also acknowledge Steve Plimpton for providing external parallel remapping routines.
PY - 2011/4
Y1 - 2011/4
N2 - We present two general discrete-time host-parasitoid models with Allee effects on the host. In the first model, it is assumed that parasitism occurs prior to density dependence, while in the second model we assume that density dependence operates first followed by parasitism. It is shown that both models have similar asymptotic behaviour. The parasitoid population will definitely go extinct if the maximal growth rate of the host population is less than or equal to one, independent of whether density dependence or parasitism occurs first. The fate of the population is initial condition dependent if this maximal growth rate exceeds one. In particular, there exists a host population threshold, the Allee threshold, below which the host population goes extinct and so does the parasitoid. This threshold is the same for both models. Numerical examples with different functions are simulated to illustrate our analytical results.
AB - We present two general discrete-time host-parasitoid models with Allee effects on the host. In the first model, it is assumed that parasitism occurs prior to density dependence, while in the second model we assume that density dependence operates first followed by parasitism. It is shown that both models have similar asymptotic behaviour. The parasitoid population will definitely go extinct if the maximal growth rate of the host population is less than or equal to one, independent of whether density dependence or parasitism occurs first. The fate of the population is initial condition dependent if this maximal growth rate exceeds one. In particular, there exists a host population threshold, the Allee threshold, below which the host population goes extinct and so does the parasitoid. This threshold is the same for both models. Numerical examples with different functions are simulated to illustrate our analytical results.
KW - Allee effect
KW - Density dependence
KW - Host-parasitoid model
KW - Local stable manifold
UR - http://www.scopus.com/inward/record.url?scp=79953284319&partnerID=8YFLogxK
U2 - 10.1080/10236190903146920
DO - 10.1080/10236190903146920
M3 - Article
AN - SCOPUS:79953284319
SN - 1023-6198
VL - 17
SP - 525
EP - 539
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 4
ER -