TY - JOUR
T1 - Species decline and extinction
T2 - Synergy of infectious disease and allee effect?
AU - Thieme, Horst
AU - Dhirasakdanon, Thanate
AU - Han, Zhun
AU - Trevino, Roy
N1 - Funding Information:
The work by Thanate Dhirasakdanon and Horst Thieme was partially supported by the NSF grants DMS-0314529 and DMS-0715451. We thank Frank Hilker for making the work of Hilker et al. [23] available to us before it was published, through which we became aware of the works by Deredec and Courchamp [15] and Lafferty and Gerber [29].
PY - 2009
Y1 - 2009
N2 - Host–parasite models with density-dependent (mass action) incidence and a critical Allee effect in host growth can explain both species decline and disappearance (extinction). The behaviour of the model is consistent with both the novel pathogen hypothesis and the endemic pathogen hypothesis for chytridiomycosis. Mathematically, the transition from decline to disappearance is mediated by a Hopf bifurcation and is marked by the occurrence of a heteroclinic orbit. The Hopf bifurcation is supercritical if intra-specific host competition increases with host density at a large power and subcritical if the power is small. In the supercritical case, host–parasite coexistence can be at equilibrium or periodic; in the subcritical case it is only at equilibrium.
AB - Host–parasite models with density-dependent (mass action) incidence and a critical Allee effect in host growth can explain both species decline and disappearance (extinction). The behaviour of the model is consistent with both the novel pathogen hypothesis and the endemic pathogen hypothesis for chytridiomycosis. Mathematically, the transition from decline to disappearance is mediated by a Hopf bifurcation and is marked by the occurrence of a heteroclinic orbit. The Hopf bifurcation is supercritical if intra-specific host competition increases with host density at a large power and subcritical if the power is small. In the supercritical case, host–parasite coexistence can be at equilibrium or periodic; in the subcritical case it is only at equilibrium.
KW - Amphibian disappearance
KW - Chytridiomycosis
KW - Epidemic
KW - Global climate change
KW - Incidence
KW - Novel versus endemic pathogen hypothesis
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U2 - 10.1080/17513750802376313
DO - 10.1080/17513750802376313
M3 - Article
C2 - 22880836
AN - SCOPUS:77954654100
SN - 1751-3758
VL - 3
SP - 305
EP - 323
JO - Journal of biological dynamics
JF - Journal of biological dynamics
IS - 2-3
ER -