Species decline and extinction: synergy of infectious disease and Allee effect?
Open Access
- 1 May 2009
- journal article
- research article
- Published by Taylor & Francis Ltd in Journal of Biological Dynamics
- Vol. 3 (2-3), 305-323
- https://doi.org/10.1080/17513750802376313
Abstract
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.Keywords
This publication has 33 references indexed in Scilit:
- POPULATION EXTINCTION IN DETERMINISTICAND STOCHASTIC DISCRETE-TIME EPIDEMIC MODELS WITH PERIODIC COEFFICIENTS WITH APPLICATIONS TO AMPHIBIAN POPULATIONSNatural Resource Modeling, 2008
- Spread of Chytridiomycosis Has Caused the Rapid Global Decline and Extinction of FrogsEcohealth, 2007
- A diffusive SI model with Allee effect and application to FIVMathematical Biosciences, 2007
- Allee effects in a discrete-time host-parasitoid modelJournal of Difference Equations and Applications, 2006
- Combined impacts of Allee effects and parasitismOikos, 2006
- Widespread amphibian extinctions from epidemic disease driven by global warmingNature, 2006
- OPEN ACCESS AND EXTINCTION OF THE PASSENGER PIGEON IN NORTH AMERICANatural Resource Modeling, 2005
- Good Medicine for Conservation Biology: the Intersection of Epidemiology and Conservation TheoryConservation Biology, 2002
- What Is the Allee Effect?Oikos, 1999
- Population biology of infectious diseases: Part INature, 1979