Allee threshold and stochasticity in biological invasions: colonization time at low propagule pressure.
We consider the problem of estimating the time needed for species colonization. The analysis is based upon the known population dynamic models by Dennis with minor modification to the Allee effect description, which allows us to obtain an analytical expression for the colonization time. For the stochastic counterpart of the models in diffusion approximation, we (1) propose the description of immigration stochasticity, (2) provide the estimates of time required for the population to overcome strong demographic Allee effect, and (3) consider the numerical results for mean colonization time and its uncertainty. Strong Allee effect strictly disallows populations at small immigration rates to colonize new habitats, unless the stochasticity in immigration, environment, or demography is present, or incorporated into the model. Immigration stochasticity, complementing with environmental and demographic stochasticity, enables the populations to overcome the Allee threshold even at low values of propagule pressure.
Department of Mathematical and Statistical Sciences and Centre for Mathematical Biology, University of Alberta, Edmonton, Canada T6G2G1. Electronic address: apotapov@ualberta.ca.
Alex
A
Potapov
Department of Biological Sciences and Centre for Mathematical Biology, University of Alberta, Edmonton, Canada T6G2G1.
Harshana
H
Rajakaruna
D000818:Animals; D004058:Diffusion; D058865:Introduced Species; D008954:Models, Biological; D011157:Population Dynamics; D013269:Stochastic Processes; D013997:Time Factors
Allee effect; Biological invasions; Colonization time; Stochastic model