Impact of stochasticity in immigration and reintroduction on colonizing and extirpating populations

Harshana Rajakaruna, Alexei Potapov, Mark Lewis

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A thorough quantitative understanding of populations at the edge of extinction is needed to manage both invasive and extirpating populations. Immigration can govern the population dynamics when the population levels are low. It increases the probability of a population establishing (or reestablishing) before going extinct (EBE). However, the rate of immigration can be highly fluctuating. Here, we investigate how the stochasticity in immigration impacts the EBE probability for small populations in variable environments. We use a population model with an Allee effect described by a stochastic differential equation (SDE) and employ the Fokker-Planck diffusion approximation to quantify the EBE probability.Wefind that, the effect of the stochasticity in immigration on the EBE probability depends on both the intrinsic growth rate (r) and the mean rate of immigration (p). In general, if r is large and positive (e.g. invasive species introduced to favorable habitats), or if p is greater than the rate of population decline due to the demographic Allee effect (e.g., effective stocking of declining populations), then the stochasticity in immigration decreases the EBE probability. If r is large and negative (e.g. endangered populations in unfavorable habitats), or if the rate of decline due to the demographic Allee effect is much greater than p (e.g., weak stocking of declining populations), then the stochasticity in immigration increases the EBE probability. However, the mean time for EBE decreases with the increasing stochasticity in immigration with both positive and negative large r. Thus, results suggest that ecological management of populations involves a tradeoff as to whether to increase or decrease the stochasticity in immigration in order to optimize the desired outcome. Moreover, the control of invasive species spread through stochastic means, for example, by stochastic monitoring and treatment of vectors such as ship-ballast water, may be suitable strategies given the environmental and demographic uncertainties at introductions. Similarly, the recovery of declining and extirpated populations through stochastic stocking, translocation, and reintroduction, may also be suitable strategies. © 2013 Elsevier Inc.
Original languageEnglish (US)
Pages (from-to)38-48
Number of pages11
JournalTheoretical Population Biology
Issue number1
StatePublished - May 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-CI013-04
Acknowledgements: The authors thank the Lewis Lab for helpful feedback on the modeling and analysis. This work was funded by the University of Alberta, Department of Biological Sciences (HR), the Canadian Aquatic Invasive Species Network (HR and AP), a Canada Research Chair (MAL) and NSERC Discovery and Accelerator Grant (MAL). This publication was based on work supported in part by Award No KUK-CI013-04 made by King Abdullah University of Science and Technology (KAUST) (MAL). The authors also thank the reviewers of this manuscript.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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