Bounds on the dynamics of sink populations with noisy immigration

Eager, Eric Alan; Guiver, Chris; Hodgson, Dave; Rebarber, Richard; Stott, Iain; Townley, Stuart

Abstract

Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics of sink populations are not easily modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined by extrinsic sources (for example, source populations, or population managers). Here we appeal to a systems and control framework to place upper and lower bounds on both the transient and future dynamics of sink populations that are subject to noisy immigration. Immigration has a number of interpretations and can fit a wide variety of models found in the literature. We apply the results to case studies derived from published models for Chinook salmon (Oncorhynchus tshawytscha) and blowout penstemon (Penstemon haydenii).

Citation

Eager, E. A., Guiver, C., Hodgson, D., Rebarber, R., Stott, I., & Townley, S. (2014). Bounds on the dynamics of sink populations with noisy immigration. Theoretical Population Biology, 92, 88-96. https://doi.org/10.1016/j.tpb.2013.12.004

• Journal Article Type: Article
• Acceptance Date: Dec 18, 2013
• Publication Date: 2014
• Deposit Date: Jul 28, 2020
• Publicly Available Date: Aug 5, 2020
• Journal: Theoretical Population Biology
• Print ISSN: 0040-5809
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 92
• Pages: 88-96
• DOI: https://doi.org/10.1016/j.tpb.2013.12.004
• Keywords: Immigration, Input-to-state stability, Population ecology, Projection model, Sink population
• Public URL: http://researchrepository.napier.ac.uk/Output/2677361