Bounds on the dynamics of sink populations with noisy immigration

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

doi:10.1016/j.tpb.2013.12.004

Bounds on the dynamics of sink populations with noisy immigration

Theor Popul Biol. 2014 Mar:92:88-96. doi: 10.1016/j.tpb.2013.12.004. Epub 2013 Dec 25.

Authors

Eric Alan Eager¹, Chris Guiver², Dave Hodgson³, Richard Rebarber⁴, Iain Stott⁵, Stuart Townley⁶

Affiliations

¹ Mathematics Department, University of Wisconsin La Crosse, 1020 Cowley Hall, 1725 State Street, La Crosse, WI, USA. Electronic address: eeager@uwlax.edu.
² Environment & Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: c.guiver@ex.ac.uk.
³ Centre for Ecology and Conservation, College of Life and Environmental Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: d.j.hodgson@ex.ac.uk.
⁴ Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA. Electronic address: rrebarber1@unl.edu.
⁵ Environment & Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: i.stott@ex.ac.uk.
⁶ Environment & Sustainability Institute, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Cornwall, TR10 9FE, UK. Electronic address: s.b.townley@ex.ac.uk.

PMID: 24373938
DOI: 10.1016/j.tpb.2013.12.004

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).

Keywords: Immigration; Input-to-state stability; Population ecology; Projection model; Sink population.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Animal Migration*
Animals
Models, Theoretical*
Population Dynamics
Salmon / physiology*