title: Bounds on the dynamics of sink populations with noisy immigration.
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).
authors.affiliation: Mathematics Department, University of Wisconsin La Crosse, 1020 Cowley Hall, 1725 State Street, La Crosse, WI, USA. Electronic address: eeager@uwlax.edu.
authors.forename: Eric Alan
authors.initials: EA
authors.lastname: Eager
authors.affiliation: 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.
authors.forename: Chris
authors.initials: C
authors.lastname: Guiver
authors.affiliation: 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.
authors.forename: Dave
authors.initials: D
authors.lastname: Hodgson
authors.affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, USA. Electronic address: rrebarber1@unl.edu.
authors.forename: Richard
authors.initials: R
authors.lastname: Rebarber
authors.affiliation: 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.
authors.forename: Iain
authors.initials: I
authors.lastname: Stott
authors.affiliation: 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.
authors.forename: Stuart
authors.initials: S
authors.lastname: Townley
mesh_terms: D025041:Animal Migration; D000818:Animals; D008962:Models, Theoretical; D011157:Population Dynamics; D012474:Salmon / Q000502:physiology*
keywords: Immigration; Input-to-state stability; Population ecology; Projection model; Sink population