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

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).

Highlights

Many populations are in a state of predictable decline in the absence of immigration, or of deliberate bolstering by conservation management strategies (Pulliam, 1988; Gonzalez and Holt, 2002; Holt et al, 2003; Roy et al, 2005; Matthews and Gonzalez, 2007)
The dynamics of sink populations are not modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined by extrinsic sources
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

Summary

Introduction

Many populations are in a state of predictable decline in the absence of immigration, or of deliberate bolstering by conservation management strategies (Pulliam, 1988; Gonzalez and Holt, 2002; Holt et al, 2003; Roy et al, 2005; Matthews and Gonzalez, 2007). In many cases, such immigration events vary dramatically in magnitude or structure throughout the lifespan of the population. In this paper we provide a relevant modelling framework, and analyse populations in this framework

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