Sensitivity and elasticity analysis of a Lur’e system used to model a population subject to density-dependent reproduction

• Published in: Mathematical biosciences Vol. 282; pp. 34 - 45
• Main Authors: Eager, Eric Alan, Rebarber, Richard
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.12.2016; Elsevier Science Ltd
• Subjects: Animals; Cirsium canescens; Ecological monitoring; Elasticity; Elasticity analyzes; Equilibiria; Equilibrium; Fecundity; Integral projection models; Integrals; Lur’e systems; Mathematical analysis; Mathematical models; Matrix methods; Models, Theoretical; Nonlinear systems; Nonlinearity; Oncorhynchus tshawytscha; Population biology; Population density; Population Dynamics; Projection model; Sensitivity analysis; Sensitivity analyzes; Viscoelasticity; Integral projection models; Population dynamics; Elasticity analyzes; Equilibiria; Lur’e systems; Sensitivity analyzes
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2016.09.016

•Sensitivity formulas are derived for the equilibrium of a Lur’e system.•Both matrix and integral projection models are considered.•Formulas are interpreted ecologically for a Salmon model and a Platte thistle model.•For IPMs the sensitivities may involve Dirac distributions. Sensitivity and elasticity analyzes have become central to the analysis of models in population biology and ecology. While much work has been done applying sensitivity and elasticity analysis to study density-independent (linear) matrix and integral projection models, little work has been done to study the sensitivity and elasticity of density-dependent models, especially integral projection models. In this paper we derive sensitivity and elasticity formulas for the equilibrium population n* of a structured population modeled by a Lur’e system, which consists of a linear system plus a nonlinearity modeling density-dependent fecundity. Sensitivity and elasticity formulas are easy to interpret ecologically, and we apply these formulas to published models for Chinook Salmon and Platte thistle (Cirsium canescens). In the C. canescens example we show that models with identical equilibrium populations can have sensitivities that are an order-of-magnitude apart, depending on the functional form for the nonlinearity.