title: Sensitivity and elasticity analysis of a Lur'e system used to model a population subject to density-dependent reproduction.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics and the River Studies Center, University of Wisconsin - La Crosse, 1725 State St., La Crosse Wisconsin, 5401, United States. Electronic address: eeager@uwlax.edu.
authors.forename: Eric Alan
authors.initials: EA
authors.lastname: Eager
authors.affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68688, United States.
authors.forename: Richard
authors.initials: R
authors.lastname: Rebarber
mesh_terms: D000818:Animals; D008962:Models, Theoretical; D011157:Population Dynamics
keywords: Elasticity analyzes; Equilibiria; Integral projection models; Lur’e systems; Population dynamics; Sensitivity analyzes