Sensitivity Analysis: Matrix Methods in Demography and Ecology

Description

This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics. Front Matter ....Pages i-xviii Front Matter ....Pages 1-1 Introduction: Sensitivity Analysis – What and Why? (Hal Caswell)....Pages 3-12 Matrix Calculus and Notation (Hal Caswell)....Pages 13-28 Front Matter ....Pages 29-29 The Sensitivity of Population Growth Rate: Three Approaches (Hal Caswell)....Pages 31-43 Sensitivity Analysis of Longevity and Life Disparity (Hal Caswell)....Pages 45-65 Individual Stochasticity and Implicit Age Dependence (Hal Caswell)....Pages 67-113 Age × Stage-Classified Models (Hal Caswell)....Pages 115-138 Front Matter ....Pages 139-139 Transient Population Dynamics (Hal Caswell)....Pages 141-158 Periodic Models (Hal Caswell)....Pages 159-178 LTRE Decomposition of the Stochastic Growth Rate (Hal Caswell)....Pages 179-195 Front Matter ....Pages 197-197 Sensitivity Analysis of Nonlinear Demographic Models (Hal Caswell)....Pages 199-252 Front Matter ....Pages 253-253 Sensitivity Analysis of Discrete Markov Chains (Hal Caswell)....Pages 255-280 Sensitivity Analysis of Continuous Markov Chains (Hal Caswell)....Pages 281-299