Sensitivity analysis: matrix methods in demography and ecology
Demographic research monographs 16
308 pages. Cham, Springer (2019)
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.
Keywords: demography, longevity, Markov chains, models, population, population growth
Introductory and Methodological
Introduction: Sensitivity Analysis – What and Why?
Matrix Calculus and Notation
The Sensitivity of Population Growth Rate: Three Approaches
Sensitivity Analysis of Longevity and Life Disparity
Individual Stochasticity and Implicit Age Dependence
Age × Stage-Classified Models
Time-Varying and Stochastic Models
Transient Population Dynamics
LTRE Decomposition of the Stochastic Growth Rate
Sensitivity Analysis of Nonlinear Demographic Models
Sensitivity Analysis of Discrete Markov Chains
Sensitivity Analysis of Continuous Markov Chains