Sensitivity analysis: matrix methods in demography and ecology

TitleDemographic research monographs 16
308 pages. Cham, Springer (2019)
Open Access


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

Full Text

Front Matter

Introductory and Methodological

Front Matter

Introduction: Sensitivity Analysis – What and Why?

Matrix Calculus and Notation

Linear Models

Front Matter

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

Front Matter

Transient Population Dynamics

Periodic Models

LTRE Decomposition of the Stochastic Growth Rate

Nonlinear Models

Front Matter

Sensitivity Analysis of Nonlinear Demographic Models

Markov Chains

Front Matter

Sensitivity Analysis of Discrete Markov Chains

Sensitivity Analysis of Continuous Markov Chains

The Max Planck Institute for Demographic Research (MPIDR) in Rostock is one of the leading demographic research centers in the world. It's part of the Max Planck Society, the internationally renowned German research society.