Sensitivity Analysis : : Matrix Methods in Demography and Ecology.

• Superior document: Demographic Research Monographs
• Author: Caswell, Hal.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; ©2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: Demographic Research Monographs
• Physical Description: 1 online resource (308 pages)

Table of Contents

• Intro
• Preface
• Bibliography
• Acknowledgements
• Contents
• Part I Introductory and Methodological
• 1 Introduction: Sensitivity Analysis - What and Why?
• 1.1 Introduction
• 1.2 Sensitivity, Calculus, and Matrix Calculus
• 1.3 Some Issues
• 1.3.1 Prospective and Retrospective Analyses: Sensitivity and Decomposition
• 1.3.2 Uncertainty Propagation
• 1.3.3 Why Not Just Simulate?
• 1.3.4 Sensitivity and Identifying Targets for Intervention
• 1.3.5 The Dream of Easy Interpretation
• 1.4 The Importance of Change
• Bibliography
• 2 Matrix Calculus and Notation
• 2.1 Introduction: Can It Possibly Be That Simple?
• 2.2 Notation and Matrix Operations
• 2.2.1 Notation
• 2.2.2 Operations
• 2.2.3 The Vec Operator and Vec-Permutation Matrix
• 2.2.4 Roth's Theorem
• 2.3 Defining Matrix Derivatives
• 2.4 The Chain Rule
• 2.5 Derivatives from Differentials
• 2.5.1 Differentials of Scalar Function
• 2.5.2 Differentials of Vectors and Matrices
• 2.6 The First Identification Theorem
• 2.6.1 The Chain Rule and the First IdentificationTheorem
• 2.7 Elasticity
• 2.8 Some Useful Matrix Calculus Results
• 2.9 LTRE Decomposition of Demographic Differences
• 2.10 A Protocol for Sensitivity Analysis
• Bibliography
• Part II Linear Models
• 3 The Sensitivity of Population Growth Rate: Three Approaches
• 3.1 Introduction
• 3.2 Hamilton's Equation for Age-Classified Populations
• 3.2.1 Effects of Changes in Mortality
• 3.2.2 Effects of Changes in Fertility
• 3.2.3 History and Perspectives
• 3.3 Stage-Classified Populations: Eigenvalue Perturbations
• 3.3.1 Age-Classified Models as a Special Case
• 3.3.2 Sensitivity to Lower-Level DemographicParameters
• 3.3.3 History
• 3.4 Growth Rate Sensitivity via Matrix Calculus
• 3.5 Second Derivatives of Population Growth Rate
• 3.6 Conclusion
• Bibliography.
• 4 Sensitivity Analysis of Longevity and Life Disparity
• 4.1 Introduction
• 4.2 Life Expectancy in Age-Classified Populations
• 4.2.1 Derivation
• 4.3 A Markov Chain Model for the Life Cycle
• 4.3.1 A Markov Chain Formulation of the Life Cycle
• 4.3.2 Occupancy Times
• 4.3.3 Longevity
• 4.3.4 Age or Stage at Death
• 4.3.5 Life Lost and Life Disparity
• 4.4 Sensitivity Analysis
• 4.4.1 Sensitivity of the Fundamental Matrix
• 4.4.2 Sensitivity of Life Expectancy
• 4.4.3 Generalizing the Keyfitz-Pollard Formula
• 4.4.4 Sensitivity of the Variance of Longevity
• 4.4.5 Sensitivity of the Distribution of Age at Death
• 4.4.6 Sensitivity of Life Disparity
• 4.5 A Time-Series LTRE Decomposition: Life Disparity
• 4.6 Conclusion
• Bibliography
• 5 Individual Stochasticity and Implicit Age Dependence
• 5.1 Introduction
• 5.1.1 Age and Stage, Implicit and Explicit
• 5.1.2 Individual Stochasticity and Heterogeneity
• 5.1.3 Examples
• 5.2 Markov Chains
• 5.2.1 An Absorbing Markov Chain
• 5.2.2 Occupancy Times and the Fundamental Matrix
• 5.2.3 Sensitivity of the Fundamental Matrix
• 5.3 From Stage to Age
• 5.3.1 Variance in Occupancy Time
• 5.3.2 Longevity and Life Expectancy
• 5.3.3 Variance in Longevity
• 5.3.4 Cohort Generation Time
• 5.4 The Net Reproductive Rate
• 5.4.1 Net Reproductive Rate in Periodic Environments
• 5.4.2 Sensitivity of the Net Reproductive Rate
• 5.4.3 Invasion Exponents, Selection Gradients, and R0
• 5.4.4 Beyond R0: Individual Stochasticity in Lifetime Reproduction
• 5.5 Variable and Stochastic Environments
• 5.5.1 A Model for Variable Environments
• 5.5.2 The Fundamental Matrix
• 5.5.3 Longevity in a Variable Environment
• 5.5.3.1 Variance in Longevity
• 5.5.4 A Time-Varying Example: Lomatium bradshawii
• 5.6 The Importance of Individual Stochasticity
• 5.7 Discussion.
• A Appendix: Derivations
• A.1 Variance in Occupancy Times
• A.2 Life Expectancy
• A.3 Variance in Longevity
• A.4 Net Reproductive Rate
• A.5 Cohort Generation Time
• A.5.1 Sensitivity of Generation Time
• Bibliography
• 6 AgeStage-Classified Models
• 6.1 Introduction
• 6.2 Model Construction
• 6.3 Sensitivity Analysis
• 6.4 Examples
• 6.4.1 Population Growth Rate and Selection Gradients
• 6.4.2 Distributions of Age and Stage at Death
• 6.4.2.1 Perturbation Analysis
• 6.5 Discussion
• 6.5.1 Reducibility and Ergodicity
• 6.5.2 A Protocol for AgeStage-Classified Models
• A Appendix: Population Growth and Reducible Matrices
• Bibliography
• Part III Time-Varying and Stochastic Models
• 7 Transient Population Dynamics
• 7.1 Introduction
• 7.2 Time-Invariant Models
• 7.3 Sensitivity of What? Choosing Dependent Variables
• 7.4 Elasticity Analysis
• 7.5 Sensitivity of Time-Varying Models
• 7.6 Sensitivity of Subsidized Populations
• 7.7 Sensitivity of Nonlinear Models
• 7.8 Sensitivity of Population Projections
• 7.9 Discussion
• Bibliography
• 8 Periodic Models
• 8.1 Introduction
• 8.1.1 Perturbation Analysis
• 8.2 Linear Models
• 8.2.1 A Simple Harvest Model
• 8.3 Multistate Models
• 8.4 Nonlinear Models and Delayed Density Dependence
• 8.4.1 Averages
• 8.4.2 A Nonlinear Example
• 8.5 LTRE Decomposition Analysis
• 8.6 Discussion
• Bibliography
• 9 LTRE Decomposition of the Stochastic Growth Rate
• 9.1 Introduction
• 9.2 Decomposition with Derivatives
• 9.3 Kitagawa and Keyfitz: Decomposition Without Derivatives
• 9.4 Stochastic Population Growth
• 9.4.1 Environment-Specific Sensitivities
• 9.5 LTRE Decomposition Analysis for logλs
• 9.5.1 Case 1: Vital Rates Differ, Environments Identical
• 9.5.2 Case 2: Vital Rates Identical, Environments Differ
• 9.5.3 Case 3: Vital Rates and Environments Differ.
• 9.6 An Example: Fire and an Endangered Plant
• 9.6.1 The Stochastic Fire Environment
• 9.6.2 LTRE Analysis
• 9.7 Discussion
• Bibliography
• Part IV Nonlinear Models
• 10 Sensitivity Analysis of Nonlinear Demographic Models
• 10.1 Introduction
• 10.2 Density-Dependent Models
• 10.2.1 Linearizations Around Equilibria
• 10.2.2 Sensitivity of Equilibrium
• 10.2.3 Dependent Variables: Beyond
• 10.2.4 Reactivity and Transient Dynamics
• 10.2.5 Elasticity Analysis
• 10.2.6 Continuous-Time Models
• 10.3 Environmental Feedback Models
• 10.4 Subsidized Populations and Competition for Space
• 10.4.1 Density-Independent Subsidized Populations
• 10.4.2 Linear Subsidized Models with Competitionfor Space
• 10.4.3 Density-Dependent Subsidized Models
• 10.5 Stable Structure and Reproductive Value
• 10.5.1 Stable Structure
• 10.5.2 Reproductive Value
• 10.5.3 Sensitivity of the Dependency Ratio
• 10.5.4 Sensitivity of Mean Age and Related Quantities
• 10.5.5 Sensitivity of Variance in Age
• 10.6 Frequency-Dependent Two-Sex Models
• 10.6.1 Sensitivity of the Population Structure
• 10.6.2 Population Growth Rate in Two-Sex Models
• 10.6.3 The Birth Matrix-Mating Rule Model
• 10.7 Sensitivity of Population Cycles
• 10.7.1 Sensitivity of the Population Vector
• 10.7.2 Sensitivity of Weighted Densities and TimeAverages
• 10.7.3 Sensitivity of Temporal Variance in Density
• 10.7.4 Periodic Dynamics in Periodic Environments
• 10.8 Dynamic Environmental Feedback Models
• 10.9 Stage-Structured Epidemics
• 10.10 Moments of Longevity in Nonlinear Models
• 10.11 Summary
• References
• Part V Markov Chains
• 11 Sensitivity Analysis of Discrete Markov Chains
• 11.1 Introduction
• 11.2 Absorbing Chains
• 11.2.1 Occupancy: Visits to Transient States
• 11.2.2 Time to Absorption
• 11.2.3 Number of States Visited Before Absorption.
• 11.2.4 Multiple Absorbing States and Probabilities of Absorption
• 11.2.5 The Quasistationary Distribution
• 11.3 Life Lost Due to Mortality
• 11.4 Ergodic Chains
• 11.4.1 The Stationary Distribution
• 11.4.2 The Fundamental Matrix
• 11.4.3 The First Passage Time Matrix
• 11.4.4 Mixing Time and the Kemeny Constant
• 11.4.5 Implicit Parameters and Compensation
• 11.5 Species Succession in a Marine Community
• 11.5.1 Biotic Diversity
• 11.5.2 The Kemeny Constant and Ecological Mixing
• 11.6 Discussion
• A Appendix A: Proofs
• A.1 Derivatives of the Moments of Occupancy Times
• A.2 Derivatives of the Moments of Time to Absorption
• B Appendix B: Marine Community Matrix
• References
• 12 Sensitivity Analysis of Continuous Markov Chains
• 12.1 Introduction
• 12.1.1 Absorbing Markov Chains
• 12.2 Occupancy Time in Transient States
• 12.3 Longevity: Time to Absorption
• 12.4 Multiple Absorbing States and Probabilities of Absorption
• 12.5 The Embedded Chain: Discrete Transitions Within a Continuous Process
• 12.6 An Example: A Model of Disease Progression
• 12.6.1 Sensitivity Results
• 12.6.2 Sensitivity of the Embedded Chain
• 12.7 Discussion
• References.