Table of Contents: Sensitivity Analysis :

Sensitivity Analysis : Matrix Methods in Demography and Ecology.

Bibliographic Details
Main Author:	Caswell, Hal.
Format:	eBook
Language:	English
Published:	Cham : Springer International Publishing AG, 2019.
Edition:	1st ed.
Series:	Demographic Research Monographs
Subjects:	Electronic books.
Online Access:	Click to View

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.

Sensitivity Analysis : Matrix Methods in Demography and Ecology.

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