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Format: 1 online resource (308 pages)

Edition: 1st ed.

ISBN: 9783030105341

Series Statement: Demographic Research Monographs

Note: 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.

Additional Edition: Print version: Caswell, Hal Sensitivity Analysis: Matrix Methods in Demography and Ecology Cham : Springer International Publishing AG,c2019 ISBN 9783030105334

Language: English

Subjects: Economics , Sociology

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Format: 1 online resource (XVIII, 299 p. 134 illus.)

Edition: 1st ed. 2019.

ISBN: 3-030-10534-2

Series Statement: Demographic Research Monographs, A Series of the Max Planck Institute for Demographic Research,

Content: 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. .

Note: I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains. , English

Additional Edition: ISBN 3-030-10533-4

Language: English

DOI: 10.1007/978-3-030-10534-1

UID:

Format: XVIII, 299 p. 134 illus. , online resource.

Edition: 1st ed. 2019.

ISBN: 9783030105341

Series Statement: Demographic Research Monographs, A Series of the Max Planck Institute for Demographic Research,

Content: 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. .

Note: I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783030105334

Additional Edition: Printed edition: ISBN 9783030105358

Language: English

DOI: 10.1007/978-3-030-10534-1

URL: https://doi.org/10.1007/978-3-030-10534-1

UID:

Format: 1 online resource (XVIII, 299 p. 134 illus.)

Edition: 1st ed. 2019.

ISBN: 3-030-10534-2

Series Statement: Demographic Research Monographs, A Series of the Max Planck Institute for Demographic Research,

Content: 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. .

Note: I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains. , English

Additional Edition: ISBN 3-030-10533-4

Language: English

DOI: 10.1007/978-3-030-10534-1

UID:

Format: 1 online resource (XVIII, 299 p. 134 illus.)

Edition: 1st ed. 2019.

ISBN: 3-030-10534-2

Series Statement: Demographic Research Monographs, A Series of the Max Planck Institute for Demographic Research,

Content: 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. .

Note: I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains. , English

Additional Edition: ISBN 3-030-10533-4

Language: English

DOI: 10.1007/978-3-030-10534-1

UID:

Format: 1 online resource (XVIII, 299 p. 134 illus.)

Edition: 1st ed. 2019.

ISBN: 3-030-10534-2

Series Statement: Demographic Research Monographs, A Series of the Max Planck Institute for Demographic Research,

Content: 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. .

Note: I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains. , English

Additional Edition: ISBN 3-030-10533-4

Language: English

DOI: 10.1007/978-3-030-10534-1