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Matrix Population Models: Construction, Analysis, and Interpretation, Second Edition

Hal Caswell, Woods Hole Oceanographic Institution

October 2000
727 pages, 216 illustrations
paper

About This Title

Matrix Population Models, Second Edition, is a comprehensive treatment of matrix population models and their applications in ecology and demography. It begins with simple cases, presented in detail so that beginning students can learn how to use these powerful models. It goes on to cover advanced topics in stochastic and nonlinear models. Analytical methods and theoretical issues are illustrated with empirical examples throughout.

The decade since the publication of the First Edition of this book has seen enormous progress in the theory and application of matrix population models. The new edition includes greatly expanded treatment of stochastic and density-dependent models, sensitivity analysis, and statistical inference, and new chapters on parameter estimation, structured population models, demographic stochasticity, and applications of matrix models in conservation biology.

Matrix Population Models, Second Edition, is an indispensable reference for graduate students and researchers in ecology, population biology, conservation biology, and human demography.

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About the Author(s)

Hal Caswell is a Senior Scientist in the Biology Department at the Woods Hole Oceanographic Institution, where he holds the Robert W. Morse Chair for Excellence in Oceanography. He earned a Ph.D. in Zoology in 1974 at Michigan State University. In addition to Matrix Population Models, Dr. Caswell is a coauthor (with S. Tuljapurkar) of Structured Population Models in Marine, Terrestrial and Freshwater Systems (Chapman and Hall, 1997). A former Guggenheim Fellow and a Fellow of AAAS, he has also served as Chairman of the Theoretical Ecology Section of the Ecological Society of America. Dr. Caswell's research interests include mathematical ecology, structured population models, stochastic models for spatial processes, conservation of marine mammals and seabirds, plant population ecology, ecotoxicology, and nonlinear dynamics in ecology.

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Reviews and Commentary

". . . for those with a taste for mathematical elegance and an interest in the full array of approaches available for modeling populations with complex life cycles, this book is a must."
—Larry Barnthouse, SETAC Globe

"Both the scope of issues and the means by which they are exposed show the author's desire to create a book that might be interesting and useful not only for the beginner, but for the expert too. Hal Caswell has succeeded remarkably in doing both."
—Dmitrii O. Logofet, Ecological Modelling

"To say that the extent of material covered in this book is impressive is an understatement. If your research endeavors include population biology, or you teach a course in population biology, you need this text."
—Floyd W. Weckerly, Natural Resource Modeling

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Table of Contents

Preface

Preface to the First Edition

1. Introduction

• The Life Cycle: Linking the Individual and the Population
• Demography
• Overview of the Book
• Construction, Analysis, and Interpretation
• Mathematical Prerequisites
• Notation

2. Age-classified Matrix Models

• The Leslie Matrix
• Projection: The Simplest Form of Analysis
• The Leslie Matrix and the Life Table
• Constructing Age-classified Matrices
• Assumptions: Projection vs. Forecasting
• History

3. Stage-classified Life Cycles

• State Variables
• Age as a State Variable: When Does it Fail?
• Statistical Evaluation of State Variables
• Conclusions

4. Stage-classified Matrix Models

• The Life Cycle Graph
• The Matrix Model
• Metapopulation and Multistate Models
• Solution of the Projection Equation
• Ergodicity
• Reproductive Value
• Transient Dynamics and Convergence
• Computation of Eigenvalues and Eigenvectors
• Assumptions Revisited

5. Events in the Life Cycle

• A = T + F
• Lifetime Event Probabilities
• Age-specific Traits

6. Parameter Estimation

• Identified Individuals
• Inverse Methods for Time Series
• Stable Stage-distribution Methods
• Stage-duration Distributions
• Multiregional or Age-size Models
• Size Categories: The Vandermeer-Moloney Algorithms
• Fertilities in Stage-classified Models
• Overview

7. Analysis of the Life Cycle Graph

• The z-Transform
• Reduction of the Life Cycle Graph
• The Characteristic Equation
• The Stable Stage Distribution
• Reproductive Value
• Partial Life Cycle Analysis
• Annual Organisms

8. Structured Population Models

• Partial Differential Equation Models
• Delay-differential Equation Models
• Integrodifference Equation Models
• i-state Configuration Models
• Choosing a Model

9. Sensitivity Analysis

• Eigenvalue Sensitivity
• Elasticity Analysis
• Sensitivity Analysis of Transient Dynamics
• Sensitivities of Eigenvectors
• Generalized Inverses in Sensitivity Analysis
• Sensitivity Analysis of Markov Chains
• Second Derivatives of Eigenvalues

10. Life Table Response Experiments

• Fixed Designs
• Random Designs and Variance Decomposition
• Regression Designs
• Extensions
• Prospective and Retrospective Analyses

11. Evolutionary Demography

• Fitness
• Sensitivity, Elasticity, and Selection
• Lifetime Reproductive Success and Individual Fitness
• Fitness and Reproductive Value

12. Statistical Inference

• Confidence Intervals and Uncertainty
• Loglinear Analysis of Transition Matrices
• Randomization Tests

13. Periodic Environments

• Periodic Matrix Products
• Annual Organisms
• Other Approaches to Periodic Environments
• Deterministic, Aperiodic Environments

14. Environmental Stochasticity

• Formulation of Stochastic Models
• Stochastic Ergodic Theorems
• Stochastic Population Growth
• Sensitivity and Elasticity Analyses
• Examples of Stochastic Models
• Evolution in Stochastic Environments
• Deterministic and Stochastic Sensitivity
• Extinction in Stochastic Environments
• Short-term Stochastic Forecasts

15. Demographic Stochasticity

• Stochastic Simulations
• The Galton-Watson Branching Process
• Multitype Branching Processes
• Analysis of Multitype Branching Processes
• Combining Demographic and Environmental Stochasticity
• Assumptions Revisited

16. Density-dependent Models

• Model Construction
• Asymptotic Dynamics and Attractors
• Stable and Unstable Invariant Sets
• Local Stability Analysis
• Bifurcation Diagrams
• Bifurcations of Equilibria: A Field Guide
• Chaos
• Transient Dynamics
• Multiple Attractors and Qualitative Unpredictability
• Tribolium: Models and Experiments
• Perturbation Analysis and Evolutionary Demography
• Stochasticity

17. Two-sex Models

• Sexual Dimorphism in the Vital Rates
• Dominance, Sex Ratio, and the Marriage Squeeze
• Two-sex Models
• Competition for Mates
• The Birth MatrixñMating Rule Model
• More Detailed Models of Mating
• Frequency- and Density-dependence Combined
• Extinction and the Sex Ratio

18. Conservation and Management

• Conservation
• Pest Control
• Harvesting
• Conclusion

19. Concluding Remarks

Appendix: The Basics of Matrix Algebra

• Motivation
• Definitions
• Operations
• Matrix Inversion
• Determinants
• Eigenvalues and Eigenvectors
• Similarity
• Norms of Vectors and Matrices

Suggested Reading

Bibliography

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Pricing and Options

Titles	Product Code	Price (USD)
Matrix Population Models: Construction, Analysis, and Interpretation, Second Edition	0-87893-121-x	$79.95	Purchase	Request Exam Copy
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