An Introduction to Structured Population Dynamics

About this book

Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? An Introduction to Structured Population Dynamics introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In An Introduction to Structured Population Dynamics, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics.

Contents

Preface

1. Discrete Models
Matrix Models
Autonomous Single Species Models
Some Applications
A Case Study
Multispecies Interactions

2. Continuous Models
Age-Structured Models
Autonomous Age-Structured Models
Some Applications
Multispecies Interactions
Other Structured Models

3. Population Level Dynamics
Ergodicity and Nonlinear Models
The Linear Chain Trick
Hierarchical Models
Total Population Size in Age-Structured Models

Appendix A. Stability Theory for Maps
Linear Maps
Linearization of Maps

Appendix B. Bifurcation Theorems
A Global Bifurcation Theorem
Local Parameterization

Appendix C. Miscellaneous

Proofs
Bibliography
Index

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