An introduction to structured population dynamics / J.M. Cushing.

Format:

Book

Author/Creator:

Cushing, J. M. (Jim Michael), 1942-

Contributor:

Conference Board of the Mathematical Sciences.

Series:

CBMS-NSF regional conference series in applied mathematics ; 71.

CBMS-NSF regional conference series in applied mathematics ; 71

Language:

English

Subjects (All):

Population biology--Mathematical models.

Population biology.

Physical Description:

1 online resource (xiii, 193 p. ) ill. ;

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1998.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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? This monograph 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 this monograph, 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. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

Contents:

Preface

Chapter 1: Discrete models. Matrix models; Autonomous single species models; Some applications; A case study; Multispecies interactions

Chapter 2: Continuous models. Age-structured models; Autonomous age-structured models; Some applications; Multispecies interactions; Other structured models

Chapter 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.

Notes:

Outgrowth of a series of lectures given at a conference held at North Carolina University, Raleigh, during June of 1997.

"Sponsored by Conference Board of the Mathematical Sciences"--Cover.

Includes bibliographical references (p. 171-190) and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-000-8

Publisher Number:

CB71 SIAM