Softcover ISBN:  9781470473341 
Product Code:  STML/106 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
eBook ISBN:  9781470476434 
Product Code:  STML/106.E 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
Softcover ISBN:  9781470473341 
eBook: ISBN:  9781470476434 
Product Code:  STML/106.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $94.40 $70.80 
Softcover ISBN:  9781470473341 
Product Code:  STML/106 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
eBook ISBN:  9781470476434 
Product Code:  STML/106.E 
List Price:  $59.00 
Individual Price:  $47.20 
MAA Member Price:  $47.20 
Softcover ISBN:  9781470473341 
eBook ISBN:  9781470476434 
Product Code:  STML/106.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $94.40 $70.80 

Book DetailsStudent Mathematical LibraryVolume: 106; 2024; 274 ppMSC: Primary 92; 39; Secondary 37; 15
This book offers an introduction to the use of matrix theory and linear algebra in modeling the dynamics of biological populations. Matrix algebra has been used in population biology since the 1940s and continues to play a major role in theoretical and applied dynamics for populations structured by age, body size or weight, disease states, physiological and behavioral characteristics, life cycle stages, or any of many other possible classification schemes. With a focus on matrix models, the book requires only first courses in multivariable calculus and matrix theory or linear algebra as prerequisites.
The reader will learn the basics of modeling methodology (i.e., how to set up a matrix model from biological underpinnings) and the fundamentals of the analysis of discrete time dynamical systems (equilibria, stability, bifurcations, etc.). A recurrent theme in all chapters concerns the problem of extinction versus survival of a population. In addition to numerous examples that illustrate these fundamentals, several applications appear at the end of each chapter that illustrate the full cycle of model setup, mathematical analysis, and interpretation. The author has used the material over many decades in a variety of teaching and mentoring settings, including special topics courses and seminars in mathematical modeling, mathematical biology, and dynamical systems.
ReadershipUndergraduate and graduate students interested in discrete time models in population, epidemic, and evolutionary dynamics.

Table of Contents

Chapters

Population models

Linear matrix models for structured populations

Nonlinear matrix models for structured populations

Disease and epidemic models

Darwinian dynamics

Appendices


Additional Material

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This book offers an introduction to the use of matrix theory and linear algebra in modeling the dynamics of biological populations. Matrix algebra has been used in population biology since the 1940s and continues to play a major role in theoretical and applied dynamics for populations structured by age, body size or weight, disease states, physiological and behavioral characteristics, life cycle stages, or any of many other possible classification schemes. With a focus on matrix models, the book requires only first courses in multivariable calculus and matrix theory or linear algebra as prerequisites.
The reader will learn the basics of modeling methodology (i.e., how to set up a matrix model from biological underpinnings) and the fundamentals of the analysis of discrete time dynamical systems (equilibria, stability, bifurcations, etc.). A recurrent theme in all chapters concerns the problem of extinction versus survival of a population. In addition to numerous examples that illustrate these fundamentals, several applications appear at the end of each chapter that illustrate the full cycle of model setup, mathematical analysis, and interpretation. The author has used the material over many decades in a variety of teaching and mentoring settings, including special topics courses and seminars in mathematical modeling, mathematical biology, and dynamical systems.
Undergraduate and graduate students interested in discrete time models in population, epidemic, and evolutionary dynamics.

Chapters

Population models

Linear matrix models for structured populations

Nonlinear matrix models for structured populations

Disease and epidemic models

Darwinian dynamics

Appendices