A Biologist's Guide to Mathematical Modeling in Ecology and Evolution / Sarah P. Otto, Troy Day.

Format:

Book

Author/Creator:

Otto, Sarah P., author.

Day, Troy, author.

Language:

English

Subjects (All):

Ecology--Mathematical models.

Ecology.

Evolution (Biology)--Mathematical models.

Evolution (Biology).

Physical Description:

1 online resource (x, 732 p. ) ill. ;

Place of Publication:

Princeton, NJ : Princeton University Press, [2011]

Language Note:

English

Summary:

Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available

Contents:

Frontmatter

Contents

Preface

Chapter 1: Mathematical Modeling in Biology

Chapter 2: How to Construct a Model

Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology

Chapter 4: Numerical and Graphical Techniques-Developing a Feeling for Your Model

Chapter 5: Equilibria and Stability Analyses-One-Variable Models

Chapter 6: General Solutions and Transformations-One-Variable Models

Chapter 7: Equilibria and Stability Analyses-Linear Models with Multiple Variables

Chapter 8: Equilibria and Stability Analyses-Nonlinear Models with Multiple Variables

Chapter 9: General Solutions and Tranformations-Models with Multiple Variables

Chapter 10: Dynamics of Class-Structured Populations

Chapter 11: Techniques for Analyzing Models with Periodic Behavior

Chapter 12: Evolutionary Invasion Analysis

Chapter 13: Probabilistic Models

Chapter 14: Analyzing Discrete Stochastic Models

Chapter 15: Analyzing Continuous Stochastic Models-Diffusion in Time and Space

Epilogue: The Art of Mathematical Modeling in Biology

Appendix 1: Commonly Used Mathematical Rules

Appendix 2: Some Important Rules from Calculus

Appendix 3: The Perron-Frobenius Theorem

Appendix 4: Finding Maxima and Minima of Functions

Appendix 5: Moment-Generating Functions

Index of Definitions, Recipes, and Rules

General Index

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and indexes.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 23. Mai 2019)

ISBN:

9781400840915

1400840910

OCLC:

749265040