A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Front Cover
Princeton University Press, Sep 19, 2011 - Science - 744 pages
1 Review

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
 

What people are saying - Write a review

LibraryThing Review

User Review  - amarcobio - LibraryThing

This is the kind of technical book I'd love to write if I could. Starts with very basic concepts and it leads you to more complex issues. At the end of the book, if you follow the arguments, you end up with a solid knowledge in biological models. This is one ofmmy favourite technical books ever. Read full review

Contents

Mathematical Modeling in Biology
1
How to Construct a Model
17
Deriving Classic Models in Ecology and Evolutionary Biology
54
Functions and Approximations
89
Numerical and Graphical TechniquesDeveloping a Feeling for Your Model
110
Equilibria and Stability AnalysesOneVariable Models
151
General Solutions and TransformationsOneVariable Models
191
Linear Algebra
214
Probability Theory
513
Probabilistic Models
567
Analyzing Discrete Stochastic Models
608
Analyzing Continuous Stochastic ModelsDiffusion in Time and Space
649
The Art of Mathematical Modeling in Biology
692
Commonly Used Mathematical Rules
695
Some Important Rules from Calculus
699
The PerronFrobenius Theorem
709

Equilibria and Stability AnalysesLinear Models with Multiple Variables
254
Equilibria and Stability AnalysesNonlinear Models with Multiple Variables
294
General Solutions and TransformationsModels with Multiple Variables
347
Dynamics of ClassStructured Populations
386
Techniques for Analyzing Models with Periodic Behavior
423
Evolutionary Invasion Analysis
454
Finding Maxima and Minima of Functions
713
MomentGenerating Functions
717
Index of Definitions Recipes and Rules
725
General Index
727
Copyright

Other editions - View all

Common terms and phrases

About the author (2011)

Sarah P. Otto is Professor of Zoology at the University of British Columbia. Troy Day is Associate Professor of Mathematics and Biology at Queen's University

Bibliographic information