A Biologist's Guide to Mathematical Modeling in Ecology and Evolution
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.
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LibraryThing ReviewUser 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
Deriving Classic Models in Ecology and Evolutionary Biology
Functions and Approximations
Numerical and Graphical TechniquesDeveloping a Feeling for Your Model
Equilibria and Stability AnalysesOneVariable Models
General Solutions and TransformationsOneVariable Models
Analyzing Discrete Stochastic Models
Analyzing Continuous Stochastic ModelsDiffusion in Time and Space
The Art of Mathematical Modeling in Biology
Commonly Used Mathematical Rules
Some Important Rules from Calculus
The PerronFrobenius Theorem
Equilibria and Stability AnalysesLinear Models with Multiple Variables
Equilibria and Stability AnalysesNonlinear Models with Multiple Variables
General Solutions and TransformationsModels with Multiple Variables
Dynamics of ClassStructured Populations
Techniques for Analyzing Models with Periodic Behavior
Evolutionary Invasion Analysis