A Biologist's Guide to Mathematical Modeling in Ecology and EvolutionThirty 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 computerbased 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 firstyear calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate classstructured 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 Review
User Review  amarcobio  LibraryThingThis 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
1  
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 
725  
727  