Biologist's Guide to Mathematical Modeling in Ecology and Evolution

ISBN-10: 0691123446
ISBN-13: 9780691123448
Edition: 2007
List price: $85.00 Buy it from $43.20 Rent it from $27.29
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Description: Bridging the gap in training between mathematics and biology is extremely important and this text guides students across this gap. It will enable any interested reader to learn how mathematical models are born, how they develop and what they can  More...

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Book details

List price: $85.00
Copyright year: 2007
Publisher: Princeton University Press
Publication date: 3/12/2007
Binding: Hardcover
Pages: 744
Size: 8.00" wide x 10.00" long x 1.75" tall
Weight: 2.420
Language: English

Bridging the gap in training between mathematics and biology is extremely important and this text guides students across this gap. It will enable any interested reader to learn how mathematical models are born, how they develop and what they can tell us.

Preface
Mathematical Modeling in Biology
Introduction
HIV
Models of HIV/AIDS
Concluding Message
How to Construct a Model
Introduction
Formulate the Question
Determine the Basic Ingredients
Qualitatively Describe the Biological System
Quantitatively Describe the Biological System
Analyze the Equations
Checks and Balances
Relate the Results Back to the Question
Concluding Message
Deriving Classic Models in Ecology and Evolutionary Biology
Introduction
Exponential and Logistic Models of Population Growth
Haploid and Diploid Models of Natural Selection
Models of Interactions among Species
Epidemiological Models of Disease Spread
Working Backward-Interpreting Equations in Terms of the Biology
Concluding Message
Functions and Approximations
Functions and Their Forms
Linear Approximations
The Taylor Series
Numerical and Graphical Techniques-Developing a Feeling for Your Model
Introduction
Plots of Variables Over Time
Plots of Variables as a Function of the Variables Themselves
Multiple Variables and Phase-Plane Diagrams
Concluding Message
Equilibria and Stability Analyses-One-Variable Models
Introduction
Finding an Equilibrium
Determining Stability
Approximations
Concluding Message
General Solutions and Transformations-One-Variable Models
Introduction
Transformations
Linear Models in Discrete Time
Nonlinear Models in Discrete Time
Linear Models in Continuous Time
Nonlinear Models in Continuous Time
Concluding Message
Linear Algebra
An Introduction to Vectors and Matrices
Vector and Matrix Addition
Multiplication by a Scalar
Multiplication of Vectors and Matrices
The Trace and Determinant of a Square Matrix
The Inverse
Solving Systems of Equations
The Eigenvalues of a Matrix
The Eigenvectors of a Matrix
Equilibria and Stability Analyses-Linear Models with Multiple Variables
Introduction
Models with More than One Dynamic Variable
Linear Multivariable Models
Equilibria and Stability for Linear Discrete-Time Models
Concluding Message
Equilibria and Stability Analyses-Nonlinear Models with Multiple Variables
Introduction
Nonlinear Multiple-Variable Models
Equilibria and Stability for Nonlinear Discrete-Time Models
Perturbation Techniques for Approximating Eigenvalues
Concluding Message
General Solutions and Tranformations-Models with Multiple Variables
Introduction
Linear Models Involving Multiple Variables
Nonlinear Models Involving Multiple Variables
Concluding Message
Dynamics of Class-Structured Populations
Introduction
Constructing Class-Structured Models
Analyzing Class-Structured Models
Reproductive Value and Left Eigenvectors
The Effect of Parameters on the Long-Term Growth Rate
Age-Structured Models-The Leslie Matrix
Concluding Message
Techniques for Analyzing Models with Periodic Behavior
Introduction
What Are Periodic Dynamics?
Composite Mappings
Hopf Bifurcations
Constants of Motion
Concluding Message
Evolutionary Invasion Analysis
Introduction
Two Introductory Examples
The General Technique of Evolutionary Invasion Analysis
Determining How the ESS Changes as a Function of Parameters
Evolutionary Invasion Analyses in Class-Structured Populations
Concluding Message
Probability Theory
An Introduction to Probability
Conditional Probabilities and Bayes' Theorem
Discrete Probability Distributions
Continuous Probability Distributions
The (Insert Your Name Here) Distribution
Probabilistic Models
Introduction
Models of Population Growth
Birth-Death Models
Wright-Fisher Model of Allele Frequency Change
Moran Model of Allele Frequency Change
Cancer Development
Cellular Automata-A Model of Extinction and Recolonization
Looking Backward in Time-Coalescent Theory
Concluding Message
Analyzing Discrete Stochastic Models
Introduction
Two-State Markov Models
Multistate Markov Models
Birth-Death Models
Branching Processes
Concluding Message
Analyzing Continuous Stochastic Models-Diffusion in Time and Space
Introduction
Constructing Diffusion Models
Analyzing the Diffusion Equation with Drift
Modeling Populations in Space Using the Diffusion Equation
Concluding Message
Epilogue: The Art of Mathematical Modeling in Biology
Commonly Used Mathematical Rules
Rules for Algebraic Functions
Rules for Logarithmic and Exponential Functions
Some Important Sums
Some Important Products
Inequalities
Some Important Rules from Calculus
Concepts
Derivatives
Integrals
Limits
The Perron-Frobenius Theorem
Definitions
The Perron-Frobenius Theorem
Finding Maxima and Minima of Functions
Functions with One Variable
Functions with Multiple Variables
Moment-Generating Functions
Index of Definitions, Recipes, and Rules
General Index

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