A biologist's guide to mathematical modeling in ecology and evolution
 Responsibility
 Sarah P. Otto and Troy Day.
 Imprint
 Princeton, NJ : Princeton University Press, c2007.
 Physical description
 x, 732 p. : ill., map ; 26 cm.
Course reserve
 Course
 BIO287A01  Advanced Topics in Mathematical Evolutionary Biology
 Instructor(s)
 Rosenberg, Noah Aubrey
At the library
Marine Biology Library (Miller)
Stacks
Call number  Status 

QH541.15 .M3 O88 2007  Unknown 
Science Library (Li and Ma)
Stacks
Call number  Status 

QH541.15 .M3 O88 2007  On reserve at Li and Ma Science Library 2hour loan 
More options
Description
Creators/Contributors
 Author/Creator
 Otto, Sarah P., 1967
 Contributor
 Day, Troy, 1968
Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Contents

 Preface ix
 Chapter 1: Mathematical Modeling in Biology 1 1.1 Introduction 1 1.2 HIV 2 1.3 Models of HIV/AIDS 5 1.4 Concluding Message 14
 Chapter 2: How to Construct a Model 17 2.1 Introduction 17 2.2 Formulate the Question 19 2.3 Determine the Basic Ingredients 19 2.4 Qualitatively Describe the Biological System 26 2.5 Quantitatively Describe the Biological System 33 2.6 Analyze the Equations 39 2.7 Checks and Balances 47 2.8 Relate the Results Back to the Question 50 2.9 Concluding Message 51
 Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology 54 3.1 Introduction 54 3.2 Exponential and Logistic Models of Population Growth 54 3.3 Haploid and Diploid Models of Natural Selection 62 3.4 Models of Interactions among Species 72 3.5 Epidemiological Models of Disease Spread 77 3.6 Working BackwardInterpreting Equations in Terms of the Biology 79 3.7 Concluding Message 82
 Primer
 1: Functions and Approximations 89 P1.1 Functions and Their Forms 89 P1.2 Linear Approximations 96 P1.3 The Taylor Series 100
 Chapter 4: Numerical and Graphical TechniquesDeveloping a Feeling for Your Model 110 4.1 Introduction 110 4.2 Plots of Variables Over Time 111 4.3 Plots of Variables as a Function of the Variables Themselves 124 4.4 Multiple Variables and PhasePlane Diagrams 133 4.5 Concluding Message 145
 Chapter 5: Equilibria and Stability AnalysesOneVariable Models 151 5.1 Introduction 151 5.2 Finding an Equilibrium 152 5.3 Determining Stability 163 5.4 Approximations 176 5.5 Concluding Message 184
 Chapter 6: General Solutions and TransformationsOneVariable Models 191 6.1 Introduction 191 6.2 Transformations 192 6.3 Linear Models in Discrete Time 193 6.4 Nonlinear Models in Discrete Time 195 6.5 Linear Models in Continuous Time 198 6.6 Nonlinear Models in Continuous Time 202 6.7 Concluding Message 207
 Primer
 2: Linear Algebra 214 P2.1 An Introduction to Vectors and Matrices 214 P2.2 Vector and Matrix Addition 219 P2.3 Multiplication by a Scalar 222 P2.4 Multiplication of Vectors and Matrices 224 P2.5 The Trace and Determinant of a Square Matrix 228 P2.6 The Inverse 233 P2.7 Solving Systems of Equations 235 P2.8 The Eigenvalues of a Matrix 237 P2.9 The Eigenvectors of a Matrix 243
 Chapter 7: Equilibria and Stability AnalysesLinear Models with Multiple Variables 254 7.1 Introduction 254 7.2 Models with More than One Dynamic Variable 255 7.3 Linear Multivariable Models 260 7.4 Equilibria and Stability for Linear DiscreteTime Models 279 7.5 Concluding Message 289
 Chapter 8: Equilibria and Stability AnalysesNonlinear Models with Multiple Variables 294 8.1 Introduction 294 8.2 Nonlinear MultipleVariable Models 294 8.3 Equilibria and Stability for Nonlinear DiscreteTime Models 316 8.4 Perturbation Techniques for Approximating Eigenvalues 330 8.5 Concluding Message 337
 Chapter 9: General Solutions and TranformationsModels with Multiple Variables 347 9.1 Introduction 347 9.2 Linear Models Involving Multiple Variables 347 9.3 Nonlinear Models Involving Multiple Variables 365 9.4 Concluding Message 381
 Chapter 10: Dynamics of ClassStructured Populations 386 10.1 Introduction 386 10.2 Constructing ClassStructured Models 388 10.3 Analyzing ClassStructured Models 393 10.4 Reproductive Value and Left Eigenvectors 398 10.5 The Effect of Parameters on the LongTerm Growth Rate 400 10.6 AgeStructured ModelsThe Leslie Matrix 403 10.7 Concluding Message 418
 Chapter 11: Techniques for Analyzing Models with Periodic Behavior 423 11.1 Introduction 423 11.2 What Are Periodic Dynamics? 423 11.3 Composite Mappings 425 11.4 Hopf Bifurcations 428 11.5 Constants of Motion 436 11.6 Concluding Message 449
 Chapter 12: Evolutionary Invasion Analysis 454 12.1 Introduction 454 12.2 Two Introductory Examples 455 12.3 The General Technique of Evolutionary Invasion Analysis 465 12.4 Determining How the ESS Changes as a Function of Parameters 478 12.5 Evolutionary Invasion Analyses in ClassStructured Populations 485 12.6 Concluding Message 502
 Primer
 3: Probability Theory 513 P3.1 An Introduction to Probability 513 P3.2 Conditional Probabilities and Bayes' Theorem 518 P3.3 Discrete Probability Distributions 521 P3.4 Continuous Probability Distributions 536 P3.5 The (Insert Your Name Here) Distribution 553
 Chapter 13: Probabilistic Models 567 13.1 Introduction 567 13.2 Models of Population Growth 568 13.3 BirthDeath Models 573 13.4 WrightFisher Model of Allele Frequency Change 576 13.5 Moran Model of Allele Frequency Change 581 13.6 Cancer Development 584 13.7 Cellular AutomataA Model of Extinction and Recolonization 591 13.8 Looking Backward in TimeCoalescent Theory 594 13.9 Concluding Message 602
 Chapter 14: Analyzing Discrete Stochastic Models 608 14.1 Introduction 608 14.2 TwoState Markov Models 608 14.3 Multistate Markov Models 614 14.4 BirthDeath Models 631 14.5 Branching Processes 639 14.6 Concluding Message 644
 Chapter 15: Analyzing Continuous Stochastic ModelsDiffusion in Time and Space 649 15.1 Introduction 649 15.2 Constructing Diffusion Models 649 15.3 Analyzing the Diffusion Equation with Drift 664 15.4 Modeling Populations in Space Using the Diffusion Equation 684 15.5 Concluding Message 687 Epilogue: The Art of Mathematical Modeling in Biology 692
 Appendix 1: Commonly Used Mathematical Rules 695 A1.1 Rules for Algebraic Functions 695 A1.2 Rules for Logarithmic and Exponential Functions 695 A1.3 Some Important Sums 696 A1.4 Some Important Products 696 A1.5 Inequalities 697
 Appendix 2: Some Important Rules from Calculus 699 A2.1 Concepts 699 A2.2 Derivatives 701 A2.3 Integrals 703 A2.4 Limits 704
 Appendix 3: The PerronFrobenius Theorem 709 A3.1: Definitions 709 A3.2: The PerronFrobenius Theorem 710
 Appendix 4: Finding Maxima and Minima of Functions 713 A4.1 Functions with One Variable 713 A4.2 Functions with Multiple Variables 714
 Appendix 5: MomentGenerating Functions 717
 Index of Definitions, Recipes, and Rules 725 General Index 727.
 (source: Nielsen Book Data)
 Summary

Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. It is 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. It is a howto guide for developing new mathematical models in biology. It provides stepbystep recipes for constructing and analyzing models. It covers interesting biological applications. It explores classical models in ecology and evolution. There are questions at the end of every chapter. Primers cover important mathematical topics. Exercises are provided with answers. Appendixes summarize useful rules. Labs and advanced material are available.
(source: Nielsen Book Data)  Supplemental links

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Publisher description
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Bibliographic information
 Publication date
 2007
 ISBN
 9780691123448 (cloth : alk. paper)
 0691123446 (cloth : alk. paper)