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More copies of this ISBNA Biologist's Guide to Mathematical Modeling in Ecology and Evolutionby Sarah P. Otto and Troy Day
Synopses & ReviewsPublisher Comments: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 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.
Synopsis:"A wonderfully pedagogical introduction to mathematical modeling in population biology: an ideal first course for biologists."Simon A. Levin, Princeton University
"This book is an amazing teaching resource for developing a comprehensive understanding of the methods and importance of biological modeling. But more than that, this book should be read by every student of evolutionary biology and ecology so that they can come to a deeper appreciation of the fundamental ideas and models that underlie these fields."Patrick C. Phillips, University of Oregon
"There is an increasing use of mathematics throughout the biological sciences, yet the training of most biologists still woefully lacks crucial mathematical tools. Sally Otto and Troy Day are themselves two masters at the deft use of theoretical models to crystallize conceptual insights about ecological and evolutionary problems, and in this wonderful book they make accessible to a broad audience the essential mathematical tool kit biologists need, both to read the literature and to craft and analyze models themselves."Robert D. Holt, University of Florida
"I am often asked by biologists to recommend a book on mathematical modeling, but I must tell them that there is no single good book that will guide them through the difficult first stages of learning to make models. Otto and Day's book fills the gap. The quality is high throughout, the scholarship is sound, the book is comprehensive. The authors are both firstrate scientists. I think this will be a classic."Steven A. Frank, author of Immunology and Evolution of Infectious Disease
"This book provides a general introduction to mathematical modelingin particular, to population modelingin the biological sciences. This past year I taught a 400level course in mathematical modeling of biological systems, and I had to do so without a textbook because no adequate text existed. Otto and Day's book would have met my needs beautifully. This book is an important addition to the field."Carl Bergstrom, University of Washington
"This book has the ambitious and worthy goal of teaching biologists enough about modeling and about mathematical methods to be both intelligent consumers of models and competent creators of their own models. Its concentration on the process of building rather than analyzing models is its strongest point."Frederick R. Adler, author of Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
Synopsis: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 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.
About the AuthorSarah 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
Table of ContentsPreface ix
Chapter 1: Mathematical Modeling in Biology 1 Chapter 2: How to Construct a Model 17 Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology 54 Primer 1: Functions and Approximations 89 Chapter 4: Numerical and Graphical TechniquesDeveloping a Feeling for Your Model 110 Chapter 5: Equilibria and Stability AnalysesOneVariable Models 151 Chapter 6: General Solutions and TransformationsOneVariable Models 191 Primer 2: Linear Algebra 214 Chapter 7: Equilibria and Stability AnalysesLinear Models with Multiple Variables 254 Chapter 8: Equilibria and Stability AnalysesNonlinear Models with Multiple Variables 294 Chapter 9: General Solutions and TranformationsModels with Multiple Variables 347 Chapter 10: Dynamics of ClassStructured Populations 386 Chapter 11: Techniques for Analyzing Models with Periodic Behavior 423 Chapter 12: Evolutionary Invasion Analysis 454 Primer 3: Probability Theory 513 Chapter 13: Probabilistic Models 567 Chapter 14: Analyzing Discrete Stochastic Models 608 Chapter 15: Analyzing Continuous Stochastic ModelsDiffusion in Time and Space 649 Appendix 1: Commonly Used Mathematical Rules 695 Appendix 2: Some Important Rules from Calculus 699 Appendix 3: The PerronFrobenius Theorem 709 Appendix 4: Finding Maxima and Minima of Functions 713 Appendix 5: MomentGenerating Functions 717 Index of Definitions, Recipes, and Rules 725 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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