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.
- A how-to guide for developing new mathematical models in biology
- Provides step-by-step recipes for constructing and analyzing models
- Interesting biological applications
- Explores classical models in ecology and evolution
- Questions at the end of every chapter
- Primers cover important mathematical topics
- Exercises with answers
- Appendixes summarize useful rules
- Labs and advanced material available
"A gentle but thorough introduction to the mathematical techniques employed in ecological and evolutionary theory. Readers who . . . finish this well-written book will be prepared to read and understand a sizeable fraction of the current literature."--Donald L. DeAngelis, Quarterly Review of Biology
"At long last, Sally Otto and Troy Day have provided relief for biologists and epidemiologists in search of an easily read, practical, and thorough starting point from which to learn mathematical modeling. . . . We would recommend this book over shorter texts that are labeled as 'introductory'. . . . The depth and detail that Otto and Day have included in this text arc appealing rather than intimidating, and the structure of the text is empowering rather than didactic or formulaic."--Sanjay Basu and Alison P. Galvani, Siam Review
"[T]he great value of the Otto/Day book is that it attempts pedagogical soundness, and so is useful for teaching. Besides being perfectly readable, it engages and impresses the reader quickly not only with the subject matter, but also with the quality of printing and layout which have to be seen to be believed. These praises may sound lavish by many a reader of these columns but first see the book or better still buy the volume and you will see our passion and rage for going all out in praise of this volume."--Current Engineering Practice
"I highly recommend this book for every university biology department because it provides both a unique, and often uplifting, introduction and a comprehensive reference of techniques for building and analysing mathematical models."--Volker Grimm, Basic and Applied Ecology
"A wonderfully pedagogical introduction to mathematical modeling in population biology: an ideal first course for biologists."--Simon A. Levin, Princeton University
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