Mathematical modeling has become an indispensable tool for biologists seeking to understand complex ecological and evolutionary processes. Where once a rudimentary grasp of mathematics sufficed, today’s biologist must be fluent in building and interpreting sophisticated models. Sarah Otto and Troy Day’s book provides a comprehensive guide for biology students navigating this increasingly quantitative landscape.
The book assumes a foundation of high school mathematics and first-year calculus, progressively introducing classic models in ecology and evolution, and then advancing to more intricate, class-structured and probabilistic models. Primers on linear algebra and probability theory equip readers with the mathematical background necessary to tackle these complex topics. Through numerous examples, the authors demonstrate how models can illuminate diverse phenomena such as the spread of HIV, chaos in population dynamics, the impact of age structure, and the processes of speciation and extinction.
Ecologists and evolutionary biologists now require sufficient mathematical training to critically assess the strengths and limitations of biological models, and to develop their own theoretical frameworks. This book serves as an indispensable resource, empowering the next generation of biologists to confidently engage with the world of mathematical modeling.
Building Blocks of Biological Models
Otto and Day emphasize a step-by-step approach to model construction and analysis. This practical focus enables readers to develop the skills needed to translate biological questions into mathematical formulations. By deconstructing existing models and providing clear instructions, the authors demystify the modeling process.
Key Ecological and Evolutionary Concepts Through a Mathematical Lens
The book’s strength lies in its ability to illustrate abstract concepts with concrete examples. Topics covered include:
- Population Dynamics: Exploring models of population growth, competition, and predator-prey interactions.
- Evolutionary Genetics: Investigating the dynamics of allele frequencies, natural selection, and genetic drift.
- Community Ecology: Modeling interactions between species, including mutualism, commensalism, and parasitism.
- Phylogenetics: Using mathematical models to reconstruct evolutionary relationships.
A Practical Toolkit for Biologists
The book provides a range of tools and resources to support learning and application:
- End-of-chapter questions: Reinforce understanding and encourage critical thinking.
- Mathematical primers: Offer concise reviews of essential mathematical concepts.
- Exercises with answers: Allow students to practice and assess their progress.
- Appendixes: Summarize useful mathematical rules and formulas.
- Supplementary Materials: Labs and advanced material available online.
Reviews and Recognition
The book has garnered widespread acclaim for its pedagogical soundness and comprehensive coverage.
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“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.” – Quarterly Review of Biology
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“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.” – Siam Review
Conclusion: Empowering the Next Generation of Biologists
In conclusion, “A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution” is an indispensable resource for students and researchers seeking to integrate mathematical approaches into their biological studies. By providing a clear and accessible pathway to mastering modeling techniques, this book empowers biologists to address complex questions and advance our understanding of the natural world. For those seeking a deeper dive, supplementary materials including labs and Mathematica notebooks are available at the authors’ site: http://www.zoology.ubc.ca/biomath/
