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In 1999-2000, while on sabbatical at Florida State, I worked on a problem of life histories in fluctuating environments with Joe Travis and we needed to construct log-normal random variables of specified means and variances. I did the calculation during and realized that although this was something pretty easy and important in ecology and evolutionary biology, it was also something difficult to find in the standard textbooks on probability or statistics. It was then that I decided to offer a six-quarter graduate sequence in quantitative methods starting the following fall when I returned to Santa Cruz. I advertised the course initially as "Quantitative tricks that I've learned that can help you" but mainly as "The Voyage of Quantitative Methods", "The Voyage Continues", etc. (As Jack Aubrey would tell us, there is much to do, so not a minute to lose.) This book is the result of that course. There is an approximate "Part I" and "Part II" structure. In the first three chapters, I develop some basic ideas about modeling (Chapter 1), differential equations (Chapter 2), and probability and some statistics (Chapter 3). The remainder of the book involves the particular applications that interested me and the students at the time of the course: the evolutionary ecology of parasitoids (Chapter 4), the population biology of disease (Chapter 5), some problems of sustainable fisheries (Chapter 6), the basics and application of stochastic population theory in ecology, evolutionary biology and biodemography (Chapters 7 and 8). It took me two years of once a week meetings plus one quarter of twice a week meetings with classes to get through the material (in Chapter 1, I offer some guidelines on how to use the book), so I expect that this volume will be a long-term companion rather than a quick read. And I hope that you will make it so. Like my other books, my goal is to bring people -- keen undergraduates, graduate students, post-docs, and perhaps even a faculty colleague or two -- to a skill level in theoretical biology where they will be able to read the primary literature and conduct their own research. I do this by developing tools and showing how they can be used. Suzanne Alonzo, a student of Bob Warner, post-doc with me and now on the faculty at Yale University, once told me that she carried Mangel and Clark (1988) everywhere she went for the first two years of graduate school. In large part, I write this book for the future Suzannes. I told the students in the courses if you stuck with it, you would be able to read and understand almost anything in the literature of theoretical biology.

MISPRINTS. I regret that there are misprints in the book, but am happy to say that I continue to get ideas about the material. You can find out about both here

SOLUTIONS. I will put solution sets up as I work with students on the book. Here are solutions for most of the exercises in Chapters 1-3 done by Erin Middleton. My new student Valerie Brown has recently (Aug 2008) found some misprints in these solutions. I will try to correct them in September.

Excerpts from reviews:

...this is a hugely engaging and interesting book. It's written with many asides and snippets of information about the topic, and particularly about the key figures in the history of theoretical biology. I do recommend this book as an excellent read and insight into the methodology of the theoretical biologist at work--- The Biologist

....[the author] goes to considerable lengths to generate the necessary thirst through metaphor, humour, and through the clarity with which he writes about the subject. At the same time he is realistic about the need ultimately to get out a pencil and paper, and to work through the exercises, as the key to making real progress in understanding...The blend of deterministic and stochastic modelling nicely captures the pulse of current thinking in theoretical ecology, and is a real strength of this book...For me, part of the charm of the book is its quirkiness, and I will be recommending it to my graduate students --- Richard Law, Fish and Fisheries

Having bought this book at the BES meeting in Oxford I spent the return train journey reading the first and third chapters. Afterwards I thought of writing a thank you e-mail to the author. I had been waiting for a book like this for some time. Mangel aims to propagate a quantitative intuition about biological systems and mathematical methods, predicting a considerable compound interest from investment made in the book's contents. This is a central theme of the first part of the book that runs through concepts and methods of modelling, differential equations and probability, using examples such as the prediction of propagule size, a useful revisit of Lokta-Volterra and a readily comprehensible drift through distribution functions. These 3 chapters provide the platform to understanding the deeper concepts and methodologies of their application found in the second half. Exercises are provided throughout the book with an avuncular warning of their difficulty. From working out the rate of energy flow of the general forager ('Easy') in Chapter 1, the exercises are aimed to bring us to a stage where we are aware of how time is subtlety used in the derivation of a differential equation ('Medium') in the final chapter. Mangel sticks to the principle that a scientific book has neither to be thick nor hard to read. Each chapter's 'Connection' section points to areas we may like to explore in more detail, giving not just a list but a brief discussion of the interest and background of each one. It is in such details and undoubted broad knowledge that Mangel's style breathes extra confidence into the reader. Well-placed examples and metaphor give enjoyable introductions into subjects in which I have previously felt I was sinking. Mangel hopes to give his reader the skills to go on and confidently acquire further knowledge. I'm looking forward to re-reading some theoretical papers and approaching somemore complex analyses with a new outlook and knowledge of their workings. This is why I had been waiting for this book --- Greg McInern, Bulletin of the British Ecological Society

...the author covers an impressive amount of material that, while not a comprehensive review of population biology, behavioral ecology, or evolutionary biology, certainly covers all of the major bases and, in doing so, illustrates the mathematical tools employed by theoretical biologists. The book is more than a toolbox, perhaps a better description would be a workshop -- where you get to not only see the tools but see them in action. The writing style in this book is lively enough to hold the attention of most readers despite what some empiricists might consider a dry subject matter...The author also does a good job of highlighting why certain key results from models are important. The book has a range of potential users and uses, in large part because Mangel adeptly summarizes both theory in evolutionary ecology and relevant quantitative methods...For many graudate students this book would be a good investments based solely on the 'Connections' section that comes at the end of each chapter that serves as an excellent introduction to the literature on a wide and diverse range of topics. --- John Latto and Matt Daugherty, Ecology 88:1872-1873 (2007)

The Theoretical Biologist's Toolbox is a how-to guide with applications. The book is a graduate-level text that covers modeling ideas, differential equations, and probability in the first three chapters, and then, in the five sub - sequent ones, the evolutionary ecology of parasitoids, diseases, fisheries, and stochastic population theory, both the basics and its applications in ecology, evolution, and demography. It is an accessible introduction to different models and analyses in theoretical population biology?Each chapter is self-contained (apart from some basic calculus skills, which are available from any good reference guide), yet there is considerable benefit to starting at the beginning of this book and finishing at the end?it serves aptly as a learning guide as well as a toolbox. The reader can learn how to use one tool well before moving to the next, although knowing how to use a mallet is invaluable, knowing how to use one with a chisel can lead to works of art... Developing a skill set and populating your own toolbox will not only provide personal edification but also offer unprecedented opportunity to help resolve a growing number of real-world problems that require sets of mathematical sensibilities. Research in areas such as bioinformatics, epidemiology, population ecology, and immunology recently has seen record growth. The application of mathematics to both large-scale patterns (climate change) and fine-scale patterns (cell regulation and gene expression) is revealing detailed insight into the underlying biological phenomena that generate the patterns. The challenge is open for those who are motivated to learn mathematics and biology. Mangel's book should be an inspiration. -- M. Bonsall, BioScience, 57:982-983 (2007)

In the introduction to his book, Marc Mangel explicitly states that its purpose is to teach the use of quantitative skills?and clearly also to let his audience know just how enthusiastic he is about what he does as a scientist. He provides readers with a very inclusive definition of theory that suggests that we are all theoreticians because we formulate ideas about how the world works, and adds that models are a good tool for investigating how well formulated these ideas are. He stresses that his goal is not necessarily to turn all readers into model builders, but rather to increase their ability to read and appreciate the literature of theoretical biology. This is particularly evident in the 'connections' sections at the end of each chapter, where Mangel provides a lot of interesting additional commentary and musings on topical issues, key papers, and alternative models (e.g., in the fisheries chapter, this extends to his fondness for salmon and the behavior of fishermen [and scientists]). In this context, I should note that one of the things I liked most about this book was the very entertaining and literary style throughout, which in no way detracted from the central aim of teaching quantitative approaches to biology. Examples include the 'Black & Decker' and 'mean Joe Green' metaphors, which nicely encapsulated much of the philosophy behind this book. I really enjoyed all of the various asides and references to other reading material scattered throughout. However, underneath the relatively informal approach, there is a real desire to encourage enthusiastic participation, and a general sense of excitement about the use of theory in biology, helped along by the many references to classic studies in ecology and evolutionary biology. Overall, I think the inclusive approach taken in this book will certainly help entice empirical biologists into the theoretical pool. . . . To me, it seems that Mangel, through his focus on a small set of key ecological problems, is better placed to work through how to gain useful insight into these biological issues, and through this lens, teaches the reader how to apply rigorous quantitative thinking to biology. In that context, he does perhaps assume a higher degree of mathematical sophistication than Otto and Day. To use the complementarity of these two books for their greatest effect, read Otto and Day first and then appreciate Mangel for the infectious enthusiasm and excitement he brings to the discipline. --- P.H. Thrall. Evolution 2007.