The Theoretical Biologist's Toolbox: Quantitative Methods for Ecology and Evolutionary Biology [Paperback]

Marc Mangel (Author)

Book Description

ISBN-10: 0521537487 | ISBN-13: 978-0521537483 | Publication Date: August 7, 2006

Mathematical modelling is widely used in ecology and evolutionary biology and it is a topic that many biologists find difficult to grasp. In this new textbook Marc Mangel provides a no-nonsense introduction to the skills needed to understand the principles of theoretical and mathematical biology. Fundamental theories and applications are introduced using numerous examples from current biological research, complete with illustrations to highlight key points. Exercises are also included throughout the text to show how theory can be applied and to test knowledge gained so far. Suitable for advanced undergraduate courses in theoretical and mathematical biology, this book forms an essential resource for anyone wanting to gain an understanding of theoretical ecology and evolution.

Editorial Reviews

Review

"This book is more than a toolbox, perhaps a better description would be workshop--where you get to not only see the tools but seem them in action."
Ecology, Vol. 88, No. 7

"...an accessible introduction to different models and analyses in theoretical population biology. ...replete with exercises...allowing easy reference to (and reinforcement of) particular topics. ...an inspiration."
BioScience

"... invite[s] the quantitatively minded empiricist to do just that."
J. Thompson, EVOLUTION

Book Description

In this textbook, Marc Mangel provides a no-nonsense introduction to the skills needed to understand the principles of theoretical and mathematical biology. Suitable for advanced undergraduate courses in theoretical and mathematical biology, this book forms an essential resource for anyone wanting to gain an understanding of theoretical ecology and evolution.

See all Editorial Reviews

Product Details

• Paperback: 390 pages
• Publisher: Cambridge University Press (August 7, 2006)
• Language: English
• ISBN-10: 0521537487
• ISBN-13: 978-0521537483
• Product Dimensions: 9.6 x 6.8 x 0.7 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,107,255 in Books (See Top 100 in Books)

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4 of 4 people found the following review helpful:

5.0 out of 5 stars It will get you in the game if you are not, and up your game if you are, September 13, 2010

By 

LabKitty (Anywhere, USA) - See all my reviews

This review is from: The Theoretical Biologist's Toolbox: Quantitative Methods for Ecology and Evolutionary Biology (Paperback)

If you're like us, you faced the following chasm sometime in your professional development: "...I understood my math classes well enough, but every time I try to apply these techniques and model a real-world problem, there seems to be something I'm missing." Or, alternatively: "... every time I try to read a modeling paper, there seems to be details the authors leave out that make the paper impenetrable." You can see the potential of using modeling in your work, but putting the idea into practice is proving difficult.

The best way to become skilled at modeling, of course, is to work with other modelers. But if you're restricted to self-study (or even if you're not), we believe you'll find no better guide than "The Theoretical Biologist's Toolbox." What makes it stand out?

The topics skew evolution and population biology, but don't let that scare you off if these are not your field. Mangel's book is really about the big three: differential equations, difference equations, and probability. What Mangel does, time and time again, is provide critical details that other authors gloss over. Details that are left out of introductory treatments because the author assumes they would confuse the reader, and that are left out of advanced treatments because the author assumes the reader already knows them. The details needed for the whole schmeer to Make Sense.

Perhaps an example can demonstrate this better than more hand-waving praise. Page 22 (at least in our edition): derivation that constant predation risk leads to an exponentially-distributed lifetime. Nine out of ten authors will begin this derivation as follows: "...consider a constant probability, p, of death. Then the probability of dying in time delta-t is p times delta-t." This is *wrong*. The correct expression is "p times delta-t plus o(delta-t)." Not only is Mangel the one in ten authors that will include the additional "Landau" term, he is also the one in a hundred that goes back after deriving the main result and shows that the Landau term corresponds to the non-linear terms in the Taylor series expansion of the exponential. The higher-order terms vanish as delta-t goes to zero (as they must), but they also restrict the probability to be less than one when delta-t is large.

Few authors take the trouble to make this connection. And without it, your understanding of the Landau term is just some "higher-order stuff" that gets ignored. Read a thousand other books that don't make the connection, and your understanding remains incomplete.

It is this kind of attention to detail that makes "The Theoretical Biologist's Toolbox" stand out. There's a number of books on modeling currently available, many of which are quite good. But Mangel's treatment is something special - a bridge between introductory and advanced texts. It really is a book that will get you in the game if you are not, and up your game if you are.

5.0 out of 5 stars Mathematical ecology without the agonizing pain**, November 23, 2011

By 

Neil Frazer (Kailua, HI United States) - See all my reviews
(REAL NAME)   

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This review is from: The Theoretical Biologist's Toolbox: Quantitative Methods for Ecology and Evolutionary Biology (Paperback)

As a way to learn a lot of useful math, this book is right up there with Edelstein-Keshet's classic "Mathematical Models in Biology." The many problems are embedded in the text, so you can do them as you read, which builds confidence and makes you feel like an active participant. Moreover, by having the reader fill in some of the details of each derivation the author makes space for more discussion. An especially nice touch is that the problems are labeled for difficulty (easy, medium or hard) and the labels are nearly always accurate. At the end of each chapter there is a detailed guide to the research literature. I haven't read the whole book, just Chapters 7 & 8, on stochastic models and their applications, and parts of chapter 6 on fisheries science and marine reserves. As I worked my way through chapters 7 & 8, doing each problem by scribbling in the conveniently wide margins, I began to like the book so much I ordered a second copy to keep at work. For a book of this length and depth, there are surprisingly few typos and errors.

Note added Jan 6, 2012:

** The title of this review honors Richard Shewchuk whose unpublished (but freely available) 1994 tutorial on conjugate gradients has earned him the undying gratitude of thousands of numerical analysts.