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Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics [Hardcover]

Thomas L. Vincent , Joel S. Brown
4.2 out of 5 stars  See all reviews (4 customer reviews)

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Book Description

July 11, 2005 0521841704 978-0521841702
All of life is a game, and evolution by natural selection is no exception. The evolutionary game theory developed in this 2005 book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.

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Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics + Game-Theoretical Models in Biology (Chapman & Hall/CRC Mathematical and Computational Biology)
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Editorial Reviews


Review of the hardback: 'It's complicated, but it's where biology is at, and Vincent and Brown clarify the issues wonderfully.' Biologist

Review of the hardback: '... even-handedness, together with its peerless reasoning, helps this book stand out in a crowded field ... masterly book. ... time and again, Shanahan convinces us that Darwin's approach was relentlessly reconciliatory, pluralistic, and non dogmatic ... Because it is equally ardent and articulate, Shanahan's own relentlessly moderate voice is likely to survive the fashionable Sturn und Drang.' Journal of the History of the Behavioral Sciences

Review of the hardback: '... provides a formal game-theoretic framework for addressing an impressive array of biological questions.' Journal of Mammalian Evolution

Review of the hardback: 'The book is written in an enthusiastic style. In several places you can still perceive the excitement the authors must have felt when they embarked on their work in evolutionary dynamics ... a must-read for those interested in the history of evolutionary game theory ...'

Book Description

In this 2005 book, many topics in natural selection are investigated including co-evolution, speciation, and extinction. It may be described as a book on mathematical Darwinism. Darwin used logical verbal arguments to understand evolution. These arguments are presented here in a mathematical setting useful for both understanding evolution and allowing for prediction as well.

Product Details

  • Hardcover: 400 pages
  • Publisher: Cambridge University Press (July 11, 2005)
  • Language: English
  • ISBN-10: 0521841704
  • ISBN-13: 978-0521841702
  • Product Dimensions: 9.1 x 7.1 x 0.8 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #2,557,130 in Books (See Top 100 in Books)

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4.2 out of 5 stars
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11 of 14 people found the following review helpful
2.0 out of 5 stars A little bit disappointing April 18, 2006
I am not a biologist, but an engineer interested in evolution and mathematics.

The mathematics of the book is very easy, the only (very) confusing issue are the indices.

The G-function is introduced a bit ad-hoc, but as a definition, this might not matter much. It is very clear, that by allowing the strategy to vary, one can get optimal (at least stationary) values. The strategy dynamics are introduced in a rather confusing way, without much of an explanation.

For the rest, it seems, that 80% of the book are numerical examples, which seem to prove mostly, that with nonlinear differential equations, the behaviour of (e.g.) stationary points can vary quite a bit, if the coefficients in those equations are changed.

Maybe a professional biologist gets a lot out of this book, but for the interested layman it offers little (except upteen numerical examples, see above)
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5 of 7 people found the following review helpful
5.0 out of 5 stars Mathematical Darwinism November 16, 2005
First, full disclosure: I am a colleague and friend of the authors, Thomas L. Vincent and Joel S. Brown, and I reviewed the entire book during its writing.

Game theory is a fairly recent development in mathematics, having been introduced in the 1940's. Evolutionary Game Theory is more recent yet - Maynard Smith and Price put it on the map with their publication in Nature in 1973 on the Logic of Animal Conflict. Maynard Smith then more fully elaborated the application of matrix games to evolution with his 1982 volume, Evolution and the Theory of Games. Vincent and Brown trace their contribution to the pioneering developments of Maynard Smith, but in this volume, they go much further. As I reviewed the eleven chapters as they were first written, I felt the privilege of observing, first hand, the construction of a great edifice. In this edifice, the dynamics of ecology is dovetailed with the dynamics of heritable strategies. The tool that accomplishes this is the fitness generating function, known as the G-function. Particularly brilliant is the invention of the virtual strategy, a scalar or vector "place holder" in the G-function. The great virtue of the virtual strategy is that it represents any focal individual taking on any strategy within the entire strategy set of the species. The fitness generating function then determines the fitness for that virtual strategy within the biotic and abiotic environment defined by the set of arguments (e.g., resident strategies, their population sizes, abundance of resources, etc.) defining the G-function.
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5 of 7 people found the following review helpful
5.0 out of 5 stars Life is a game August 28, 2005
Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics by Thomas L. Vincent and Joel S. Brown is a book that not only belongs among the classics of evolutionary theory, but should have pride of place on the shelf right after Darwin's Origin of Species and Maynard Smith's Evolution and the Theory of Games.

This book makes a novel, interesting and readable contribution to the proper understanding of Darwinian processes in evolution. Based on more than twenty years of collaboration between the authors, the book is a comprehensive review of Darwinian theory newly cast in an over-arching mathematical framework. Unlike Stephen Jay Gould's recent overview of evolutionary theory (The Structure of Evolutionary Theory, 2002, 1433 pages), Vincent & Brown's book is concise (382 pages), uncluttered, and supported by an elegant skeleton of mathematical theory.

Don't let the math dissuade you however. If you have read Origin of Species and have a familiarity with classic evolutionary games, you won't have trouble understanding this book. Text and numerous examples provide a clear conceptual explanation of equations throughout.

The book's premise is that life is a game and its players have strategies. Understood as such, the authors present fitness-generating functions (G-functions) that encompass strategy, population, and Darwinian dynamics to model evolutionary outcomes. The first chapter introduces this philosophy; the next six chapters develop the theory, presenting classic population models (Ch. 2) and evolutionary games (Ch. 3), then forging new theory through deriving G-functions (Ch. 4), modeling Darwinian dynamics (Ch. 5), finding the evolutionary stable strategies (ESS, Ch. 6) and developing their general ESS maximum principle (Ch. 7).
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6 of 10 people found the following review helpful
5.0 out of 5 stars A Mathematical Approach to Evolution August 2, 2005
Charles Darwin published his primary thesis 'The Origin of Species' in 1859. It was a masterpiece of logical deduction based on the observations he had made while serving as a naturalist aboard the H.M.S. Beagle on a scientific expedition around the world. His views were both orthodox for the day and flawed.

Only seven years later Mendel published the results of his research on genetics. Over time these sciences were merged together into what is now called the 'Modern Synthesis.' Genetics explains the why and the how of species begetting species, and how changes in the species are made when a change is made in the genes.

In 1944, with the advances in mathematics, von Neumann and Morgenstern published 'Theory of Games and Economic Behavior.' Over time the modern synthesis of the genertic approach to evolution has been fit into game theory to help understand how the randomness of genetic evolution can be predicted using game theory.

This book gives a rigorous introduction to the mathematics of game theory as applied to Natural Selection. The book presents the tools necessary for understanding many of Nature's mysteries.
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