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Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics (Hardcover)

~ (Author), Joel S. Brown (Author)
Key Phrases: coalition vector, ecological equilibrium point, convergent stable point, Maynard Smith, Time Figure, Strategy Figure (more...)
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Editorial Reviews

Review

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

'... 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 own relentlessly moderate voice is likely to survive the fashionable Sturn und Drang.' Journal of the History of the Behavioral Sciences

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

'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 ...' www.PalArch.nl


Product Description

All of life is a game and evolution by natural selection is no exception. The evolutionary game theory developed in this 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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Product Details

  • Hardcover: 400 pages
  • Publisher: Cambridge University Press (July 11, 2005)
  • Language: English
  • ISBN-10: 0521841704
  • ISBN-13: 978-0521841702
  • Product Dimensions: 9 x 6.1 x 0.9 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.com Sales Rank: #545,845 in Books (See Bestsellers in Books)

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More About the Author

Thomas L. Vincent
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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Inside This Book (learn more)
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
coalition vector, ecological equilibrium point, convergent stable point, ecologically stable equilibrium, fitness generating function, evolutionarily stable minimum, convergent stability, extant genetic variability, scalar strategies, rare alternative strategies, species archetypes, scalar strategy, population dynamics equations, stable maxima, adaptive landscape, heritable phenotypes, reproductive yield, bully game, single prey species, classical game theory, incumbent replacement, foraging game, niche axis, matrix game, proper maximum
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Maynard Smith, Time Figure, Strategy Figure, North America, Strategy Strategy Frame, Fisher's Fundamental Theorem of Natural Selection
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6 of 8 people found the following review helpful:
2.0 out of 5 stars A little bit disappointing, April 18, 2006
By PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews
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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4 of 6 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. With G-function in hand, Evolutionary Game Theorists now have a mathematical Darwinism - a formal mathematical expression of Darwin's three postulates: a) like begets like; b) organisms struggle for existence; c) heritable traits help determine the outcome of the struggle. With the G-function, we can predict both the dynamics of heritable strategies and the adaptive outcome of natural selection.

Vincent and Brown begin, in Chapter 1, with an historical and philosophical overview of Evolutionary Game Theory and its relationship to the more traditional approach of Evolutionary Genetics. They then proceed to lay the mathematical foundations (Chapters 2 - 7), constructing the theory of Evolutionary Games and the G-function. These chapters each contain useful examples, teaching the student of evolutionary games how to apply the G-function. Noteworthy is that most all of the examples in these chapters represent continuous, as opposed to matrix games. In matrix games, which constitute the bulk of early development of Evolutionary Game Theory, and with which most readers are probably most familiar, strategies are discrete rather than continuous. However, the continuous games elaborated by Vincent and Brown (and now, many others) are of far more useful application in Evolutionary Ecology. Key contributions here are the precise mathematical definition of Maynard Smith's seminal Evolutionarily Stable Strategy (ESS) in Chapter 6, and the formulation of the ESS Maximum Principle in Chapter 7. This principle establishes the well-recognized properties of the ESS of invasion resistance and convergent stability, but also the fit of form and function - the ESS strategy is an adaptation - it maximizes individual fitness given the circumstances.

Chapter 8, which treats species concepts, speciation, and extinction, is particularly enlightening. Here the G-function shines! Under traditional approaches, a huge chasm, conceptual and methodological, separates microevolution and macroevolution. Vincent and Brown, armed with the G-function, unify the two: Microevolution is repeatable and reversible evolutionary dynamics within a G-function. Macroevolution is the production of novel G-functions. They demonstrate the versatility of the G-function approach to Evolutionary Game Theory in their discussion of three contexts for extinction (which is as integral to evolution as is speciation). Vincent and Brown introduce many key concepts in Chapter 8. Perhaps most important is their strategy species concept, which relies on their definition of the species archetype. They provide a particularly cogent definition of a species that is ecologically keystone (its presence promotes the persistence, in ecological time, of other species in the community), but they also point out that a species can by evolutionarily keystone - when its presence increases the numbers of species at an ESS. Using these developments, Vincent and Brown investigate mechanisms of speciation, including sympatric speciation, allopatric speciation, adaptive radiations, coevolution, Wright's shifting balance theory, and incumbent replacement. They conclude with a tour de force: a concise and brilliant discussion of the Procession of Life. As they aptly demonstrate, with the G-function approach to the Game of Life, theories such as Punctuated Equilibrium, oft cited as a contradiction of Darwinian Evolution, instead result naturally from Darwin's three postulates!

Chapter 9 is perhaps the least exciting chapter, but it serves the utilitarian purpose of melding the matrix approach to Evolutionary Game Theory with the G-function approach. This is, indeed, required reading for those who think matrix games are the only game in town.

Chapters 10 and 11 are well worth the wait and development. In these chapters, Vincent and Brown apply the G-function to an impressive diversity of problems arising in the beautiful metaphor of Hutchinson, the Ecological Theater and Evolutionary Play. Though the diversity of topics covered in these two chapters is impressive, as Vincent and Brown state, it represents only a subset of the problems that can be investigated with G-functions. Chapter 10 addresses "basic" issues of Evolutionary Ecology - a who's who of fundamental subjects. These include: Habitat selection and the ideal free distribution; Consumer-resource games, with examples on plant competition and root-shoot ratio; Carcinogenesis (a must read for all interested in Darwinian Medicine); Flowering time for annual plants; Root competition; and Foraging games.

Chapter 11 turns to the G-function as a fundamental tool for Applied Evolutionary Ecology. Here Vincent and Brown examine: Evolutionary responses to harvesting; Resource management and conservation; and Chemotherapy-driven evolution. They contrast management based on ecological enlightenment with that based on evolutionary enlightenment (prescriptions based on each emphasis are not always identical!). They point out the resemblance of control of a cancer with chemotherapy with control of a population through hunting. The analysis is striking, with the main message that if all cancer cells are not destroyed by a chemotherapy session, the survivors will evolve as the first step of what they call chemotherapy-driven evolution. If ever Evolutionary Ecologists were looking for a raison d'être, here they have it!
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4 of 6 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).

The authors are able to side-step population-genetics models (and notably, are able to explain WHY this is possible), and build a general model of Darwinian evolution. An immediate insight of their general model is the concept of flexible landscapes, which re-envisions the notion that natural selection cannot cross valleys on evolutionary landscapes, one of the fundamental criticisms of Darwinian theory since the New Synthesis. Exploration of Vincent & Brown's model illustrates that flexible landscapes can shift under evolving populations so that "valleys" are spanned by continuously uphill routes, re-forming behind evolving populations after they have passed. Further, Vincent & Brown derive the general conditions where flexible landscapes will or will not occur (frequency-dependent vs. -independent evolution respectively).

Armed with their general theory, Vincent & Brown are not content to stop after illuminating the valley conundrum, however, and go on in subsequent chapters to apply their theory to classic problems in evolution (Ch. 8; sympatric and allopatric speciation, co-evolution, the difference between micro- and macro-evolution) and ecology (Ch. 9 & 10; sex ratios, cooperation, ideal free distribution, consumer-resource competition), and even medicine (Ch. 10; the ontogenesis of cancer, chemotherapy) and ecosystem management (Ch. 11, evolutionary stable and ecologically enlightened resource management).

In short, Vincent and Brown have written a marvelous book; and from the day it was published, any evolutionary scholar who has not read it has been behind in the field, and has some catching up to do. It should also be read by ecologists, behaviorists, medical researchers and resource managers interested in evolutionary aspects of their work.
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