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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.
1. Understanding natural selection
2. Underlying mathematics and philosophy
3. The Darwinian game
4. G-functions for the Darwinian game
5. Darwinian dynamics
6. Evolutionary stable strategies
7. The ESS maximum principle
8. Speciation and extinction
9. Matrix games
10. Evolutionary ecology
11. Managing evolving systems
Dr Vincent is Professor Emeritus with the Aerospace and Mechanical Engineering at the University of Arizona. His main research interests are in the area of Nonlinear Control System Design, Optimal Control and Game Theory, and Evolution and Adaptation of Biological Systems. He has 153 publications including 79 journal articles, and 8 books.
Dr Brown is a Professor of Biology at the University of Illinois at Chicago. His main research interests lie in applying concepts from natural selection to behavioral, population and community ecology with applications to conservation biology. Specific interests include the Ecology of Fear that studies the ecological and evolutionary implications of the non-lethal effects of predators on prey. He has 102 publications including 88 journal articles.
"It's complicated, but it's where biology is at, and Vincent and Brown clarify the issues wonderfully."
"[...] 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
"[...] 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 [...]"