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Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well.
Game-Theoretical Models in Biology describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner's dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use MATLAB to solve various games.
Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behavior, and the existence of adornments (for example, the peacock's tail), have been explained using ideas underpinned by game theoretical modeling. Suitable for readers studying and working at the interface of mathematics and the life sciences, Game-Theoretical Models in Biology shows how evolutionary game theory is used in the modeling of these diverse biological phenomena.
What Is a Game?
The Underlying Biology
Some Classical Games
Further Concepts in Game Theory
The Evolution of Cooperation
Mating Games I: Obtaining Mates
Mating Games II: Selecting Mates
Food Competition I: Indirect Competition
Food Competition II: Direct Competition
Life History Theory
Selection below the Level of the Organism
Summary and Overview
Jan Rychtář is Associate Professor of Mathematics at the University of North Carolina at Greensboro, USA. He received his PhD in from University of Alberta, Edmonton, Canada in 2004 for his work in functional analysis, topology and optimization. Since 2004 he works on game theoretical models, prevalently collaborating with Mark Broom on mathematical models of kleptoparasitism. In 2006, he started a math-biology research group involving faculty and students from departments of biology and mathema
"In the biological sciences, there is probably no better time to become a game theorist, and anyone who so aspires will value this text as a guide. Assuming only a modicum of mathematics, Broom and Rychtář lead their readers all the way from the rudiments of evolutionary game theory to the research frontier. They are appealingly candid on how their scope reflects their taste. Nonetheless, their coverage is remarkably wide-ranging, from old standards like the Hawk-Dove game to newer applications such as epidemiology. The authors strike an excellent compromise between breadth and depth by limiting the generality of some theoretical treatments, choosing good examples, and using up-to-date references to round out their coverage. By focusing on evolutionary stable strategy as a "static concept," Broom and Rychtář convincingly demonstrate the power of game-theoretic models to describe real animal behaviour, in ways that mathematicians who specialize on evolutionary dynamics are apt to overlook. Thus the book brings a timely sense of balance to the range of texts now available. At the research frontier, the trail has many forks; but whichever fork readers decide to explore, this book will leave them admirably well prepared for the way ahead."
- Mike Mesterton-Gibbons, Florida State University
"Many books on evolutionary game dynamics are on my shelf – why would I put another one there? The first thing that caught my attention in the new book of Mark Broom and Jan Rychtář are the exercises. Reading a book on mathematics is a fruitless exercise for me without a pencil and paper and maybe a computer. The wonderful exercises in this book are sufficiently deep to provoke some serious thinking, but not so difficult that the reader turns them down in despair. Broom and Rychtář cover a multitude of subjects, from the vary basics of game theory to concrete biological applications. Some of them have not found their place into the minds of many young scientists, such as food competition and the ideal free distribution, but it pays to learn about these classical applications. The book focuses on static aspects. However, with complex dynamical considerations, theoreticians are often going too far and it is absolutely fascinating to see how far you can get from such a focus on static properties of games. I highly recommend this book – not for your shelf, but for your desk!"
- Arne Traulsen, Max Planck Gesellschaft
"Evolutionary game theory originally flourished some thirty years ago as a means to predict individual behavior in biological systems through its static game-theoretic solution concept of an evolutionarily stable strategy (ESS). Since then, the advancement of the theory has increasingly occurred in other disciplines. In their timely book, Broom and Rychtář have returned the theory to its biological roots and illustrated the relevance of these recent developments to biology. Their careful mathematical analysis of diverse biological models based on such current topics as nonlinear and multi-player games, structured population effects and the stochastic effects of finite populations provide a comprehensive set of applications. The book will serve both as an important resource for researchers in the field and as a valuable text for students at a graduate or senior undergraduate level. Students will especially appreciate the extensive set of exercises for each chapter and that the book is exceptionally well-written and self-contained."
- Ross Cressman, Wilfrid Laurier University