Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics

by Vincent, Thomas L.; Brown, Joel S.

Publication: Cambridge, New York, Cambridge
   University Press, 2005.

 

Book Description

All of life is a game and evolution by natural selection is no exception. Games have players, strategies, payoffs, and rules. In the game of life, organisms are the players, their heritable traits provide strategies, their births and deaths are the payoffs, and the environment sets the rules. The evolutionary game theory developed in this book provides the tools necessary for understanding many of Nature’s mysteries. These include coevolution, speciation, and extinction as well as the major biological questions regarding fit of form and function, diversity of life, procession of life, 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). The G-function is a tool that simplifies notation and plays an important role in the development of the Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy or 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.

 

About the Author

Thomas L. Vincent is Professor Emeritus of Aerospace and Mechanical Engineering at the University of Arizona. His main research interests are in the areas 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.

Joel S. 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.

 

Contents

List of figures page x

Preface xv

1 Understanding natural selection 1

1.1 Natural selection 2

1.2 Genetical approaches to natural selection 7

1.3 Natural selection as an evolutionary game 10

1.4 Road map 21

2 Underlying mathematics and philosophy 26

2.1 Scalars, vectors, and matrices 28

2.2 Dynamical systems 33

2.3 Biological population models 39

2.4 Examples of population models 42

2.5 Classical stability concepts 49

3 The Darwinian game 61

3.1 Classical games 62

3.2 Evolutionary games 72

3.3 Evolution by natural selection 83

4 G-functions for the Darwinian game 88

4.1 How to create a G-function 89

4.2 Types of G-functions 91

4.3 G-functions with scalar strategies 92

4.4 G-functions with vector strategies 93

4.5 G-functions with resources 96

4.6 Multiple G-functions 99

4.7 G-functions in terms of population frequency 103

4.8 Multistage G-functions 106

4.9 Non-equilibrium dynamics 110

5 Darwinian dynamics 112

5.1 Strategy dynamics and the adaptive landscape 113

5.2 The source of new strategies: heritable variation and mutation 116

5.3 Ecological time and evolutionary time 119

5.4 G-functions with scalar strategies 120

5.5 G-functions with vector strategies 131

5.6 G-functions with resources 140

5.7 Multiple G-functions 141

5.8 G-functions in terms of population frequency 143

5.9 Multistage G-functions 144

5.10 Non-equilibrium Darwinian dynamics 145

5.11 Stability conditions for Darwinian dynamics 147

5.12 Variance dynamics 149

6 Evolutionarily stable strategies 151

6.1 Evolution of evolutionary stability 153

6.2 G-functions with scalar strategies 160

6.3 G-functions with vector strategies 168

6.4 G-functions with resources 170

6.5 Multiple G-functions 174

6.6 G-functions in terms of population frequency 180

6.7 Multistage G-functions 183

6.8 Non-equilibrium Darwinian dynamics 188

7 The ESS maximum principle 197

7.1 Maximum principle for G-functions with scalar strategies 198

7.2 Maximum principle for G-functions with vector strategies 205

7.3 Maximum principle for G-functions with resources 211

7.4 Maximum principle for multiple G-functions 213

7.5 Maximum principle for G-functions in terms of population frequency 219

7.6 Maximum principle for multistage G-functions 222

7.7 Maximum principle for non-equilibrium dynamics 225

8 Speciation and extinction 231

8.1 Species concepts 234

8.2 Strategy species concept 236

8.3 Variance dynamics 243

8.4 Mechanisms of speciation 251

8.5 Predator–prey coevolution and community evolution 264

8.6 Wright’s shifting balance theory and frequency-dependent selection 266

8.7 Microevolution and macroevolution 268

8.8 Incumbent replacement 272

8.9 Procession of life 273

9 Matrix games 275

9.1 A maximum principle for the matrix game 277

9.2 The 2 × 2 bi-linear game 284

9.3 Non-linear matrix games 295

10 Evolutionary ecology 304

10.1 Habitat selection 304

10.2 Consumer-resource games 309

10.3 Plant ecology 324

10.4 Foraging games 333

11 Managing evolving systems 343

11.1 Evolutionary response to harvesting 344

11.2 Resource management and conservation 350

11.3 Chemotherapy-driven evolution 359

References 364

Index 377

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