Evolutionary game theory, natural selection, and Darwinian dynamics

✍ Scribed by Vincent T.L., Brown J.S.

• Publisher: CUP
• Year: 2005
• Tongue: English
• Leaves: 401
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Half-title......Page 2
Title......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Figures......Page 11
Preface......Page 16
1 Understanding natural selection......Page 20
1.1.1 Historical perspective......Page 21
1.1.2 As Darwin saw it......Page 24
1.1.3 The Modern Synthesis......Page 25
1.2 Genetical approaches to natural selection......Page 26
1.3 Natural selection as an evolutionary game......Page 29
1.3.1 Game theory and evolution......Page 34
1.3.2 Games Nature plays......Page 36
1.3.3 ESS concept......Page 37
1.3.4 Scope of evolutionary game theory......Page 39
1.4 Road map......Page 40
1.4.2 Vector strategies......Page 42
1.4.5 Frequency dynamics......Page 43
1.4.7 Non-equilibrium dynamics......Page 44
2 Underlying mathematics and philosophy......Page 45
2.1 Scalars, vectors, and matrices......Page 47
2.1.1.1 Addition......Page 50
2.1.1.3 Division......Page 51
2.2 Dynamical systems......Page 52
2.2.1 Difference equations......Page 53
2.2.2 Differential equations......Page 55
2.3.1 A special class of dynamical systems......Page 58
2.3.2 The fitness concept with scalar Fi......Page 59
2.3.3 Continuous versus discrete modeling with scalar fitness......Page 60
2.4.2 Lotka–Volterra models for many species of individuals......Page 61
2.4.3 Leslie model of one prey and one predator......Page 62
2.4.4 Many prey and many predators model......Page 63
2.4.5 Identifying strategies in the Lotka—Volterra model......Page 64
2.4.6 Consumer-resource models......Page 65
2.4.7 Multistage models......Page 66
2.5 Classical stability concepts......Page 68
2.5.1 Equilibrium solutions......Page 69
2.5.2 Asymptotic stability......Page 70
2.5.3 Linearization......Page 71
2.5.4 Equilibrium point stability for linear difference equations......Page 72
2.5.5 Equilibrium point stability for linear differential equations......Page 75
2.5.7 Non-equilibrium dynamics......Page 77
3 The Darwinian game......Page 80
3.1 Classical games......Page 81
3.1.1 The optimization problem......Page 82
3.1.2 Matrix games......Page 84
3.1.3 Solution concepts: max-min, Nash equilibrium, etc.......Page 88
3.1.4 Continuous games......Page 89
3.2 Evolutionary games......Page 91
3.2.1 Collapsing a population’s fitness functions into a single G-function......Page 94
3.2.2 Bauplans, G-functions, and taxonomic hierarchies......Page 100
3.3.1 Tautology and teleology in Darwinian evolution......Page 102
3.3.2 Darwin's postulates in evolutionary game theory......Page 103
3.3.3 Heritable variation and fitness......Page 104
4 G -functions for the Darwinian game......Page 107
4.1 How to create a G-function......Page 108
4.2 Types of G-functions......Page 110
4.3 G-functions with scalar strategies......Page 111
4.4 G-functions with vector strategies......Page 112
4.5 G-functions with resources......Page 115
4.6 Multiple G-functions......Page 118
4.7 G-functions in terms of population frequency......Page 122
4.8 Multistage G-functions......Page 125
4.9 Non-equilibrium dynamics......Page 129
5 Darwinian dynamics......Page 131
5.1 Strategy dynamics and the adaptive landscape......Page 132
5.2 The source of new strategies: heritable variation and mutation......Page 135
5.3 Ecological time and evolutionary time......Page 138
5.4 G-functions with scalar strategies......Page 139
5.4.1 Mean strategy dynamics......Page 141
5.4.1.1 Large difference in time scales......Page 145
5.4.1.2 Small difference in time scales......Page 149
5.5 G-functions with vector strategies......Page 150
5.6 G-functions with resources......Page 159
5.8 G-functions in terms of population frequency......Page 162
5.9 Multistage G-functions......Page 163
5.10 Non-equilibrium Darwinian dynamics......Page 164
5.11 Stability conditions for Darwinian dynamics......Page 166
5.12 Variance dynamics......Page 168
6 Evolutionarily stable strategies......Page 170
6.1 Evolution of evolutionary stability......Page 172
6.2 G-functions with scalar strategies......Page 179
6.2.2 Ecological stability......Page 180
6.2.3 Evolutionary stability......Page 182
6.2.4 Convergent stability......Page 184
6.2.5 Using G-functions with scalar strategies......Page 185
6.3 G-functions with vector strategies......Page 187
6.3.1 Using G-functions with vector strategies......Page 188
6.4 G-functions with resources......Page 189
6.4.1 Using G-functions with resources......Page 191
6.5 Multiple G-functions......Page 193
6.5.1 Using multiple G-functions......Page 196
6.6 G-functions in terms of population frequency......Page 199
6.6.1 Using G-functions in terms of population frequency......Page 200
6.7 Multistage G-functions......Page 202
6.7.1 Using multistage G-functions......Page 206
6.8 Non-equilibrium Darwinian dynamics......Page 207
6.8.1 Using G-functions with non-equilibrium dynamics......Page 210
7 The ESS maximum principle......Page 216
7.1 Maximum principle for G-functions with scalar strategies......Page 217
7.2 Maximum principle for G-functions with vector strategies......Page 224
7.3 Maximum principle for G-functions with resources......Page 230
7.4 Maximum principle for multiple G-functions......Page 232
7.5 Maximum principle for G-functions in terms of population frequency......Page 238
7.6 Maximum principle for multistage G-functions......Page 241
7.7 Maximum principle for non-equilibrium dynamics......Page 244
8 Speciation and extinction......Page 250
8.1 Species concepts......Page 253
8.2.1 Species archetypes......Page 255
8.2.2 Definition of a species......Page 261
8.3.1 Strategies over a fixed interval......Page 262
8.3.2 Clump of strategies following a mean......Page 266
8.4.1 Sympatric speciation at an evolutionarily stable minimum......Page 270
8.4.2 Stable maxima and allopatric speciation......Page 275
8.4.3 Adaptive radiation......Page 279
8.5 Predator–prey coevolution and community evolution......Page 283
8.6 Wright's shifting balance theory and frequency-dependent selection......Page 285
8.7 Microevolution and macroevolution......Page 287
8.8 Incumbent replacement......Page 291
8.9 Procession of life......Page 292
9 Matrix games......Page 294
9.1.1 Frequency formulation......Page 296
9.1.2 Strategies......Page 297
9.1.3 Payoff function......Page 298
9.1.4 Frequency dynamics......Page 299
9.1.5 Matrix-ESS......Page 300
9.1.6 Maynard Smith’s original ESS definition......Page 301
9.2 The 2 × 2 bi-linear game......Page 303
9.2.1.1 Coalition of one......Page 304
9.2.1.2 Coalition of two......Page 306
9.2.2.1 Coalition of one......Page 311
9.2.3 Evolution of cooperation......Page 312
9.3 Non-linear matrix games......Page 314
9.3.1 Sex ratio game......Page 316
9.3.1.1 The politically correct solution......Page 317
9.3.1.2 Other possible solutions......Page 318
9.3.2 Kin selection......Page 320
10.1 Habitat selection......Page 323
10.1.1 Ideal free distribution......Page 324
10.2 Consumer-resource games......Page 328
10.2.1 Competition between plants......Page 329
10.2.2 Carcinogenesis......Page 336
10.2.2.1 Conditions promoting carcinogenesis......Page 338
10.2.2.2 A route to carcinogenesis......Page 340
10.3.1 Flowering time for annual plants......Page 343
10.3.2 Root competition......Page 348
10.4.1 Gerbil–owl fear game......Page 352
10.4.2 Patch-use model of fierce predators seeking wary prey......Page 357
10.4.2.1 Prey with imperfect information......Page 358
10.4.2.2 Predator's response to prey with imperfect information......Page 360
11 Managing evolving systems......Page 362
11.1 Evolutionary response to harvesting......Page 363
11.1.1 Necessary conditions for an ESS coalition of one......Page 364
11.1.2 Necessary conditions for an ESS coalition of two......Page 365
11.1.3 Specific examples......Page 366
11.2.1 Evolutionarily stable harvest strategies......Page 369
11.2.1.1 Yield......Page 372
11.2.1.3 Evolutionarily enlightened manager......Page 373
11.2.3 The Schaeffer model in an evolutionary context......Page 374
11.3 Chemotherapy-driven evolution......Page 378
References......Page 383
Index......Page 396