Evolutionary game theory, natural selection, and Darwinian dynamics

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Title:

Personal Author:

Vincent, Thomas L.

Publication Information:

Cambridge, UK : Cambridge University Pr., 2005

ISBN:

9780521841702

Subject Term:

Evolution -- Mathematical models

Natural selection -- Mathematical models

Game theory

Added Author:

Brown, Joel S. (Joel Steven), 1959-

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010167581	QA269 V56 2005	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000010155692	QA269 V56 2005	Open Access Book	Book	Searching... Unknown

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.

Author Notes

Joel S. Brown is a Professor of Biology at the University of Illinois at Chicago.

List of figures	p. x
Preface	p. xv
1 Understanding natural selection	p. 1
1.1 Natural selection	p. 2
1.2 Genetical approaches to natural selection	p. 7
1.3 Natural selection as an evolutionary game	p. 10
1.4 Road map	p. 21
2 Underlying mathematics and philosophy	p. 26
2.1 Scalars, vectors, and matrices	p. 28
2.2 Dynamical systems	p. 33
2.3 Biological population models	p. 39
2.4 Examples of population models	p. 42
2.5 Classical stability concepts	p. 49
3 The Darwinian game	p. 61
3.1 Classical games	p. 62
3.2 Evolutionary games	p. 72
3.3 Evolution by natural selection	p. 83
4 G-functions for the Darwinian game	p. 88
4.1 How to create a G-function	p. 89
4.2 Types of G-functions	p. 91
4.3 G-functions with scalar strategies	p. 92
4.4 G-functions with vector strategies	p. 93
4.5 G-functions with resources	p. 96
4.6 Multiple G-functions	p. 99
4.7 G-functions in terms of population frequency	p. 103
4.8 Multistage G-functions	p. 106
4.9 Non-equilibrium dynamics	p. 110
5 Darwinian dynamics	p. 112
5.1 Strategy dynamics and the adaptive landscape	p. 113
5.2 The source of new strategies: heritable variation and mutation	p. 116
5.3 Ecological time and evolutionary time	p. 119
5.4 G-functions with scalar strategies	p. 120
5.5 G-functions with vector strategies	p. 131
5.6 G-functions with resources	p. 140
5.7 Multiple G-functions	p. 141
5.8 G-functions in terms of population frequency	p. 143
5.9 Multistage G-functions	p. 144
5.10 Non-equilibrium Darwinian dynamics	p. 145
5.11 Stability conditions for Darwinian dynamics	p. 147
5.12 Variance dynamics	p. 149
6 Evolutionarily stable strategies	p. 151
6.1 Evolution of evolutionary stability	p. 153
6.2 G-functions with scalar strategies	p. 160
6.3 G-functions with vector strategies	p. 168
6.4 G-functions with resources	p. 170
6.5 Multiple G-functions	p. 174
6.6 G-functions in terms of population frequency	p. 180
6.7 Multistage G-functions	p. 183
6.8 Non-equilibrium Darwinian dynamics	p. 188
7 The ESS maximum principle	p. 197
7.1 Maximum principle for G-functions with scalar strategies	p. 198
7.2 Maximum principle for G-functions with vector strategies	p. 205
7.3 Maximum principle for G-functions with resources	p. 211
7.4 Maximum principle for multiple G-functions	p. 213
7.5 Maximum principle for G-functions in terms of population frequency	p. 219
7.6 Maximum principle for multistage G-functions	p. 222
7.7 Maximum principle for non-equilibrium dynamics	p. 225
8 Speciation and extinction	p. 231
8.1 Species concepts	p. 234
8.2 Strategy species concept	p. 236
8.3 Variance dynamics	p. 243
8.4 Mechanisms of speciation	p. 251
8.5 Predator-prey coevolution and community evolution	p. 264
8.6 Wright's shifting balance theory and frequency-dependent selection	p. 266
8.7 Microevolution and macroevolution	p. 268
8.8 Incumbent replacement	p. 272
8.9 Procession of life	p. 273
9 Matrix games	p. 275
9.1 A maximum principle for the matrix game	p. 277
9.2 The 2 x 2 bi-linear game	p. 284
9.3 Non-linear matrix games	p. 295
10 Evolutionary ecology	p. 304
10.1 Habitat selection	p. 304
10.2 Consumer-resource games	p. 309
10.3 Plant ecology	p. 324
10.4 Foraging games	p. 333
11 Managing evolving systems	p. 343
11.1 Evolutionary response to harvesting	p. 344
11.2 Resource management and conservation	p. 350
11.3 Chemotherapy-driven evolution	p. 359
References	p. 364
Index	p. 377

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Author Notes

Table of Contents