Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics

by Thomas L. Vincent , Joel S. Brown

• ISBN13: 9780521841702
• ISBN10: 0521841704
• Format: Hardcover
• Copyright: 2005-07-11
• Publisher: Cambridge University Press

Summary

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.

Author Biography

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

Table of Contents

List of figures	x
Preface	xv
1 Understanding natural selection	1	(25)
1.1 Natural selection	2	(5)
1.2 Genetical approaches to natural selection	7	(3)
1.3 Natural selection as an evolutionary game	10	(11)
1.4 Road map	21	(5)
2 Underlying mathematics and philosophy	26	(35)
2.1 Scalars, vectors, and matrices	28	(5)
2.2 Dynamical systems	33	(6)
2.3 Biological population models	39	(3)
2.4 Examples of population models	42	(7)
2.5 Classical stability concepts	49	(12)
3 The Darwinian game	61	(27)
3.1 Classical games	62	(10)
3.2 Evolutionary games	72	(11)
3.3 Evolution by natural selection	83	(5)
4 G-functions for the Darwinian game	88	(24)
4.1 How to create a G-function	89	(2)
4.2 Types of G-functions	91	(1)
4.3 G-functions with scalar strategies	92	(1)
4.4 G-functions with vector strategies	93	(3)
4.5 G-functions with resources	96	(3)
4.6 Multiple G-functions	99	(4)
4.7 G-functions in terms of population frequency	103	(3)
4.8 Multistage G-functions	106	(4)
4.9 Non-equilibrium dynamics	110	(2)
5 Darwinian dynamics	112	(39)
5.1 Strategy dynamics and the adaptive landscape	113	(3)
5.2 The source of new strategies: heritable variation and mutation	116	(3)
5.3 Ecological time and evolutionary time	119	(1)
5.4 G-functions with scalar strategies	120	(11)
5.5 G-functions with vector strategies	131	(9)
5.6 G-functions with resources	140	(1)
5.7 Multiple G-functions	141	(2)
5.8 G-functions in terms of population frequency	143	(1)
5.9 Multistage G-functions	144	(1)
5.10 Non-equilibrium Darwinian dynamics	145	(2)
5.11 Stability conditions for Darwinian dynamics	147	(2)
5.12 Variance dynamics	149	(2)
6 Evolutionarily stable strategies	151	(46)
6.1 Evolution of evolutionary stability	153	(7)
6.2 G-functions with scalar strategies	160	(8)
6.3 G-functions with vector strategies	168	(2)
6.4 G-functions with resources	170	(4)
6.5 Multiple G-functions	174	(6)
6.6 G-functions in terms of population frequency	180	(3)
6.7 Multistage G-functions	183	(5)
6.8 Non-equilibrium Darwinian dynamics	188	(9)
7 The ESS maximum principle	197	(34)
7.1 Maximum principle for G-functions with scalar strategies	198	(7)
7.2 Maximum principle for G-functions with vector strategies	205	(6)
7.3 Maximum principle for G-functions with resources	211	(2)
7.4 Maximum principle for multiple G-functions	213	(6)
7.5 Maximum principle for G-functions in terms of population frequency	219	(3)
7.6 Maximum principle for multistage G-functions	222	(3)
7.7 Maximum principle for non-equilibrium dynamics	225	(6)
8 Speciation and extinction	231	(44)
8.1 Species concepts	234	(2)
8.2 Strategy species concept	236	(7)
8.3 Variance dynamics	243	(8)
8.4 Mechanisms of speciation	251	(13)
8.5 Predator-prey coevolution and community evolution	264	(2)
8.6 Wright's shifting balance theory and frequency-dependent selection	266	(2)
8.7 Microevolution and macroevolution	268	(4)
8.8 Incumbent replacement	272	(1)
8.9 Procession of life	273	(2)
9 Matrix games	275	(29)
9.1 A maximum principle for the matrix game	277	(7)
9.2 The 2 x 2 bi-linear game	284	(11)
9.3 Non-linear matrix games	295	(9)
10 Evolutionary ecology	304	(39)
10.1 Habitat selection	304	(5)
10.2 Consumer-resource games	309	(15)
10.3 Plant ecology	324	(9)
10.4 Foraging games	333	(10)
11 Managing evolving systems	343	(21)
11.1 Evolutionary response to harvesting	344	(6)
11.2 Resource management and conservation	350	(9)
11.3 Chemotherapy-driven evolution	359	(5)
References	364	(13)
Index	377