Analysis of Evolutionary Processes : The Adaptive Dynamics Approach and Its Applications

by Dercole, Fabio; Rinaldi, Sergio

• ISBN13: 9781400828340
• ISBN10: 1400828341
• Copyright: 2008-03-02
• Publisher: Princeton Univ Pr

Summary

Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. InAnalysis of Evolutionary Processes, Fabio Dercole and Sergio Rinaldi have written the first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones. The book shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics. After introducing the basics of evolutionary processes and classifying available modeling approaches, Dercole and Rinaldi give a detailed presentation of the derivation of the AD canonical equation, an ordinary differential equation that focuses on evolutionary processes driven by rare and small innovations. The authors then look at important features of evolutionary dynamics as viewed through the lens of AD. They present their discovery of the first chaotic evolutionary attractor, which calls into question the common view that coevolution produces exquisitely harmonious adaptations between species. And, opening up potential new lines of research by providing the first application of AD to economics, they show how AD can explain the emergence of technological variety. Analysis of Evolutionary Processeswill interest anyone looking for a self-contained treatment of AD for self-study or teaching, including graduate students and researchers in mathematical and theoretical biology, applied mathematics, and theoretical economics.

Table of Contents

Preface	p. xi
Introduction to Evolutionary Processes	p. 1
Origins of Evolutionary Theory	p. 1
Genotypes and Phenotypes	p. 5
Mutations	p. 9
Selection	p. 10
Evolution	p. 13
The Red Queen Hypothesis	p. 16
The Emergence of Diversity	p. 17
Evolutionary Extinction	p. 21
Examples	p. 24
Modeling Approaches	p. 43
Overview	p. 43
Population Genetics	p. 47
Individual-based Evolutionary Models	p. 53
Quantitative Genetics	p. 55
Evolutionary Game Theory	p. 59
Replicator Dynamics	p. 62
Fitness Landscapes	p. 64
Adaptive Dynamics	p. 67
A Comparative Analysis	p. 70
The Canonical Equation of Adaptive Dynamics	p. 74
The Evolving Community	p. 74
The Resident-Mutant Model	p. 76
The Example of Resource-Consumer Communities	p. 79
Does Invasion Imply Substitution?	p. 83
The AD Canonical Equation	p. 88
Evolutionary State Portraits	p. 95
Evolutionary Branching	p. 99
The Role of Bifurcation Analysis	p. 110
What Should We Expect from the AD Canonical Equation	p. 116
Evolutionary Branching and the Origin of Diversity	p. 119
Introduction	p. 119
A Market Model and Its AD Canonical Equation	p. 121
A Simple Example of Technological Branching	p. 129
Discussion and Conclusions	p. 135
Multiple Attractors and Cyclic Evolutionary Regimes	p. 138
Introduction	p. 138
A Model of Resource-Consumer Coevolution	p. 139
The Catalog of Evolutionary Scenarios	p. 144
Discussion and Conclusions	p. 151
Catastrophes of Evolutionary Regimes	p. 153
Introduction	p. 153
A Model for the Evolution of Cooperation	p. 154
Catastrophic Disappearance of Evolutionary Attractors	p. 159
Evolutionary Branching and the Origin of Cheaters	p. 166
Discussion and Conclusions	p. 169
Branching-Extinction Evolutionary Cycles	p. 172
Introduction	p. 172
A Model of Cannibalistic Demographic Interactions	p. 174
Coevolution of Dwarfs and Giants	p. 177
The Branching-Extinction Evolutionary Cycle	p. 182
Discussion and Conclusions	p. 183
Demographic Bistability and Evolutionary Reversals	p. 186
Introduction	p. 186
Biological Background	p. 188
Asymmetric Competition and the Occurrence of Evolutionary Reversals	p. 189
Slow-Fast Approximation of the AD Canonical Equation	p. 195
Discussion and Conclusions	p. 200
Slow-Fast Populations Dynamics and Evolutionary Ridges	p. 204
Introduction	p. 204
Biological Background	p. 207
The AD Canonical Equation for General Demographic Attractors	p. 209
Evolutionary Sliding and Pseudo-equilibria	p. 221
Results and Discussion	p. 224
Concluding Remarks	p. 229
The First Example of Evolutionary Chaos	p. 231
Introduction	p. 231
A Tritrophic Food Chain Model and Its AD Canonical Equation	p. 233
The Chaotic Evolutionary Attractor	p. 235
Feigenbaum Cascade of Period-doubling Bifurcations	p. 238
Discussion and Conclusions	p. 241
Second-order Dynamical Systems and Their Bifurcations	p. 243
Dynamical Systems and State Portraits	p. 243
Structural Stability	p. 248
Bifurcations as Collisions	p. 250
Local Bifurcations	p. 252
Global Bifurcations	p. 259
Catastrophes, Hysteresis, and Cusp	p. 261
Extinction Bifurcations	p. 265
Numerical Methods and Software Packages	p. 267
The Invasion Implies Substitution Theorem	p. 272
The Probability of Escaping Accidental Extinction	p. 277
The Branching Conditions	p. 281
Bibliography	p. 287
Index	p. 325
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