Analysis of Evolutionary Processes :The Adaptive Dynamics Approach and Its Applications ( Princeton Series in Theoretical and Computational Biology )

Publication subTitle :The Adaptive Dynamics Approach and Its Applications

Publication series :Princeton Series in Theoretical and Computational Biology

Author: Dercole Fabio;Rinaldi Sergio;;  

Publisher: Princeton University Press‎

Publication year: 2008

E-ISBN: 9781400828340

P-ISBN(Paperback): 9780691120065

Subject: O Mathematical Sciences and Chemical;O29 applied mathematics;Q1 General Biology

Keyword: 普通生物学,数理科学和化学

Language: ENG

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Description

Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. In Analysis 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 Processes will 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.

Chapter

Chapter 2. Modeling Approaches

2.1 Overview

2.2 Population Genetics

2.3 Individual-based Evolutionary Models

2.4 Quantitative Genetics

2.5 Evolutionary Game Theory

2.6 Replicator Dynamics

2.7 Fitness Landscapes

2.8 Adaptive Dynamics

2.9 A Comparative Analysis

Chapter 3. The Canonical Equation of Adaptive Dynamics

3.1 The Evolving Community

3.2 The Resident-Mutant Model

3.3 The Example of Resource-Consumer Communities

3.4 Does Invasion Imply Substitution?

3.5 The AD Canonical Equation

3.6 Evolutionary State Portraits

3.7 Evolutionary Branching

3.8 The Role of Bifurcation Analysis

3.9 What Should We Expect from the AD Canonical Equation

Chapter 4. Evolutionary Branching and the Origin of Diversity

4.1 Introduction

4.2 A Market Model and Its AD Canonical Equation

4.3 A Simple Example of Technological Branching

4.4 Discussion and Conclusions

Chapter 5. Multiple Attractors and Cyclic Evolutionary Regimes

5.1 Introduction

5.2 A Model of Resource-Consumer Coevolution

5.3 The Catalog of Evolutionary Scenarios

5.4 Discussion and Conclusions

Chapter 6. Catastrophes of Evolutionary Regimes

6.1 Introduction

6.2 A Model for the Evolution of Cooperation

6.3 Catastrophic Disappearance of Evolutionary Attractors

6.4 Evolutionary Branching and the Origin of Cheaters

6.5 Discussion and Conclusions

Chapter 7. Branching-Extinction Evolutionary Cycles

7.1 Introduction

7.2 A Model of Cannibalistic Demographic Interactions

7.3 Coevolution of Dwarfs and Giants

7.4 The Branching-Extinction Evolutionary Cycle

7.5 Discussion and Conclusions

Chapter 8. Demographic Bistability and Evolutionary Reversals

8.1 Introduction

8.2 Biological Background

8.3 Asymmetric Competition and the Occurrence of Evolutionary Reversals

8.4 Slow-Fast Approximation of the AD Canonical Equation

8.5 Discussion and Conclusions

Chapter 9. Slow-Fast Populations Dynamics and Evolutionary Ridges

9.1 Introduction

9.2 Biological Background

9.3 The AD Canonical Equation for General Demographic Attractors

9.4 Evolutionary Sliding and Pseudo-equilibria

9.5 Results and Discussion

9.6 Concluding Remarks

Chapter 10. The First Example of Evolutionary Chaos

10.1 Introduction

10.2 A Tritrophic Food Chain Model and Its AD Canonical Equation

10.3 The Chaotic Evolutionary Attractor

10.4 Feigenbaum Cascade of Period-doubling Bifurcations

10.5 Discussion and Conclusions

Appendix A. Second-order Dynamical Systems and Their Bifurcations

A.1 Dynamical Systems and State Portraits

A.2 Structural Stability

A.3 Bifurcations as Collisions

A.4 Local Bifurcations

A.5 Global Bifurcations

A.6 Catastrophes, Hysteresis, and Cusp

A.7 Extinction Bifurcations

A.8 Numerical Methods and Software Packages

Appendix B. The Invasion Implies Substitution Theorem

Appendix C. The Probability of Escaping Accidental Extinction

Appendix D. The Branching Conditions

Bibliography

Index

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