The Stability Concept of Evolutionary Game Theory

1. Front Matter

   Pages N2-VIII

   PDF

2. Introduction

   • Ross Cressman

   Pages 1-3

3. Frequency-Dependent Evolution in a Single Haploid Species

   • Ross Cressman

   Pages 4-30

4. Frequency-Dependent Evolution in a Two-Species Haploid System

   • Ross Cressman

   Pages 31-56

5. Frequency-Dependent Evolution in a Randomly-Mating Diploid Species

   • Ross Cressman

   Pages 57-76

6. Frequency- and Density-Dependent Evolution in a Haploid Species

   • Ross Cressman

   Pages 77-94

7. Evolutionarily Stable Sets and Contestant Information

   • Ross Cressman

   Pages 95-122

8. Back Matter

   Pages 123-129

   PDF

These Notes grew from my research in evolutionary biology, specifically on the theory of evolutionarily stable strategies (ESS theory), over the past ten years. Personally, evolutionary game theory has given me the opportunity to transfer my enthusiasm for abstract mathematics to more practical pursuits. I was fortunate to have entered this field in its infancy when many biologists recognized its potential but were not prepared to grant it general acceptance. This is no longer the case. ESS theory is now a rapidly expanding (in both applied and theoretical directions) force that no evolutionary biologist can afford to ignore. Perhaps, to continue the life-cycle metaphor, ESS theory is now in its late adolescence and displays much of the optimism and exuberance of this exciting age. There are dangers in writing a text about a theory at this stage of development. A comprehensive treatment would involve too many loose ends for the reader to appreciate the central message. On the other hand, the current central message may soon become obsolete as the theory matures. Although the restricted topics I have chosen for this text reflect my own research bias, I am confident they will remain the theoretical basis of ESS theory. Indeed, I feel the adult maturity of ESS theory is close at hand and I hope the text will play an important role in this achievement.

• Evolutionary biology
• Fitness
• biological processes
• game theory
• mathematical modelling

• Department of Mathematics, Wilfrid Laurier University, Waterloo, Canada

  Ross Cressman

Policies and ethics