Skip to main content

1992 | Buch

The Stability Concept of Evolutionary Game Theory

A Dynamic Approach

herausgegeben von: Ross Cressman

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Biomathematics

insite
SUCHEN

Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
1. Introduction
Abstract
Over the past two decades, evolutionary game theory has become a powerful unifying force to analyze evolutionary processes that are driven by individual selection pressures. It is now the accepted theoretical explanation of such diverse biological phenomena as the prevalence of equal male/female sex ratios in diploid species and the evolution of ritualistic fighting behaviors in many animal species (Maynard Smith 1982; Hofbauer and Sigmund 1988). A random check of current research publications in (theoretical) biology shows both the growing breadth and depth of evolutionary game theory’s influence. American Naturalist in 1991 published articles that extend the theory of evolutionary games (Christiansen 1991); its range of biological applications (Motro 1991); and its consistency with empirical data (Petersen 1991). Even more convincing for me is that the majority of articles in these volumes contain some form of strategic reasoning (e.g. the analysis of individual behavioral alternatives in a given biological system).
Ross Cressman
2. Frequency-Dependent Evolution in a Single Haploid Species
Abstract
Most researchers in the area agree that the approach of Maynard Smith (1974; 1982) to model the behavioral evolution in a single animal species was the beginning of evolutionary game theory. In this approach, individuals are characterized by their behavior type (or strategy). These strategies may be bona fide behaviors such as aggression or altruism that can be used in pairwise interactions; physical characteristics such as size or color; or life-cycle patterns such as dispersal rate or sex ratio. An individual with a strategy of the latter type is often thought of as playing the field in that payoffs are not given through pairwise contests. In any case, an individual’s strategy is fixed over its lifetime or, alternatively, the life history of an individual is its strategy. [This assumption contrasts markedly with that of classical (i.e. economic or non-biological) game theory where individuals may change their strategies based on rational decisions concerning alternative payoffs.] An individual’s strategy, in conjunction with the prevalence of strategies of other individuals, determines its frequency-dependent fitness and thereby its reproductive success. [For further elaboration on these points, see Hofbauer and Sigmund (1988, Section 15.3).]
Ross Cressman
3. Frequency-Dependent Evolution in a Two-Species Haploid System
Abstract
Chapter 2 emphasized the dynamic consequences of the original ESS theory that Maynard Smith (1974; 1982) developed to explain the observed frequency evolution of behavioral types in a single species. At the same time, the presentation provided a foundation from which to generalize evolutionary game theory to other biological systems. This and the following two chapters examine extensions of the original theory. By the end of Chapter 5, I expect all readers to appreciate both the power of ESS theory in these particular biological settings and the enormous potential of game-theoretic reasoning in general evolutionary processes.
Ross Cressman
4. Frequency-Dependent Evolution in a Randomly-Mating Diploid Species
Abstract
The main cause for skepticism concerning the biological relevance of evolutionary game theory as developed in the last two chapters is the implied asexual reproduction of the population. This criticism is overcome in the present chapter by assuming throughout that individuals in the large diploid population mate randomly and that each mating pair produce the same number of offspring (i.e. equal fecundity) in 1:1 sex ratio through Mendelian segregation. I feel strongly that the results contained here will convince all readers of the importance of ESS theory in population genetics.
Ross Cressman
5. Frequency- and Density-Dependent Evolution in a Haploid Species
Abstract
Chapters 2 and 3 systematically developed the stability conditions for the frequency-dependent haploid dynamic in two biological contexts (the single-species and two-species systems respectively). Based on these heuristic conditions, Chapter 4 gave a game-theoretic interpretation to classical results in the genetic evolution of a diploid species. The present chapter assumes a new game-theoretic aspect in that individual fitness may also depend on population size (i.e density). For this reason, new stability conditions for a density-dependent evolutionarily stable strategy (DDESS) must be developed before their dynamic consequences are ascertained.
Ross Cressman
6. Evolutionarily Stable Sets and Contestant Information
Abstract
The preceding four chapters have each analyzed a general theoretical model in evolutionary biology. The limited examples of particular evolutionary games played a secondary role to the theory. That is, their main purpose was to illustrate the theory at hand.
Ross Cressman
Backmatter
Metadaten
Titel
The Stability Concept of Evolutionary Game Theory
herausgegeben von
Ross Cressman
Copyright-Jahr
1992
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-49981-4
Print ISBN
978-3-540-55419-6
DOI
https://doi.org/10.1007/978-3-642-49981-4