Mais uma abordagem matemática para quaisquer jogos evolutivos de estrutura populacional

Evolutionary dynamics in set structured populations

1. Corina E. Tarnitaa,
2. Tibor Antala,
3. Hisashi Ohtsukib and
4. Martin A. Nowaka,1

+Author Affiliations

1. aProgram for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138; and

2. bDepartment of Value and Decision Science, Tokyo Institute of Technology, Tokyo 152-8552, Japan

1. Communicated by Robert May, University of Oxford, Oxford, United Kingdom, April 2, 2009 (received for review February 8, 2009)

Abstract

Evolutionary dynamics are strongly affected by population structure. The outcome of an evolutionary process in a well-mixed population can be very different from that in a structured population. We introduce a powerful method to study dynamical population structure: evolutionary set theory. The individuals of a population are distributed over sets. Individuals interact with others who are in the same set. Any 2 individuals can have several sets in common. Some sets can be empty, whereas others have many members. Interactions occur in terms of an evolutionary game. The payoff of the game is interpreted as fitness. Both the strategy and the set memberships change under evolutionary updating. Therefore, the population structure itself is a consequence of evolutionary dynamics. We construct a general mathematical approach for studying any evolutionary game in set structured populations. As a particular example, we study the evolution of cooperation and derive precise conditions for cooperators to be selected over defectors.

* cooperation
* game
* social behavior
* stochastic dynamics

Footnotes

* 1To whom correspondence should be addressed. E-mail: martin_nowak@harvard.edu

* Author contributions: C.E.T., T.A., H.O., and M.A.N. performed research and wrote the paper.

* The authors declare no conflict of interest.

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