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On a Notion of Linear Replicator Equations

  • Nihat Ay
  • Ionas Erb
Article

Abstract

We show that replicator equations follow naturally from the exponential affine structure of the simplex known from information geometry. It is then natural to call replicator equations linear if their fitness function is affine. For such linear replicator equations an explicit solution can be found. The approach is also demonstrated for the example of Eigen’s hypercycle, where some new analytic results are obtained using the explicit solution.

Keywords

Replicator equation exponential affine structure logarithmic linearity hypercycle system. 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Nihat Ay
    • 1
    • 3
    • 4
  • Ionas Erb
    • 2
    • 3
  1. 1.Santa Fe InstituteSanta FeUSA
  2. 2.Bioinformatik, Institut für InformatikUniversity of LeipzigLeipzigGermany
  3. 3.Max-Planck Institute for Mathematics in the SciencesLeipzigGermany
  4. 4.Mathematical InstituteFriedrich-Alexander-University Erlangen-NurembergErlangenGermany

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