On a Notion of Linear Replicator Equations

Authors: Ay, Nihat¹; Erb, Ionas²

Source: Journal of Dynamics and Differential Equations, Volume 17, Number 2, April 2005 , pp. 427-451(25)

Publisher: Springer

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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

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10884-005-4574-3

Affiliations: 1: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA, 2: Bioinformatik, Institut für Informatik, University of Leipzig, Kreuzstr. 7b, 04103, Leipzig, Germany, Email: ay@mi.uni-erlangen.de

Publication date: 2005-04-01