Journal of Mathematical Biology

, Volume 42, Issue 5, pp 455–488 | Cite as

Mutation and recombination with tight linkage

  • Ellen Baake

Abstract.

An exact solution of the mutation-recombination equation in continuous time is presented, with linear ordering of the sites and at most one mutation or crossover event taking place at every instant of time. The differential equation may be obtained from a mutation-recombination model with discrete generations, in the limit of short generations, or weak mutation and recombination. The solution relies on the multilinear structure of the dynamical system, and on the commuting properties of the mutation and recombination operators. It is obtained through diagonalization of the mutation term, followed by a transformation to certain measures of linkage disequilibrium that simultaneously linearize and diagonalize the recombination dynamics. The collection of linkage disequilibria, as well as their decay rates, are given in closed form.

Key words or phrases: Mutation – Recombination – Linkage disequilibria 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ellen Baake
    • 1
  1. 1.Zoologisches Institut, Universität München, Luisenstr. 14, D-80333 München, Germany. e-mail: baake@zi.biologie.uni-muenchen.deDE

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