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The geometry of recombination. (English) Zbl 1429.92107
Summary: With the tools of information geometry, we can express relations between marginals of a joint distribution in geometric terms. We develop this framework in the context of population genetics and use this to interpret the famous Ohta-Kimura formula [T. Ohta and M. Kimura, “Linkage disequilibrium due to random genetic drift”, Genet. Res. 13, No. 1, 47–55 (1969; doi:10.1017/s001667230000272x)] and discuss its generalizations for linkage equilibria in Wright-Fisher models with recombination with several loci. The state space associated with the Ohta-Kimura model is simply a Riemannian manifold of constant positive curvature. Furthermore, the equilibria states for recombination can be interpreted geometrically as a product of spheres. In the case of only 2 loci, we also derive the behavior of the mutual information between these two loci.
92D10 Genetics and epigenetics
Full Text: DOI
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