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Markovian approximation to the finite loci coalescent with recombination along multiple sequences
Affiliation:1. Bioinformatics Research Center, Aarhus University, Denmark;2. Department of Mathematics, Aarhus University, Denmark;1. Infection, Prevention, and Control, Alberta Health Services, Calgary, AB, Canada;2. Computational Epidemiology and Public Health Informatics Laboratory, University of Saskatchewan, Saskatoon, SK, Canada;3. Department of Computer Science, University of Saskatchewan, Saskatoon, SK, Canada;4. School of Public Health, University of Saskatchewan, Saskatoon, SK, Canada;1. Department of Health Sciences, University of Leicester, UK;2. Department of Computer Science, University of York, UK;1. Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat Gan, Israel;2. Department of Chemical Engineering and Network Biology Research Lab, Technion, Haifa, Israel;1. Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, IL 60637, USA;2. Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria;3. Department of Applied Mathematics, Brown University, Providence, RI 02912, USA;4. Departments of Computer Science and Mathematics, The University of Chicago, Chicago, IL 60637, USA;1. Université Montpellier 2, CNRS, Institut des Sciences de l’Évolution, France;2. Institut de Biologie Computationnelle, Montpellier, France;3. Section of Integrative Biology, University of Texas, Austin, TX 78712, USA
Abstract:The coalescent with recombination process has initially been formulated backwards in time, but simulation algorithms and inference procedures often apply along sequences. Therefore it is of major interest to approximate the coalescent with recombination process by a Markov chain along sequences. We consider the finite loci case and two or more sequences. We formulate a natural Markovian approximation for the tree building process along the sequences, and derive simple and analytically tractable formulae for the distribution of the tree at the next locus conditioned on the tree at the present locus. We compare our Markov approximation to other sequential Markov chains and discuss various applications.
Keywords:Coalescent with recombination  Conditional approach  Distance between segregating sites  Markov along sequences
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