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Originally published as Genetics Published Articles Ahead of Print on May 16, 2007.
Genetics, Vol. 176, 2307-2315, August 2007, Copyright © 2007
doi:10.1534/genetics.107.074344
Prediction of Multilocus Identity-by-Descent
William G. Hill1 and Jules Hernández-Sánchez
Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh, EH9 3JT, United Kingdom
1 Corresponding author: Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, W. Mains Rd., Edinburgh, EH9 3JT, United Kingdom.
E-mail: w.g.hill{at}ed.ac.uk
Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in random-mating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD XABC at each of ordered loci A, B, and C can be well approximated by XABC = XABXBC/XB and generalizes to X123...k = X12X23...Xk–1,k/Xk–2, where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.
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