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Am J Hum Genet. 1994 Jun;54(6):1104-9.

Computation of identity-by-descent proportions shared by two siblings.

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Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor 48109-2029.


I provide a novel approach to computing the mean and variance of the proportion of genetic material shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, conditional on observed marker data. I first show that each chromosome in an offspring can be represented by a two-state Markov chain, with the time parameter being the map distance along the chromosome. On this basis, I show that IBD proportion can be written as a stochastic integral and that the computation of its mean and variance can be reduced to evaluation of an integral of some elementary functions. In addition, I show how Goldgar's model can be extended to include dominance effects. Several examples are provided to illustrate the calculation.

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