title: Computation of identity-by-descent proportions shared by two siblings.
abstract: 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.
authors.affiliation: Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor 48109-2029.
authors.forename: S W
authors.initials: SW
authors.lastname: Guo
mesh_terms: D000704:Analysis of Variance; D002874:Chromosome Mapping / Q000379:methods* / Q000706:statistics & numerical data; D002877:Chromosomes, Human; D008040:Genetic Linkage; D005819:Genetic Markers; D006801:Humans; D008390:Markov Chains; D008957:Models, Genetic; D015233:Models, Statistical
chemical_list: D005819:Genetic Markers