The generalized sib pair IBD distribution: its use in the detection of linkage

General expression for the distribution of identity by descent (IBD) scores at a marker locus have been derived given neither, one or both sibs affected with a disorder determined by a linked trait locus with arbitrary gene frequency and penetrance vector. It is shown that the distirbution of IBD scores depends only on the additive and dominance variances and the population prevalence of the disorder. A one-sided test is suggested as an appropriate means of statistically testing the hypothesis that the recombination fraction is significantly less than 1/2. This sib pair approach is designed primarily to detect the presence of a critical disease susceptibility locus but when the assumptions of the incompletely penetrant single locus model are correct the methodology proposed here results in consistent estimates of the recombination fraction. The affected sib pair methodology seems especially suited to traits determined by single loci with non-Mendelian transmission.