To the Editor: Kruglyak and Lander (1995) provide an important synthesis of methods for identity-by-descent (IBD) sib-pair linkage mapping, with an emphasis on theuse of complete multipoint inheritance information for each sib pair. These procedures are implemented in the computer program MAPMAKER/SIBS, which performs interval mapping for dichotomous and quantitative traits. The authors present three methods for mapping quantitative trait loci (QTLs): a variant of thecommonly used Hase-man-Elston regression approach (Haseman and Elston 1972), a maximum-likelihood procedure involving variance components, and a rank-based nonparametric procedure. These approaches and related work (Amos and Elston 1989; Fulker and Cardon 1994; Olson 1995) use the magnitude of the difference in the sibling phenotype values for each sib pair as the observation for analysis. Linkage is detected if siblings sharing more alleles IBD have similar phenotypes (ie, a small difference in the phenotype values), while siblings sharing fewer alleles IBD have lesssimilar phenotypes. Such techniques have been used to detect linkage for a number of quantitative traits (eg, Cardon et al. 1994; DeMeester et al. 1995). However, the exclusive reliance on the phenotypic differences may be due in large part to historical inertia. A likelihood argument is presented here to show that, under certain classical assumptions, the phenotypic differences do not contain the full likelihood information for QTL mapping. Furthermore, considerable gains in power to detect linkage can be achieved with an ex-panded likelihood model. The development here is related to previous work (Amos 1994; Amos et al. 1996), which incorporates the full set of phenotypic data using likelihood and robust quasi-likelihood methods. The purpose of this letter is not to endorse a particular approach but to spur research in alternative and perhaps more powerful linkage tests. Using the notation from Kruglyak and Lander (1995), for the ith sib pair let vi be the number of alleles (0, 1, or 2) shared IBD by the siblings at a marker locus. For simplicity, the arguments here are initially developed under the assumption that the vi are known exactlyie, the marker is fully informative for each individual. However, the overall conclusions do not depend strongly on this assumption. The phenotypes of siblings 1 and 2 (arbitrarily ordered) in the ith pair are denoted 01i, 02i, with difference Di= 41i-42i. The differences have mean zero, and are assumed to be normally distrib-uted with variances aov= Var (Di vi). The power to detect linkage derives from the fact that a marker linked to the QTL should exhibit o2o> ac2> a22, and Kruglyak and Lander (1995) recommend a test based on maximum-likelihood estimation of these variances. Note that from the value Di alone one cannot recover the original pair {41i, 02J}, and it is reasonable to speculate that the original phenotypes may carry additional information for linkage.

We assume that the phenotype pair is bivariate normally distributed, with E (41i)= E (42i)= A, and Var (qii)= Var (02i)= 42, regardless of IBD status. Here it is the correlation pVi= corr (O1i, 2i vi) that varies with vi, and a linked marker should exhibit 0: