The Haseman-Elston (1972) method, widely used for studying linkage, has been criticized for incomplete utilization of sib-pair information. As an alternative, Amos (1994) created and advocates the “variancecomponents” approach; Wright (1997), using a “likelihood argument,” found that the phenotypic difference discards sib-pair linkage information; and Fulker and Cherny (1996) came to a similar conclusion after an analysis of sib-pair covariances (Fulker et al. 1995). Here, I propose an extension of the Haseman-Elston (1972) method that puts the sib-trait sum into linkage testing.

Suppose a trait X has a normal distribution with a mean genetically determined and environmental (residual) variance; each sib pair has i alleles identical by 2 je descent (IBD) at the trait locus,, 1, or 2; and the i 0 sib pair–trait vector has joint normal (bi-T T X {(X, X)