The proportions of affected sibs sharing 2, 1 or 0 identical by descent parental marker alleles have
been shown to conform to the ‘triangle constraints’ (Suarez, 1978; Holmans, 1993). It has also been
shown (Dudoit & Speed, 1999) that the constraints are verified provided certain assumptions hold.
In this study we explore a realistic situation in which the constraints fail due to the presence of a
factor in which the sibs differ, a factor on which penetrance depends. This factor may be a
characteristic of the trait (severe vs. mild form), or the presence/absence of an associated trait or an
environmental factor. We show that under such situations, using the triangle constraints may lead
to important loss of power to detect linkage by the MLS test. We propose here an alternative
approach in order to detect both linkage and heterogeneity.