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.

The current challenge in biomedical research is to detect genetic risk factors involved in common complex diseases. The power to detect their role is generally poor in populations that have been large for a long time. It has been suggested that the power may be increased by taking advantage of the specificity of founder populations; linkage disequilibrium spanning larger regions and kinship coefficients being stronger than in large populations. A new method is proposed here, the Maximum Identity Length Contrast (MILC) which, in contrast with other existing methods, does not make the assumption of unique ancestry for the genetic risk factors. It is thus appropriate for a search for common genetic risk factors for complex diseases. Statistical properties of the method are discussed in realistic contexts.