Likelihood Models for Multivariate Traits in Human Genetics¹

The formulation of likelihood functions for multivariate genetic traits in humans is discussed, and exact computing formulas presented for families and simple pedigrees. The model described incorporates all the features of the original ELSTON and STEWART (1971) formulation and that of LANGE et al. (1976, 1983); the integration of the two models is achieved through the introduction of quantities we call “relatedness coefficients.” These are subsequently used to define “status indices,” which turn out to be the key to the computational problem, for the polygenic and mixed models of genetic transmission. The highest order of matrices that enter into the calculation is pXp for a p ‐variate trait, instead of npXnp , where n is the size of the pedigree. The expressions that are presented can be extended to complex pedigree structures.