Asymptotic distribution of the lod score for familial data

Using a linkage model with mixed parental mating types between a trait locus and a marker locus the asymptotic null distribution of the statistic U = 2ln(10)Z(theta) was stimulated and compared to the chi square type distribution function 1/2 + 1/2 Pr [chi 2(1) less than mu]. The stimulation results show that the chi square approximation fits the asymptotic null distribution well when both loci are predominated by either one of the two alleles at their loci, respectively, or the linkage phase tends to disequilibrium.