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The present paper demonstrates algorithms for applying gene counting estimation of haplotype frequencies in very large genetic systems. A factor union representation of phenotypes is used which conveniently yields the sets of potential haplotypes and diplotypes for each phenotype. Methods for storing and rapidly retrieving the relevant haplotypes are given. An example with several hundred frequencies is given which required a few seconds computing time for each estimation iteration on a small computer. A computer program employing the methods described has been written in Fortran-77 and is available to any investigator on request.

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Data are now available on 9 pedigrees in detail and 4 pedigrees as lod scores only. Linkage to HLA is significant (Z = 5.53 at recombination rates of 0.223 in males and 0.327 in females). Tight linkage is excluded. Nine pedigrees which appear to be typical olivopontocerebellar atrophy (OPCA I) have recombination rates of 0.150 in males and 0.300 in females. The remaining 4 pedigrees are clinically atypical or include discrepant data and give no evidence for linkage. The symbol SCA1 is proposed for a locus on chromosome 6 (loosely linked to HLA), at which at least one allele produces OPCA I (Menzel type). It is not yet clear whether other clinical types are determined by alleles at different loci, although this is suggested by several pedigrees, including a Danish pedigree of OPCA with dementia. Linkage evidence will be decisive in delineating the ataxias.

40 multiplex multiple sclerosis (MS) families were analyzed for evidence of an MS susceptibility gene linked to the HLA region of the sixth chromosome. We assumed that population associations between specific HLA alleles and MS are due to linkage disequilibrium, so preference was given to hypotheses compatible with tight linkage, and explanations were sought for conflicting evidence. The analyses proceeded in two steps: (1) segregation analysis using the computer program POINTER, and (2) linkage analysis using LINKAS, first assuming linkage equilibrium and then allowing for linkage disequilibrium and etiological heterogeneity. The results of the segregation analyses were indeterminate. The results of the linkage analyses suggest that analyses that do not allow for disequilibrium lose substantial evidence on linkage. Of the models that were investigated under linkage disequilibrium, the best fit is with a model of complete linkage (Θ = 0.0) in 75% of tghe pedigrees and no linkage in the remaining pedigrees. We were unable, however, to statistically reject another model involving loose linkage and no heterogeneity.