Ancestral Inference Research Articles

Ancestral inference. II. The founders of Tristan da Cunha.

The Tristan da Cunha data for the MN-blood types and for retinitis pigmentosa are analysed according to the methods for ancestral inference developed in the preceding paper. Joint and marginal likelihoods for the MN data show that it is possible to make inferences about the types of original founder genes, although relative values are in some cases not large. Although relative likelihoods are robust against small changes in gene frequency, they can be distorted by assuming values that differ widely from the maximum likelihood estimate. In the case of retinitis pigmentosa, under an assumed allele frequency of 0.01, we conclude, contrary to expectations, that the couple (975, 798) are substantially the most likely founders to have been responsible for the introduction of the allele. The inferences for this trait are complicated by the fact that it is recessive, and genotypes are therefore not observable. Extinction probabilities for a variety of sets of original founder genes on the Tristan da Cunha ancestral pedigree are also computed and discussed.

Ancestral inference: I. The problem and the method

A method for inferring the ancestral genotypes for the founders of a population is developed. This method uses the algorithms for the computation of probabilities on pedigrees of arbitrary complexity, developed by Cannings et al. (1978) and implemented by Thompson (1977b). When characteristics are simply determined by underlying genotypes the inference problem is simplified, and larger and more complex pedigrees may therefore be analysed. The problem of estimating the allele frequencies to be used in computing prior genotype probabilities for those founders on whom a likelihood function is not required is discussed. The same method allows us to compute extinction probabilities for any combination of original founder genes; these probabilities are interesting parameters of pedigree structure, which, since they relate to the actual genes present in a population, help to provide a clearer understanding of observed distributions of autosomal traits.