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.