Efficient computation of genotype probabilities for loci with many alleles: I. Allelic peeling

Genetic marker data are likely to be obtained from a relatively small proportion of the individuals in many livestock populations. Information from genetic markers can be extrapolated to related individuals without marker data by computing genotype probabilities using an algorithm referred to as peeling. However, genetic markers may have many alleles and the number of computations in traditional peeling algorithms is proportional to the number of alleles raised to the sixth or eighth power, depending on pedigree structure. An alternative algorithm for computing genotype probabilities of marker loci with many alleles in large, nonlooped pedigrees with incomplete marker data is presented. The algorithm is based on recursive computations depending on alleles instead of genotypes, as in traditional peeling algorithms. The number of computations in the allelic peeling algorithm presented here is proportional to the square of the number of alleles, which makes this algorithm more computationally efficient than traditional peeling for loci with many alleles. Memory requirements are roughly proportional to the number of individuals in the pedigree and the number of alleles. The recursive allelic peeling algorithm cannot be applied to pedigrees that include full sibs or loops. However, it is a preliminary step toward a more complex and encompassing iterative approach to be described in a companion paper.