Parentage and sibship exclusions: higher statistical power with more family members

Parentage exclusion probabilities are now routinely calculated in genetic marker-assisted parentage analyses to indicate the statistical power of the analyses achievable for a given set of markers, and to measure the informativeness of a set of markers for parentage inference. Previous formulas invariably assume that parentage is to be sought for a single offspring, while in practice multiple full siblings might be sampled (for example, seeds, eggs or young from a pair of monogamous parents) and their father, mother or both are to be assigned among a number of candidates. In this study, I derive formulas for parentage exclusion probabilities for an arbitrary number (n) of fullsibs, which reduce to previous equations for the special case of n=1. I also derive sibship exclusion probabilities, and investigate the power of differentiating half-sib, avuncular and grandparent-grandoffspring relationships using unlinked autosomal markers among different numbers of tested individuals. Applications of the formulas are demonstrated using both theoretical and empirical data sets of allele frequencies. The results from the study highlight the conclusion that the power of genealogical relationship inferences can be enhanced enormously by analysing multiple individuals for a given set of markers. The equations derived in this study allow more accurate determination of marker information and of the power of a parentage/sibship analysis. In addition, they can be used to guide experimental designs of parentage analyses in selecting markers and determining the number of offspring to be sampled and genotyped.