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

Abstract

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 ¼ 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.

Parentage and Sibship Inference From Multilocus Genotype Data Under Polygamy

“…Typically, the probability of the marker data of a dyad under each of a number of candidate relationships is calculated as the likelihood of the relationship, and the inferred relationship is the one with the maximum likelihood (e.g., Epstein et al 2000;McPeek and Sun 2000). Although simple to implement and potentially capable of inferring any possible relationships between two individuals, pairwise methods fail to use the valuable marker information efficiently (Sieberts et al 2002;Wang 2007).…”

“…These markers have 5-10 alleles per locus and could have elevated rates of genotyping errors because genotypes were obtained from fecal samples. The probability that a random unrelated individual is excluded as a parent of an offspring by using the 13 SSRs is 0.9862, calculated by the formula in Wang (2007).…”

“…Few methods exist for estimating simultaneously parentage and full and half sibship among any number of individuals (Emery et al 2001;Jones et al 2007). This is unfortunate because, on one hand, background relationship interferes with the inference of the focal relationship and thus reduces the statistical power (Wang 2004), and, on the other, taking the background relationship into account by inferring multiple relationships among three or more individuals gains enormously more power (Sieberts et al 2002;Wang 2007). 1 Second, most methods estimate the relationship between a pair of individuals in isolation, causing two major problems.…”

“…In parentage assignments, for example, one offspring provides information for just one allele at a locus in the parent. The probability that both parental alleles are present in the genotypes of a number of n offspring is 1 À 2 1Àn , and the power of parentage assignment rises dramatically with an increasing number of offspring whose parentage is considered jointly (Wang 2007).…”

Kin assortment in juvenile shoals in wild guppy populations

“…The program searches for the maximum likelihood partition of a sample of individuals into fulland half-sib clusters. It is more powerful than the pairwise approach because more information on entire families rather than just pairs of individuals is extracted and utilised (Wang, 2007;Wang and Santure, 2009). Bootstrapping (over individuals) was used to assess whether the average relatedness, calculated from the inferred sibship assignments, or the frequency of sibship was significantly greater within than between shoals, for each population.…”