Estimating seven coefficients of pairwise relatedness using population genomic data

Abstract

Population structure can be described by genotypic correlation coefficients between groups of individuals, the most basic of which are the pair-wise relatedness coefficients between any two individuals. There are nine pair-wise relatedness coefficients in the most general model, and we show that these can be reduced to seven coefficients for biallelic loci. Although all nine coefficients can be estimated from pedigrees, six coefficients have been beyond empirical reach. We provide a numerical optimization procedure that estimates them from population-genomic data. Simulations show that the procedure is nearly unbiased, even at 3x coverage, and errors in five of the seven coefficients are statistically uncorrelated. The remaining two coefficients have a negative correlation of errors, but their sum provides an unbiased assessment of the overall correlation of heterozygosity between two individuals. Application of these new methods to four populations of the freshwater crustacean Daphnia pulex reveal the occurrence of half-siblings in our samples, as well as a number of identical individuals that are likely obligately asexual clone-mates. Statistically significant negative estimates of these pair-wise relatedness coefficients, including inbreeding coefficents that were typically negative, underscore the difficulties that arise when interpreting genotypic correlations as estimations of the probability that alleles are identical by descent.