Population structure is described by genotypic correlation coefficients between individuals, the most basic of which are Jacquard's nine condensed coefficients. These correlation coefficients form the basis of quantitative genetic analysis, and geneticists perform experimental crosses or pedigree analysis in order to recover them. Previously molecular techniques could only recover four of these coefficients, but we can recover seven coefficients using biallelic loci and a maximum likelihood method. This approach should allow for more robust estimation of the components of genetic variance from population genomic data.
Simulations show that the procedure is nearly unbiased, even at the minimally informative 3x coverage, and that 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. These methods are applied to four populations of the freshwater crustacean Daphnia pulex, and revealed several interesting characteristics that are not apparent with other techniques. The use of a maximum likelihood method also allows us to assess statistical significance of relationships using a log likelihood ratio test, and we find statistically significant negative estimates of many of these pair-wise relatedness coefficients. Although these coefficients are traditionally regarded as measure of the probability of identity, which cannot be negative, we treat them as measures of conditional association, which can be negative. These methods are implemented as part of the mapgd package (maximum likelihood analysis of population genomic data) available from https://github.com/LynchLab/MAPGD.