The coefficient of dominance is not (always) estimable with biallelic markers

The genetic relationship among individuals at one locus is characterized by nine coefficients of identity. The coefficients of inbreeding, coancestry and dominance (or fraternity) are just linear functions of them. Here, it is shown how they can be estimated using biallelic and triallelic markers using the method of moments, and comparisons are made with other methods based on molecular coancestry or molecular covariance. It is concluded that in the general case of dominance and inbreeding with biallelic markers, only the coefficients of inbreeding and coancestry can be estimated, but neither the single coefficients of identity nor the coefficient of dominance can be estimated. More than two alleles are required for a full estimation as illustrated with the triallelic situation.