Non-identifiability of identity coefficients at biallelic loci

We analyze precisely how different IBD modes combine into identical genotype distributions at diallelic loci. In particular, we describe IBD mode mixtures that result in identical genotype distributions at all allele frequencies, implying the non-identifiability of the identity coefficients from independent loci. Our analysis yields an exhaustive characterization of relatedness statistics that are always identifiable. Importantly, we show that identifiable relatedness statistics include the kinship coefficient (probability that a random pair of alleles are identical by descent between individuals) and inbreeding-related measures, which can thus be estimated consistently from genotype distributions at independent loci.