Total allelic relationship (TA) as a possible alternative to the pedigree-derived additive genetic relationship (RA) is defined. The TA measures the actual allelic identity between individuals for loci segregating for the trait concerned. Its value was studied by simulation in populations of different family structure, different numbers of loci, different numbers of alleles per locus, and different heritability levels. The alternative types of relationship matrices were used in mixed model equations to derive best linear unbiased prediction estimates (EBV) of breeding values (BV). Accuracies of evaluations were calculated as correlations of EBV with true breeding values. In populations with random selection and mating, EBVTA derived using TA had higher accuracies than EBVRA derived using RA. In populations with selection, EBVTA was more accurate and resulted in higher responses than selection on EBVRA. We conclude that not accounting for variation in average measures of relationship and identity in state can be important sources of variance of prediction error, and taking account of them increases the accuracy of selection.