The additive genetic relationship is estimated using the pedigree. But how accurate is that? We know that parents pass exactly half of their genetics on to their offspring. However, we also know that two full brothers may have received different alleles from the same parents. ON AVERAGE they share half of their genes. However, it could be half, it could be a bit more and it could be a bit less. If we only consider a single gene, two full brothers may even share no alleles at all due to Mendelian sampling. This is illustrated in Figure 7, where you see a pedigree of mice. The mother has alleles A and B, and the father has alleles C and D. Each of the four offspring received one allele from the father and one from the mother. In this example, each of the mice received a different combination of these two alleles. On average you would expect that these mice share half of their genes as each of them got half from the same parents. But if you compare two of the four mice, they may share one allele or they share none. So instead of a = ½ these mice would have a = 0, at least for this specific gene.
Of animals course have not only a single, but very many genes. So on average, across all the genes, two full brothers share half of their genes. However, as illustrated in Figure 8, there is some variation around the average, some share a bit more than half and some a bit less. Likewise, half sibs on average share ¼ of their genes. Also here some share a bit more and some a bit less. The variation is half that in full sibs, because half sibs share only one parent instead of two.
