Appendix B - ACCURACY AND RELIABILITY OF THE COEFFICIENT OF RELATIONSHIP

Parent-offspring

Because of a meiotic cell division, where the number of chromosomes is halved in the formation of sperms and eggs, both sexes pass on exactly half of their autosomal genes (i.e. those not on the sex chromosomes) to each individual offspring. In this respect (R = 1/2) is very accurate in describing the proportion of genes held in common by parent and offspring.

However, there is a slight correction needed due to the difference in size between the two sex chromosomes. The female has two long X chromosomes, whereas the male has only one X and a much smaller one called Y

For practical purposes most of the important sex-linked genes are present on the X chromosome. The consequence of this is to make the parent-offspring relationship higher (for sex-linked genes) between opposite sexes than between parent and offspring of the same sex. However, the overall effect is that the deviation of R from 50% is quite small. Since the difference only involves one out of 23 pairs of chromosomes, the error is probably in the region of 3 to 5%. It is interesting that of the four different parent-offspring relationships, mother-daughter is the only one where parent and offspring have exactly 50% of both sex-linked and autosomal genes in common.

1.      Sib Relationship (Excluding identical twins)

The relationship between full sibs and between half sibs is also slightly affected by the irregular sex chromosomes. In the case of full sibs, two brothers or two sisters have slightly more of their inheritance in common than a brother and a sister.

A further problem, on an individual basis, is the effect of sampling. Each full sib receives half of his or her genes from the father and half from the mother. The half received by one sib from the father is not the same as the half received by the other sib from the father, it is an independent sample. On average only one half of the half received from the father will be held in common by the two sibs (1/2 x 1/2 = 1/4). Similarly, of the mother's contribution, only about 1/4 will be held in common by the two sibs. Thus, although the average common inheritance over many pairs of full sibs will be 1/2, in individual cases it can vary from 0 to 1.0 and will follow a normal distribution curve. This explains why, in rare cases, two brothers may look like identical twins on the one hand, and more like unrelated individuals on the other. Therefore, although most pairs of full sibs will have close to 50% of their genes in common, there is a small probability that excessive deviations can occur on either side due to extreme sampling.

2.      Other Relationships

Other relationships, such as grandparent-grandchild, uncle/aunt-nephew/niece and various types of cousins are all subject to sampling variation and sex chromosome anomalies. In the case of grandparent-grandchild, of the 50% of genes a parent receives from a single grandparent, on average 50% of them will be passed on to the grandchild, but can vary on either side because of sampling effects. Since all other relationships, i.e. uncle/aunt-nephew/niece and all types of cousins involve sib relationships somewhere in the chain, it follows that they will also be subject to sampling variation.

To summarise, many relationships described, are subject to minor variations in R due to sex chromosome anomalies; but only parent-offspring relationships are free from sampling errors. When R values are used for other purposes in quantitative genetics, e.g. to estimate the heritability of a character or the genetic correlation between two characters, large numbers of individuals are used and these sampling errors cancel out. [19]