Definitions

# Coefficient of relationship

In population genetics, Sewall Wright's coefficient of relationship or coefficient of relatedness or relatedness or r is defined as 2 times the coefficient of kinship. The coefficient of kinship is defined as the probability that the alleles at a particular locus chosen at random from two individuals are identical by descent.

For example, in a diploid species (e.g. all mammals), the coefficient of relationship between parent and offspring is 0.5, meaning half of the offspring's genome comes from that parent. Or, more precisely said, half the genomes are identical by descent.

Some other relatedness examples: (assuming no consanguinity, for diploid species unless noted otherwise)

r relationship
0.5 (½) parent-offspring
0.25 (¼) grandparent-grandchild
0.125 (⅛) great grandparent-great grandchild
1 identical twins
0.5 (½) full siblings
0.25 (¼) half siblings
0.03125 (1/32) second cousins
0.75 (¾) full hymenoptera sisters

Some of these definitions of r are tricky to calculate. For example, consider that you are one of a family of half brothers with the same mother but different fathers. Call rm the coefficient of matrilineal relatedness and call rp the coefficient of patrilineal relatedness. What is the coefficient of relatedness to each of your half brothers?

rm=0.5 as it does for normal siblings, since there is a 1 in 2 chance that you and your half brother developed from eggs from harboring the same haploid genome selected during maternal meiosis. But rp=0 since there is no chance that any two brothers inherited the same allele from different fathers by descent. The average of these rs equals 0.25, as we see above. You and your half brother are one quarter genetically identical by descent.

In the example above, the differentiation between maternal and paternal coefficients of relatedness was made in order to introduce the phenomenon of imprinting, or parent-specific gene expression into the calculation of r.

To illustrate how an imprinting turns normal siblings into half siblings, consider that you are one of a cadre of full siblings. What is your coefficient of relatedness to one of your siblings at an imprinted locus in a maternally inherited allele? (Maternally inherited alleles are called "madumnal," and paternally inherited alleles are called "padumnal".)

The value of r at this imprinted locus is equal to the value of r for the entire genome of the half brothers. For the brothers above, rm=0.5 and rp=0. For the madumnal locus in the family of full siblings rm=0.5 too, since all expression is from the mother's allele. Normally, rp=0.5 for full siblings with the same father, but the effect of imprinting is to negate paternal expression, hence rp=0. Therefore you and your full siblings resemble half-siblings at imprinted loci.