Coefficient of relationship

The coefficient of relationship is a measure of the degree of consanguinity (or biological relationship) between two individuals. A coefficient of inbreeding can be calculated for an individual, as a measure for the amount of pedigree collapse within that individual's genealogy. The term coefficient of relationship was defined by Sewall Wright in 1922, and was derived from his definition of the coefficient of inbreeding of 1921. The measure is most commonly used in genetics and genealogy.

In general, the higher the level of inbreeding the closer the coefficient of relationship approaches a value of 1, expressed as a percentage, and approaches a value of 0 for individuals with arbitrarily remote common ancestors.

The coefficient of inbreeding ("f") is a measure of the likelihood of genetic effects due to inbreeding to be expected based on a known pedigree (i.e. a fully documented genealogy e.g. due to a fixed system of breeding). The measure expresses the expected percentage of homozygosity arising from a given system of breeding.

For a given gene with equally common dominant and recessive variants A and a, a random-bred stock will be 50% homozygous (25% AA and 25% aa), while a closely inbred population will be 100% homozygous (100% AA or 100% aa). The coefficient of inbreeding f is thus designed to run from 0 for an expected 50% homozygosis to 1 for an expected 100% homozygosis, f=2h-1, where h is the chance of finding homozygosis in this gene.

Note that f is an expectation value for an unspecified, hypothetical, perfectly Mendelian gene. Its definition holds regardless of whether the organism's genome actually contains such a gene. Therefore, the coefficient of inbreeding is a statistical value derived from the individual's pedigree and cannot be verified or "measured" exactly by looking at the individual's genome.

The coefficient of relationship ("r") between two individuals B and C is obtained by a summation of coefficients calculated for every line by which they are connected to their common ancestors. Each such line connects the two individuals via a common ancestor, passing through no individual which is not a common ancestor more than once. A path coefficient between an ancestor A and an offspring O separated by n generations is given as:

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