Inbreeding coefficient, pairwise relatedness, and genetic contribution

The inbreeding coefficient (F) is defined as the probability that a pair of alleles at any locus in an individual are identical by descent, and it is calculated by the following formula³⁴:

where n₁ = number of generations from one parent back to the common ancestor, n₂ = number of generations from the other parent back to the common ancestor, and F_A = inbreeding coefficient of the common ancestor.

Pairwise relatedness (r) or coancestry coefficient, the degree of relationship by descent of two parents, equals the inbreeding coefficient of their prospective progeny.

The genetic contribution (GC) of a founder to a cultivar is calculated by the following formula³⁵:

where n = number of generations in a pedigree pathway between the founding clone and the cultivar and x = number of pathways between the founding clone and the cultivar. The three parameters were calculated using the SAS INBRED procedure (SAS 9.4 SAS Institute, Cary, NC, USA).

In summary, the inbreeding coefficient measures the probability that two alleles in a locus are identical by descent and so copies of the same allele from a previous generation. The pairwise relatedness measures the probability that two alleles at any locus are identical by descent (copies of the same allele in a previous generation) between two different individuals. F and r range from 0 to 1, with values close to 0 indicating a low degree of inbreeding or relatedness and values close to 1 indicating a high degree of inbreeding or relatedness. The genetic contribution estimates the proportion of genome that comes from the same individual. Thus, a child will have 0.5 genome of either parent and a grandchild will have 0.25 genomes of his grandparents.