Revised calculation of the coefficient of parentage in plant breeding

The knowledge of the genetic similarity between two individuals has been useful for animal breeders for a long time, and one of the most common measures of similarity is the Coefficient of Parentage (COP). For two individuals X and Y, it is defined as the probability that an allele taken from a particular locus in individual X is equal by descent to another allele taken from the same locus in individual Y; thus, the COP between two individuals is the same as the expected inbreeding of their offspring, and it is now a routine calculation among plant breeders as part of crop improvement programmes. Nevertheless, plant breeders deal with the genealogy between strains or groups of individuals, and here, we provide a mathematical proof that in this case the application of standard formulae replicated from animal breeding may result in overestimation of the true amount of inbreeding between two strains.