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 programs. 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.