100 years ago: Sewell Wright's inbreeding coefficient

The negative effects of inbreeding had already been described by Darwin in the 19th century. However, he, and animal breeders, were aware that uniformity of offspring and anchoring of positive traits in a breed is not possible without kinship breeding. With smaller populations, as in pigeon breeding, the mating of closer relatives, inbreeding, occurs automatically. The question of potential negative effects in highly inbred strains was tackled by Sewell Wright in the 1920s. He sought a balance between the positive effects of purebredness (uniformity of offspring and heritability of positive traits) and the negative ones (vitality and fertility).

Uniformity of offspring in constituent traits of breeds such as size, feather structures, behaviour

For many traits homozygosity is desirable and from experience not negative for vital functions. Those who breed plain-headed pigeons are not happy when a youngster with a feather crest occasionally lies in the nest due to heterozygosity for the crest. Where a medium body size is aimed at, oversize and undersize are disturbing in the offspring. The goal is pure heredity for the expression of a trait as defined in the standard. From this point of view, mating with other strains is associated with the risk of losing a strain that has been painstakingly achieved in terms of pure heredity.

Uncovering of negative traits in the strain through kinship breeding

Inbreeding also reveals recessive vitality-reducing and, in extreme cases, lethal factors in a strain. From this point of view, web-foot up to lethal web-lethal, polydactyly and others are the negative face of inbreeding. But it is not only negative that they show themselves. This is because consistent breeders have the opportunity to determine carriers and potential carriers and to eliminate the trait in the strain. D and E are latent carriers in the example due to their descent from B. The siblings of D and E are also highly likely carriers, as are the siblings of the affected homozygous individual.

Outwardly imperceptible traits

With advances in molecular genetics, one can look deeper into the genome than with the naked eye. For example, different alleles in the feather keratin gene and also in the LDH gene, which plays a role in the conversion of lactic acid (lactate), can be detected (cf. the overview article by Eberhard Haase 2021). While studies in racing pigeons showed that even top flyers do not necessarily have to be homozygous for the same alleles, earlier studies on transferrin genotypes, which play a role in the transport of iron produced in the liver, showed that homozygosity for certain alleles can have a negative influence on vital functions. In the case of permanent inbreeding, negative constellations can also accumulate in families for other genes that have not been studied so far and thus trigger what is called inbreeding depression.

The calculation of the inbreeding coefficient

The inbreeding coefficient developed by Wright calculates the potential inbreeding degree of an animal from a pedigree, as shown in the example. Potential, because it determines the probability that two genes of a gene locus are of the same parentage. The same or identical parentage means that they come from the same ancestor and have been passed down through the generations.

In the example, it is ancestor B who is common on both the maternal and paternal sides through parents D and E. According to Wright, if A, B, C have no common ancestors to be considered, then the coefficient Fj for the individual j is

Fj = Σ (1/2)n1+n2+1, where n1 is the number of generations from parent D to common ancestor B (here = 1) and n2 is the number of generations from E to common ancestor B (here also = 1). The summation sign Σ refers to the fact that there can be several common ancestors. A value is then calculated for each ancestor and then added together. For the half-sibling pairing shown, an inbreeding coefficient of

Fj = (1/2)3 = 0.125.

For the mating of full siblings, the value will double, 0.250.

The parallels to inheritance processes

The formula for the coefficient may look like magic at first glance. But it has as its background the same genetic understanding that is also expressed in Mendel's laws and in the representation of Punnett's squares. Let us assume that full siblings are mated with each other whose parents are genetically unrelated. On a locus in the genome, let one parent have alleles 1 and 2 and the other alleles 3 and 4. With a large number of offspring, four gene combinations could fall out of this, (1//3), (1//4) and (2//3) as well as (2//4). With a very large number of random full sibling matings, 1/16 of the young in the subsequent generation are homozygous for allele 1. In the statistical expectation, 1/16 of the young are also homozygous for each of the other three alleles, making a total of 4/16 or ¼ or the 0.250 given in Wright's formula. Almost more significant for the above discussion of inbreeding depression: the probability that a young of F2 does not have a gene, e.g. gene 1, is one quarter. If by chance two such young animals are mated with each other for further breeding the next generation, then allele 1 has disappeared in the inbred line. The probability of such a coincidence is statistically ¼ x ¼ = 1/16. This seems small, but it also applies to the definitive loss of one of the other alleles and to other genes of the entire genome. There is an increase in pure heredity over the generations and, as the other side of the coin, a loss of alleles in the family. With the transferrin genotypes, traits have been found where this can be harmful. This will only be the tip of the iceberg.

On the usefulness of the inbreeding coefficients

The calculations are not comparable to the molecular genetic analysis of individuals, ancestries and similarities within populations. These were not possible in Wright's time and are hardly possible for pigeon fanciers today. What remains is the coefficient as an easier point of reference to determine. The absolute numbers are not so important in themselves, the differences in different breeding strategies perhaps even more so. At least they show the beginner that it is better to start breeding with two pairs than with one pair. The measured inbreeding coefficient when siblings of the offspring from unrelated parents are mated with each other is calculated as 0.250, when siblings are mated again it rises to 0.375. If offspring of another unrelated pair are available for cross breeding, the measured coefficient of the offspring of the first generation drops to zero, when cross breeding it rises to a more moderate 0.125 in the second generation and opens up the possibility of less close relationship breeding for some time. For a more detailed analysis see Sell 2012, 2019. (AS)


Haase, Eberhard, Molekulargenetik und Brieftaubenzucht, Die Brieftaube no. 25, June 26, 2021, pp. 6-10.

Sell, Critical Issues in Pigeon Breeding. What we know and what we believe to know, Part VI, Achim 2021

Sell, Pigeon Genetics. Applied Genetics in the Domestic Pigeon, Achim 2012

Sell, Taubenzucht. Möglichkeiten und Grenzen züchterischer Gestaltung, Achim 2019.

Wright, Sewall, Coefficients of Inbreeding and Relationships, The American Naturalist Vol. 56, No. 645 (Jul. - Aug., 1922), pp. 330-338.


Homozygous family of Thuringian White-Bib Pigeon in respect to constitutional characteristics of the breed



Defective web-feet in a family that from time to time shows up in inbred families. As is shown, the webs also lead to a curvature of the toe position. 


Inbreeding Coefficients of Wright in different inbreeding strategies. Source: Sell, Taubenzucht. Möglichkeiten und Grenzen züchterischer Gestaltung. Zucht und Vererbung in Theorie und Praxis, Achim 2019

IMG_4681 Ausschnitt

Youngsters in the same age with different inbreeding coefficient due to cross-fertilization (young in the background). Source: Sell, Taubenzucht, Achim 2019.