The correlation between relatives on the supposition of Mendelian inheritance: biometry and Mendelism reconciled
An analysis showing that the correlations between relatives which the biometricians had measured for the stature of parents, children and siblings are exactly those that must arise if a trait is determined by many Mendelian factors of small effect, each segregating on its own.
The analysis was made in 1918 by the Englishman Ronald Fisher. For this he introduced the word 'variance' and its partition into hereditary and environmental, additive and dominance parts, that is, the analysis of variance. The dispute of biometricians and Mendelians, running since 1900, ended not in the victory of one side but in a formula in which both are right.
The paper became the foundation of quantitative and population genetics. The lane is life because this is a theory of inheritance; math is added because the whole apparatus is statistical. In 1936 the same Fisher accused Mendel of data that were 'too good', and that dispute is still alive.
Why this date
The date is that of publication: R. A. Fisher, 'The Correlation between Relatives on the Supposition of Mendelian Inheritance', Transactions of the Royal Society of Edinburgh 52, part 2 (1918), pp. 399-433 (DOI 10.1017/S0080456800012163, checked against Wikidata Q7727667). The reference list of Visscher and Goddard (2019) gives volume 53, which is an error. Fisher printed a popular account in the Eugenics Review in 1919.
What it grew from
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'Versuche über Pflanzen-Hybriden': segregation of characters and numerical ratios
influenced · Confidence: high
Fisher showed that the 'pea vs. height debate' is removed if a trait is determined by many factors, each obeying Mendelian rules and segregation ratios. Mendel's experiments of 1866 enter the paper of 1918 not as something cited but as the model of inheritance from which the observed correlations between relatives are derived.
Dispute: Fisher's attitude to Mendel is double, and this is a well known dispute. In the 1936 paper 'Has Mendel's work been rediscovered?' the same Fisher asserted that the data of most of Mendel's experiments had been falsified to agree with expectation, and in private called the finding 'abominable' and 'shocking'. Hartl and Fairbanks go through both series of experiments and conclude that there is no factual basis for the allegation of falsification, the discrepancy being explained by which character Mendel actually scored and how many seedlings he examined. The dispute over data that are 'too good' continues, but it does not affect the 1866 to 1918 link: Fisher's 1918 paper rests on the Mendelian mechanism regardless of how Mendel himself counted.
Link sources
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
In his paper, Fisher showed that this “pea vs. height debate” could be reconciled by postulating that multiple genes contribute to variation in the population, each of them obeying Mendelian rules and segregation ratios.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
A century ago, a paper from R.A. Fisher reconciled Mendelian and biometrical genetics in a landmark contribution that is now accepted as the main foundation stone of the field of quantitative genetics.
- Churchill Eisenhart, «Pearson, Karl», Complete Dictionary of Scientific Biography (2008) Verified 20 Sep 2026
he improved upon the kinds of models that Pearson, Weldon, and Yule had been considering 10–20 years before, and showed clearly that the correlations observed between human relatives not only could be interpreted on the supposition of Mendelian inheritance, but also that Mendelian inheritance must lead to precisely the kind of correlations observed.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
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The biometric-Mendelian debate: continuous or discontinuous heredity
influenced · Confidence: high
The 1918 paper was written for the sake of this dispute and closed it: the biometricians led by Pearson held that the inheritance of continuous traits such as height could not be explained by Mendelian principles, the Mendelians led by Bateson held the opposite, and Fisher showed that both sides are right if the factors are many and each is small.
Dispute: Historians also differ over whether the dispute was closed by the 1918 paper as such: Visscher and Goddard note that attempts to reconcile the observations with Mendelism had been made earlier by Pearson, Yule and Weinberg, and that actual acceptance came later, with the work of Wright (1921) and others in the 1920s.
Link sources
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
After Mendel’s laws were rediscovered in 1900, there was a vigorous debate between the “Biometricians,” led by Pearson, and the “Mendelians,” led by Bateson. The Biometricians argued that the inheritance of continuous traits, such as human height, could not be explained by Mendelian principles.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
Nevertheless, attempts to reconcile the observed results with Mendelian inheritance had been made before 1918 by Pearson, Yule, and Weinberg, but it was Fisher’s 1918 paper that formed the basis for quantitative genetics in the future.
- Churchill Eisenhart, «Pearson, Karl», Complete Dictionary of Scientific Biography (2008) Verified 20 Sep 2026
In fact, geneticists today ascribe the reconciliation of the “ancestral” and “Mendelian” positions and “Mendelian” positions, and definitive synthesis of the two theories, to Fisher’s first genetical paper, “The Correlations to be Expected Between Relatives on the Supposition of Mendelian Inheritance” (1918)
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
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Pearson's correlation coefficient and the chi-square test
influenced · Confidence: high
Fisher was computing precisely those correlations between relatives that were measured with Pearson's coefficients, and he built on models which Pearson, Weldon and Yule had been considering ten to twenty years before him. Visscher and Goddard say outright: 'Fisher built upon previous work by Yule and Pearson'.
Dispute: The relations of Pearson and Fisher were hostile: according to Eisenhart, in 1920 Pearson returned to Fisher the manuscript on the distribution of the correlation coefficient, and the work appeared in another journal. Continuity of method and personal conflict do not coincide here, and that is worth remembering when reading the link.
Link sources
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
However, its purpose was clearly set out in the introductory paragraph, namely, to interpret empirical results from biometry, in particular the correlations between relatives, in accordance with Mendelian inheritance, to provide a more precise analysis of the causes of variation in human complex traits. Fisher built upon previous work by Yule and Pearson.
- Churchill Eisenhart, «Pearson, Karl», Complete Dictionary of Scientific Biography (2008) Verified 20 Sep 2026
he improved upon the kinds of models that Pearson, Weldon, and Yule had been considering 10–20 years before, and showed clearly that the correlations observed between human relatives not only could be interpreted on the supposition of Mendelian inheritance, but also that Mendelian inheritance must lead to precisely the kind of correlations observed.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
Links under review
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The journal Biometrika: the statistics of life gets a journal of its own
influenced · Confidence: low
No historian links the journal as an institution to Fisher's 1918 paper; the sources confirm only that Fisher relied on Pearson and Lee's data printed in Biometrika.
The numbers Fisher was explaining are the tables of correlations between relatives for stature published by the biometricians. Visscher and Goddard point out that Fisher's inference about dominance variance rested on earlier data on human traits, namely Pearson and Lee 1903; the Pearson and Lee paper appeared in the second volume of Biometrika.
Dispute: The confidence is deliberately low: the quotation asserts that Fisher relied on the data of Pearson and Lee 1903, while the fact that they were printed in Biometrika comes from that paper's reference list rather than from a statement about the link. A historian stating outright that the journal as an institution made Fisher's work possible could not be found here.
Link sources
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019) Verified 25 Sep 2026
In addition, earlier results on human traits (mainly stature) showed a somewhat larger correlation between full siblings than between parent and offspring, consistent with dominance variance (Pearson and Lee 1903), but also consistent with sibs sharing a common environment.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019) Verified 25 Sep 2026
Pearson K, Lee A, 1903 On the laws of inheritance in man: I. inheritance of physical characters. Biometrika 2: 357–462.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019) Verified 25 Sep 2026
Node sources
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
A century ago, a paper from R.A. Fisher reconciled Mendelian and biometrical genetics in a landmark contribution that is now accepted as the main foundation stone of the field of quantitative genetics.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
If there are many genes contributing to trait variation then total (phenotypic) variance in a trait (such as height) can be partitioned into variance components due to genetic factors and environmental factors, and genetic variance itself can be partitioned into variance due to the average effects of alleles and variance due to dominance deviations.
- Peter M. Visscher, Michael E. Goddard, From R.A. Fisher's 1918 Paper to GWAS a Century Later, Genetics 211 (4), 1125-1130 (2019)
The now ubiquitous term variance was first introduced in this paper, as was the method of the ANOVA (Charlesworth and Edwards 2018).
- R. A. Fisher, The Correlation between Relatives on the Supposition of Mendelian Inheritance, Transactions of the Royal Society of Edinburgh 52 (2), 399-433 (1918) Verified 5 Oct 2026
The Correlation between Relatives on the Supposition of Mendelian Inheritance
- Daniel L. Hartl, Daniel J. Fairbanks, Mud Sticks: On the Alleged Falsification of Mendel's Data, Genetics 175 (3), 975-979 (2007) Verified 5 Oct 2026
The allegation that has impugned Mendel's integrity is Fisher's (1936, p. 132) assertion that “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel's expectations,” a discovery that Fisher regarded as “abominable” and “shocking” (Box 1978, pp. 296 and 197, respectively).
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.