Commentary: Fisher 1918: the foundation of the genetics and analysis of complex traits

Written while a high school teacher in 1916, Fisher’s article (1918)¹ and its easier to understand summary² are landmark papers that founded the field of quantitative genetics, or in modern parlance, complex trait genetics. Like many landmark papers, it was not recognised as such at the time. With a century-worth of hindsight, Fisher 1918 did not suffer from a rejection by the Proceedings of the Royal Society, although it may have hurt Fisher’s pride. Fisher 1918 is notoriously difficult to read and understand. It also contains an awful lot of new material—new theory, concepts and analysis methods, most if not all of which have stood the test of time.

It is important to place these papers in their historical context. In the 1880s, Francis Galton pioneered the quantification of the resemblance between relatives for traits like height, using linear regression and correlation. Mendel’s laws were rediscovered in 1900, and a question that occupied a number of scientists (including Karl Pearson, George Udny Yule, John Brownlee and others) for the next few decades was whether the hereditary and evolutionary properties for a trait like human height were the same as those for Mendel’s peas. A particular question was whether inheritance of complex traits was by ‘blending’ of parental phenotypes, which was seen as different to the inheritance of discrete characters as in Mendel’s peas. The incompatibility between blending inheritance and natural selection (and therefore indirectly between blending inheritance and complex traits) was pointed out as early as 1867, in a critique of Darwin’s Origin of Species by Fleemin Jenkin.³

Pearson and Lee in 1903⁴ quantified the correlation between first-degree relatives for height and related measures using a large sample size of 1000s of families, and incorrectly concluded ‘Thus for most practical purposes we may assume parental heredity for all species and all characters to be approximately represented by a correlation of .5’. The ‘pea versus height’ debate was lively and involved some big egos—a thorough historical account of the discoveries in population and quantitative genetics in the early part of the 20th century is given in the book by Provine.⁵

Enter Fisher (1918). In 35 pages packed with derivations and results, Fisher sets out to derive the theory of the resemblance between relatives due to their genetic covariance at 1, 2 and many loci. He defined the term ‘variance’ and introduced the analysis of variance to partition observed variation into underlying ‘causal’ factors. Fisher partitioned genetic variation into additive genetic (the variance of what we now call ‘breeding values’) and the variance of dominance deviations. He also showed the effect of epistatic variance on the resemblance between relatives. Fisher showed how phenotypic variance could be partitioned into meaningful genetic and non-genetic sources of variance, without knowing anything about the underlying genes. Fisher defined quantities that are now called narrow sense and broad sense heritability (variance due to ‘essential genotypes’ and ‘genotypes’, respectively). It was a masterful reconciliation between Mendelian inheritance and biometric analysis of quantitative traits.

In Fisher (1919),² he gives a mostly non-technical summary of his discoveries. The importance of the analysis of variance is first discussed and its meaning in terms of causes of variability. Fisher then discusses the application of the analysis of variance to quantify the total effect of ‘ancestry’ (genetic factors) on quantitative trait variation, with numerical examples of human height. Fisher points out that in addition to the parental contribution of variation in offspring (measured as the squared correlation of offspring-parent correlation, i.e. the variance explained in offspring by parental phenotypes), segregation variance (‘segregation of hereditary qualities’) should also be considered. This solved the problem of ‘blending’ inheritance mentioned previously. Fisher (1919) concludes that the ‘facts’ of biometry are consistent with the theory of cumulative Mendelian factors, and that the ‘percentage of variance due to heritable factors’ (i.e. what we now called heritability) could be estimated numerically from observations on the resemblance between different pairs of relatives. Fisher also makes an important observation that a large heritability would still allow ‘considerable scope for the action of environment’.

Interestingly, Fisher (1919) states that his greatest analytical difficulty was the problem of how to allow for the observed phenotypic correlation in trait value between spouses (assortative mating). Indeed, it is easy to miss, but 24 out of the 35 pages in Fisher (1918) are devoted to assortative mating! In comparison, epistasis (‘epistacy’ by Fisher) only gets 1.5 pages, where two-locus epistasis was modelled. Notably and with great insight, Fisher wrote ‘In addition it is very improbable that any statistical effect, of a nature other than that which we are considering, is actually produced by more complex somatic connections’. Indeed, even in the presence of multi-locus higher-order epistasis, Maki-Tanila and Hill (2014)⁶ showed that most of this variation maps onto the additive variance, indicating very little contribution from non-additive genetic variances.

Fisher derived two important aspects of the theory of assortative mating, namely the effect of non-random mating on genetic variation in the population, and the effect on the resemblance between relatives. The theory of assortative mating was re-visited in the 1970s and 1980s in a number of important contributions by Lande, Nagylaki, Gimelfarb, Crow, Felsenstein and Bulmer, and empirically modelled mostly by twin researchers. However, with the advent of molecular genetic data it is now possible to revisit these old questions with new data, and test different hypotheses about the causes of trait similarity in spouses⁷ and the effect of assortative mating on the genome.

Fisher appeared to adhere to the principle of ‘I trust my own theory and somebody else’s data’, because he seemed somewhat uncritical of the inference he drew about the contribution of the different sources of variation to human height—Fisher noted the sampling variance of the estimates but did not seem to question the models (assumptions) themselves. He concluded, effectively, that the broad sense heritability was nearly 100%. The conclusions from variance partitioning were that 62%, 21% and 17% of variance were due to additive genetic variance, dominance deviations and assortative mating, respectively. These parameters are not wildly different from estimates obtained subsequently over the past century, apart from the contribution of non-additive (dominance) variation, which seems large by today’s standards.⁸

Conflict of interest: None declared.