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Commentary: Height and Mendel's theory: the long and the short of it.

In this paper1 Brownlee explores mathematical genetic models that are consistent with the observed resemblance between relatives for traits with a continuous distribution, such as height in human populations. It is important to place the paper in its historical context – it was read in 1910 and published in 1911. In the 1880s, the Victorian polymath Francis Galton, a cousin of Charles Darwin, pioneered the quantification of the resemblance between relatives for traits like height using regression and correlation. In 1901, Mendel’s laws were rediscovered and a question that occupied a number of scientists for the next few decades was whether the hereditary and evolutionary properties for a trait like 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. 
 
A paper by Pearson and Lee in 19032 gave a detailed breakdown of the correlation between first-degree relatives for height and related measures, using what must have been quite large sample sizes at that time – thousands of families. Pearson and others thought that they were discovering new laws of inheritance for quantitative traits – the title of Pearson and Lee was On the Laws of Inheritance in Man: I. Inheritance of Physical Characters. It was maybe unfortunate that the correlation of parents and offspring for height was about 0.5 (it still is these days) and that other ‘complex’ traits for which there were data at the time – both in humans and in other species – also showed a parent-offspring correlation close to 0.5, because it led Karl Pearson to conclude ‘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’. In 1910, RA Fisher was studying at Cambridge and it was not until 1918 that Fisher’s now famous article was published, reconciling the Mendelian and biometrical approaches to complex traits, and laid the foundation for the new field of quantitative genetics.3 
 
The ‘pea versus height’ debate (Mendelians vs biometricians) was lively and involved some big egos (something else that hasn’t changed). A thorough historical account of the discoveries in population and quantitative genetics in the early part of the 20th century, and the personalities involved, is given in the book by Provine.4 
 
So Brownlee’s paper lies between the rediscovery of Mendel’s law, Galton and Pearson’s quantification of the correlation of quantitative traits between relatives and Fisher (1918). The terminology in Brownlee is a bit different from what we use nowadays. He used ‘allomorph’ and ‘element’ for what we now call ‘allele’, and used ‘blending’ to denote additivity. 
 
Brownlee used multiple gene models to study the resulting distribution of the trait and the resulting correlation between relatives. For a particular locus, he modelled both additive and dominance modes of gene action. Segregation at each individual gene followed Mendelian rules. Importantly, he did not model any environmental or residual factors, so that all variation and resemblance between relatives is genetic. In that sense, the trait he modelled was more like finger ridge count than stature. Brownlee showed that with only few independent loci, the distribution of the resulting ‘phenotype’ becomes normal, as Pearson and Lee observed with real data on human height. This was an important result, because it showed that, in principle, Mendelian inheritance could be consistent with the observed distribution of quantitative traits. He also showed that under an additive model, the observed ‘phenotypic’ correlation between first- and second-degree relatives was one-half and one-quarter, similar to what was observed for height. This is the right result but for the wrong reason. Brownlee effectively modelled the correlation between relatives’ additive genetic values (‘breeding values’), which are indeed factors of one-half. But the phenotypic correlation between relatives depends on the heritability, the proportion of phenotypic variation that is due to additive genetic factors. Phenotypic resemblance between close relatives can also be due to shared environmental factors. For human height, the heritability is high, approximately 80%, and there is also evidence for a small covariance between family members due to a shared environment. The resulting correlation of first-degree relatives is close to half but that’s just fortuitous. It seems that Pearson was also led astray by this factor of one-half. Nevertheless, Brownlee showed that for a trait with a heritability of one, its distribution could look normal, as observed for real data, and the resemblance between relatives could be close to what was observed for some traits, and both from postulating only a few ‘genes’ that segregate in a Mendelian manner. These conclusions were important and have stood the test of time. In his own words ‘I have shown that there is nothing necessarily antagonistic between the evidence advanced by the biometricians and the Mendelian theory’. 
 
Brownlee was not the first to point out that the continuous distribution of quantitative traits and the observed resemblance between relatives is consistent with Mendelian theory. For example, Yule and Weinberg did that before him. For a detailed history of early papers on the theory and analysis of quantitative traits, see Hill (1984).5 It took another eight years for Fisher’s landmark paper to appear (not helped by an earlier rejection from the Royal Society), in which he modelled many genes of small effect plus environmental effects, derived the resemblance between relatives analytically and showed how phenotypic variance could be partitioned into meaningful genetic and non-genetic sources of variance, without knowing anything about the underlying genes.