Era 0, Part I: Heredity observed from variation

Series authors · Domen Jemec, Jason Chin, and Bianca Lauro

Quantitative foundations: biometry and statistical genetics, 1830s–1918

Before heredity was explained with molecular data, scientists analyzed it through phenotypes. Breeders and naturalists watched variation across generations both in ordinary inheritance and through forced cross-breeding.¹⁶⁷ The visible patterns they observed and the records they kept of those traits led to some of the earliest foundations of computational biology. These foundations allowed scientists to begin to hypothesize about the hidden structures driving those traits and statistics gave scientists a way to turn observations that had long been anecdotal into hand-calculated quantities.⁶⁷¹⁷

Once scientists could quantify resemblance, they could analyze populations numerically. Population traits could be treated as distributions with means, variances, correlations, and more. Because this was a new way of evaluating biology, the datasets, descriptive language, and research community had to be developed from the ground up but they did not have to start from scratch. Many scientific and analytical practices were already established such as the rigorous logging of observations, newly developed statistical measurement techniques, information sharing through journals, and using assistants to increase manual calculation throughput.¹¹¹² As the research progressed, this new way of collecting evidence made its way into paper records and printed exchanges but, due to the field still being fragmented, some findings could remain obscure for decades. Despite these limitations, this new approach to analyzing biology started to show it was capable of underpinning new theories. For example, in 1918, Ronald Fisher used a computational foundation to show that continuous biometric traits could arise from discrete Mendelian factors.¹⁷

Image 1. Mendel's surviving notes on flower-color experiments, written on the same sheet as editing marks for a sermon.²⁸

Inheritance without a mechanism

By the mid-nineteenth century, natural history still depended largely on collecting, classifying, and comparing observations. Darwin's On the Origin of Species (1859) proposed natural selection but it left one key assumption exposed. Selection could only accumulate change if some variations survived across generations and Darwin did not yet know what carried them. He later tried to answer this question with pangenesis, a mechanism in which tiny "gemmules" from across the body contributed to reproduction, though he privately called the theory "abominably wildly, horridly speculative."¹ Despite this, Darwin and others knew an answer was needed, because without a mechanism of transmission, selection rested on an unexplained assumption.¹ But Darwin's need for persistent heredity ran into a common view at the time called "blending inheritance," in which offspring seemed to inherit an average of their parents' traits. Many scientists found the idea intuitive because offspring often did have traits that looked like a blend of their parents. The trouble with this theory came when analyzing it across many generations. If a tall parent and a short parent produced intermediate children, and that blending continued each generation, variation should wash out toward an average. The differences that breeders and naturalists kept seeing should have faded away, and selection would lose the persistent variation it needed to work on.²³

Francis Galton approached that persistence as something that could be measured. Rather than looking for the physical carrier of heredity, he focused on understanding how strongly traits in families and more distant relatives resembled one another.⁸ Gregor Mendel had already published evidence in 1866 that inheritance could behave as discrete factors rather than blended resemblance, but that evidence did not reshape the field until its rediscovery around 1900.⁵⁶ Since Mendelian inheritance proposed factors that could hold their identity across generations, disappear from view, and return in countable ratios, once the field discovered it, it quickly gained popularity.⁵⁶¹⁵ After this, Walter Sutton and Theodor Boveri's work in cytology connected Mendelian segregation to chromosome behavior in the early 1900s, and Thomas Hunt Morgan's fly work made sex-linked inheritance traceable in 1910.²

Despite these advances, scientists were still unsure what the mechanism of inheritance was. Mendelian factors gave scientists rules for predicting inheritance, and chromosome-focused cytological work suggested where the factors of the mechanism might sit, but the factors themselves were still known only through their effects. Wilhelm Johannsen's pure-line beans made that gap sharper. He could select visible differences within a uniform line, but the descendants did not keep shifting, which showed that the measured trait and the inherited type were not the same thing. In 1909, he named that split "genotype" and "phenotype."²²⁵ Even with this knowledge the researchers still could not isolate and experiment directly on the inheritance factor. They still did not know how to connect a visible trait to a particular hereditary factor, for instance, how a seed shape followed from a particular factor. Statistics had made visible resemblance quantifiable, and cytology gave the factors a possible cellular location, but the factor itself remained an open, contested question.²¹⁵

What made quantification possible

Making progress on understanding inheritance without knowing the mechanism was only possible because of advances in statistics. Scientists in physics and astronomy had seen that repeated measurements scattered around a true value and created a bell-shaped "law of error" leading to the normal distribution theory.³ In 1835, Belgian astronomer-statistician Adolphe Quetelet applied the same logic to human traits. Human measurements varied from person to person, but Quetelet argued that they still formed regular population patterns around average values, represented by the "average man," or l'homme moyen.³ While Quetelet focused on the population mean, Galton used that mean as a baseline for inheritance. He wanted to understand how much of a parent's departure from the mean appeared again in the child versus how much fell back toward the population mean.⁷⁸

Scientists found that applying statistics to inheritance required data to be collected in the right structure. Through the nineteenth century, data collection had come from census-like social statistics, anthropometric surveys, and breeding records.³⁴²⁹ Those records were useful, but they were not built around family comparison, so Galton began looking to collect measurements that connected relatives across generations that could be statistically analyzed. At the 1884 International Health Exhibition in London, he set up an Anthropometric Laboratory and measured 9,337 visitors, recording height, weight, grip strength, hearing, vision, and other personal data while actually charging each person.⁴ Those rows of comparable measurements let Galton ask whether relatives departed from the population mean together, and whether one trait tended to correlate with another. In that tabular form, human variation could be compared in the way Galton needed so that he could begin to develop modern statistical regression and correlation.⁷⁸⁹

Image 2. Left: a measurement card from Galton's Anthropometric Laboratory, dated December 1, 1888. Right: a page from Galton's family-heights notebook, where parent and child heights were recorded in tabular form. Together they show the paper form of the data Galton wanted statistics to explain.²⁷

By the end of the nineteenth century there were new methods for measuring heredity but there was still no consensus on what the results meant for inheritance. Around 1900, this question led to a sharp divide when three botanists, Hugo de Vries, Carl Correns, and Erich von Tschermak, rediscovered what would become a pivotal paper. That paper was Mendel's. Historians still debate the independence and priority of that rediscovery,⁵ but the paper's return turned heredity into a fight between two groups known as the biometricians and Mendelians.¹⁵

The fight over heredity

After Mendel's work was rediscovered around 1900, biologists split into two camps that argued bitterly over what inheritance was and how it worked.¹⁵ Biometricians treated heredity as a statistical pattern of resemblance across families and populations, built from many ancestral contributions while Mendelians treated heredity as the transmission of discrete factors revealed by controlled crosses.¹⁵

The biometricians, led by Karl Pearson and W. F. R. Weldon, measured continuous variation in wild populations and described it with correlations and distributions. From their side, Mendelian ratios could look too clean, experimental, and detached from the smooth variation visible in real populations. To build out evidence for the biometricians' position, in 1893 Weldon measured different body dimensions of adult female shore crabs from Naples and Plymouth. He found that crab anatomy varied continuously but not randomly, with body dimensions covarying within each measured population rather than varying independently. His later work even suggested that broader-fronted crabs were selectively eliminated in silty water, providing a quantification of natural selection.¹⁴ Instead of relying on population measurements, the Mendelians, led by William Bateson, collected evidence from controlled multi-generational crosses. Bateson spent years collecting cases where variation appeared in discontinuous forms, including organisms with extra or missing parts. His 1894 Materials for the Study of Variation treated discontinuity as a biological clue rather than statistical noise.¹⁵ From their perspective the biometric averages looked too smooth. A curve could describe a population with high accuracy but it would miss that a trait could reappear unchanged in a cross after a generation. The reappearance of Mendel's paper in 1900 gave Bateson the mechanism he had been looking for. Mendel's work showed that traits could segregate, disappear from view, and return in predictable ratios. Bateson turned this interpretation into the basis of his work and, in 1905, gave the new study of heredity its name, "genetics."¹⁵

Image 3. Bateson's Fig. 16 shows a sawfly with one normal antenna and one antenna bearing a foot-like structure. Cases like this made discontinuity look like evidence rather than stray measurement error.³⁰

By 1906, the Weldon-Bateson dispute had become both technical and openly hostile. The technical question was whether Mendel's pea crosses could support the broad claims Bateson made for them. Weldon argued that other crosses showed variable dominance and that the ancestry of the lines still mattered. To him that made Mendel's results look too narrow to serve as a general theory of inheritance. Bateson's 1902 reply called Weldon's criticism "baseless and for the most part irrelevant." For Bateson, the crucial point was that a trait could disappear from view in one generation and return in predictable proportions later. Weldon's death in 1906 left Pearson as the main defender of the biometric position.¹⁵ By this point, each side had found a real issue in the other. Bateson saw that the older ancestral-contribution picture could not explain everything heredity did. If inheritance was only graded resemblance from ancestors, it struggled to explain traits that skipped generations and returned intact in predictable ratios. Pearson and Weldon saw that clean Mendelian crosses made heredity look simpler than it was in wild populations, where variation was usually continuous and selection worked through small measured differences.¹⁴¹⁵

A bridge between the two groups came in two parts. First, in 1908, Godfrey Hardy and Wilhelm Weinberg each independently showed mathematically that Mendelian inheritance could be calculated in a population, not only in a controlled cross. In their proposal they showed that if mating was random and no outside force changed the frequency of a hereditary factor, the different forms of that factor would appear in predictable genotype proportions in the next generation. Since the factors themselves were still unseen, observable trait counts were the evidence biologists could use as the calculation's foundation and a population could remain stable without blending inheritance. Hardy and Weinberg's proposals gave biologists an idealized baseline for what Mendelian heredity did by itself.¹⁶ While their proposal explained some of the gap, the harder case was continuous traits, the kind the biometricians had been focused on. Plant breeders unknowingly had the solution since they had shown that in wheat, maize, and tobacco, measured traits could grade smoothly when several Mendelian factors contributed to the same character.²⁶ A solution to the second part of the bridge came formally in 1918 when Fisher presented a mathematical answer showing how discrete inheritance could still generate continuous variation.¹⁷ He showed that a trait could be shaped by many Mendelian factors, each with a small effect. When added together and blurred by the environment and error, those factors could produce the smooth distributions and family correlations that Pearson and Weldon had measured. Fisher focused on showing how much of the observed variation could be traced to inheritance. He partitioned the measured trait variation into hereditary and environmental components, then related it back to Mendelian factors acting together, changing how biometric data could be interpreted. This change meant that parent-child resemblance, correlations, and distributions were foundational to estimating how hidden hereditary factors contributed to visible variation. This reframing bridged the remaining disagreement between biometricians and Mendelians and was the first step into what would become quantitative genetics.¹⁷

Eugenics and the biometric program

While the fight over Mendelism was unfolding, Galton and Pearson were also tying biometry to eugenics. Galton coined the word in 1883, then defined it in 1904 as the study of influences that improve "inborn qualities."¹⁸ Galton saw biometric evidence not only as a way to understand heredity, but as a possible tool for guiding marriage, reproduction, and social policy though he did caution that more work was needed and that findings should be used only "so far as they are surely known."¹⁸ This caution was echoed by several scientists questioning how far the evidence could go. Weldon defended Galton's statistical methods but warned that limited breeding experiments could not be turned directly into eugenic rules, H. G. Wells worried that family status could be mistaken for inherited ability, and Robert Hutchison argued that food and childhood environment could shape physical and mental development enough to be mistaken for inherited weakness.¹⁸ Even with those reservations and disagreements on what the biometric measurements could prove, eugenics gave biometric heredity a public purpose, funding, and institutional force.¹⁸¹⁹

Galton then worked to build an institutional home for eugenics. He began the Eugenics Record Office in 1904 and, in 1907, Pearson took over the work. After Galton died in 1911, his estate endowed the Francis Galton Professorship of Eugenics, with Pearson as the first holder.¹⁹ For Galton and Pearson, eugenics was the practical promise of biometry. If heredity appeared in family resemblance, then enough family records could show which traits, diseases, abilities, and social outcomes ran through a lineage. To support this research, the laboratory collected and standardized family data on the belief that heredity could be turned into tables, analyzed statistically, and then applied to eugenic policy. While Fisher's 1918 proposal resolved the division between Mendelians and biometricians, it also strengthened the statistical heredity that eugenic arguments depended on. The lab continued this research and Fisher would later hold the Galton Professorship from 1933 to 1943.²⁰ It would take much of the next century to separate heritability from the claim that a trait was fixed in any one person.²²

Key quantitative ideas

Gregor Mendel, an Augustinian friar in Brünn, began with a hybridization problem. He wrote that artificial fertilizations in ornamental plants had revealed a "striking regularity" in the return of hybrid forms.⁶ The missing step, as he saw it, was to follow those forms through later generations and establish their numerical ratios. Mendel's insight arose from the agricultural world around Brünn, where sheep breeders, plant hybridizers, and his own abbot had treated inheritance as something that could be tested rather than only described.²⁹ He found that peas fit his goal because they offered constant, sharply distinguishable traits, controllable pollination, and fertile hybrid offspring. From 1856 to 1863, he turned the monastery garden into a counting experiment.⁶ The work spanned many seasons and required counting traits by hand. In one second-generation cross for seed shape, he counted 5,474 round seeds against 1,850 wrinkled, a ratio of 2.96 to 1.⁶ From that count he inferred a hidden hereditary element behind the visible trait. Mendel used several terms for the visible traits and the inherited factors that produced them, including Merkmale (or characters), Anlage, and Factoren. In his publication he represented the factors with letters such as \(A\) and \(a\).⁶ He argued that, in a hybrid, egg and pollen cells carried those factors "on average in equal numbers," and combined by chance at fertilization.⁶ A character, or physical trait, could vanish from appearance without the factor being diluted away. Despite not knowing about genes, the Mendel could see from the factor counts that there had to be a hidden hereditary unit. The paper landed in a local natural-history society journal and was written in the language of plant hybridization. Since it appeared before cytology and chromosomes had become central to heredity, and it was printed in a local publication, the work did not become part of mainstream heredity theory for three decades.⁵⁶¹⁵

Francis Galton focused on the problem of understanding family resemblance. He postulated that if heredity showed up as resemblance among relatives, then resemblance had to be measured across families, rather than argued from individual examples. He first saw the pattern in sweet peas. Galton had friends grow packets of carefully weighed seeds and found that the offspring seeds tended back toward an ordinary size.⁸ For humans, he saw the same evidence in stature. In his 1886 paper, he described the object of the work as the "degrees of family likeness in different degrees of kinship." Studying 930 adult children from 205 families, he found that the children of tall parents were usually tall, though less extreme than their parents. Their heights retained about two-thirds of the mid-parent deviation from the population mean.⁷ Galton then generalized the problem, writing that "the large do not always beget the large," yet population proportions stayed surprisingly regular across generations.⁸ From statistics, correlation gave him a way to measure that regularity between traits and relatives while the mechanism of inheritance remained unknown. Through his work of applying statistics to the observed traits, Galton made a hereditary relationship measurable as a single number.

Karl Pearson took Galton's family-resemblance problem and pushed it toward larger samples and stricter formulas. He called this "inheritance in the mass."⁹ A single family could mislead, but a population of measured parents and children could show how strongly traits moved together. In 1896, building on Galton's correlation idea and Francis Edgeworth's mathematical groundwork, Pearson developed the product-moment coefficient, which gives correlation the \(r\) we still use today.⁹ In this paper Pearson argued that heredity and regression had been discussed too loosely, with speculation about causes, and needed precise definitions, measurements, formulas, and probability-based analysis before anyone could claim to explain heredity.⁹ In 1900, Pearson developed the chi-square \(\chi^2\) test, which he described as a way to judge whether observed deviations could reasonably have arisen from random sampling.¹⁰ Pearson also founded the journal Biometrika in 1901 with Galton and Weldon, giving the new quantitative biology a home of its own.¹¹ Its first issue said the journal would collect biological data and spread the statistical theory needed for their "scientific treatment."¹¹ In 1902, Weldon applied Pearson's method to Mendel's pea counts and found that one set of results fit Mendel's hypothesis with exceptional closeness.¹⁰ For the 639 plants in Mendel's three-character cross, Weldon calculated that a repeated experiment would give a worse fit about 95 times in 100 (\(P \approx 0.95\)), making the original counts look almost too close to the predicted ratios.¹⁰ In 1903, at UCL, Pearson's biometric work was formalized as the Drapers' Biometric Laboratory, where assistants helped turn measurements into usable tables.¹² In this lab, labor was the computation scaler, with people copying measurements, checking arithmetic, and turning scattered observations into numbers a journal could print.¹²

William Sealy Gosset brought statistics into his work at Guinness in Dublin. He faced a practical limit because large-scale experiments on barley and malt were too expensive for a working brewery and he saw that the normal curve worked best with large samples. He needed a way to measure uncertainty in small samples because of his data limitations. For example, in one experiment with barley he only had two pot-culture comparisons and in another experiment, he had eleven paired seed experiments, seven varieties in one year and four in the next. In 1908 he published his answer, the t-distribution, which could estimate a mean when the sample is small and the true population variation is unknown.¹³ This distribution looks like a normal curve with heavier tails, which means it gives more honest uncertainty for small experiments where a few measurements can swing the average. The ability to handle small samples made the t-test useful far beyond brewing, because biological experiments were often small and noisy for exactly those reasons.¹³

Godfrey Hardy and Wilhelm Weinberg made Mendelian inheritance calculable in populations. While Mendel had shown how factors behaved in crosses, Hardy and Weinberg asked what those factors would do across a whole population. In 1908, each independently showed that under random mating, the frequency of a factor's alternatives could predict genotype proportions in the next generation.¹⁶ A stable population no longer had to imply blending inheritance and the biometricians' theory. It could be what Mendelian heredity looked like when no outside force was changing the factor's frequency.¹⁶

Ronald A. Fisher showed in 1918 that continuous traits did not rule out Mendelian inheritance. Many Mendelian factors, each with a small effect, could add together, while environmental variation blurred the result, producing the smooth variation biometricians had measured.¹⁷ Fisher proposed splitting observed variation into inherited and environmental components. Parent-child resemblance and population spread became ways to estimate hidden hereditary contributions, decades before anyone could read the molecules carrying those factors.¹⁷

What the era left

By the end of this period, biologists could use visible variation to reason about hidden inheritance. There was now a common thread from Mendel's ratios through Fisher's variance. Each method used visible patterns to make claims about hidden inheritance. The hereditary factor itself was still unknown, yet there were ways to quantify its effects. Since the analysis methods were starting to align, data collection and sharing efforts standardized to support them and other scientists could peer review. New journals and biometric laboratories improved the scale at which the work could be done across institutions.¹¹¹²

After 1918, the application of statistics would be carried into population genetics. Haldane's mathematical theory of selection began appearing in 1924. Fisher and Wright then built on the same base in 1930 and 1931, turning the 1918 reconciliation into a theory of how hereditary factors change in populations.²¹ The question would shift from resemblance among relatives to movement across generations. At the same time, another branch of quantitative biology was taking shape from work that treated living forms and processes as physical and mathematical problems.²⁴ This branch used instruments, equations, and physical explanations to make living processes calculable. We'll dive deeper into this branch in our next Era 0 post.

Endnotes