30. Statistics against Biometrics 1895-1906

Francis Galton was 25 years older than Ray Lankester and for some years they had lived nearby on the southern side of Hyde Park where they often talked about their different attitudes to science.

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Galton believed the answer to the question of life could be measured, yet his main problem was that he didn’t have much data. He offered a challenge to Lankester about his elaborate plans for an Anthropometric Laboratory, with which he was going to collect a lot of data and analyse them. The project was being set up just down the road in South Kensington to measure physical and behavioural features from visitors to the International Health Exhibition. It was a small roving exhibition and volunteers were measured for things like head size and shape, then the results were compared to social status and other factors. Galton was also collecting data about the intelligence of whole families, though a lot of the detail seemed even then to be of dubious social, let alone scientific, acceptability. One of his expectations was to devise an index to measure the range of human intelligence.

Interested and able to get involved with this kind of analysis was Carl Pearson, a student of marine biology and statistics who Lankester had encouraged to go to Naples with Weldon. Pearson was brought up in archetypal Victorian middle class family tradition. His domineering father was a successful hard-working barrister who paid no attention to his family during term-time. Holidays were for that kind of thing and it was then that the youngsters would be taken shooting and fishing, all strictly under his control.  Carl was sent to school at Rugby and then studied mathematics at Cambridge. In 1879 he got a First and was elected to the Fellowship of King’s College Cambridge. He hated anything compulsory and argued with his colleagues about the divinity classes that he had to attend with all the other Fellows.

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The freedom of the Cambridge life-style allowed Pearson to visit Berlin and Heidelberg regularly and he took an interest in the contemporary German philosophers who were so busy then. He admired the new left wing politics and JBS Haldane argued later that it was Marx’s influence that caused him to change his name from Carl to Karl. But statistical mathematics excited him most and the new data being accumulated by people like Francis Galton presented him with very attractive applications.

Statistical analysis is an advance from what he’d been doing with Raphael Weldon at the Marine Station in Naples a few years previously. Weldon had followed Lankester’s main interest in marine life and spent time at the Naples laboratory and later at Plymouth, but was more and more aware that evolution was a statistical problem. Then, a major challenge was to provide more data for analysis and Weldon obtained measurements of the death rates of crabs and snails. In 1889 he took Lankester’s job at University College where he became well known as a great teacher. He also continued Lankester’s fight to defend the independence of University College and King’s College against their amalgamation as a new Albert University. Lankester had left London for an unhappy decade at Oxford, leaving the young scientists to take over many of his projects. It also put them under the influence of Galton and enlisted them both in the programme for a statistical solution to the problems of heredity and evolution.

Earlier, while he was an undergraduate at Cambridge, Weldon had been friendly with William Bateson who strongly favoured mutation as the cause of most change in evolution. Bateson presented the idea as his theory of discontinuous evolution, showing it as two peaks in the population of an earlier single species. He explained it in detail in what he hoped would become a student bible, Materials for the Study of Variation published in 1894. But he over-emphasising the role of mutation and gave no place for environmental influences. With Lankester out of the way in Oxford there was peace between these four quantitative scientists and they teamed up as Galton and Pearson, Bateson and Weldon. The harmony was not going to last for very long.

None of them gave much attention to Darwin’s ideas on natural selection until Alfred Wallace was asked to review Bateson Materials book. The next day he had the good chance to bump into Weldon in London and they talked about Bateson’s dismissal of many ideas that Darwin had cherished. Sharing their anger after that initial exchange Wallace and Weldon went away intent on going public with their criticisms of the biased approach and they both gave bad notices for the book. What had been a strong friendship at Cambridge between Bateson and Weldon became a bitter and nasty battle in their later lives. Galton continued to support the book because it added to the cause of his own polyhedron model and was one in the eye for his cousin’s old-fashioned insistence on gradualism.

A rare defender of mainstream Victorian values, and Charles Darwin in particular, was Sir William Thistleton-Dyer, the new Director of Kew Gardens who took over from Hooker in 1885. He shared the need for stability of the mean and agreed with Weldon about Bateson’s neglect of outside influences on evolution. Dyer made that same point in 1895 when he suggested that different coloured varieties of the ornamental flowering plant Cineraria were hybrids and not random mutants.

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His observations were that the different colours formed gradually not suddenly, though whether that meant they weren’t mutants wasn’t very clear then. This intervention attracted the wrath of Bateson in the correspondence columns of Nature and Weldon soon joined in. Bateson took the criticism personally and from then on his Cambridge group, studying mutations in what became Mendelian Genetics, were at war with the London school of statistical biometrics.

Most biologists agreed that experiments were needed to settle these questions and that some statistical analysis of the results could be very useful. The argument about mutations had divided those with a quantitative outlook on evolution, leaving hapless observers like Lankester and Wallace on the side-lines, feeling useless relics of another age. Their interests in evolution were far away from the mathematical theory that had entered the discussions and they felt isolated from the young generation. A serious divide had been made much deeper and science was moving on faster all the time.

So with this in mind, over a working lunch at his club in 1893, Herbert Spencer entertained Galton, Weldon, Wallace and Lankester to a discussion about “conducting statistical enquiry into the variability of organisms.” They agreed that the statistical method was the only one by which Darwin’s hypothesis could be experimentally checked.

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Later this group became the Evolution Committee of the Royal Society, which confirmed to Lankester that he was one of the few biologists then who still wanted to look outside at the whole organism and then towards the physical environment. Most others were on the new mission to the smallest part of the cell, expecting to join with the chemists and physicists and find mathematically defined laws. It frightened him that both directions of study were so vast, suggesting that progress in understanding the biology of life was going to be very slow, however fast one part of the science might be moving.

Despite the attempts of Wallace and Weldon to bring the sides together, the last few years of the nineteenth century saw a rapid decline in support for natural selection, encouraged by the Bateson affair and the continuing absence of evidence for adaptation. Galton worried that he might die before the elusive agent of heredity was discovered and to add to that despair his wife did die in 1898. Accidentally, he was kept going by stumbling across some very exciting new data, the pedigree of a large family of Basset hounds with white and yellow patches and he was able to trace the heritage back several generations. He used the data to establish the distribution of each parent’s contribution going back four and more generations. Overjoyed with such good data for analysis, Karl Pearson described the patterns of inheritance for the white and yellow patches with a series of new equations. To cheer up his depressed boss he incorporated them into a Happy New Year card, and through Galton’s warm reaction it gave all the London biometricians a new lease of life for the next battle with Cambridge.

That came sooner than they expected because Bateson was the referee of the manuscript setting out Pearson’s equations, and though the mathematics may have been original, the biology was bad. Bateson took great delight in rejecting the manuscript. In anger, the London group decided to begin a journal of their own for such articles on topics crossing the boundaries of traditional disciplines. They called it Biometrika, a name like Pearson’s own, spelt with a k not a c (and which is still publishing high quality work). Even with this divided opposition, Lankester was side-lined in his defence of Darwin and the holistic view he still had for all of nature.

No-one would have guessed anything special was going to happen when William Bateson caught the train from Cambridge to London one morning in May 1900. He had been invited to give a lecture to the Royal Horticultural Society in Chelsea, about what was being called Galton’s Law. It came from the conclusions of Galton’s analysis of the white and yellow patches on Basset hounds that had just been published and stated that parents contributed equally to their offspring’s inherited matter. On the slow train journey Bateson happened to turn to some papers that he had bundled into his bag and there he found an unread reprint of an article published 34 years earlier. The author was Gregor Mendel.

Bateson realised that the characters that Mendel had counted over several generations of peas showed a pattern was carried from one generation to the other. Whatever this mechanism, Bateson thought the forty year old manuscript by Mendel had some important messages for plant breeders, a different kind of detail to Galton’s and that difference was important. Legend has it that before his train reached Liverpool Street Station in London he had decided to change his lecture and share Mendel’s work with his audience at the Chelsea Society. The audience remained silent, unaware of the importance of the monk’s breeding experiments, let alone why such dull work should be presented with such excitement. It was an uncanny repeat of the silence after the Darwin and Wallace paper was read out to the Linnean Society 42 years earlier.


Wanting to share his discovery further, Bateson wrote to alert Galton to the manuscript “in case you may miss it. Mendel’s work seems to me one of the most remarkable investigations yet made on heredity, and it is extraordinary that it should have got forgotten.” Like the audience in Chelsea, Galton did not respond and it took several years for the penny to drop in other peoples’ minds. To be fair to these observers, it was easy to miss the point from Mendel’s funny little experiments crossing different varieties of peas. For the uninitiated, and that was the vast majority, counts of which pea types had shown up in the next generation were a long way from finding Darwin’s missing units of inheritance.

Attracting hardly any interest, Bateson was left feeling that he had over-reacted to the Mendel article and that his own idea was best after all. It was six years since he had first suggested that hereditary features were transmitted by vibrations rather than by discrete particles. He became so pre-occupied with this hypothesis that he preferred to dismiss all other explanations of evolution out of hand. He summarised Darwin in one line: “Selection is a true phenomenon; but its function is to select, not to create”. He was convinced that Darwin had got it wrong and the London group around Galton and Pearson were beyond the pale.

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After all, there was still a possibility that his own theory of vibrating messages would show Mendelian ratios and that he had been right to get excited about the re-discovered manuscript. So with this always in his mind he never did accept the chromosomal account of inheritance.

Some people, like de Vries, saw mutation as hereditary change showing up as splitting one species into two, big evolutionary jumps, more dramatic than anything Darwin had anticipated in the world of gradual change. Later in the decade “mutation” became associated with smaller changes, encouraged by replacing the difficult expression “Mendelian Factor” with the simple term “gene”.

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These changes in single characters were usually happening within a species, one simple character controlled by one gene. Even Darwin had expected that mechanisms such as mutation might account for evolutionary change in addition to the more important process of natural selection. In the last sentence of the Introduction to the Origin he wrote: “I am convinced that Natural Selection has been the main but not exclusive means of modification.”

In all parts of the life sciences the quantitative approach was gaining ground. With this trend were Pearson and Weldon who used mathematics to test the validity of Mendel’s own data and whose results appeared to be too good to be true: there was nearly 100% validity, an unheard-of result that made them suspect that someone had fiddled the calculation. But who would want to do such a thing, and with what motive?  Bateson did not accept the criticism and saw Weldon’s questioning of Mendel’s conclusions as an over-reaction. Ever more determined, Weldon went on looking for evidence of adaptation in his snails and crabs, measuring their death rates, looking for signs of extinction of old species and origin of new ones. But he didn’t find any new evidence and blamed that on the complexity of the way his organisms showed their adaptation and selection. This was no way of gaining support from an already disillusioned group of Darwin supporters.

Bateson took an even stronger line against the London statisticians in Pearson’s circle and the bitter dispute about the nature of evolution and the value of the statistical method continued to rage. The battle over Mendel’s data reached its climax at the 1904 British Association meeting that happened to be in Cambridge where the audience was hostile to the London side. In response, a complacent Bateson was the proud host and felt confident that his students would give some good talks. In the event there was a series of dull displays of statistical analysis from the Londoners and the presentations of breeding experiments from Bateson’s Cambridge group were not much better. At the end, Pearson offered to bring the two sides together: the chairman looked around at the blank faces of the Cambridge audience and saw little enthusiasm for this: “But what I say is: let them fight it out!” The audience broke up into small groups, each wondering which side another was on, and many thinking that strong leadership could have led the scientists out of this hole. Instead, most of the positive work was being done miles away in New York and the English contribution was about to turn into tragedy.

Weldon was eager to accept the challenge from that meeting and his first chance for reconciliation came later in the year when the Royal Society asked him to referee a manuscript from one of Bateson’s supporters. It took data from the pedigrees of race horses and found what the author argued to be Mendelian ratios in the coat colours: bay and brown being dominant to the chestnut recessive. Weldon was unhappy with the author’s colour assignments, fearing they had been altered to give good results, and asked the author to clarify the methodology and the definition of his characters. The great row that inevitably followed ended in the work eventually being published, but with a brief footnote. It highlighted some of the changes that Weldon had demanded, but the fact that the article was published at all gave victory to Bateson’s group.

In despair at this outcome Weldon put all his energy into disproving the article’s results, and that meant him finding evidence of a chestnut mare, crossed with another chestnut, giving birth to a brown or a bay foal. He worked frantically, saying “I cannot leave this thing unsettled” and causing his good friend Pearson to measure the seriousness of the situation by observing that “he used stronger language than I have ever heard him use.” Eventually Weldon found the information he had hoped for and was persuaded to take a family holiday with the Pearsons. That was when the 45 year old Weldon caught a chest infection and he died a few weeks later. It was generally agreed this was from the exhaustion, worry and over-work.

All these incidents between London and Cambridge were based on uncertainty and the battles they created were really about their lack of belief in what Darwin or Mendel had been telling them. More particularly, Darwin’s theory was aggressively rejected by Bateson’s group and Mendel’s was not accepted by Weldon and his London friends. But neither group had anywhere else to turn, other than to the hope that somehow the numbers games would come up with something unexpected.

That was exactly what happened when new calculations laid another of Darwin’s ghosts to rest, the one about the age of the earth and the time that had most likely been available for animal and plant evolution to have happened. In 1904, during one of his public lectures, Rutherford announced his new radiometric dating techniques which measured the half-life of elements such as radium present in particular rocks. His first results suggested a much older age of the earth than had been advocated by Thomson.

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Afterwards, Rutherford is said to have described his shocked reaction to seeing Thomson in the audience as he began the lecture. “To my relief Thomson fell fast asleep, but as I came to the important part, I saw the old bird sit up, open an eye and cock a baleful glance at me. Then a sudden inspiration came, and I said Thomson had limited the age of the earth, provided no new source of heat was discovered. That prophetic utterance refers to what we are now considering tonight, radium!” Just as Thomson saw through Lyell’s shaky edifice of uniformity, Rutherford had seen through Thomson’s single-tracked thinking about the cooling planet earth: more than one thing was going on at once and that had clouded each process.

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