WELDON, WALTER FRANK RAPHAEL

(b. London, England, 15 March 1860; d. Oxford, England, 13 April 1906), biometrics.

One of the founders of biometrics, Weldon was born into a wealthy London family (his father was an industrialist and a Swedenborgian) and was initially educated by private tutors and at fashionable boarding schools. In 1876 he entered University College, London, and began to study zoology under E. Ray Lankester. Two years later he moved to St. John’s College, Cambridge, where he continued his study of zoology under Francis Balfour; he graduated in 1881 with a first-class degree in the natural sciences tripos.

At this point Weldon seemed on his way to becoming an orthodox zoologist. He spent some time at the Naples zoological station (1881), was demonstrator for W. T. Sedgwick at Cambridge (1882), completed a dissertation on invertebrate morphology and embryology (1883), and became a fellow of St. John’s and a university lecturer in invertebrate morphology (1884). Weldon’s style of life was perfectly suited to his profession; he spent two terms of each year in Cambridge, and from June to January he and his wife (whom he had married in 1883) traveled and did research at various marine laboratories. In 1883 he became associated with the laboratory of the Marine Biological Association at Plymouth, and in 1890 he succeeded Lankester as professor at University College.

The move to University College signaled a profound transformation in Weldon’s interest. After reading Francis Galton’s Natural Inheritance (1889), he became convinced that statistical studies of variation would contribute more toward solving the problems of Darwinism than the embryological work in which he had been engaged.

Between 1890 and 1892 Weldon published two papers that were classics of their kind, on variation in the shrimp Crangon rulgaris. In the first he demonstrated that body measurements for large populations of shrimp (carapace length, for example) are normally distributed; this was the first normal distribution observed in a wild population subject to the influence of natural selection. The second paper presented the first correlation coefficients derived for a wild population; Weldon demonstrated that in the shrimp pairs of organ lengths are highly correlated in individuals of the same species. Weldon hoped that these correlations would yield quantitative definitions of species and races, replacing the older descriptive definitions, which were based upon a single type specimen. In 1893, in studies of the crab Carcina moenas, Weldon found an asymmetrical distribution for frontal breadth. He thus concluded that he was actually measuring two different races of crab that inhabited the same environment but were physically distinguishable.

In 1891 Weldon began to learn probability theory and sought the help of his colleague Karl Pearson. Pearson soon became enthusiastic about the prospect of solving the problems of evolution statistically; he and Weldon began a collaboration that lasted until Weldon’s death. One of the first fruits of their combined effort was the formation in 1893 of the Royal Society Evolution Committee (with Galton as chairman), dedicated to large-scale studies of variation.

Weldon’s most significant contribution to biometrics was his study of differential death rates in crabs (1894), which was sponsored by the Evolution Committee. He reasoned that if natural selection works by killing “unfit” individuals before they can breed, it should be possible to correlate death rates in youthful populations with physical characteristics. To test this assumption he raised 7,000 young female crabs in jars filled with polluted water from their natural environment, assiduously measured several characteristics of each crab at different times during its growth, and discovered that individuals with greater than normal frontal breadths were more likely to die before reaching reproductive age. From these results Weldon concluded that natural selection can operate on small, apparently insignificant variations and that there is no need to postulate large jumps or discontinuous variations (as had been suggested by Galton in 1889 and by Bateson in 1894) in order to understand how evolution progresses. Weldon knew that his results were tentative, since the experimental procedure was quite faulty; but he was not prepared for the storm of protest that broke about his head. Naturalists were not ready to admit that regression lines and correlation coefficients were relevant in what had been, until then, a purely descriptive science.

The controversy between the advocates of continuous variation and the proponents of discontinuity grew increasingly acrimonious, and eventually the biometricians resigned from the Evolution Committee and founded a journal, Biometrika (1901), in which to publish and to propagandize for their new science. After the rediscovery of Mendel’s work and the founding of Biometrika, two separate schools of genetics developed in England: the Mendelians, who believed in discontinuous variation and devoted themselves to breeding studies; and the biometricians (including Weldon and Pearson), who believed in continuous variation and devoted themselves to statistical study of variation. In 1900 Weldon moved to Oxford, where he became Linacre professor; but the distance between Weldon and Pearson did not dampen their collaboration. Weldon undertook studies of moths (unpublished), snails, thoroughbred horses, poppies, mice, and men in an effort to find clear-cut cases of evolutionarily significant continuous variation; but none of these studies was as fruitful, either methodologically or substantively, as his earlier work on shrimp and crabs. Perhaps because of his frustration, Weldon worked at a pace and with an intensity that worried his friends. His debate with the Mendelians became even more acrimonious; and a stream of critical articles flowed from his pen, to be published in Biometrika. In the midst of an Easter holiday devoted to biometric research Weldon collapsed and died. Many of his colleagues considered his death particularly tragic for having come when he seemed to be entering a very promising phase of his career.

BIBLIOGRAPHY

Weldon’s most significant biometric papers are “The Variations Occurring in Certain Decapod Crustacea. I. Crangun rulgaris,” in Proceedings of the Royal Society, 47 (1890), 445–453; “On Certain Correlated Variations in Crangon vulgaris,” ibid., 51 (1892), 2–21; “On Certain Correlated Variations in Carcina moenas,” ibid., 54 (1893), 318–329; and “Attempt to Measure the Death Rate due to the Selective Destruction of Carcina moenas With Respect to a Particular Dimension,” ibid., 57 (1895), 360–379.

For an understanding of his theoretical dispute with the Mendelians see “Remarks on Variation in Animals and Plants,” in Proceedings of the Royal Society, 57 (1895), 379–382; “Mendel’s Laws of Alternative Inheritance in Peas,” in Biometrika, 1 (1901-1902), 228–254; “Professor de Vries on the Origin of Species,” ibid., 365–374; and “On the Ambiguity of Mendel’s Categories,” ibid., 2 (1902), 44–55.

The best source for information about Weldon is Karl Pearson, “Walter Frank Raphael Weldon,” in Biometrika, 5 (1906), 1–50.

Ruth Schwartz Cowan