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References
Charles Darwin, The Origin of Species, a Variorum Text, ed. Morse Peckham (Philadelphia, 1959), p. 164, sentence 13.
C. Darwin and A. R. Wallace, Evolution by Natural Selection (Cambridge, 1958). See the “Sketch of 1842.”
Darwin, The Origin of Species, p. 202, sentence 227.
Ibid., p. 178, sentence 95.11.e.
Ibid., p. 267, sentence 382.65.0.50.369.
Darwin's changes of view on the matter of which forms of variation were evolutionarily significant and his reactions to his critics are well dealt with in Peter Vorzimmer, “Charles Darwin and Blending Inheritance,” Isis, 54 (1963), 371–390.
Not explicable in the sense of being Strictly predictable, for one of the central points about variation seemed to be that one could not tell in advance what new features might be produced.
Francis Galton, Hereditary Genius, 2nd. ed. (London, 1892).
Fleeming-Jenkin, “The Origin of Species,” North British Review, 46, (1867), 285. Jenkin also criticized the notion of evolution having been brought about by the emergence of “sports”. For, believing in a blending theory of heredity, he was able to argue that any novelty of feature would soon be “swamped” by crossing with normal forms.
Hugo De Vries, Intracellulare Pangenesis (Jena, 1889), trans. C. S. Gager as Intracellular Pangenesis (Chicago, 1910).
Francis Galton, Natural Inheritance (London, 1889), pp. 18–34. Galton's presentation of these ideas is discussed in J. S. Wilkie, “Galton's Contribution to the Theory of Evolution, with Special Reference to His Use of Models and Metaphors,” Annals of Science, 11 (1955), 194–205.
Galton, Hereditary Genius, “Prefatory Chapter to the Edition of 1892”.
William Bateson, Materials for the Study of Variation, Treated with Especial Regard to Discontinuity in The Origin of Species (London, 1894).
G. S. Carter, A Hundred Years of Evolution (London, 1958), pp. 78–92. Quoting from B. Bateson, William Bateson F.R.S. (Cambridge, 1928), p. 42, Carter illustrates his point by showing that Bateson found it difficult to obtain permanent employment because he had gone “too far afield” from morphological work. Weldon, before moving to London in 1891, had been a Cambridge lecturer in invertebrate morphology.
See F. Galton, Memories of My Life (London, 1909), chap. 5. Weldon's first paper on selection incorporated ideas rather similar to those contained in the section on “Natural Selection” in Galton's Natural Inheritance, pp. 119–124. It should be noted that Galton's primary interest was with anthropology, not with biology, and that he always operated as a private citizen, never as the holder of an academic post.
Karl Pearson, “Walter Frank Raphael Weldon 1860–1906,” Biometrika 5 (1906), 1–52, esp. pp. 17–19. This memoir is the only biography of Weldon. Pearson explains Weldon's adoption of biometric methods as partly due to the fact that, shortly before reading Natural Inheritance, he was working on morphological problems involving the idea of correlation.
Galton, Natural Inheritance, pp. 95–100.
F. Galton, letter to Nature, 55 (1897), 605.
The invalidity is compound. Galton wrongly assumed that regression coefficients could be multiplied together, a false assumption discussed in Karl Pearson, The Life, Letters and Labours of Francis Galton (Cambridge, 1914–1930), pp. iiia, 23–24. But, after this, his reasoning is invalid. This, and the relation between his statistical and physiological theories of heredity, are clearly discussed in R. G. Swinburne, “Galton's Law—Formulation and Development,” Annals of Science, 21 (1965), 15–31.
Galton, Natural Inheritance, pp. 134–137.
F. Galton, “The Average Contribution of Each Several Ancestor to the Total Heritage of the Offspring”, Proc. Roy. Soc., 61, (1897), 401–413. Why Galton felt able to apply his law to discontinuous attributes when he had “derived” it from data for stature is a puzzling matter. Swinburne concluded that Galton's law was in fact derived from his physiological theory (see e.g., Natural Inheritance, 7–14, 192–198) and was “merely tested later against the painfully accumulated data.” This supposition would certainly explain Galton's amazing extrapolation if we further assumed that he regarded discontinuous attributes as controlled by the development of a single hereditary particle (or linked group), and continuously varying dimensions as controlled by a large number of independent particles, with the individual particles following the same inheritance pattern in each case.
Galton, Hereditary Genius, p. xvii.
Galton, letter to Nature, 1897.
Karl Pearson, “Regression, Heredity and Panmixia,” Phil. Trans. Roy. Soc., 197A (1896), 253–318.
Karl Pearson, “Mathematical Contributions to the Theory of Evolution. On the Law of Ancestral Heredity,” Proc. Roy. Soc., 62 (1898), 386–412. For a detailed account of Pearson's work see my 1970 M.Phil. thesis, Theories of Evolution of the Biometric School (University of London).
Ibid., p. 396.
Ibid., p. 401.
Hugo De Vries, The Mutation Theory (Chicago, 1910), pp. i, 104.
Karl Pearson, “Walter Frank Raphael Weldon 1860–1906,” Biometrika 5 (1906), 19.
W. F. R. Weldon, “On Certain Correlated Variations in Carcinus moenas,” Proc. Roy. Soc., 54 (1893), 329.
Karl Pearson, The Ethic of Freethought (London, 1887), p. 320.
Bateson, Materials for the Study of Variation. A good account of Bateson's pre-Mendelian work is given in chapter one of E. A. Carlson, The Gene: A Critical History (London, 1966). See also W. Coleman, “Bateson and Chromosomes: Conservative Thought in Science”, Centaurus, 15 (1970), 228–314. Coleman is concerned primarily to explain Bateson's opposition to the chromosome theory, but in so doing gives an account of the development of Bateson's thought patterns.
Before his move to University College London in 1891 Weldon had been lecturer in invertebrate morphology at Bateson's Cambridge college, St. John's, and, according to Mrs. Bateson, was at the time Bateson's “most intimate friend.” Weldon was instrumental in securing a grant for Bateson to study at the Chesapeake Bay Zoology Station under W. K. Brooks. Brooks, unlike Weldon, was not committed to the evolutionary insignificance of discontinuous variation, and it appears to have been during his American period that Bateson formulated his notions of evolutionary discontinuity. (See W. Bateson and others, “William Keith Brooks. A Sketch of His Life by Some of His Former Pupils and Associates,” J. Exp. Zool., 9 [1910], 1–52). Bateson's adoption of new ideas led to a rift with Weldon, for Mrs. Bateson records that “extreme divergence of their views undermined this friendship which later dissolved in bitterness.” Weldon certainly studied all that Bateson wrote, as instanced by his unfavorable review of the Materials in Nature, 50 (1894), 25–26. It is interesting to note that Galton wrote favorably of Bateson's work in his “Discontinuity in Evolution,” Mind, n.s., 3 (1894), 362–372.
Bateson, Materials for the Study of Variation, pp. 1–17.
Darwin, The Origin of Species, p. 321, sentences 6–7.
Bateson, Materials for the Study of Variation, p. 63.
Ibid., p. 61.
Pearson, The Life... of Francis Galton, pp. iiia, 287.
Pearson, “Walter Frank Raphael Weldon,” p. 24.
W. F. R. Weldon, “An Attempt to Measure the Death Rate Due to the Selective Destruction of Carcinus moenas with Respect to a Particular Dimension”, Proc. Roy. Soc., 57, (1895), 360–379.
W. F. R. Weldon, “Remarks on Variation in Animals and Plants”, Proc. Roy Soc., 57 (1895), 379–382.
In Weldon's terminology, if a population representable by a frequency curve with a median ordinate y 1 and a standard deviation (S.D.) σ1 was reduced symmetrically about the median, to another with a median ordinate y 2 and standard deviation σ2, then the death rate would be regarded as consisting of two parts—a nonselective part which reduced the population y 1 σ1 to the population y 2 σ1, and a selective part, responsible for reducing the population y 2 σ1 to the population y2 σ2.
Weldon, “Remarks on Variation”, p. 381.
Pearson, “Walter Frank Raphael Weldon”, p. 26.
In the Galton papers, which are kept at University College London, there are several letters from Weldon to Galton which mention other, critical letters sent to the committee by Bateson. These letters are not very instructive, and so far I have not succeeded in tracing the letters which Weldon refers to. I would like to thank the Librarian for permission to examine these papers.
Nature, 54 (1896), 245, 294, 366, 413.
Ibid., 460.
Nature, 55 (1896), 155.
Pearson, “Walter Frank Raphael Weldon,” p. 26. I would like to thank the Librarian of the Royal Society for permission to consult the minute book and other papers of the Evolution Committee.
Ibid. In a footnote, Pearson remarks that “no sufficiently general formula of growth can yet be applied to allow of the completion of Weldon's work in this direction.”
Report of the British Association for the Advancement of Science (1898), pp. 887–902.
Karl Pearson, Phil. Trans. Roy. Soc., 197A (1896), 257.
Karl Pearson, The Grammar of Science 2nd ed. (London, 1900), p. 408. In this work Pearson expounded his phenomenalistic philosophy of science. Weldon sympathized with Pearson's view that statements should be analyzed for their observational content. (Pearson, for instance, regarded scientific statements containing “theoretical” terms referring to unobservable entities—e.g., “atom”—as logically equivalent to a concatenation of statements which referred only to the sense impressions of some observer.) Thus we find Weldon consciously avoiding traditional Darwinian terminology, and instead of speaking of characters as being “useful” or “adaptive,” he speaks only of their effect on death rate. This methodological outlook is surely another reason for Weldon's undertaking death rate studies; it must have impressed him with the necessity for analyzing Darwin's statements about “the great and complex battle for life” for their observational content, and also for testing this content empirically. Certainly the Biometricians were characterized by a devotion to mathematics and to the formulation of a metaphysics-free science. See, for example, the editorial to the first number of their own journal, Biometrika (1901). Pearson did not use the method he described in any field investigation of death rates.
Pearson spoke of the death rate as composed of two components: a constant part, (1-m/n), and a selective part, (m/n.df/d5).
Pearson, The Grammar of Science, p. 408.
W. F. R. Weldon, “A First Study of Natural Selection in Clausilia laminata” Biometrika, 1 (1901), 109–124.
The distance of the plane of section from the reference plane was determined as follows: Suppose that in Fig. 4 AC was not 5 mm but 4.68 mm long, and that the next columellar radius AC′ was 5.27 mm long. Then, assuming that the columellar spiral was sensibly equiangular through 180°, the angle between the section and the reference plane would be % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% aI1aaccaGae8hiaaIae8hiaaIaeyOeI0IaaGinaiaac6cacaaI2aGa% aGioaaqaaiaaiwdacaGGUaGaaGOmaiaaiEdacqGHsislcqWFGaaica% aI0aGaaiOlaiaaiAdacaaI4aaaaiab-bcaGiGacIhacqWFGaaicaaI% XaGaaGioaiaaicdadaahaaWcbeqaaiaaicdaaaGccqWFGaaicqGH9a% qpcqWFGaaicaaIWaGaaiOlaiaaiwdacaaI0aGaaGOmaiaaisdacqWF% GaaiciGG4bGae8hiaaIaaGymaiaaiIdacaaIWaWaaWbaaSqabeaaca% aIWaaaaOGaaiOlaaaa!56C5!\[\frac{{5 - 4.68}}{{5.27 - 4.68}} \operatorname{x} 180^0 = 0.5424 \operatorname{x} 180^0 .\]. Since all measures in any section were 180° apart, the positionof one relative to the reference plane determined that of all the others.
Weldon, “A First Study,” p. 124. I would like to thank Dr. R. C Olby of the University of Leeds for having drawn my attention to the work of H. C. Bumpus, who also studied death rates. See, e.g., his “The Elimination of the Unfit as Illustrated by the Introduced Sparrow Passer domesticus,” Woods Hole Mar. Biol. Lab. Lect. (1898), 209–226. Bumpus's work is discussed in chap. 7 of J. Maynard Smith's The Theory of Evolution (Penguin Books, 1958). His result was similar to Weldon's in that he found evidence of a selective elimination of extremes. With selection following this pattern, one might expect the successive generations of a population to become less and less variable, but Smith explains why this process does not lead necessarily to genetic uniformity among a population's members. Weldon, in his paper, did not mention the work of Bumpus. It is interesting to note that in his later paper, “Note on a Race of Clausilia itala,” Biometrika, 3 (1903), 299–307, Weldon reported that he had been unable to find evidence of selective destruction among the C. itala taken from Brescia.
See above, nn. 24–27.
See above n. 18.
See above, n. 9. Galton in 1879 (see above n. 18) had offered what was in effect a mathematical reformulation of Jenkin's point, but it was formulated in ignorance of the mathematics of multiple regression. These are explained in C. E. Weatherburn, A First Course in Mathematical Statistics (Cambridge, 1968), pp. 242–260.
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Norton, B.J. The biometric defense of Darwinism. J Hist Biol 6, 283–316 (1973). https://doi.org/10.1007/BF00127611
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DOI: https://doi.org/10.1007/BF00127611