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Karl pearson's mathematization of inheritance: From ancestral heredity to Mendelian genetics (1895–1909)

Pages 35-94 | Received 20 Jun 1996, Published online: 18 Sep 2006

  • Punnett , Reginald . August 1916 . Referee Report [for R. A. Fisher's paper] on the Correlation between Relatives on the Supposition of Mendelian inheritance August , 8 Library of the Royal Society/RR.1916.
  • Fisher , R.A. 1936 . Has Mendel's work been Rediscovered? . Annals of Science , 1 : 115 – 137 .
  • See Bowler Peter The Mendelian Revolution. The Emergence of Hereditarian Concepts in Modern Science and Society London 1984 103 103 112; Augustine Brannigan, ‘The Reification of Mendel’, Social Studies of Science, 9 (1979), 422–54 (see 422–9); Robert Olby, ‘Mendel no Mendelian’, History of Science, 17 (1979) 53–72; reprinted in Origins of Mendelism, 2nd edn, (London, 1985), 253.
  • Brannigan . 1984 . The Mendelian Revolution. The Emergence of Hereditarian Concepts in Modern Science and Society 422 – 422 . London
  • Bateson , William . 1902 . Mendel's Principles of Heredity: A Defence Cambridge see especially 104–208, and William Ernest Castle, ‘The laws of heredity of Galton and Mendel, and some laws governing race improvement by selection’, Proceedings of the American Academy of Arts and Science, 39 8 (November 1903), 224–32.
  • Haldane , J.B.S. 1957 . Karl Pearson . Speeches Delivered at a Dinner held at University College London on the Occasion of Karl Pearson's Centenary Celebration , May in 13 (privately issued by the Biometrika Trustees, 1958); Lancelot Hogben, Statistical Theory: The Relationship of Probability, Credibility and Error (London, 1957), 235; Julian Huxley, Evolution: The Modern Synthesis, 2nd edn (London, 1963), 24; Reginald Punnett, ‘Early days of genetics’, Heredity, 4 (1950), 2–10; A. H. Sturtevant, A History of Genetics (New York, 1959), 58; and Sewall Wright, ‘The foundations of population genetics’ or ‘Evolution in Mendelian populations’ Genetics, 16 (1934), 97–159 (98).
  • Box , Joan Fisher . 1978 . R. A. Fisher. The Life of a Scientist 3 – 3 . New York Bernard Norton, ‘Biology and Philosophy: The Methodological Foundations of Biometry’, Journal of the History of Biology, 8 (1975), 85–93; Olby (note 3), 129; William Provine, The Origins of Theoretical Population Genetics (Chicago, 1971), 69; R. G. Swinburne, ‘Galton's Law: Formulation and Development’, Annals of Science, 24 (1965), 227–46.
  • Froggatt , P. and Nevin , N.C. 1971 . The “Law of Ancestral Heredity and the Mendelian-Ancestrian Controversy in England 1889–1906 . Journal of Medical Genetics , 8 : 1 – 36 . (see especially 20–4).
  • Haldane . 1957 . Karl Pearson . Speeches Delivered at a Dinner held at University College London on the Occasion of Karl Pearson's Centenary Celebration , May : 9 – 9 . in 13 Norton (note 7), 87–8; Olby (note 3), 129.
  • Pearson , Karl . 1904 . Mathematical Contributions to the Theory of Evolution. XII. On the generalised theory of alternative inheritance with special references to Mendel's laws . Philosophical Transactions of the Royal Society , A 203 : 53 – 86 . Pearson read the paper on 26 November 1903. Idem, ‘Mendel's Law’, Nature, 70 (27 October 1904), 626–7.
  • Karl , Pearson . 1909 . The theory of ancestral contributions of a Mendelian population mating at random . Proceedings of the Royal Society , 81 : 225 – 229 .
  • See, for example Swinburne R. A. Fisher. The Life of a Scientist New York 1978 Provine (note 7); Norton (note 7); Donald Mackenzie, Statistics in Britain 1865–1930: The Social Construction of Scientific Knowledge (Edinburgh, 1981).
  • For a fuller account of the nineteenth-century mathematics training, see Warwick Andrew Exercising the student body. Mathematics and Athleticism in Victorian Cambridge Carnal Knowledge: The Physical Representation of intellectual Selves Lawrence Chris Shapin Steven Chicago in forthcoming
  • See Pearson Karl Gresham Lecture on ‘The Geometry of Statistics (A) 1891 KP:UCL/49
  • Pearson , Karl . 1902 . On the fundamental conception of biology . Biometrika , 1 : 322 – 344 . (324).
  • Magnello , M. Eileen . 1996 . Karl Pearson's Gresham lectures: W. F. R. Weldon, speciation and the origins of Pearsonian statistics . British Journal for the History of Science , 29 : 43 – 63 .
  • Magnello , M. Eileen . 1996 . Karl Pearson's Gresham lectures: W. F. R. Weldon, speciation and the origins of Pearsonian statistics . Birtish Journal for the History of Science , 29 : 43 – 63 .
  • Magnello , M. Eileen . “ Karl Pearson: Quantification, Mathematical Statistics and the transformation of medical research in the twentieth century ” . In Mathematical Developments in the History of Medicine Edited by: Magnello , M. Eileen and Hardy , Anne . in (in preparation)
  • See, for example Castle William Ernest Has Mendel's work been Rediscovered? Annals of Science 1936 1 221 221 Ruth Schwartz Cowan, ‘Nature and Nurture: The Interplay of Biology and the Politics in the work of Francis Galton’, Studies in the History of Biology, 1 (1977), 133–208 (197); Peter Froggatt and N. C. Nevin, ‘Galton's “Law of Ancestral Heredity”: Its influence on the Early Development of Human Genetics’, History of Science, 10 (1971), 1–27 (passim); Punnett (note 6), 2 and 9; Swinburn (note 7), 21–2 and 30.
  • Donald Mackenzie mentions multiple regression and the tetrachoric correlation whilst Steve Stigler addresses both multiple regression and multiple correlation Mackenzie (note 12), 67–8 Stigler Steve The History of Statistics. The Measurement of Uncertainty before 1900 Cambridge, MA 1986
  • Swinburne . 1978 . R. A. Fisher. The Life of a Scientist 20 – 21 . New York
  • Swinburne . 1978 . R. A. Fisher. The Life of a Scientist 30 – 30 . New York
  • Froggatt and Nevin . 1971 . “ Galton’s “Law of Ancestral Heredity”: Its influence on the Early Development of Human Genetics ” . In History of Science Vol. 10 , 8 – 8 .
  • Peter Bowler (personal correspondence, 16 May 1991). See also Froggatt Nevin Evolution: The History of an Idea Berkeley and Los Angeles 1984 240 240
  • Darwin , Charles . 1868 . “ Provisional Hypothesis of Pangenesis ” . In The Variation of Plants and Animals under Domestication , Vol. II , 370 – 370 . John Murray . in page number refers to 2nd edn 1875
  • Darwin , Charles . 1868 . “ Provisional Hypothesis of Pangenesis ” . In The Variation of Plants and Animals under Domestication , Vol. II , 389 – 390 . John Murray . in page number refers to 2nd edn 1875
  • Galton , Francis . 1871 . Experiments in Pangenesis, by Breeding from Rabbits of a pure variety, into whose circulation blood taken from other varieties had previously been largely transfused . Proceedings of the Royal Society , 19 : 393 – 410 . (394).
  • Galton , Francis . 1871 . Experiments in Pangenesis, by Breeding from Rabbits of a pure variety, into whose circulation blood taken from other varieties had previously been largely transfused . Proceedings of the Royal Society , 19 : 396 – 396 .
  • Galton , Francis . 1871 . Experiments in Pangenesis, by Breeding from Rabbits of a pure variety, into whose circulation blood taken from other varieties had previously been largely transfused . Proceedings of the Royal Society , 19 : 404 – 404 .
  • Darwin , Charles . 1871 . Pangenesis . Nature , 3 April : 502 – 502 . 27
  • Galton , Francis . 1872 . On Blood Relationships . Proceedings of the Royal Society , 20 : 394 – 402 . (395).
  • Geison , Gerald . 1969 . Darwin, Heredity and the Evolution of his Hypothesis of Pangenesis . Journal of the History of Medicine , 24 : 375 – 411 . (377).
  • Galton , Francis . 1876 . Theory of Heredity . Journal of the Anthropological Institute of Great Britain and Ireland , 5 : 328 – 348 . (330).
  • Galton , Francis . 1890 . Sexual Generation and Cross Fertilisation unpublished manuscript FG: UCL, 2.
  • Swinburne . 1978 . R. A. Fisher. The Life of a Scientist 15 – 15 . New York For a further account of theories of inheritance in the nineteenth century see Olby (note 3). Weismann's theory appeared in various articles in the 1880s, and in his Germ Plasm in 1893. Weismann thought that ‘the germ plasm of an organism was developed entirely from that of its parents, and that there was no influence by bodily parts on the germ-plasm’.
  • Swinburne . 1978 . R. A. Fisher. The Life of a Scientist 15 – 15 . New York
  • Bowler . 1984 . The Mendelian Revolution. The Emergence of Hereditarian Concepts in Modern Science and Society 70 – 70 . London Cowan (note 16) has also discussed Galton's statistical work, but she has rather overemphasized the role of eugenics in the development and use of Galton's statistics. Though Galton discussed how statistics could be, in principle, used for problems of eugenics, his statistical methods were, in practice, devised for his anthropometric and hereditarian work.
  • Darwin . 1871 . Pangenesis . Nature , 3 April : 368 – 368 . 27
  • Galton , Francis . 1908 . Memories of my Life 300 – 300 . London
  • Galton . 1876 . Theory of Heredity . Journal of the Anthropological Institute of Great Britain and Ireland , 5 : 330 – 330 . Derek Forest has traced Galton's interest in heredity to 1864 when Galton began writing his papers on ‘Heredity Talent’ which appeared in Macmillan Magazine in the following year. D. W. Forest, Francis Galton: The Life and Work of a Victorian Genius (New York: Taplinger Publishing, 1974), 85. See also Francis Galton, ‘Heredity Talent and Character’ Macmillan Magazine, 12 (1865), 157–66, and ‘Typical Laws of Heredity. Part I’, Nature, 15 (5 April 1877), 492–3.
  • Galton . 1876 . Theory of Heredity . Journal of the Anthropological Institute of Great Britain and Ireland , 5 : 330 – 330 .
  • Galton , Francis . 1877 . Typical Laws of Heredity, Part III . Nature , 15 April : 532 – 537 . 19 (532).
  • Galton , Francis . 1877 . Typical Laws of Heredity, Part III . Nature , 15 April : 532 – 533 . 19
  • Galton , Francis . 1885 . Regression towards Mediocrity in Hereditary Stature . Journal of the Anthropological Institute of Great Britain and Ireland , 15 : 246 – 263 . (252–3).
  • Pearson , Karl . 1930 . Life, Letter and Labours of Francis Galton Vol. IIIA , 20 – 20 . Cambridge (3 vols in 4 parts)
  • Pearson , Karl . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 253 – 318 . (288).
  • Pearson , Karl . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 307 – 307 .
  • In this paper, which he read at the Royal Institution on 27 February 1874, he ordered the stature of boys at Marlborough College into ‘quartiles’: the first quartile, q1, was at the 25th percentile, the second, q2, was the median which was at the 50th percentile and the third, q3, was at the 75th percentile. From these quartiles, he devised what he termed the semi-interquartile range; this was found by taking the difference between q1 and q3. Galton Francis On a Proposed Statistical Scale Nature March 1874 9 342 343 5
  • Galton , Francis . 1886 . Family Likeness in Stature with Appendix by J. D. Hamilton Dickson . Proceedings of the Royal Society , 40 : 42 – 71 . (43).
  • Galton , Francis . 1886 . Family Likeness in Stature with Appendix by J. D. Hamilton Dickson . Proceedings of the Royal Society , 40 : 53 – 53 .
  • Galton . 1876 . Theory of Heredity . Journal of the Anthropological Institute of Great Britain and Ireland , 5 : 302 – 302 .
  • Galton . 1876 . Theory of Heredity . Journal of the Anthropological Institute of Great Britain and Ireland , 5 : 302 – 303 .
  • Galton . 1885 . Regression towards Mediocrity in Hereditary Stature . Journal of the Anthropological Institute of Great Britain and Ireland , 15 : 260 – 260 .
  • Galton , Francis . 1888 . Co-relation and their Measurement Chiefly from Anthropometric Data . Proceedings of the Royal Society , 45 : 135 – 145 . (143).
  • Galton , Francis . 1888 . Co-relation and their Measurement Chiefly from Anthropometric Data . Proceedings of the Royal Society , 45 : 135 – 135 .
  • Galton , Francis . 1888 . Co-relation and their Measurement Chiefly from Anthropometric Data . Proceedings of the Royal Society , 45 : 143 – 143 .
  • Grove , William Robert . 1846 . Correlation of Physical Forces London Grove viewed correlation as a ‘mutual convertibility’ of forces that would enable him to establish (a non-mathematical) correlation between vital and physical forces. The physiologist, William Benjamin Carpenter (1813–85) used Grove's theory of correlation of forces four years later to determine relationships between electricity and magnetism. W. B. Carpenter, ‘On the Mutual Relations of the Vital and Physical Forces’, Philosophical Transactions, 140 (1850), 744, as cited in Vance M. D. Hall, ‘The Contribution of the Physiologist William Benjamin Carpenter (1813–1885), to the Development of the Principles of the correlation of forces and the conservation of Energy’, Medical History, 23 (1979), 135–45 (143).
  • Darwin . 1868 . “ Provisional Hypothesis of Pangenesis ” . In The Variation of Plants and Animals under Domestication , Vol. II , 347 – 347 . John Murray . in see also 313–17.
  • Stigler . 1986 . The History of Statistics. The Measurement of Uncertainty before 1900 97 – 97 . Cambridge, MA
  • Pearson . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 307 – 307 .
  • Stigler . 1986 . The History of Statistics. The Measurement of Uncertainty before 1900 97 – 97 . Cambridge, MA
  • Edgeworth , F.Y. 1892 . Correlated Averages . Philosophical Magazine , 34 : 429 – 438 . 5th series
  • Weldon , W.F.R. 1890 . The variations occurring in Crangon vulgaris . Proceedings of the Royal Society , 47 : 445 – 453 .
  • See Magnello Karl Pearson's Gresham lectures: W. F. R. Weldon, speciation and the origins of Pearsonian statistics British Journal for the History of Science 1996 29 43 63 for a fuller account of Weldon's impact on Pearson's Gresham Lectures in 1892–3, which led to the creation of the Biometric School at University College, London, in October 1894.
  • Yule , G. Udny . 1895 . Notes of Karl Pearson's Lectures: 1894–1896 (“Correlation”) Vol. III , Yule's lecture notes have been bound in five volumes; he presented this set to the Department of Applied Statistics, University College London, shortly after Pearson's death in 1936, KP:UCL.
  • Pearson , Karl . June 1895 . Letter to Francis Galton June , 4 – 5 . 18 FG:UCL
  • Pearson , Karl . June 1895 . Letter to Francis Galton June , 6 – 6 . 18 FG:UCL
  • Pearson , Karl . June 1895 . Letter to Francis Galton June , 7 – 8 . 18 FG:UCL
  • See Stigler The History of Statistics. The Measurement of Uncertainty before 1900 Cambridge, MA 1986 281 281 who considered Galton's conceptual use of the normal distribution as ‘perhaps, the single major breakthrough in statistics in the last half of the nineteenth century’.
  • Pearson , Karl and Heron , David . 1913 . On Theories of Association . Biometrika , 9 : 139 – 315 . (164).
  • Weldon . November 1896 . Letter to Karl Pearson November , 1 – 1 . 21 KP:UCL
  • Pearson . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 253 – 318 . For details of Pearson's examples, see 296.
  • Pearson , Karl . 1895 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Proceedings of the Royal Society , : 69 – 71 . (Abstract) (70).
  • Pearson . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 292 – 292 .
  • Pearson . 1885 . Regression towards Mediocrity in Hereditary Stature . Journal of the Anthropological Institute of Great Britain and Ireland , 15 : 332 – 332 . Pearson would have most likely come across the word Geschwister in his work on folklore and literature in Germany where the word had certainly been used since at least the seventeenth century. See Hans Meier, ‘Welfare and Health of Children and Adolescents in Early Modern England and Southern Germany. The case of Bampton in Oxfordshire and Oettingen in Southern Germany in the 17th and 18th centuries’ (unpublished DPhil thesis, University of Oxford, 1995). The word ‘god-sibling’ was used in the seventeenth century in England as ‘someone invited to witness the birth for the subsequent purpose of the child's baptism’. See Adrian Wilson, ‘The ceremony of childbirth and its interpretation’ in Women as Mothers in Pre-industrial England, edited by Valerie Fildes (London, 1990), 68–107. I am grateful to Natsu Hattori for bringing this to my attention.
  • Pearson . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 240 – 241 .
  • Pearson , Karl . 1895 . Note on Regression and Inheritance in the Case of Two Parents . Proceedings of the Royal Society , 58 : 240 – 241 .
  • Pearson , Karl . 1895 . Note on Regression and Inheritance in the Case of Two Parents . Proceedings of the Royal Society , 58 : 272 – 272 .
  • Pearson , Karl . 1895 . Note on Regression and Inheritance in the Case of Two Parents . Proceedings of the Royal Society , 58 : 265 – 265 .
  • Edgeworth . 1892 . Correlated Averages . Philosophical Magazine , 34 : 194 – 204 . 5th series
  • Yule , G.U. 1897 . On the Theory of Correlation . Journal of the Royal Statistical Society , 60 : 833 – 833 .
  • Pearson . 1930 . Life, Letter and Labours of Francis Galton Vol. IIIA , 21 – 21 . Cambridge (3 vols in 4 parts)
  • Pearson . 1930 . Life, Letter and Labours of Francis Galton Vol. IIIA , 21 – 21 . Cambridge (3 vols in 4 parts)
  • Pearson . 1930 . Life, Letter and Labours of Francis Galton Vol. IIIA , 21 – 21 . Cambridge (3 vols in 4 parts)
  • Pearson . 1930 . Life, Letter and Labours of Francis Galton Vol. IIIA , 21 – 21 . Cambridge (3 vols in 4 parts)
  • Pearson . 1930 . Life, Letter and Labours of Francis Galton Vol. IIIA , 21 – 21 . Cambridge (3 vols in 4 parts) See also Karl Pearson, ‘Further remarks on the Law of Ancestral Heredity’, Biometrika, 8 (1911), 239–43; idem, ‘On the Multiple Correlation of Brothers, being a Note on Mr. J. O. Irwin's Memoir [‘The Further Theory of Francis Galton's Individual Difference Problem’] and on my statement of the Application of Galton's Difference Problem to the Determination of the Degree of Relationship of Brothers, made in August 1902’, Biometrika, 17 (1925), 129–41.
  • Pearson , Karl . 1903 . The law of ancestral heredity . Biometrika , 2 : 211 – 229 .
  • Cayley was the Sadlerian Professor of Pure Mathematics when Pearson was at Cambridge. Cambridge University Reporter (1878–9), 38. See Anon, Cayley Arthur Nature January 1895 51 323 323 31 John Michael Dubby, ‘Arthur Cayley’ in A Bibliographical Dictionary of Scientists, edited by Trevor Williams (London, 1969), p. 101.
  • Pearson . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 253 – 318 .
  • Pearson . 1896 . Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia . Philosophical Transaction of the Royal Society , A 187 : 253 – 318 .

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