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\noindent{\bf Walter Frank Raphael WELDON}\footnote{Abridged version of an article
in the {\it Encyclopedia of Statistical Sciences (update)} and published
by kind permission of John Wiley \& Sons, Ltd.}\\
b. 15 March 1860 - d. 13 April 1906\\
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\noindent{\bf Summary.} Zoologist W.F.R. Weldon's efforts to make biology
more rigorous and
quantitative provided strong stimulus to K. Pearson, and through him the
Biometric movement and the laying of the foundations of much of modern
statistics.
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W.F.R. Weldon, born in Highgate (London),
was the second child of the journalist and industrial chemist,
Walter Weldon and his wife Anne Cotton. His father changed residences so
frequently that Weldon's early education was desultory until he became a
boarder in 1873 at Caversham near Reading. Weldon matriculated at University
College London (UCL) in the autumn of 1876 with the intention of pursuing a
medical career. During his time at UCL, he acquired a respectable knowledge of
mathematics from the Danish mathematician, Olaus Henrici, and attended the
lectures of the zoologist, E. Ray Lankester.. In the following year he
transferred to Kings College, London and on 6 April 1878, he entered St.
John's College, Cambridge as a bye-term student.
Once at Cambridge, he met the zoologist, Francis Maitland Balfour, and
subsequently gave up his medical studies for zoology. In 1881, he gained a
first-class degree in the natural science Tripos: in the autumn he left for
the Naples Zoological Station to begin the first of his studies in marine
biological organisms. Upon returning to Cambridge in 1882, he was appointed
university lecturer in Invertebrate Morphology, and in the following year
he married Florence Tebb. He became a founding member of the Marine
Biological Station in Plymouth in 1884 and resided there until 1887. From
1887 until his death in 1906, Weldon's work was centred around the development
of a fuller understanding of marine biological phenomena and, in particular,
the examination of the relationship between various organs of crabs and
shrimps to determine selective death rates in relation to the laws of growth.
During his first five years at the Marine Biological Station, Weldon's
investigations were directed to the study of classification, morphology and
the development of Decapod crustacea. His only work on invertebrate
morphology contained an account of the early stage of segmentation and the
building of the layers of shrimp. Weldon was both a master of histological
techniques and a powerful and accurate draughtsman. In 1889 he succeeded
E. Ray Lankester in the Joddrell Chair of Zoology at University College
London.
During this time Weldon read Francis Galton's
{\it Natural Inheritance}.
In this book Galton (q.v.) had shown that the frequency distributions of the
average size of certain organs in man, plants and in moths were normally
distributed. Similar investigations had been pursued by the Belgian
statistician, Adolphe Quetelet (q.v.), whose work was confined to ``civilised man".
Weldon was interested in investigating the variations in organs in a species
living in a wild state which acted upon natural selection and other
destructive influences.
When Galton was writing on heredity in 1889, he had predicted that
selection would not change the shape of the normal distribution; he expected
that his frequency distributions would remain normally distributed in all
cases whether or not animals were under the action of natural selection.
Around this time, Weldon began to study the variation of four organs in the
common shrimp (Crangon vulgaris) and he collected five samples from waters
fairly distant from Plymouth. His statistical analysis which he published
in 1890, confirmed Galton's prediction. Shortly after the paper was
published, Weldon was elected a Fellow of the Royal Society.
During the Easter vacation of 1892, Weldon and his wife collected
23 measurements from 1000 adult female shore crabs (Carcinus m{\oe}nas) from
Malta and the Bay of Naples. Weldon discovered that all but one of the 23
characters he measured in the Naples group were normally distributed; he
found that this one character (the frontal breadth of the carapace) was
instead a `double-humped' (i.e., bi-modal) curve. His first attempt to
interpret the data involved breaking up the curve into two normal
distributions as Galton had advocated. Weldon then approached Karl
Pearson (q.v.)
(who had been appointed as Professor of Mechanism and Applied Mathematics at
UCL in 1884) for assistance with interpreting his data. At that time, Pearson
was teaching applied mathematics to engineering students at UCL and was also
giving his Gresham lectures of Geometry at Gresham College. (This ancient
educational foundation, located in the City of London, offered lectures to
members of the public on an annual basis.)
By the end of 1892 Pearson began to devise a probability system of
curve fitting for Weldon's data, and he used this material in his Gresham
lectures in the following year. From his analysis of Weldon's data, Pearson
concluded that two separate species had arisen. Up until the middle of the
nineteenth century species were defined in terms of types or essences. Charles
Darwin's recognition that species comprised different sets of `statistical'
populations rather than types or essences, prompted a reconceptualization of
statistical populations by Pearson and Weldon. Moreover, this required the
use of new statistical methods. Following Pearson's work on curve fitting of
asymmetrical distributions, in his Gresham lecture of 23 November 1893, he
devised a goodness of fit test for asymmetrical distributions for Weldon's
data. These statistical innovations formed much of the basis of Pearson's
work in the nineteenth century, and in 1900 Pearson devised the chi-square
$({\chi}^2 , P)$ goodness of fit test (his single most important contributions to
modern statistical theory). When Pearson was working out the mathematical
properties of simple correlation and regression in 1896, Weldon suggested to
Pearson the idea of a negative correlation. (Galton had used positive
correlations only.) Pearson regarded Weldon as `one of the closest friends
he ever had'. Their relationship could be characterised by an emotional and
intellectual intimacy that engendered a symbiotic alliance. It is thus not
surprising that one of the most extensive sets of letters in Pearson's
archives are those of Weldon and his wife Florence, which consist of nearly
1,000 pieces of correspondence.
Though not a statistician by training, it was Weldon's interest in
finding statistical tools to demonstrate empirical evidence of Darwin's theory
of natural selection in marine organisms that provided the impetus to
Pearson's development of the modern theory of statistics. Weldon also
provided Pearson with the basis of a programme that underpinned the
construction of his statistical innovations in the 1890s which, in turn,
provided the infrastructure for Pearson's statistical developments in the
twentieth century. Weldon's influence, which exceeded that of any other
person in the emergence and development of Pearsonian statistics, arose from
the following factors: he provided the stimulus for new statistical methods
by asking Pearson biological and statistical questions that could be
answered only by devising a new statistical approach, he offered continual
moral support as well as encouragement; and he promulgated the Pearsonian
corpus of statistics to `serious students of animal evolution' throughout
the 1890s and until his death in 1906. Though some of the statistical work
of John Venn (q.v.) and Francis Ysidro
Edgeworth (q.v.) played a role in Pearson's early
work on probability, there seems to have been no other person whose
influence on the emergence and development of Pearsonian statistics was as
rapid and immediate in its impact as that of Weldon.
When Weldon went up to Oxford in 1899, to take up the Linacre Chair
of Comparative Anatomy, he carried on the biometric tradition by gathering
a number of students who began to look for empirical evidence of natural
selection acting upon various animals and plants. Despite Weldon's move, he
and Pearson made arrangements to be together every year during the Easter
and Christmas vacations and throughout the summer months. They continued
their collaborative work investigating biometrical problems such as natural
selection, inheritance and, in particular, Mendelian inheritance. These joint
biometrical projects were pursued until Weldon's untimely death in
Oxford in 1906.
Weldon's death was for Pearson the single greatest loss in his life.
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\noindent{\bf References}
\noindent Bourne, Gilbert Charles (1906). Walter Frank Raphael Weldon.
(1860-1906). {\it Dictionary of National Biography}. Oxford University Press,
629-630.
\noindent Cowan, Ruth Schwartz (1981). Walter Frank Raphael Weldon. (1860-1906).
{\it Dictionary of Scientific Biography},
ed. Charles C. Gillispie, Vol. XIV, Charles Scribner's Sons, New York,
251-252.
\noindent Magnello, M. Eileen (1996). 'Karl Pearson's Gresham lectures:
W.F.R. Weldon, speciation and the origins of Pearsonian Statistics', {\it British
Journal for the History of Science}, {\bf 29}, 43-63.
\noindent Magnello, M. Eileen (Forthcoming). 'Karl Pearson's mathematisation
of inheritance. From Galton's ancestral heredity to Mendelian Genetics
(1895-1909)', {\it Annals of Science}.
\noindent Pearson, Karl (1906). Walter Frank Raphael Weldon. 1860-1906.
{\it Biometrika}, {\bf 5}, 1-52. Also reprinted in E.S. Pearson and Maurice Kendall,
{\it Studies in the History of Statistics and Probability}, Volume 1,
Griffin, London, 1970.
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\hfill{Eileen Magnello}
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