2 
riiOFESSOK K. PEARSON ON THE INFLUENCE OF NATURAL 
(1.) Introductory. On the Influence of Selection upon Correlation. 
At an earlier stage in the development of the statistical theory of evolution it 
was suggested that the coefficient of correlation (Galtox’s function) might he found 
constant for all races of the same species—in fact, it was considered possible that this 
coefficient might be the long-soiight-for criterion of identity in species. Professor 
Weldox, following up this suggestion of Mr. Galtox’s, then made the elaborate 
series of measurements on crabs with whicli his name will ahvays he closely associated. 
To a first approximation these researches seemed to confirm the j^ossihility of 
Galton’s function being a true criterion of species. When, however, a finer 
mathematical test was applied to Professor Wei.don’s observations as well as to 
other statistical series for organs in man,'^ it became clear that the coefficient of 
correlation varied from local race to local race, and could not be used as a criterion 
of species. A slight investigation undertaken in the summer of 1896 convinced me 
that the coefficient of correlation between any two organs, is just as much peculiar and 
characteristic of a local race as the means and variations of tliose organs. In fact, 
if local races he the outcome of natural selection, then their coefficients of correlation 
must ill general differ. The object of the present paper is to show, not only that 
natural selection must determine the amount of correlation, hut that it is jirohably 
the chief factor in the production of correlation. If selection, natural or artificial, 
he cajiahle of producing correlation, then it seems impossible to regard all correlation 
as evidence of a causal nexus, f although the converse proposition that all causal 
nexus denotes correlation, is undoubtedly the most jihilosophical method of regarding 
causality. 
In dealing with the influence of selection on correlation, I shall supjDOse the distri¬ 
bution of complex groups of organs to follow the normal correlation surface—the 
generalised Gaussian law of frequency. I shall further assume the selection surfaces 
to be normal in character. Neither of these assumjjtions is absolutely true, but the 
Gaussian law in a good many cases describes the fi-equency sufficiently closely to 
enable us to obtain fair numerical results by its application. Probably in all cases it 
will enable us to reach qucditative if not accurate quantitative theoretical deductions. 
I have the less hesitation in asserting this, as Mr, G. U. Yule has recently succeeded 
in deducing the chief formulm for correlation and regression as given by the 
Gaussian law from general principles, which make no appeal to a special law of 
frequency. I 
* “ Mathematical Contributions to the Theory of Evolution.—III.,” ‘Phil. Trans.,’ A, voi. 189, 266 
and 280. See also E. Warren, “Variation in Purtunus depurator,” ‘Roy. Soc. Proc.,’ vol. 60, 
pp. 233-4. 
t See a series of letters in ‘ Nature,’vol. 54, 1896, arising from a discussion upon a paper by A. R. 
Wallace. 
J ‘Roy. Soc. Proc.,’ vol. 60, p. 477. 
