PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 259 
The importance of determining whether there is any correlation between repro¬ 
ductivity and a given organ of either parent appears to be great. For, if there be, it 
is not easy to understand how, even in the absence of both natural and sexual, 
selection, a population can remain in a stable state. For example, suppose the mean 
father or the mean mother or both to be taller than the mean man or the mean 
woman or both, then this reproductive selection would appear to involve a gradual 
increase of height in the population in the same manner as selective breeding of 
animals by man might do. It is probable, therefore, that if reproductive selection be 
demonstrated by a finite value of the correlation constants, the instability of the 
population which results is partially or completely screened by natural selection.*' 
( f ) Heredity. —Given any organ in a parent and the same or any other organ in 
its offspring, the mathematical measure of heredity is the correlation of these organs 
for pairs of parent and offspring. If the organs be the same for parent and offspring, 
the heredity may be spoken of as direct, if they be different as cross. The word organ 
here must he taken to include any characteristic which can he quantitatively measured. 
If the organs are not those of parent and offspring, but of any two individuals 
with a given degree of blood relationship, the correlation of the two organs will 
still he the proper measure of the strength of heredity for the given degree of 
relationship. Cf. § 6. 
(g.) Regression .—Regression is a term which has been hitherto used to mark the 
amount of abnormality which falls on the average to the lot of offspring of parents of 
a given degree of abnormality. The mathematical measure of this special regression 
is the ratio of the mean deviation of offspring of selected parents from the mean of 
all offspring to the deviation of the selected parents from the mean of all parents. 
This may be further elucidated as follows :—Let parents, having an organ or charac¬ 
teristic of given deviation from the average or normal, be termed a “parentage/’ let 
the offspring of a parentage be termed a “ fraternity.” Then the coefficient of 
regression may be defined as the ratio of the mean deviation of the fraternity from 
the mean offspring to the deviation of the parentage from the mean parent. Both 
parentage and fraternity may be either male or female. It will he noted that we 
have so framed our definition of regression, that it marks the deviation of the 
fraternity from the filial and not the parental mean. We are thus able to allow for 
secular natural selection and reproductive selection. We shall see in the sequel that 
the coefficient of regression is a function of the variations in parents and offspring, 
and further of the correlations which define parental heredity and assortative mating. 
Further, as in heredity, the deviation or abnormality in parentage and fraternity may 
be measured with respect to the same or different organs ; we have thus direct and 
cross regression. 
From this special definition of regression in relation to parents and offspring, we 
* I hope shortly to publish a paper on “ Reproductive Selection in Man,” and show how completely 
it appears to screen Natural Selection in the case of civilised man. 
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