SELECTION OX THE YARTxlBILITY xLXD CORRELATION OF ORGANS. 
3!) 
Illustratiox I.— Tv find the Influence on the Intensity of Parental Herediiy of 
the Selection of Parents. 
Let the subscripts I, 2, 3 refer respectively to farther, mother, child. Let us first 
select one parent—say, the father—very stringently, i.e., sja^ ■= is small. Then we 
need onlv equations (xlix.) and (li.). These give us : 
,._ 
and 
= cr/ (1 ~ (1 ~ I\~) 
The first may he vnitten 
or, we see that iq- will decrease, as decreases. Thus if vqg = A we have for 
y ^ = 1/2, 1^3 = '2132, ^2/0"^ = '8367, 
p-j = 1/4, 1^3 = '1085, ^2/^2 — '7906, 
Pj = 1 / 8 , ri3 = "0545, —■’/h'2 ~ ' 7786 . 
It is clear, therefore, that the correlation of parent and child will be much reduced by 
such a selection. On the other hand, the regression coeificient will not Ije altered, ?.r., 
^ 2 lT 3 A‘i = have seen. Hence in problems of heredity, where we 
suspect a parent to have been highly selected, we should seek for the regression of son 
on parent rather than for the correlation. Thus in the case of Basset Hounds,some 
if not all the reduction in correlation between sire and ofispring may be due to 
selection of the sire. A test of whether the reduction in correlation is due to 
selection of a parent ought to be given by a comparison of .5/ and We cannot, 
I think, suppose, unless natural selection he very stringent, that cr^ difiers much from 
<T^. Hence it follows that ought generally to be large, if there be selection of 
a parent. We can hardly test this point eftectively in the case of the Basset Hounds, 
owing to the nature of the classification. In racehorses, although the sire appears 
to be far more selected than the dam, there is not a great reduction of the coefficient 
of correlation between sire and offspring,! 5^ appears to be less than but not so 
greatly and certainly less, that we can be surprised that the correlation of sire and 
offspring is not much less than we have found it for material in which selection of the 
father is certainly far less marked. We must accept the warning as to the reduction 
* ‘Roy. Soc. Proc.,’ vol. 66, p. 157. 
t See ‘Phil. Trans.,’ A, vol. 195, p. 93. 
