SELECTION ON THE VARIABILITY AND CORRELATION OF ORGANS. 
43 
Hence if we put = ‘5, and r = ’4, 
I's-i = 
T8 + + Pjo) 
'68 + ■32//q®(l + Pjj) 
(Ixxxii.). 
The following table will sulEce to indicate the changes which take place, when we 
give a series of A^aliies to /x, and Thus the first row gives the influence of selecting 
parents without any assortative mating. We see that with increasing stringency of 
selection the reduction of correlation is very considerable, and that with such selection 
the influence of assortative mating becomes less and less. Nevertheless, assortative 
mating can produce quite sensible results, if there be little or no selection. I am, 
indeed, inclined to think that a good deal of the high values found for the fraternal 
colour correlation in the thorouo’hbred foals"* is due to much ass(U’tative C()lour matino- 
o o 
in sire and dam. Of course it cannot be all due to this source. 
Values of Fraternal Correlation with Parental Selection. 
p.l=l. 
P-\ = 'S- 
/'■i= 
Pi = ■ t- 
/n=-2. 
P-i = 0. 
P\i = 0 
•5000 
•4349 
•3712 
■3162 
•2783 
•2647 
Pl-2 = • 1 
•5155 
•4477 
• 3802 
•3209 
•2796 
•2647 
n 
/>12= - 
•5301 
• 4599 
• 3889 
-.3256 
•2809 
•2647 
Pl2 = ■ 3 
• 5438 
•4716 
•3974 
• 3303 
•2823 
•2647 
Pl2= -5 
•5690 
•4935 
•4137 
•3392 
• 2849 
•2647 
Pl2= 1 
•6212 
•5411 
•4508 
• 3609 
•2914 
•2647 
On the whole, I think, we may conclude, so far as the relative influences of sexual 
selection in the form of assortative mating and natural selection go, that: 
Both sexual and natural selection can sensildy 'modify the intensity of inheritance 
as measured hy the coefficient of correlation, the former tends to raise, the latter to 
lower, its intensity. But the effect of the latter, if at edl stringent, is to completely 
mash the effect of the former. 
In fact, we may write 
l-., = 1 _ 
1 — 2/'” + 2r-fif{l + Pjo) 
Hence the smaller yf pf, the smaller will be fraternal correlation. This 
varies as the square of and only as the linear power of 1 + p^o. Thus we see at once 
why stringency of selection is far more potent than assortative mating. 
Illustkatiox hi.— To fnd the hifuence of selecting two organs A and B in 
a parent, on the correlation of the like organs A' and B' in the offsjyring. 
Let the organs in the parent be denoted by 1 and 2, and in the offspring by 3 and 4. 
Suppose the organic correlation of the two organs in the general population to be ? 
* ‘ Phil. Trans.,’ A, voL 195, p. 93. 
G 2 
