42 
PROFESSOR K. PEARSON ON THE INFLUENCE OF NATURAL 
Illustration II.— To Find the Influence of Parental Selection on Modifying 
Fraternal Correlation. 
I^et the subscripts 1, 2 represent the parents, and 3 and 4 two of their offspring. 
Let us first select one parent only, tlie selection being given as before by Si/o-j = 
Our formuke will now lie (liv.) and (Ivi.). So far as the change in variability is 
concerned, we have already discussed it under our first illustration, so we need only 
consider : 
Vmx = 
v/ {1 - (1 - pd) ’-iClT 1 - a - p?) ri/} • 
Now 7’j.j = if tlie offspring are of one sex ; hence : 
^’i.T (f 
(Ixxvii.). 
Li — 
f '^’ 1 . 3 “ (1 “ /^i") 
If we take = ’4 and r.^^ = '5 as reasonable values, we have 
•34 + T6pj'’ 
(Ixxviii.). 
Li — 
84 + -16;.I. 
Thus I'si, Avill lie greatest when is greatest, i.e., Avhen there is no selection, and 
will decrease with p^ until it reaches ’4048, when p^ = 0, or there is selection of 
fathers of one value of the character only."^ 
The selection of one jiarent only does not, therefore, immensely modify the 
correlation of brothers. Still, if we Avork sensibly with one class of the community— 
say, men of genius—we should expect to find their sons rather less like each other 
tiian if we Avorked Avith the general population of brothers. 
Noav let us select both parents. Here again the A^ariability of the offspring has 
already been dealt wdth. We are concerned wdth equation (Ixix.), and Ave shall put 
7-J3 = =; 7’23 = = r, or make jiarental influence equijiotent for the two sexes. 
Hence 
r 
+ '^'12 ’ 
^13 — /^33 — Ar — Ar — ^ ^ 
where r is the parental correlation, and the coefficient of assortatiAm mating. 
Hence Ave find 
L-i — 
{1 py T 1 pv + 2 (7'^2 
1 — /3^ {1 — pd + 1 — pd + 2 (rjo — P 10 P 1 P 2 )} 
(Ixxx.). 
To reduce to numbers, suppose p^ = p.„ and = 0 for the general population. We 
have 
’’m — 2r” {1 — pd(l + P13)} 
Lr — 
l_2rHl-pd(l + />i2)} 
(Ixxxi.) 
In general the value of rsi ranges from 734 down to 
734 - I'lS' 
l-ri3- 
