414 
R. A. FISHER ON THE CORRELATION BETWEEN 
Supposing A determinate, we may determine the association coefficients f for 
r 2 r '2 f — ^ (iP - A'R)(i P -AR) , I 
1 1 /u “ prig — , y ^ n 
Hence 
f 1 
Pqf 18“ (T^Ap V M 
\ 
. -^y 2b ( 2 - 
-i+ 
iP — &R t 2 
! p ■ Y> 
and so 
T . A iP - &R 
1 - A p 
Similarly 
v v A »P - &R 
1 -A g 
and 
J =j- A - P --? (iP-KR) 
J 1-A Ipq V . 
(XXIII) 
(XXIY) 
So that the sense in which the mean value of the heterozygote is changed by 
assortative mating depends only on whether p or q is greater. In spite of perfect 
dominance, the mean value of the heterozygote will be different from that of the 
dominant phase. 
The value of the variance deduced from the expression 
Y = 2(PH + 2Q/J + R&K) 
reduces to a similar form. For evidently 
V = 2“ 2 + • 2(^P - *R)fr(» -j) + ~ m 
Hence 
v = °- 2 + tAh 2 ( xxv ) 
1 - A 
Therefore the equation for A finally takes the form 
/xr 2 = YA(1 - A) = A(1 - A)o- 2 + A 2 t 2 , 
and may be otherwise written 
A 2 e 2 — Atr 2 + /xr 2 = 0 (XXYI) 
Now, since the left-hand side is negative when A = 1, there can be only one root less 
than unity. Since, moreover, 
(/x - A 2 )r 2 = (A - A 2 )cr 2 ...... (XXVI, a ) 
it is evident that this root is less than m, and approaches that value in the limiting 
case when there is no dominance. 
A third form of this equation is of importance, for 
(XXVI, b ) 
which is the ratio of the variance without and with the deviations due to dominance. 
, A 2 
A_ t 2 t 2+ T=A t 
/ x A--A € - ^ ~ A t2 
1 - A 
