404 
R. A. FISHER ON THE CORRELATION BETWEEN 
mean by d. The steps from recessive to heterozygote and from heterozygote to 
dominant are genetically identical, and may change from one to the other in passing 
from father to son. Somatically the steps are of different importance, and the 
soma to some extent disguises the true genetic nature. There is in dominance a 
certain latency. We may say that the somatic effects of identical genetic changes 
are not additive, and for this reason the genetic similarity of relations is partly 
obscured in the statistical aggregate. A similar deviation from the addition of 
superimposed, effects may occur between different Mendelian factors. We may use 
the term Epistacy to describe such deviation, which although potentially more 
complicated, has similar statistical effects to dominance. If the two sexes are 
considered as Mendelian alternatives, the fact that other Mendelian factors affect 
them to different extents may be regarded as an example of epistacy. 
The contributions of imperfectly additive genetic factors divide themselves for 
statistical purposes into two parts : an additive part which reflects the genetic nature 
without distortion, and. gives rise to the correlations which one obtains ; and a residue 
which acts in much the same way as an arbitrary error introduced into the measure- 
ments. Thus, if for a, d, —a we substitute the linear series 
c + b, c, c-b, 
and choose b and c in such a way that 
P(c + b - a) 2 + 2Q(c - d) 2 + R(c - b + a) 2 
is a minimum, we find for this minimum value <5 2 , 
fi2 _ 4PQRcZ 2 
PQ + 2PR + QR’ 
which is the contribution to the variance of the irregular behaviour of the soma ; and 
for the contribution of the additive part, /3 2 , where 
we obtain 
and since 
we have 
/3 2 = P(c + b — to) 2 + 2Q(c — to) 2 + R(c - b - to) 2 , 
/3 2 = 2Z> 2 (PQ + 2PR + QR), f 
b = a + 
Q(P-B)d 
PQ + 2PR + QR’ 
* - + 2PE + QE) - 4Q(P - • 
5. These expressions may be much simplified by using the equation 
Q 2 = PR, 
for then 
8 2 = 4Q 2 i 2 . 
j8 2 = 2a 2 Q 2 - 4Q(P - R)arf + 2Q(P - R)|| 
which appears in the regression in Article 3 (IV), 
and 
(V) 
(VI) 
t 2 = 2a 2 Q - 4Q(P - R)ad + 2Q(P + R)d 2 
• (VII) 
