406 
R. A. FISHER ON THE CORRELATION BETWEEN 
who show a similar variation ; but they may also be changed from heterozygote to 
dominant. In the case of siblings, however, whichever change takes- place in one is 
more likely to occur in the other. 
Thus, writing i, j, k for the deviations 
a - m, d — m, - (a + m ), 
so that 
iP + 2/Q + AR = 0 (XII) 
and p 2 , pq, q 2 for P, Q, R, we can draw up association tables for different pairs of 
relatives, and readily obtain the correlations between them by substituting the 
fractions in the nine sections of the table as coefficients of a quadratic function 
in i, j, k. 
Thus the association table between parent and child is 
— 
pq(p + q) 
pq* 
■ 
pq* 
q 3 
from which we obtain the quadratic 
pH* + 2 \p*qij +pq{p + q)i 2 + 2pq*jk + q 3 k*, 
which is equal to 
while for brother and brother we have the table 
p 2 (p+k) z pMp -kk) 
W 
p *q(p + \q) pq(p 2 + 3 pq + q 2 ) 
pq\%p + q) 
\p*q* | pq\%p + q) 
q\\p + qf 
which gives us a quadratic expression exceeding that for the parental correlation by 
the terms 
- ‘lij + 4 f + 2 ik - 2 \jk + A- 2 ), 
4 
which are equal to ^ 2 , and therefore give for the fraternal correlation 
The effect of dominance is to reduce the fraternal correlation to only half- the 
extent to which the parental correlation is reduced. This allows us to distinguish, as 
far as the accuracy of the existing figures allows, between the random external effects 
of environment and those of dominance. This halving of the effect of dominance, it 
is important to notice, is independent of the relative importance of different factors, 
of their different degrees of dominance, and of the different proportions in which 
their phases occur. The correlation between the dominance deviations of siblings is, 
in all cases, 
7. To investigate the cases of uncles and cousins we must deal with all the possible 
