408 
R. A. FISHER ON THE CORRELATION BETWEEN 
of deviations due to dominance, and that with these cousins the correlation will in 
general be rather higher than it is for uncle and nephew. 
For ordinary first cousins I find the following table of the distribution of random 
pairs drawn from the six types of ordinary cousinship : — 
l p 3(4 p + q ) 
\p 2 q\7p + q) 
w 
\ p*q(7p + q) 
\pq(p 2 +Upq + q 2 ) 
}pq 2 (jp + 7q) 
1 pV 
\pq\p + 7q) 
\<f(P + 4 ?) 
which yields the correlation - - 
2 
2 1 
In a similar way the more distant kin may be investigated, but since for them 
reliable data have not yet been published, the table already given of genetic correla- 
tions will be a sufficient guide. 
8. Before extending the above results to the more difficult conditions of 
assortative mating, it is desirable to show how our methods may be developed so as 
to include the statistical feature to which we have applied the term Epistacy. The 
combination of two Mendelian factors gives rise to nine distinct phases, and there is 
no biological reason for supposing that nine such distinct measurements should be 
exactly represented by the nine deviations formed by adding i,j, or k to i r ,-j[, or k'. 
If we suppose that i,j, k, k' have been so chosen as to represent the nine actual 
types with the least square error, we have now to deal with additional quantities, 
which we may term 
e 2l e 22 e 23 
e 31 g 32 e 33 
connected by the six equations, five of which are independent. 
P\i + ' 2 P c l e 2i + 7%i = 0 
ii + 2 pqe n + q 2 e n = 0 
p\ 2 + 2pqe 22 + = ° 
P\i + 
3 22 + 2 2e 23 = ° 
p 2 e 13 + 2p>qe i3 + q 2 e 33 = 0 
p' 2 e 3l + 2p'q'i 
?32 + 
This is a complete representation of any such deviations from linearity as may 
exist between two factors. Such dual epistacy, as we may term it, is the only kind 
of which we shall treat. More complex connections could doubtless exist, but the 
number of unknowns introduced by dual epistacy alone, four, is more than can be 
determined by existing data. In addition it is very improbable that any statistical 
effect, of a nature other than that which we are considering, is actually produced by 
more complex somatic connections. 
The full association table between two relatives, when we are considering two 
distinct Mendelian factors, consists of eighty-one cells, and the quadratic expression to 
which it leads now involves the nine epistatic deviations. A remarkable simplification 
is, however, possible, since each quantity, such as e 21 , which refers to a partially or 
