432 
R. A. FISHER ON THE CORRELATION BETWEEN 
Writing £ for log* - and <r for the standard deviation of we have. 
p = e^/ 2coshJf, q = e~l£/2 cosh|£, and 2pq = J sech 2 
Hence we have to evaluate 
E = —^= f J sech 2 \i.e~ ^ = -J= j i sech 2 ~ «■ 'll . . (XXYIII) 
and the dominance ratio derived from the whole group is 
EcZ 2 
a 2 + (1 — E)d 2 ’ 
E is a function of a- only, which decreases steadily from its value \ when o- = 0, 
approaching when o- is large to the function — %=. The function (16 + 16o- 2 + —a 4 
' 2tt \ 4 
osculates it at the origin, and appears on trial to represent it effectively to three 
significant figures. This function has been used for calculating the form of the 
accompanying curves. Fig. 3 shows the course of the function E. Fig. 4 gives the 
curves comparable to those of figs. 1 and 2, showing the value of the dominance 
ratio for different values — and cr. If the assumptions upon which this diagram is 
based are justified, we are now advanced some way towards the interpretation of an 
observed dominance ratio. A ratio of '25 gives us a lower limit of about '8 for 
d 
- , and no upper limit. If the possibility of superdominance (d>a) is excluded, then 
the ratio of the phases must be so distributed that the standard ratio e a is not greater 
than about 3:1. A greater value of the standard ratio would make the effect of 
dominance too small ; a smaller value could be counteracted by a slight reduction of 
d 
— . We have therefore no reason to infer from our dominance ratios that dominance 
a 
is incomplete. We may speak of it as having at least four-fifths of its full value, 
but we can set no upper limit to it. 
26. Throughout this work it has been necessary not to introduce any avoidable 
complications, and for this reason the possibilities of Epistacy have only been 
touched upon, and small quantities of the second order have been steadily ignored. 
In spite of this, it is believed that the statistical properties of any feature determined 
by a large number of Mendelian factors have been successfully elucidated. Due 
allowance has been made for the factors differing in the magnitude of their effects, 
and in their degree of dominance, for the possibility of Multiple Allelomorphism, and 
of one important type of Coupling. The effect of the dominance in the individual 
factors has been seen to express itself in a single Dominance Ratio. Further, the 
effect of marital correlation has been fully examined, and the relation between this 
association and the coefficient of marital correlation has been made clear. 
By means of the fraternal correlation it is possible to ascertain the dominance 
