1921-22.] 
or, when /3 is small, 
On the Dominance Ratio. 
335 
Such selection is therefore equivalent to a genetic selection 
a = qfS. 
Now 
dO 
= a Jpq = fjqVpq, 
and for the variance caused by selection, instead of pqcTa^, as in Section 6, 
we now write pq^or / : we have then for the total variance produced in one 
generation in the value of 6, 
} + ~ sin- ^(1 4- cos Oy^cr^^ 
In lb 
= ^ + sin^ co.s'^ ^6 . 
and the equilibrium distribution will be 
1 
y 
yo cos® + — 
It is important to notice that this distribution, unlike those hitherto 
considered, is unsymmetrical, factors of which the dominant phase is in 
excess are in the majority. This has an important influence on the value 
of the dominance ratio. 
If 2?^a■/ is large, we can write with sufficient accuracy * 
A 1 
y 
1 •4022(2r/(o-/)^ + log (fSno-/) - § 
^sin2 
16 cos® 16* + 
1 
2?7(t/ 
The terminal ordinate therefore varies nearly as (2^i(r/)b ^nd for large 
populations in equilibrium, fj. varies as and as 
Genotypic selection resembles genetic selection in diminishing the 
amount of variability which a given frequency of mutation can maintain, 
or per contra, increasing the amount of mutation needed to maintain a 
given amount of variability; it differs, however, in being comparatively 
inactive in respect of factors in which the dominant allelomorph is in 
excess, and consequently in allowing a far greater number of factors to 
exist in this region (see fig. 4). 
* I am indebted to Mr E. Gallop, Gonville and Cains College, Cambridge, for tlie value 
of the definite integral. Mr Gallop has shown that the three terms given are the heads of 
three series in descending powers of in which the integral may be expanded. 
