1921-22.] 
On the Dominance Ratio. 
321 
XXI. — On the Dominance Ratio. By R. A. Fisher, M.A., Fellow of 
Gonville and Cains College. Communicated by Professor J. Arthur 
Thomson. 
(MS. received March 8, 1922. Read June 19, 1922.) 
Introduction. 
In 1918, in a paper published in the Transactions of the Royal Society of 
Edinburgh, the author attempted an examination of the statistical effects 
in a mixed population of a large number of genetic factors, inheritance in 
which followed the Mendelian scheme. At that time, two misapprehensions 
were generally held with regard to this problem. In the first place, it was 
generally believed that the variety of the assumptions to be made about 
the individual factors — which allelomorph was dominant ; to what extent 
did dominance occur; what were the relative magnitudes of the effects 
produced by the different factors; in what proportion did the allelomorphs 
occur in the general population; were the factors dimorphic or poly- 
morphic; to what extent were they coupled, — besides the more general 
possibilities of preferential mating (homogamy), preferential survival 
(selection), and environmental effects, rendered it possible to reproduce 
any statistical resultant by a suitable specification of the population. It 
was, therefore, important to prove that when the factors are sufficiently 
numerous, the most general assumptions as to their individual peculiarities 
lead to the same statistical results. Although innumerable constants enter 
into the analysis, the constants necessary to specify the statistical aggre- 
gate are relatively few. The total variance of the population in any 
feature is made up of the elements of variance contributed by the indi- 
vidual factors, increased in a calculable proportion by the effects of 
homogamy in associating together allelomorphs of like effect. The degree 
of this association, together with a quantity which we termed the 
Dominance Ratio, enter into the calculation of the correlation coefficients 
between husband and wife, and between blood relations. Special causes, 
such as epistacy, may produce departures, which may in general be 
expected to be very small from the general simplicity of the results ; the 
whole investigation may be compared to the analytical treatment of the 
Theory of Gases, in which it is possible to make the most varied assump- 
tions as to the accidental circumstances, and even the essential nature of 
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