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Proceedings of the Poyal Society of Edinburgh. [Sess. 
p is large, which would tend to make the distribution more symmetrical, 
this effect is exactly balanced by the increased effect of selection when p 
is small. The dominance ratio is therefore unaltered by the direct effect 
of assortative mating. 
Summary. 
The frequency ratio of the allelomorphs of a Mendelian factor is only 
stable if selection favours the heterozygote : such factors, though occurring 
rarel}^ will accumulate in the stock, while those of opposite tendency will 
be eliminated. 
The survival of a mutant gene although established in a mature and 
potent individual is to a very large extent a matter of chance ; only 
when a large number of individuals have become affected does selection, 
dependent on its contribution to the fitness of the organism, become of 
importance. This is so even for dominant mutants ; for recessive mutants 
selection remains very small so long as the mutant form is an inconsider- 
able fraction of the interbreeding group. 
The distribution of the frequency ratio for different factors may be 
calculated from the condition tha,t this distribution is stable, as is that of 
velocities in the Theory of Gases : in the absence of selection the distribu- 
tion of log is given in fig. 1. Fig. 2 represents the case of steady decay 
in variance by the action of random survival (the Hagedoorn effect). 
Fig. 3 shows the distribution in the somewhat artificial case of uniform 
genetic selection : this would be the distribution to be expected in the 
absence of dominance. Fig. 4 shows the asymmetrical distribution due to 
uniform genotypic selection with or without homogamy.' 
Under genotypic selection the dominance ra^io for complete dominance 
comes to be exactly J, in close agreement with the value obtained from 
human measurements. 
The rate of mutation necessary to maintain the variance of the species 
may be calculated from these distributions. Very infrequent mutation 
will serve to counterbalance the effect of random survival ; for equilibrium 
with selective action a much higher level is needed, thqugh still mutation 
may be individually rare, especially in large populations. 
It would seem that the supposition of genotypic selection balanced by 
occasional mutations fitted the facts deduced from the correlations of 
relatives in mankind. 
