RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE. 40l 
twelfth of his Mathematical Contributions to the Theory of Evolution '(“ On a 
Generalised Theory of Alternative Inheritance, with special reference to Mendel’s 
Laws,” Phil. Trans., vol. cciii, A, pp. 53-87. The subject had been previously 
opened by Udny Ytjle, New Phytologist, vol. i). For a population of n equally 
important Mendelian pairs, the dominant and recessive phases being present in equal 
numbers, and the different factors combining their effects by simple addition, he 
found that the correlation coefficients worked out uniformly too low. The parental 
correlations were ^ and the fraternal 
These low values, as was pointed out by Yule at the Conference on Genetics in 
1906 (Horticultural Society’s Report), could be satisfactorily explained as due to the 
assumption of complete dominance. It is true that dominance is a very general 
Mendelian phenomenon, but it is purely somatic, and if better agreements can be 
obtained without assuming it in an extreme and rigorous sense, we are justified in 
testing a wider hypothesis. Yule, although dealing with by no means the most 
general case, obtained results which are formally almost general. He shows the 
similarity of the effects of dominance and of environment in reducing the correlations 
between relatives, but states that they are identical, an assertion to which, as I shall 
show, there is a remarkable exception, which enables us, as far as existing statistics 
allow, to separate them and to estimate how much of the total variance is due to 
dominance and how much to arbitrary outside causes. 
In the following investigation we find it unnecessary to assume that the different 
Mendelian factors are of equal importance, and we allow the different phases of each 
to occur in any proportions consistent with the conditions of mating. The hetero- 
zygote is from the first assumed to have any value between those of the dominant and 
the recessive, or even outside this range, which terms therefore lose their polarity, 
and become merely the means of distinguishing one pure phase from the other. In 
order to proceed from the simple to the complex we assume at first random mating, 
the independence of the different factors, and that the factors are sufficiently numerous 
to allow us to neglect certain small quantities. 
* The case of the fraternal correlations has been unfortunately complicated by the belief that the correlation on a 
Mendelian hypothesis would -depend on the number of the fraternity. In a family, for instance, in which four 
Mendelian types are liable to occur in equal numbers, it was assumed that of a family of four, one would be of each 
type ; in a family of eight, two of each type ; and so on. If this were the case, then in such families, one being of the 
type A would make it less likely, in small families impossible, for a second to be of this type. If, as was Mendel’s 
hypothesis, the different qualities were carried by different gametes, each brother would have an independent and 
equal chance of each of the four possibilities. Thus the formulae giving the fraternal correlations in terms of the 
number of the fraternity give values too small. The right value on Mendel’s theory is that for an infinite fraternity. 
As Peajrson suggested in the same paper, “probably the most correct way of looking at any fraternal correlation 
table would be. to suppose it a random sample of all pairs of brothers which would be obtained by giving a large, or 
even indefinitely large, fertility to each pair, for what we actually do is to take families of varying size and take as 
many pairs of brothers as they provide.” In spite of this, the same confusing supposition appears in a paper by 
Snow “ On the Determination of the Chief Correlations between Collaterals in the Case of a Simple Mendelian 
Population Mating at Random” (E. C. Snow, B.A., Proc. Boy. Soc., June 1910); and in one by John Brownlee, 
“ The Significance of the Correlation Coefficient when applied to Mendelian Distributions ” (Proc. Boy. Soc. Edin., 
Jan. 1910). 
