410 
R. A. FISHER ON THE CORRELATION BETWEEN 
9. With assortative mating all these coefficients will be modified. There will be 
association between similar phases of different factors, so that they cannot be 
treated separately. There will also be an increase in the variance. 
We must determine the nature of the association between different factors, 
and ascertain how it is related to the degree of assortative mating necessary to 
maintain it. Then we shall be able to investigate the statistical effects of this 
association on the variance of the population and on the correlations. 
If fj- be the marital correlation, then in a population with variance V the frequency 
of individuals in the range dx is 
*dx = M, 
and the frequency in the , range dy is 
j2irY e ' 
* V dy = N; 
but the frequency of matings between these two groups is not simply MN, as would 
be the case if there were no marital correlation, but 
1 x'-Zi&y+y* 
2nY — /j? 
dx dy, 
which is equal to 
MN 
jr-y 
i -2^gy+j»V 
2V(1 — fj. 2 ) 
In studying the effect of assortative mating we shall require to know the 
frequency of matiugs between two groups, each with a variance nearly equal to 
that of the whole population, but centred about means a and b. The frequencies 
of such groups in any ranges dx, dy can be written down, and if the chance of any 
mating depends only on x and y, the frequency of mating between these two groups 
can be expressed as a double integral. If M and N are the frequencies in the two 
groups, the frequency of mating between them is found to be 
liab 
MNe V 
10. We shall apply this expression first to determine the equilibrium value of 
the frequencies of the three phases of a single factor. Of the six types of mating 
which are possible, all save two yield offspring of the same genetic phase as their 
parents. With the inbreeding of the pure forms DxD and R x R obviously no 
change is made, and the same is true of the crosses D x H and RxH, for each of 
these yields the pure form and the heterozygote in equal numbers. On the other 
hand, in the cross DxR we have a dominant and a recessive replaced in the next 
generation by two heterozygotes, while in the cross HxH half of the offspring 
return to the homozygous condition. For equilibrium the second type of mating 
