PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 317 
(iii.) Panmixia for Human Stature. —It is instructive to note the value of these 
expressions for the case of stature in man. We have at once from the numbers on 
p. 31J, supposing p-selections of male and female populations averaging 4" and 3" above 
the present mean, the following results : 
(a.) Without Assortative Mating. 
u p = 3-9549 (-2933)^- ] + '0451 (-9581)^-\ 
Vp = 3-0538 (*2933)^- 1 - -0538 (-9581)?- 1 . 
Thus, in five generations (p = 5) u 5 = ’0673 and v- = — -0227, or the male and 
female means have been raised 3 // *9327 and 3 // '0227 respectively. Thus, we see that 
the males have been raised by selection very near to the selection average, while the 
females have actually been raised beyond it. # Thus, continued selection would now 
keep down, and not raise, the female mean, panmixia corresponding to a rise in the 
mean. 
(b.) With Assortative Mating. 
Up = 3-9893 ("3560) ?_1 + '0107 (•9656)^" 1 
Vp — 3-0136 (-3560)?- 1 - -0136 (■9656)^-h 
Thus, in five generations, u- = "0744 and v 5 = *0366, or the male and female means 
have been raised 3 ,/ "9256 and2 / '"9634 respectively. The means are accordingly raised 
less rapidly with this form of sexual relation, the female mean, indeed, having in the 
five generations not yet overshot the selection mean. 
(iv.) Concluding Remarks on Regression and Fixedness of Character. —Accordingly 
on this hypothesis, with the correlation coefficients of inheritance anything like their 
value in man, five generations of selections of the type required in both parents would 
suffice to establish a breed. This seems more or less consonant with breeders’ 
opinions, which, in part at any rate, may be presumed to represent their experience. 
If, however, anything like this hypothesis be true, then the suspension of natural 
selection would not be followed by a rapid regression, or even a slow persistent 
regression, that would require a reversal of natural selection, i.e., a selection of those 
previously destroyed and a destruction of those previously selected. On this hypo¬ 
thesis, indeed, it would be probably best to keep the term panmixia for that 
suspension of assortative mating which we have seen assists, rather than retards, the 
processes of natural selection. 
Several fairly sound reasons could be given why the focus of regression should be 
taken as the mean of the population from which the parents have been selected, but 
the sole safe argument appears to be experiment. 
* This results, of course, from breeding from an average father very much taller relatively than the 
average mother selected. 
