312 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
(b.) With Assortative Mating.—We must take the values of the /3 s from 
Table XIII.: 
= -4176, yS 3 = -2997, B' 2 = -2895, B' s = '2609. 
We find 
y, = -6440 y 2 = *0344. 
Aj = 3-9893 A 3 — -0107, 
whence 
g p = 3-9893 (•6440)? 3 - 1 + '0107 (-0344)?'- 1 , 
f p = 3-0136 ("6440)^ _1 - *0136 (-0344)* -1 . 
As before, we note the small importance of the second terms. After four genera¬ 
tions (p = 5), we have g p — "6862 and g p = "5184 ; while after nine generations we 
have g p = "1L80 and g n = "0892. 
Now the effect of assortative mating here, even so little of it as may be detected 
in regard to stature in human mating, is of the exactly opposite character to what 
some of the current language on panmixia would have led us to believe. The more 
assortative mating the more rapid is the regression. The maximum of regression 
would be reached, if this factor of sexual selection exhibited perfect correlation.* 
Hence, assortative mating, if unaccompanied by a stringent natural selection, appears 
rather to emphasize than retard the action of panmixia. 
(v.) Effect of Panmixia on Variation. —We now turn to the second part of our 
pioblem, the determination of the standard deviations after p generations of 
suspended natural selection and assortative mating. This involves the solution of 
the equations e p and g p on p. 310. 
We find 
„ 3 = ^ + C, 
Of- 1 - 1 , n 9A~ l - 1 
9i ~ 1 
+ cy 
On, 1 
o, _ g i ri 9\ Af 9\ v 1 1 | p 9 2 A~ 9A ' ~ 1 
V p - 9\ + - — + Vo “ V » 
A 2 9i - 1 
A 3 9 - 2 - 1 
where 
9 i 
} 
W + Pi* ± v/(A* - Pi*? + iPiPi*. 
and C, and C, are to be found from 
* This is not absolutely accurate, for r 3 and r 3 are not equal, so that all tlie /3’s do not take their 
smallest value for = 1. But assuming r 2 and r 3 , r' 3 and r' 3 not very sensibly different, the result 
stated would practically follow. The whole reasoning in the text is, indeed, subject to another 
limitation, it is supposed that the constants of parental inheritance and of assortative mating are 
independent and characteristic of the race. The former, however, may really depend upon the latter. 
The dependence is very improbably so close as to reverse the principle stated. 
