536 TRANSMISSION 



all of which means that the closest selection of both parents 

 (perfect assortative mating) cannot result in the reduction of 

 variability by more than about 13 per cent. 



Moreover, if the entire back ancestry be selected, the vari- 

 ability will not be much reduced below this point. In connec- 

 tion with the law of ancestral heredity (page 534) we gave a 

 formula for the variability of the offspring of an ancestral line 

 selected back for an indefinitely large number of generations. 

 This formula is 



,\ 



2 V 2 ( 



in which 2 is the variability of the offspring of this selected 

 ancestry, a- is the variability of offspring in general for the 

 population from which selection is made, and r^ r 2 , r^ -, r n are 

 the correlation coefficients of offspring and first, second, third, 

 . . . , nth mid-parents. 



For pangamic mating, r lt r 2 , r s , -, r n may be taken as 

 0.6 0.6 0.6 0.6 



Vz (V 2 ) 2 (V^) 3 ' (VI) 

 Substituting these values in (i), we get 



2 . . 0.6 0.6 



f 0.6 0.6 



22 2 2 VI 2 



= 0.8 cr 2 . 



= <r Vo.8 = 0.8944 <r, 



which means that in the case of pangamic mating the variability 

 is reduced only about 1 1 per cent by selecting the entire 

 ancestry. 



Basing his remarks on these facts, Pearson says that the 

 10 to 13 per cent reduction obtained by the selection of two 



* The series - -f 2 -\ - + to infinity is a geometrical progression whose 

 sum is found in the usual manner by dividing the first term by i minus the ratio. 



