HEREDITY 



535 



general by multiplying this standard deviation by Vi r^ ; that 

 is, in symbolic language, ^ = <7 3 Vi rf gives the variability 

 (standard deviation) of an array of offspring whose correlation 

 with the selected parent is r lt and in which the variability of 

 offspring in general is <r 3 . 



The numerical value of this variability in a given instance 

 depends upon the value of r^ Now experimental evidence 

 shows that the correlation between parent and offspring ranges 

 all the way from 0.3, with little or no assortative mating, up to 

 about o. 5 , with the highest selection of both parents that has yet 

 been achieved (see table of coefficients of heredity, page 488). 



Now in our formula ^ = cr 3 Vi rf let us substitute these 

 values : _ 



When i\ = 0.3, V = <7 3 Vi 0.09 = 0.9539 "3 ; that is, in this 

 case, when one parent is selected we get an offspring only about 

 5 per cent less variable than the offspring in general. 



We have already seen (page 533) that when two parents are se- 

 lected, assuming them to be equipotent, the formula for the vari- 



I 2 r 2 



ability of the offspring of selected parents is jv = o- 3 \ i -- 1- . 



1 4- *s 



Let us now make the same assumption as before ; namely, take 

 r first as 0.3 for pangamic mating, and again as 0.5 for the case 

 of perfect assortative mating. 



/ 



\l 



1. If r l = 0.3 and r% = b, then V = <7 3 \ I -- ^- becomes 



~~ " 



i -- - = <r 3 Vo.82 =0.9055 a- 3 , which means that the 



selection of both parents out of a race developed by pangamic 

 mating will result in the reduction of variability by only about 

 10 per cent. 



2. If T-J = 0.5 and r B = i, that is, with perfect assortative 

 mating and with the highest correlation found in highly bred 

 races, - 



becomes 



0.25 =0.8662 <J 3 ; 



