No. 600] PIEBALD RATS AND MULTIPLE FACTORS 



737 



a case the second cross would be said to show further re- 

 duction. 



Whether this advance in the second cross returns the 

 hooded grade to about what the uncrossed race would 

 have been is a matter of what average is used to repre- 

 sent the uncrossed race. The original hooded parents 

 were the last parents to be selected in this series of 

 crosses. It seems clear then, as above reasoned in an- 

 other connection, that the average to be used in compari- 

 son with the two groups of F 2 hoodeds is that of the off- 

 spring of uncrossed parents of the same grade and gen- 

 eration as the original hooded parents used in the crosses. 

 If this average be accepted (3.84), it is plain that even 

 after the second cross there remains a considerable dif- 

 ference between the averages of the uncrossed and the 

 twice extracted hooded rats. There is reason to believe 

 that the changes produced by selection are modified by 

 crossing and that it has not been finally disproved that 

 further crossing does not cause further modification. So, 

 as far as can be judged from the data at hand, this crucial 

 test does not seem to offer a final blow to the applicability 

 of the hypothesis of multiple factors. 



On the other hand, that modification actually does re- 

 sult from crosses is strikingly proved by the conversion 

 of the minus race into the plus by means of a cross. 

 This experiment has been referred to on page 729. Six 

 successive return selections did not return the average 

 of the minus race to the "0" grade. But after minus 

 race rats were crossed with wild, a single selection of the 

 plus varieties raised the average 2 grades above "0." 



Summary 



By way of recapitulation, the points referred to are 

 summarized as follows: 



A. Seventeen generations of selection need not have en- 

 tirely eliminated modifiers, because, 

 1. Matings less close than brother and sister have 

 tended to continue heterozygosity; 



