428 



The Journal of Heredity 



generations respectively. The varia- 

 tions with a genetic basis may be due 

 either to variations of the main hooding 

 factor Sh in which case the different 

 grades should be allelomorphs of each 

 other (except for the non-genetic varia- 

 tion) or to the cooperation of inde- 

 pendent factors with the hooding factor. 

 Those who hold to an exceedingly 

 stable germ-plasm must adopt the 

 second view, at least in the main, 

 to account for the success of selection. 

 If, however, selection has worked 

 through the appearance of numerous 

 small variations these might be of either 

 kind. Professor Castle has pointed out 

 both possibilities and, indeed, has 

 proved that both kinds of variations 

 exist in particular cases. He attributes, 

 however, more weight to variations of 

 the main factor than to independent 

 ones. The writer is inclined to reverse 

 the em])hasis. 



ANALYSIS OF THE DATA 



A rough analysis of the data on the 

 assumption that both kinds of variations 

 exist yields some very interesting results. 

 Let it be assumed that the factor S is 

 varying and that each generation or 

 stock has its characteristic mean allelo- 

 morph in the series, which may be 

 represented by Sio+, Sio-, Sw, Sm, Si, 

 etc., for the tenth plus and tenth minus 

 generations and the wild, mutant and 

 Irish stocks, respectively. Assimie also 

 that there is a large array of independent 

 factors with respect to which each 

 generation and stock has a certain 

 average condition which may be repre- 

 sented by 2io+, 2io-, Sw, Sm, Si, etc. 

 Assuming variation to occur at random 

 in both directions, a given factor as 

 Sio-f- should come out of any cross at 

 the same average level, Sio+, that it 

 went in. Justification of this assum])- 

 tion may be found in the crosses of tlie 

 tenth ])lus generation with the mutant 

 rats spoken of above which came from 

 this generation. The tenth plus gen- 

 eration were of an average grade of 

 -}-3.73 on Professor Castle's scale in 

 which -|-6 is self and —4a nearly solid 

 white with only a little black on the 

 head. The mutants were about grade 

 -f 5. 50 but in F2 or later generations of 



the cross of tenth plus with mutant the 

 hooded segregates averaged very close 

 to +3.73 (actually -+-3.79) showing that 

 in a cross in which the same inde- 

 pendent factors should be present in 

 both parents, the hooding factor segre- 

 gates out unchanged after a generation 

 in nearly self rats. In regard to the 

 independent factors, the best w^orking 

 assumption for the average produced 

 by any cross or back cross seems to be 

 blending inheritance. Thus Fi from 

 tenth plus (grade -f3.73) by tenth 

 minus (grade —2.01) was +1.00 in 

 grade, about half way betw^een the 

 parents, and F2 averaged nearly the 

 same, +0.73, although with somewhat 

 greater variability showing slight indica- 

 tions of segregation. The standard 

 deviations were +0.60 and +0.87 

 in Fi and F2 respectively. This cross 

 would be presented by the s^-mbols 

 above as follows : 



S lo+S 10+S 10+ X S 10-Sio-S 10- 



= Sio+Sio- ^">++^io- 

 2 

 In F2 there should be segregation of 

 S 10+ and Sio- but the averai^e condition 

 of the independent factors should still be 

 S10++S10- 

 2 

 By this method it is possible to deduce 

 roughly the average grade of rats which 

 have derived their hooding factor from 

 one source and the entire array of 

 independent factors from another. Thus 

 Fi from the cross mutant by tenth 



minus must be SmSio- ^" ^ '°~ and 



the easily recognized hooded rats in 

 F2 must on the average be of formula 



Sio-Sio- '^""^f^'°~ . But this is the 



same as Fi between minus and a 

 hypothetical stock with the main hood- 

 ing factor of the tenth minus generation, 

 but the residual heredity of the mutant 

 stock, Sio_Sio-Sm. the Fo segre- 

 gates from the cross tenth minus with 

 mutant, then, should be just half-way 

 l^etween the tenth minus and the 

 hyi)othetical stock in grade, which 

 enables us to deduce the grade of the 

 latter. The following table is thus 

 derived from crosses given by Castle 



