132 Shull. 



determiners involved in any given cross have been based. NILSSON- 

 EHLE (1911) has described a case in which the range of variation in 

 the length of heads of wheat in the F 2 considerably exceeded the com- 

 bined ranges of the two parents. HAYES (1912) has found a similar 

 case in the number of leaves in tobacco, and EMEESON and EAST (1913) 

 have seen the same phenomenon in the length of internode and total 

 length of stalks in maize. It seems probable that such transgressive 

 variation may be the rule rather than the exception when very complex 

 characters are investigated; for it is hardly to be expected that a large 

 number of plural determiners, affecting such a character, shall all act in 

 the same direction, or that the parent having the highest development 

 of the given character shall generally contain all the genes which the 

 other chosen parent possesses. Whenever such transgressive' variability 

 is producible by the genotypic recombinations of parental characters, 

 the frequency with which F;> individuals simulate either parent, gives 

 no clue to the total number of plural determiners which have been 

 brought together, with respect to any character under consideration. 

 The difficulty of making an estimate of the number of genes which 

 affect the same character will be more fully appreciated when it is 

 kept clearly in mind that these plural determiners need not be duplicate, 

 and that consequently there is no reason for assuming that the in- 

 fluence of the several determiners is quantitatively equal. 



Qualitative and quantitative differences in the effects individually 

 produced by the several plural factors for a character will assist in 

 interpreting certain phenomena for which less simple hypotheses have 

 been offered. The now celebrated hooded rats may serve to illustrate: 

 Because the hooded -pattern reappears in all crosses as a Mendelian 

 recessive to the self-colored pelages, in the simple monohybrid proportion, 

 it is accepted by CASTLE (1912) as a case in which a single de- 

 terminer is involved. Selection of high and low extremes of this 

 pattern during a series of generations has resulted in increasing the 

 size of the pattern in the one series and in diminishing it in the other, 

 just as CUENOT (1907) found to be true in regard to the piebald- 

 pattern of mice. When hooded rats from either the plus or the minus 

 selected series are crossed with self-colored rats the hooded -pattern 

 still acts in each case as a simple monohybrid recessive, though the ex- 

 tracted pattern is somewhat larger when an individual of the plus 

 series has been used in the cross, and somewhat smaller when the 

 hooded parent was taken from the minus series. CASTLE concludes, 

 therefore, that selection does not simply sort out variations already 



