146 Shull. 



This indicates that the deficiency in the Heegeri individuals, previously- 

 reported, was probably due, in large part at least, to selective elimination. 



In one family there was an equal deficiency in the proportion of 

 recessives and of homozygous dominants, so that the ratio DD : DR : RR 

 was about 1:4:1 instead of 1:2:1. Several possible interpretations 

 of this result are considered: namely, a) that it is a purely chance 

 result; b) that a selective fertilization has favored the union of unlike 

 gametes; c) that selective elimination has affected positive and negative 

 homozygotes equally because they lack the vigor produced by hetero- 

 zygosis; and d) that some form of gametic coupling occurs between the 

 two genes C and D. Of these hypotheses a) and d) appear most promising. 



The discovery by NILSSON-EHLE and EAST that the same character 

 may be produced by any one of several independently inheritable de- 

 terminers, marks an important advance in genetic progress because it 

 has led to a well grounded Mendelian interpretation of inheritable quan- 

 titative differences. Determiners which independently produce such 

 equivalent results, I have called "duplicate" genes. 



A sharp distinction must be maintained between "duplicate 1 ' 

 determiners and "plural" determiners, the latter including all determiners, 

 of whatever nature, which produce a given characteristic or which modify 

 it in any way that does not destroy its identity. Inheritable quantita- 

 tive characters are probably the product of plural determiners, but not 

 to any considerable extent of duplicate determiners, and the develop- 

 ment of an adequate Mendelian interpretation of the inheritance of such 

 characteristics need not have awaited the discovery of duplicate determiners. 



For only four characters is the evidence of duplicate genes to be 

 deemed adequate: namely, for the presence of a ligula in oats, red 

 pericarp-color in wheat, yellow endosperm-color in maize, and the tri- 

 angular capsule-form in Bursa. For many other characters the existence 

 of plural determiners has been rendered probable, but there are weaknesses 

 in the evidence, and apparently fallacious inferences have been drawn 

 in a number of cases, owing to the failure to distinguish between plural 

 and duplicate determiners. 



For many characters the only evidence of plural Mendelian size- 

 determiners is an increased variability in Fi as compared with the Pi 

 and Fi generations. It is here shown: a) that the stimulating effect of 

 hybridity, for which the name "heterosis" is adopted, produces increased 

 variability in quantitative characters in the F2 and a pseudo-segregation 

 in Fa, independently of the existence of specific determiners for size; 

 b) that the demonstration of an increased variability in F2 does not by 



