Duplicate genes for capsule-form in Bursa bursa-pastoris. 131 



variability in the parental, Fi, and F 2 , generations, as in the F 3 , if the 

 range of the coefficients of variation in the different F 3 families is to 

 be properly evaluated. 



In thus pointing out some limitations in the legitimate interpreta- 

 tion of increased Fa variability and size-differentiations in Fs, it is 

 hoped that the reader will not mistake my attitude. I believe that all 

 of these points can be taken into account without reversing the funda- 

 mental conclusions that plural Mendelian factors exist, which may affect 

 in an apparently continuous manner the various quantitative characters 

 and complex physiological activities of plants and animals, and that 

 Mendelian segregations offer at present the most plausible interpretation 

 of most of the phenomena encountered in the inheritance of these 

 characters. 



Attempts to decide how many differentiating genes affect a certain 

 quantitative character in a given cross, have been, up to the present 

 time, premature. HAYES'S (1912) conclusion that if the number of F 2 

 individuals is large enough, the F 2 range will equal the combined ranges 

 of the parents and the Fi hybrids, is not a legitimate conclusion from 

 the evidence he presents, but only a logical necessity for the hypothesis 

 he holds, namely, that the size-differences with which he is working 

 are wholly the product of plural Mendelian determiners. It is well 

 known that the empirical range of a continuous variation increases with the 

 increase in the number of variates. The total combined range of variation 

 in number of leaves on the paternal strains and on the Fi of HAYES'S 

 < 'Sumatra"-"Broadleaf" tobacco-cross extended from 16 to 31, thus in- 

 cluding 16 classes, and that of the F 2 from 17 to 35, or 18 classes, 

 but the combined number of individuals included in the Pi and Fi were 

 only 683, while the total number in the F 2 families was 6340, besides 

 which, the former were grown on good soil, heavily fertilized. HAYES 

 shows that there is only slight modification of leaf-number on different 

 soils, and although he gives no evidence as to the relative variability 

 Mm the different soils, this also is probably but little affected, so that 

 too much stress must not be laid on the different conditions under which 

 the several generations were grown; but the extent to which the 

 combined ranges of PI and Fi would have been stretched if ten times 

 as many individuals had been available in those generations, remains 

 a question, and leaves the conclusion as to the identity of range be- 

 tween the F 2 and Pi -f- Fi incompletely supported. 



This extension of the F-_. range of variation to include the two 

 Pi ranges is the basis upon which estimates of the number of plural 



