Duplicate genes for capsule-form in Bursa bursa-pastori&^^___^ 147 



itself prove that several genes of similar nature are involved, that 

 dominance is lacking, or that all inheritable quantitative differences 

 between the parents of the particular cross are Mendelian; and c) that 

 unequal treatment of the several generations may produce a purely fac- 

 titious increase in the range and coefficients of variability of the Fa. 



Attempts to determine how many plural determiners for any quan- 

 titative character are involved in a particular cross are as yet premature. 

 Such attempts are based on the unproven hypothesis that the range of 

 variability in Fa equals the combined ranges of the Pi and Fi genera- 

 tions and the unwarranted assumption that the different plural deter- 

 miners are essentially equal in effect. 



Qualitative and quantitative inequality of plural determiners give 

 a simple explanation of CASTLE'S results with hooded rats, and EMERSON'S 

 recessive dwarf maize-segregates, without resort to coupling of the genes. 



Low coefficients of correlation do not indicate a high degree of 

 genotypic independence of characters, nor does a high correlation indicate 

 gametic coupling. Such differences in the degree of correlation are 

 produced by so many different causes that genetic inferences from them 

 should be most carefully guarded. 



The duplication of determiners for the ligula of oats is probably 

 a primitive condition, and that for the triangular capsule of Bursa a 

 derivative condition. 



If the genes are functions of the chromosomes, the simple exchange 

 of relative positions by two chromosomes would give rise at the same 

 time to the duplication of the determiner for the triangular capsule in 

 B. bursa-pastoris and the origin of the recessive mutant, B. Heegeri, 

 without a progressive mutation on the one hand, or the loss of a de- 

 terminer on the other hand. A longitudinal transfer of the capsule- 

 determiner from one chromosome to another adjacent chromosome would 

 have a like result. 



The occurrence of recessive mutants is apparently much more 

 frequent than the duplication of determiners; consequently, no con- 

 siderable portion of such mutations can have originated by the method 

 here made probable for B. Heegeri. The author can not agree with 

 those who would explain the Oenothera mutants as due to the segregation 

 of duplicate or plural Mendelian determiners. 



For the present the hypothesis that plural Mendelian genes ad- 

 equately account for the inheritance of complex quantitative and physio- 

 logical characters is valuable only to the extent that it is made a 

 working hypothesis. 



