G3S 



THE AMERICAN NATURALIST [Vol. XLVI 



it was immediately seen that where dominance is ab- 

 sent and such multiple factors are assumed, size char- 

 acters can be interpreted as coming under the Mendelian 

 law. When dominance is complete the mathematical 

 representation of an F 2 generation is (3/4 + 1/4)" 

 where n represents the number of factorial differences 

 involved; as the manifestation of dominance becomes 

 less this formula approaches the type (1/2 + 1/2 ) 2n . 

 The difference between the heredity of qualitative char- 

 acters and quantitative characters is therefore only one 

 of degree, for there is absence of dominance in cases of 

 simple monohybrid qualitative characters and there is 

 presence of multiple factors in cases of qualitative char- 

 acters showing dominance. But it is manifestly absurd 

 to expect size characters to appear in natural groups as 

 do- many qualitative characters. The marked effect of 

 environment and our ignorance of the exact effect to 

 attribute to each factor precludes it. One can determine 

 whether size inheritance compares with the inheritance 

 of qualitative characters only by the use of arbitrary bio- 

 metrical methods. In theory, homozygotes with size dif- 

 ferences when crossed should give an intermediate F x 

 of low variability and an F 2 of high variability. Vari- 

 ous F 3 populations should differ in their mean and in 

 their variability. The difference in the variability of 

 F 2 over F T should decrease as the heterozygosity of the 

 parents increases. Sometimes parents of the same size 

 should differ in the factors they contain and the F 2 gen- 

 eration should contain individuals smaller and individ- 

 uals larger than either of the parents. Each of these re- 

 quirements has been satisfied by experiment. East and 

 East and Hayes have tested it for number of rows per 

 cob, height of plant, length of ear and size of seed in 

 maize, Slmll for number of rows in maize, Emerson for 

 fruit sizes in maize, beans and gourds, Tammes for 

 various characters in flax species, Tschermak for time of 

 blooming in beans, Hayes for number of leaves in to- 

 bacco, Belling for certain characters in beans, Phillips 

 for body size in ducks, MacDowell for body size in rab- 



