346 Quantitative Characters 



and if one is homozygous for contributing genes only, whereas the 

 other is homozygous for neutral genes, the more numerous the 

 contributing genes, the less each one contributes, the more numer- 

 ous the classes between the two extremes, and the smaller the 

 difference between any two successive classes. If the contribut- 

 ing genes are very numerous, the difference between successive 

 classes may be smaller than the amount of variation which is 

 normally the result of environmental differences, and individuals 

 of one class may overlap those of another. Where these class 

 differences are so small, the variation in the F2 population seems 

 to be continuous. Where only four or six cumulative genes are 

 interacting, it may be possible to classify the F2 individuals 

 into a few classes which are sufficiently distinct to admit of ready 

 separation, but when more such genes are involved, the classes 

 usually run together. Where there are a few distinct classes, 

 the variation is said to be discontinuous. 



We have cited many examples of discontinuous variation 

 throughout this book. A few such characters are bullata and 

 normal leaves in the evening primrose; curved and normal wings 

 in Drosophila; red, white, and pink flowers in the four-o'clock; 

 crooked and normal fingers in human beings; and many other 

 characters that have been discussed in the chapters dealing with 

 the transmission of genes. In all those examples, the individuals 

 can easily be classified as possessing one or the other character, 

 and such classification can be made by simple inspection, with- 

 out resorting to any scale of measurements. When the variation 

 is continuous, however, an individual can be classified only after 

 a measurement is made, and he cannot be scored by simple 

 observation. Where the variation is discontinuous and measure- 

 ments are not necessary for classification, the character is fre- 

 quently said to be a qualitative character, whereas those char- 

 acters that can be scored only by measurement because they vary 

 continuously are quantitative. If the quantitative characters 

 are the result of numerous, duplicate, cumulative, nondominant 

 genes, such genes are frequently known as polymeric genes or 

 multiple factors. 



According to the theory of duplicate genes, a small number 

 of cumulative genes is interacting to produce a few discontinuous 

 classes. The expansion of this theory into the theory of poly- 

 meric genes, in which many such duplicate genes are interacting 



