358 Quantitative Characters 



we have discussed in chapters previous to this one resulted from 

 oligogenes, and they include characters determined by single 

 genes or by the interaction of only a small number of genes 

 with large effects. Oligogenes determine characters that show 

 discontinuous variation. Polygenic characters are controlled by 

 the joint action of a large number of genes each of which has but 

 a small effect when compared with the total nonheritable fluctu- 

 ation of the character, and hence show continuous variation. 

 Polygenes, therefore, include duplicate, cumulative, nondomi- 

 nant genes when the number of such genes is large enough so 

 that each has a small effect compared w^ith fluctuation. They 

 have individual effects which are similar to one another and are 

 small, but they may often show dominance and do not always 

 act strictly cumulatively. If there is dominance, some dominant 

 genes may increase while others decrease the expression of the 

 character, and a symmetrical frequency distribution will result 

 from the presence of an equal number of both types of dominant 

 polygenes. The interaction of polygenes is not always purely 

 additive. Some polygenes interact so as to give a perfectly sym- 

 metrical frequency distribution if a certain type of scale is used 

 to plot the measurements, but a skewed curve if the type of scale 

 is changed. Apparently, however, polygenes may also show 

 various types of epistasis with respect to one another. 



Some Statistical Constants 



In Table 19, the distribution of the plants in the Pi, Fi, F2, and 

 some F3 families is tabulated, and this is followed by three 

 columns headed ":r," ''<^," and "v.^' Since nothing has been said 

 as yet about the meaning of these terms the student will, perhaps, 

 wonder whether their presence has any significance. Most as- 

 suredly it has! These expressions, known as statistical con- 

 stants, are of great value in giving us a clear concept of the 

 family to which they refer and they enable us to compare at a 

 glance two or more families. Another important characteristic 

 of these families is the number of plants that they contain. The 

 size of each family is listed in the last column in these tw^o 

 tables. 



Although these statistical constants have been used in this 

 specific problem to describe families of plants, they are of very 

 wide application and are used in many fields of biology, psy- 



