FACTOR RELATIONS IN QUANTITATIVE INHERITANCE 181 



intermediate, for in quantitative inheritance in general the factors ap- 

 parently do not display dominance but the phenotypic expression of Aa 

 is approximately equal to the average of that of the two parents. If 

 this idea be correct the F 2 should consist in this case of IAA : 2Aa : laa, 

 which has been shown to be approximately true, if the boundaries shown 

 in Fig. 86 be accepted. It is to be noted, however, even for as simple a 

 case as this that the two parents and the F\ each have their typical ranges 

 of fluctuation. Considering the parental and FI distributions, the upper 

 limits of the smaller parent run into the lower portion of the range of the 

 FI, and the lower limits of the larger parent run into the upper limits of 

 the FI. It follows that in F 2 , even if there should be only a single factor 

 difference between the two parents, the F 2 classes would overlap. Con- 

 sequently some of the plants assumed to belong to the lower class and 

 also some of those assumed to belong to the upper class really belong to 

 the middle group, and some of those arbitrarily included in the middle 

 class belong either to the upper or to the lower class. 



The only accurate method of classifying those individuals lying near 

 the boundaries of the classes is to test them by growing their F 3 progenies. 

 If they belong to the upper or lower classes they should then give uni- 

 modal distributions corresponding to the parental distributions, whereas 

 if they belong in the middle class, they should give trimodal distributions 

 corresponding to the distribution obtained in F 2 . In another case 

 Leake has endeavored to apply this test to an entire F 3 distribution, and 

 although the evidence indicates some discrepancies probably due to the 

 presence of minor factor differences, nevertheless the agreement is such 

 as to lend support to the idea of a single main factor difference. 



Most size differences however are not so readily interpreted as this 

 one, apparently because a larger number of factors is concerned in them. 

 The general statement with regard to such size differences is that two 

 contrasted races, each of which displays a certain characteristic amount 

 of variability when grown in the pure line, when crossed produce an FI 

 intermediate between the two parents and no more variable than either 

 of them. The F 2 from such a hybrid when grown in large populations 

 displays on an average an intermediate position, but some few indi- 

 viduals at either extreme approach the sizes of the parents, and between 

 these extremes lies a continuous series of forms, in distribution usually 

 approximating a normal curve. The evidence of segregation here is the 

 increased variability in the second generation, and subsequent genera- 

 tions display a similar conformity to such an interpretation. 



This type of inheritance may best be illustrated by a typical example, 

 but one which has, perhaps, been more thoroughly investigated than 

 any other, namely the inheritance of length of corolla in tobacco. East 

 has investigated the inheritance of length of corolla in crosses between 



