Inheritance of Quantitative Characters 83 



cumulative in increasing the height of the plant. Of 

 course a single dose of one type of factor may not bring 

 the same increase in height as would a single dose of one 

 of the other types, and therefore the mathematics of the 

 situation will be slightly modified. The fundamental 

 mathematical system, however, will remain the same, 

 and we will have the satisfaction of dealing with a natural 

 mechanism rather than an artificial one. 



A few of the applications of the cumulative factor hypothesis 

 are worth considering. Assume that a practical breeder crosses 

 two extreme parent types in the hope of obtaining a hybrid com- 

 bining the desirable characters of the two parents. If the material 

 is corn, he might use one parent with large grains but few in num- 

 ber, while the other parent had many grains but small ones. Such 

 quantitative characters as these would be determined by cumula- 

 tive factors, and the hybrid would be intermediate with respect 

 to both of these characters, that is, the grains would be of medium 

 size and medium number. No matter how many crosses he made, 

 he would always get this result, and not the desired combination 

 of large grains and many of them. 



Suppose now that these intermediate hybrids are inbred in the 

 hope of obtaining the desired combination among the individuals 

 of the F2 generation. It will be realized that the chances of obtain- 

 ing a plant combining the two extreme characters of large grains 

 and numerous grains would depend upon the number of factors 

 that enter into the make-up of these quantitative characters. 

 Assume that there are five factor pairs in each case. The mathe- 

 matics of the situation would show that in order to get the desired 

 pure type from a cross between two parents, each having their 

 desirable character determined by five pairs of cumulative factors, 

 it would require 100 acres of corn to have an even chance of getting 

 one such individual in the Fj generation. It is altogether unlikely 

 that any farmer would use 100 acres and a corresponding amount 

 of labor on such an extreme chance. Even an agricultural experi- 

 ment station would not feel justified in conducting such an experi- 

 ment. 



