is I GENETICS IN RELATION TO AGRICULTURE 



in general is the type of curve obtained in segregation in quantita- 

 tive inheritance. The increased variability in F 2 is, therefore, con- 

 sistently explainable on the basis of segregation of size factors which lack 

 dominance and which display cumulative effects. 



However, in the above study of flower size inheritance the parental 

 forms were not recovered in F 2 . Elsewhere we have adopted a chromo- 

 some explanation of heredity, consequently we must inquire what 

 chromosome conditions appear to exist in tobacco. So far as known 

 the number of chromosomes in Nicotiana is forty-eight. With such a 

 large number of chromosomes a duplication of the exact chromosome 

 content of each grandparent, assuming that no crossing-over occurred, 

 would take place only once in about 365 million millions of F z individuals. 

 Consequently, if a differentiating size factor be assumed to exist in each 

 pair of chromosomes, the reappearance of the grandparental forms on 

 the assumptions outlined above would be practically inconceivable. 

 It is, however, possible from the data at hand to approximate roughly 

 the probable ratio of occurrence of the grandparental forms in F% popula- 

 tions. Assuming that the class distribution in F 2 is of the type of the 

 normal probability curve, then the larger the number of individuals 

 grown in F 2 , the greater will be the class range over which the distribu- 

 tion extends. In this particular flower size problem the average mean 

 of the smaller flowered parent is 40.54 mm., and of the larger flowered 

 parent 93.30 mm. Half the difference between the means of the two 

 parents, therefore, amounts to 26.38 mm. Our problem is to determine 

 what proportion of the individuals in an F 2 population lie beyond the 

 limits set by the value Mp t 26.38 mm., where M Fl is the value of 

 the mean for the FZ population. The mean of one F% population is 

 67.51 mm., and its standard deviation, 5.91 mm. Now by mathematical 

 methods it is possible when the standard deviation of a normal prob- 

 ability curve is known to determine what proportion of the area lying 

 under the curve is within or outside of any assigned limits. If we apply 

 these methods to the problem here set, we find that the part of the curve 



26 38 



lying outside the boundaries, _ Q1 = + 4.46<r, is equal to 0.00080 per 



o.y JL 



cent, of the total area under the curve. Since a parental value might as 

 often fall short of these modal limits as exceed them, we may fix twice 

 this value as that marking off the parental portion of the curve. It 

 would, therefore, be necessary to grow some 62,500 individuals in order 

 to recover the parental forms in such an experiment as this. Consider- 

 ing the other F 2 population with a standard deviation of 6.79 mm., the 

 limits in this case expressed in terms of the standard deviation are 

 26 38 

 TQ- = 3.88a : therefore 0.010 per cent, of the curve lies outside the 



