184 GENETICS IN RELATION TO AGRICULTURE 
in general is the type of curve obtained in segregation in quantita- 
tive inheritance. The increased variability in F, 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’,. 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 F2 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. is of the type of the 
normal probability curve, then the larger the number of individuals 
grown in Fs, 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 Ff; population le beyond the 
limits set by the value Mp, + 26.38 mm., where Mp, is the value of 
the mean for the Ff. population. The mean of one F.2 population is 
67.51 mm., and its standard deviation, 5.91mm. 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 
aie = + 4.460, is equal to 0.00080 per 
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 fF, population with a standard deviation of 6.79 mm., the 
limits in this case expressed in terms of the standard deviation are 
26.: 
ae = 3.880: therefore 0.010 per cent. of the curve lies outside the 
lying outside the boundaries, 
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