186 GENETICS IN RELATION TO AGRICULTURE 
In general the number of individuals necessary for recovery of the 
parental types depends upon the number of factors involved, so that 
with large numbers the expectations rapidly become very slight. 
5. In certain cases individuals should be produced in F, that show 
a more extreme deviation than is found in the frequency distribution 
of either grandparent. 
This follows from a consideration of cases like the following. If 
XXAABBcc and X XaabbCC be crossed, there will be obtained by re- 
combination in F’, individuals of the genetic constitutions XX AABBCC 
and X Xaabbcc which would be larger and smaller respectively than the 
grandparental types. 
6. Individuals from various points on the frequency curve of an F, 
population should give Ff; populations differing markedly in their modes 
and means. 
This of course depends on the fact that the Ff. individuals represent 
a series of genotypes which give F; populations depending on their par- 
ticular genotypic constitutions. 
7. Individuals either from the same or from different points on the 
frequency curve of an F’, population should give F’; populations of diverse 
variabilities extending from that of the original parents to that of the 
F, population. 
The variability of a population depends on the genotype of the Fe. 
plant selected. If this plant be heterozygous for many factors its 
variability obviously will exceed that of one heterozygous for but few 
factors. That plants occupying the same point on a frequency curve 
may possess different genotypes and be heterozygous for differing 
numbers of factors is self-evident, and is well illustrated by Nillson- 
Ehle’s case of color of grain in wheat, which has been treated in detail 
in a previous chapter. 
8. In generations succeeding the F2 the variability of any family may 
be less but never greater than the variability of the population from which 
it came. 
This proposition is to be taken with some reservation. Absolutely 
it holds only if the factors involved le in different chromosomes. If 
there is any linkage between size factors then the proposition is valid 
only when the number of factors involved is large. In that case breaks 
in linkage occur as often in one direction as in the other and so would not 
greatly influence the result. If the number of factors be small, however, 
and some of them coupled, then breaks in linkage might profoundly affect 
the relations in recombination and thus render invalid this proposition. 
Castle’s Hooded Rats.—Serious objections have been raised to the 
multiple factor hypothesis of size inheritance particularly on the basis of 
results of selection experiments. The multiple factor hypothesis depends 
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