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 number^ the expectations rapidly become very slight. 



5. In certain cases individuals should be produced in Fz 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 XXaabbCC be crossed, there will be obtained by re- 

 combination in Fz individuals of the genetic constitutions XXAABBCC 

 and XXaabbcc which would be larger and smaller respectively than the 

 grandparental types. 



6. Individuals from various points on the frequency curve of an F 2 

 population should give Fz populations differing markedly in their modes 

 and means. 



This of course depends on the fact that the F 2 individuals represent 

 a series of genotypes which give Fa 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 2 population should give F 3 populations of diverse 

 variabilities extending from that of the original parents to that of the 

 Fz population. 



The variability of a population depends on the genotype of the F z 

 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 F 2 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 lie 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 



