316 LEROY POWERS 



chromosome pair. In this column the situation is reversed as compared to 

 column two. Again 50 per cent of crossing over gives 244 individuals among 

 a million in the F2 possessing all twelve plus genes. This decreases with a de- 

 crease in the percentage of crossing over until with no crossing over no indi- 

 viduals in the infinite F2 population contain more than eight plus genes. 

 However, since two of the plus genes are carried on the same chromosome 

 in each of the two linkage groups, an increase in the linkage intensity results 

 in an increased number of individuals in the F2 population possessing all 

 eight plus genes in the homozygous condition. 



Here, then, is a case in which close linkage facilitates recombination of 

 desired genes up to a certain number, and from a practical standpoint further 

 advances by selection in that generation are impossible. Also, it would be 

 difhcult to make further advances by continued selection in later genera- 

 tions. In the F2 population with a crossover value of 0.075 the frequency of 



the ( T T _ ) ( T T _ ) genotype e.xpressed as a decimal fraction is 



0.183024 and of the (t t 7)(i t l) genotype is 0.014840. 



To obtain some F3 families derived from F2 plants of the latter genotype 

 would require growing at least 300 selections in the F3 generation. To sepa- 

 rate the F3 families derived from the F2 plants of the former genotype from 

 those derived from the latter genotype would require an adequately replicated, 

 well designed experiment. Anyone who has worked with the quantitative char- 

 acters either in genetics or plant breeding realizes the difficulties besetting such 

 a task. After such F3 families had been determined, only 25 per cent of the in- 

 dividuals would be of the (TTT)(TT_) genotype. These would have 

 to be tested in the F4 to separate them from F4 families derived from F3 plants 

 of the (i i 7) (i t l) and the (^ ]j] ~) (^ ][] ~) genotypes. Even 



with the small number of genes assumed in the above example, it would not be 

 a simple matter to make progress by continued selection in later generations. 

 The addition of a few more genes having the plus and minus genes alternating 

 on the same chromosome would make further progress by continued selection 

 in generations later than the F2 practically impossible. From the above it is 

 apparent that any series of plus genes being adjacent without minus genes in- 

 tervening would facilitate recombination of desirable genes in the F2 genera- 

 tion. It seems that in actual genetic and plant breeding materials many such 

 combinations do exist. 



The figures in the fourth column of Table 19.9 are the theoretical fre- 

 quency distributions for that situation in which the plus and minus genes 

 alternate on the chromosome. Again the number of individuals expected in 

 the F2 generations possessing all twelve plus genes decreases rather rapidly 

 with a decrease in the percentage of crossing over. Even in the case of 50 per 



