120 GENETICS IN RELATION TO AGRICULTURE 
The occurrence of double crossing-over accounts for the low per- 
centage of crossing-over between white and bar as compared with the 
sum of the values given by white and miniature and miniature and bar. 
The value for crossing-over between W and M is given by 
B+ ° = 28.15 + 5.05 = 33.2 per cent. 
and similarly between M and B’ 
C+ 2 = 15.45 + 5.05 = 20.5 per cent. 
consequently the distance between W and B’ as measured by adding 
together the values for W and M and M and B’ gives the equation 
B+C+D = 53.7. 
Since double crossing-over of the type D does not involve a rearrange- 
ment of the loci, W and B’, however, the actual crossing-over obtained 
experimentally must fall short of the computed distance by a value 
equal to D as given by the equation 
B+ C = 43.6 per cent. 
The lowering of the percentage of crossing-over when extreme distances 
are involved is, therefore, a logical consequence of the relations existing 
between linked factors. Obviously double crossing-over occurs much less 
frequently in short distances than in long ones. Consequently since a 
factor map is designed to give the total values for crossing-over between 
the different loci, such a map is prepared so far as possible from experi- 
ments involving short factor distances. If such data are not at hand 
simple methods of interpolation are used to locate the loci. 
It should be noted in passing that variations in linkage values some- 
times occur among members of a given set of factors. Bridges has pointed 
out that in some cases at least the percentage of crossing-over depends 
somewhat on the age of the female, and Plough has detected definite 
effects of extremely high or low temperatures on the percentage of 
crossing-over between factors of the second chromosome in Drosophila, 
although crossing-over in the first and third chromosomes was not in- 
fluenced by the changes in temperature. Besides such variations, how- 
ever, definite factors have been discovered (Sturtevant) which lower the 
percentage of crossing-over. Muller has shown that such a factor exerts a 
particularly disturbing action in the third chromosome in which it is 
located. But even in cases of variation in linkage values the order of the 
factors in the chromosome is not disturbed. The relations shown, there- 
fore, in cases involving variations in linkage are in harmony with the 
conception of linear arrangement of factors in the chromosomes. 
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