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 + "? == 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. 



