Double Crossing Over 173 



their proper order and with the proper distances between them? 

 The method is the same as that used in locating the order of 

 cities. About a thousand miles west of New York is Chicago. 

 Another two thousand miles west is Seattle. If the order in 

 which these cities are located is known and the distance between 

 any two pairs of them is also known, they can be mapped and 

 the third distance can readily be determined. If the order in 

 which they are located is not known, they could not be plotted 

 on a map unless all three distances were known. If all that was 

 known was that Seattle and New York were three thousand 

 miles apart and that New York and Chicago were one thousand 

 miles apart, they could not be mapped because Chicago might 

 be east of New York, in which case it would be four thousand 

 miles from Seattle. Similarly, to plot three genes on a chromo- 

 some map the distances between all three pairs must be known 

 or the distances between any two pairs plus the order in which 

 they occur. 



In the second chromosome of Drosophila melanogaster , the 

 genes black {h) and curved (c) show about 27 per cent of cross- 

 ing over, and curved and vestigial {vg) show about 8.5 per cent. 

 Historically, the black-curved linkage is interesting for it was 

 the first case discovered of linkage in autosomes in Drosophila. 

 It happened to be found first in the repulsion phase. These 

 three genes cannot be plotted without further information as 

 they might be arranged in either of two ways: 



27 6.5 18.5 8.5 



vg b vg 



35.5 27 



If they were arranged the first way, h and vg should show 

 35.5 per cent of recombinations; but if they were in the second 

 order, only 18.5 per cent of crossovers should be found between 

 these two genes. Since the latter figure more nearly accords with 

 experimental data, the second arrangement is the actual one. 



Double Crossing Over 



So far, we have assumed that only one chromatid of each 

 chromosome breaks between two genes. This statement is true 

 for any one place in a chromosome and is also true between any 



