Double Crossing Over 177 



22.27 43.37 



bm pr 



50.14 



In other words, an independent test of the hm and v genes 

 would show them 50.14 units apart, but bm and pr are 22.27 

 units apart and pr and v are 43.37 units apart. The laws of 

 mathematics tell us that the w^hole equals the sum of its parts, 

 but this case seems to defy the laws of mathematics. Actually, 

 of course, the discrepancy is that the value of 50.14 units be- 

 tween bm and v is inaccurate. The distance between two genes, 

 in map units, equals the percentage of crossing over between 

 them, but the examination of the testcross phenotypes when just 

 bm and v are studied does not show the true percentage of cross- 

 overs that occurred between these two genes. When all three 

 genes are considered at a time, some of the phenotypes that were 

 regarded as parental combinations are seen to be double cross- 

 overs. In determining the percentage of crossovers between bm 

 and V these double crossovers must be taken into account for, 

 instead of representing a parental type, each double crossover 

 represents two crossovers. Bearing this fact in mind, we should 

 revise the determination of the percentage of crossing over as 

 follows : 



+ pr +— 80 (40 X 2) 



bm + V— 92 (46 X 2) 



728 



= 65.64 per cent 



1109 



Now w^hen the distances between bm and pr (22.27 units) and 

 between pr and v (43.37 map units) are added together, their 

 sum (65.65 map units) equals the percentage of crossovers be- 

 tween bm and v when the double crossovers are taken into ac- 

 count. The same value could be obtained by adding to the 



