178 Locating Genes on Chromosomes 



percentage of crossovers obtained when only hm and v were 

 considered, twice the percentage of double crossovers in the 

 cross involving all three genes. It will give the same value — 

 65.64 per cent of crossing over or 65.64 map units. 



This problem shows that when genes are not close together, 

 and especially when the distance between them approaches 50 

 units, double crossing over reduces the single crossovers between 

 the two genes to about 50 per cent. For this reason, the cross- 

 over value never exceeds 50 per cent, even though two genes lie 

 more than 50 units apart. (In this problem, the value was so 

 slightly over 50 per cent that it can be considered as not exceed- 

 ing the figure.) This problem also shows that, in order to obtain 

 an accurate distance between two genes, (1) the three-point 

 method, when an intermediate gene is involved, must be used 

 and (2) genes that are close together should be used in determin- 

 ing map distances rather than genes widely separated on the 

 chromosome. 



In the discussion of two linked genes in the last chapter, it 

 was pointed out that the original cross may be made in either 

 the coupling or the repulsion phase, and that although the pa- 

 rental combinations and recombinations are different for the 

 two types of crosses, the percentage of crossing over is the same. 

 It is also true of a three-point cross. This cross in maize can 

 be made in four possible ways and will produce these four pos- 

 sible Fi plants: 



and 



hm pr V ' hm pr + ' hm + v ' + pr v 



No matter in which way the genes entered the Fi, the per cent 

 of recombinations between bm and pr, between pr and v, and 

 between bm and v will be the same. 



It will be noted that the double crossovers are less frequent 

 than either of the single crossover classes. It is naturally to be 

 expected because the chance of one break of chromatids in a 

 certain region is greater than the chance of two breaks in the 

 same region. This fact can be utilized, however, in locating the 

 genes on the chromosome. If the order of the genes in the pre- 

 vious cross was not known, the original parental combinations 

 could be written tentatively as BmBm PrPr VV X bmbm prpr vv. 

 The order of the genes here has no significance. Then, looking 



