300 INTRODUCTION TO CYTOLOGY 



percentage was 6.9, so that Sk sk had to be placed this number of units 

 from B h. Either of two positions was possible for Sk sk: to the right 

 or to the left of B h. Obviously a choice between these positions might 

 be made if the percentage of recombination between Lg Ig and Sk sk were 

 known. This turned out to be 34 ; hence Sk sk was assigned a position 

 farther away from Lg lg than was B b. The relative position of the three 

 pairs of genes was thus established. 



It will be noted that the percentage of recombination between Lg lg 

 and Sk sk is somewhat less than the sum of the percentages shown in 

 regions a and /3. This is due to the fact that two crossovers sometimes 

 occur between widely separated genes in the same chromosome pair. 

 Thus two exchanges between Lg lg and Sk sk would leave the same genes 

 linked, one crossover neutralizing the effect of the other. Since all three 

 gene pairs were studied simultaneously in the above experiment, it was 



1-9 b Sk 



Fig. 172. — Diagram of linkage relations of certain genes in chromosome II of Zea 

 Mays. The four lines represent portions of the chromatids of a synapsed pair. See text. 

 (After data from M. M . Rhoades.) 



possible to show that crossing-over had actually occurred simultaneously 

 in regions a and j3 in 11 out of the 1,392 cases. Because of such "double 

 crossing-over," the map distances often exceed the percentages of recom- 

 bination for widely separated genes. 



The observed percentages of recombination due to random crossing- 

 over between the four chromatids of a tetrad approach 50 as a limit since 

 only two of the four chromatids are altered by any one exchange (Emer- 

 son and Rhoades, 1933). In well-developed chromosome maps like those 

 of Zea and Drosophila (Figs. 171, 173) it will, however, be noted that map 

 distances may exceed 100 units. This is because the map is built up by 

 adding the distances between closely linked genes and not by observing 

 directly the recombination percentages for widely separated genes. 

 It does not take account of such modifying influences as double crossing- 

 over. Hence the map distances represent actual recombination per- 

 centages only for rather closely linked genes (not more than about 10 

 units apart in Drosophila) . It will accordingly be observed that the map 

 distance between "black" and "vestigial" in the second chromosome is 

 18.5 units, whereas the percentage of recombination is 17, as shown in 

 Fig. 169. 



