20 THE THEORY OF THE GENE 



the numerical result would be the same as when free 

 assortment occurs. That is, no linkage would be observed 

 even though the characters involved are in the same link- 

 age group. Their relation as members of the same group 

 could, nevertheless, be shown by their common linkage 

 to some third member of the series. If more than 50 per 

 cent crossing-over should be found, a sort of inverted 

 linkage would appear, since the cross-over combinations 

 would then be more frequent than the grandparental 

 types. 



The fact that crossing-over in the female of Drosophila 

 is always less than 50 per cent, is due to another corre- 

 lated phenomenon called double crossing-over. By double 

 crossing-over is meant that interchange takes place twice 

 between two pairs of genes involved in the cross. The 

 result is to lower the observed cases of crossing-over, 

 since a second crossing-over undoes the effect of a single 

 crossing-over. This will be explained later. 



The Simultaneous Interchange of Many Genes 

 in Crossing-Over. 



In the examples of crossing-over just given, two pairs 

 of characters were studied. The evidence involved only 

 those cases of crossing-over that took place once between 

 the two pairs of genes involved in the cross. In order to 

 obtain information as to how frequently crossing-over 

 takes place elsewhere, i.e., in the rest of the linkage 

 group, it is necessary to include pairs of characters that 

 cover the entire group. For example, if a female with the 

 following nine characters of Group I, scute, echinus, 

 cross-veinless, cut, tan, vermilion, garnet, forked and 

 bobbed, is crossed to a wild type male, and if the F x 

 female (Fig. 15) is back-crossed to the same multiple re- 

 cessive type, the offspring produced will give a record of 

 every crossing-over. If crossing-over had taken place 



