LINKAGE AND CROSSING-OVER 



443 



greater than the cross-over percentage between A and C, and the dis- 

 crepancy increases with the magnitude of the values involved. This 

 fact has been accounted for in two different ways. First, it may be 

 supposed that the arrangement of the genes is really not linear, that 

 B lies out of line with A and C, so that AC will be less than the sum of 

 AB and BC, and that the more distant genes are no farther apart than 

 indicated by the cross-over percentages between then?. This expla- 

 nation has met with more difficulties than it has cleared away. The 

 second explanation is that the map-distances indicate proportionate 

 numbers of breaks in the linkage chain between points, not propor- 

 tionate numbers of changes of relation between genes at particular 

 points. Thus, suppose genes ABCDE of a linkage system meet their 

 allelomorphs, abcde, in a cross and gametes are later formed by the 

 cross-bred as follows, (i) ABcde, (2) ABcdE, and (3) AbcDe. Assum- 

 ing that the arrangement is linear, we must suppose that one break 

 in the linkage chain has occurred in (i), two breaks in (2), and three 



M 



a 



M 



B C 



D 



FIG. 93. B and C illustrate Morgan's idea of the linear arrangement of the 

 genes in the chromosomes. A and D show how the composition of the chromo- 

 somes is supposed to change as the result of the crossover. On the right, a pair 

 of chromosomes, <z, before; b, during; and c, after a double crossover. (After 

 Morgan.) 



breaks in (3). But if we did not have genes BCD under observation, 

 and merely noted the relation of A to E, we should infer that in case 

 (i) and in case (3) a single crossover had occurred. We should on that 

 basis underestimate the amount of breaking in the linkage chain. 



