THE MECHANISM OF CROSSING-OVER III 



HERMANN J. MULLER 

 Columbia University 



V. An Experiment to Determine the Linkage of Many 

 Factors Simultaneously 

 A more exact knowledge of the interference of one 

 crossing-over with another required an experiment, or 

 series of experiments, in which the distance between the 

 two points of crossing-over in cases of double crossing- 

 over could be more accurately determined. In an experi- 

 ment involving only three factors— A, D and H— if a 

 double cross-over occurs, all that can be known is that 

 crossing-over has occurred at the same time somewhere be- 

 tween A and D, and somewhere between D and H, but 

 nothing can be known of the precise location and distance 

 apart of the two points of crossing-over, except that they 

 could not be further apart than A and H. On the other 

 hand, if the inheritance of four points could be followed— 

 say, A, D, F and H— then the distance between the two 

 points of crossing-over could be determined a little more 

 exactly, for a double crossing-over involving breaks be- 

 tween A and D, and between D and F, would cut out a 

 shorter segment of the chromosome than one occurring in 

 regions A-D and F-H. And the more numerous were 

 the factors that could be followed— other things being 

 equal— the more exact the determination would become. 

 At the same time, it might be possible by comparing the 

 results of a series of different experiments to arrive at the 

 desired end with the three-factor method also. For ex- 

 ample, the difference in frequency between the double 

 cross-overs obtained in an experiment involving A, B, C 

 and in an experiment involving A, B, D, must obviously 

 be due to the double cross-overs involving regions A-B 

 and C-D, 1 except in so far as these differences are due to 

 the random deviation of different samples from each 



i For region BD is made up of BC + CD. Therefore double crossovers 

 involving AB and BD really consist of double cross-overs involving AB and 

 BC plus those involving AB and CD. Consequently, if we subtract the 

 number of double cross-overs involving AB and BC from the number involv- 

 ing AB and BD, we obtain the number involving AB and CD. 



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