72 



Table 3 



BR by 1.8 instead of by 1.0. It has 

 actually been found possible to pre- 

 dict the strength of association be- 

 tween two factors by this method, 

 fair approximations having been given 

 for BR and for certain combinations 

 involving factors not treated in this 

 paper, before the crosses were made. 



DOUBLE CROSSING OVER 



On the chiasmatype hypothesis it 

 will sometimes happen, as shown by 

 Dexter ('12) and intimated by Mor- 

 gan ('11 d) that a section of, say, 

 maternal chromosome will come to 

 have paternal elements at both ends, 

 and perhaps more maternal segments 

 beyond these. Now if this can happen 

 it introduces a complication into the 

 results. Thus, if a break occurs be- 

 tween B and P, and another between 

 P and M, then, unless we can follow P 

 also, there will be no evidence of 

 crossinCT over between B and M, and 

 the fly hatched from the resulting 

 gamete will be placed in the non-cross- 

 over class, though in reality he repre- 

 sents two cross-overs. In order to see 

 if double crossing over really does 

 occur it is necessary to use three or 

 more sex-linked allelomorphic pairs in 

 the same experiment. Such cases have 

 been reported by A4organ ('11 d) and 

 Morgan and Cattell ('12) for the fac- 

 tors B, CO, and R. They made such 

 crosses as long gray red by miniature 

 yellow white, and long yellow red by 

 miniature gray white, etc. The details 



STURTEVANT 



and analyses are given in the original 

 papers, and for our present purpose it 

 is only the flies that are available for 

 observations on double crossing over 

 that are of interest. Table 4 gives a 

 graphical representation of what hap- 

 pened in the 10495 cases. 



Double crossing over does then 

 occur, but it is to be noted that the 

 occurrence of the break between B 

 and CO tends to prevent that between 

 CO and R (or vice versa). Thus where 

 B and CO did not separate, the ga- 

 metic ratio for CO and R was about 

 1 to 2, but in the cases where B and 

 CO did separate it was about 1 to 6.5. 



Three similar cases from my own 

 results, though done on a smaller scale, 

 are given in the table at the end of this 

 paper. The results are represented in 

 Tables 5, 6 and 7. 



It will be noted that here also the 

 evidence, so far as it goes, indicated 

 that the occurrence of one cross-over 

 makes another one less likely to occur 

 in the same gamete. In the case of 

 BOPR there was an opportunity for 

 triple crossing over, but it did not 

 occur. Of course, on the viev/ here 

 presented there is no reason why it 

 should not occur, if enough flies were 

 raised. An examination of the figures 

 will show that it was not to be ex- 

 pected in such small numbers as are 

 here given. So far as I know there is, 

 at present, no evidence that triple 

 crossing over takes place, but it seems 

 highly probable that it will be shown 

 to occur.- 



UnfortunateK', in none of the four 

 cases given above are two compara- 

 tively long distances involved, and in 

 only one are there enough figures to 

 form a fair basis for calculation, so 

 that it seems as yet hardly possible to 

 determine how much eff^ect double 



2 A case of triple crossing over within 

 the distance CR was observed after this 

 paper went to press. 



