OF MUTANT CHARACTERS. 



185 



black purples upon inbreeding. If both the black and the purple 

 chosen happened to have come from cross-over eggs, then the double 

 would be produced in F3 directly. In case none of the parents proved 

 to be from cross-over gametes, than at least the F3 wild-type flies are 

 equivalent to the Fi and would save a generation in the repetition. 

 The other two types of crosses would give a favorable result only if 

 both parents happened to be from cross-over eggs, in which ca.se the 

 double would appear among their progeny. 



Table 37.— Pi mating, purple, cf X black 9 ; B.C.,FicP X black purple 9 . 



It so happened that one of the black X black crosses gave a few 

 black purples in F3 directly and from these a stock was made for 

 use in back-crossing. At the same time a Pi mating of a black male 

 to a purple female was started to furnish the required Fi hetero- 

 zygotes. A single test of the Fi male showed, as expected, no crossing- 

 over whatever (table 37), 



Two back-cross tests of the female gave a total of 773 flies, of which 

 38 or 4.9 per cent were cross-overs (table 36). Of the two expected 

 values, that of 30 is excluded entirely, and that of 10 is approximated, 

 though not very closely. On this basis, the order of these genes is 

 black, purple, vestigial, and not black, vestigial, purple. 



A THREE-POINT BACK-CROSS. BLACK PURPLE CURVED. WITH 



BALANCED INVIABILITY. 



Most of the linkage experiments up to this time had involved only 

 two loci, as the three just cited, namely, purple vestigial, black ves- 

 tigial, and black purple. It was now realized that a more complex 

 type of experiment involving all three loci at once would yield returns 

 whose value far outweighed the greater labor entailed. Thus, a 

 multiple back-cross for black purple vestigial would give hnkage data 

 upon all three cross-over values simultaneously, and these values 

 would be strictly comparable, since there would be no possibihty of 

 discrepancies due to different conditions of culture or parentage. 

 Accordingly, the simple black purple back-cross was done on a scale 

 only large enough to decide between two possible values and thus show 

 what was the order of the three loci. A knowledge of this order is of 

 great advantage in synthesizing the multiple recessive. It was found, 

 as already stated, that black and vestigial are the two farthest apart and 



