No. 636] GAMETIC RATIOS IN DBOSOPHILA 



59 



ingly too low in the complementary cross, and the mean value 

 will be correct.^ 



Since the effects of in viability are likely to be more pro- 

 nounced, even disproportionately so, as the number of mutant 

 characters present simultaneously is increased, it is advisable to 

 plan any linkage experiment in which several characters are to 

 be involved, in such a way that the characters are distributed 

 as evenly as possible. The type of back-cross that gives the 

 evenest possible distribution, as well as the smallest proportion 

 of individuals in which the higher combinations occur, is that in 

 which half the mutants have entered the cross from one parent 

 and the other half from the other parent, and in which the 

 mutants are alternated" as regards their positions along the 

 chromosome. Thus, for example, let us consider a back-cross in 

 the third chromosome in which the seven mutants to be used are : 

 roughoid at 0.0 ; hairy at 25.8 ; scarlet at 35.1 ; dicliate at 38.5 ; 

 pink at 44.6 ; spineless at 54.2 ; and ebony-2 at 66.9. The two 

 parents should be roughoid scarlet pink ebony-2, and hairly 

 dichjBte spineless; and the formula for the F, multiple lieterozy- 

 gote would be : 



Tlie production of an individual possessing all seven characters 

 would re(iuire an hexuple crossover, whicli almost certainly 

 would not occur.^ 



A method that overcomes inviability effects to the greatest 

 extent where many mutants are involved, but which unfortu- 

 nately requires too great lahor for general use, was devised by 

 Muller.^" Fj females heterozygous for any number of mutants 

 are crossed, not to the multiple recessive as in the ordinary back- 

 cross, but to the wild-type. Except for the dominant mutants, 

 none "of the characters involved appears in the resulting indi- 

 viduals, and hence do not exert injurious effects. These indi- 



8 This "balancing of the inviability" has been discussed at greater length 

 by Bridges, Jour. Exper. Zool., 1915, p. 3ff.; Jour. Exin r. Zooh, 1920, pp. 

 281, 288; by Morgan and Bridges, Carnegie Pub. No. 237, p. 19, 43; and 

 by Muller, Am. Nat., 1916, p. 353. 



9 See Bridges, Jovr. Exper. Zooh, 1920, p. 295, for discussion and other 



10 Am. Nat., 1916, p. 354 ff. 



