THE AMERICAN NATURALIST 



[Vol. LV 



result will follow. Unexpected irregularities in ratios may 

 arise where many mutant characters are distributed in different 

 combinations. These peculiarities of inviability are probably 

 comparable to "specific" and "disproportionate" modifications 

 in eye-color, etc.® 



If more than one poorly viable mutant is present in a linkage 

 experiment, there is distortion in the ratios due to linkage, and 

 such experiments are either entirely worthless, or are only to be 

 regarded as rough indicators of the real relations. As we saw, 

 if only one inviable mutant is present in a cross, one of each of 

 the pairs of complementary classes remains undisturbed; and 

 correct values can be calculated from them. The presence of a 

 second inviable mutant leaves undistur'bed only that class in 

 which neither mutant occurs. The calculation of crossover 

 values under this circumstance is somewhat comparable to solv- 

 ing for two unknowns v^'ith a single equation. Solutions can be 

 obtained only by assuming some relationship between the two 

 disturbances. Thus, we may assume that the disturbances are 

 independent; that is, that there is no specific interaction of the 

 kind mentioned above, and the class in which both mutants 

 occur is accordingly of the size that would be expected from the 

 amount of the disturbance present in those classes in which each 

 occurs by itself. On this basis, the crossover values are calcu- 

 lated from the square root of the product of the two comple- 

 mentary non-crossovers, and likewise of the crossover classes, 

 instead of from the sums of such complementary classes.^ The 

 assumption of independence would be approximately correct in 

 perhaps a majority of crosses in which only two or a few loci 

 are involved. If the disturbances are related — if they tend to 

 neutralize or to exaggerate each other — a correction can still 

 be made by raising an equal number of individuals in the com- 

 plementary cross. In the two complementary back-cross^, a X b 

 (repulsion) and afc X ^^'ild-type (coupling), the character com- 

 binations that are non-crossover classes in the repulsion experi- 

 ment are crossovers in the coupling experiment, and vice versa. 

 If the presence of a particular class has given a crossover value 

 too high in the one cross, then it will give a value correspond- 



