EXAMPLES OF MULTIPLE FACTORS. 11 



unit by hypothesis is as strong as the next there would only be fifteen 

 visible combinations — that is, fourteen grades of yellow forming a con- 

 tinuous series from strong yellow to solid green. As before, the pure 

 yellow and green types would be found but once in 16,384 individuals. 

 The most completely heterozygous combinations, as in the first case, 

 would be most numerous, but the number in this class would be much 

 greater, for here would fall all individuals that had combinations with 

 seven of the possible fourteen "doses" present. In either direction 

 from this group the frequencies would become smaller as they ap- 

 proached the extremes. They would form a curve very like the normal 

 curve of error. Tammes (1911) gives a table of the distributions of 

 the frequencies on similar assumptions with from one to six equivalent 

 units involved. Castle (1911) represents the same thing graphically 

 for two, three, and four characters. 



EXAMPLES OF MULTIPLE FACTORS. 

 COLOR DIFFERENCES. 



Such multiple factors as above described are not known to occur in 

 pea colors, but comparable cases which may be explained by two or 

 more independent factors giving rise to the same visible feature have 

 been found by several investigators to whose work brief references will 

 now be made. The important and conclusive investigations of Nilsson- 

 Ehle gave rise to this theory of multiple factors. When oats with 

 black glumes were crossed with varieties with white glumes, Nilsson- 

 Ehle (1909) found that, in most cases, black behaved as a single unit- 

 factor. In the second generation the ratio 3 black to 1 white was found. 

 One variety of black oats, however, gave 630 black to 40 whites (15.8: 1) 

 in the second generation of a cross with white. This is a close approxi- 

 mation to the dihybrid ratio. Of the 43 F 2 plants carried to the third 

 generation, 4 were white and showed no segregation, 17 were black and 

 remained black in the next generation, while 22 were blacks which 

 segregated into black and white. Of these, 11 gave 428 black and 120 

 white ( = 3.6:1); 9 gave 556 black and 35 whites ( = 15.9:1). Two of 

 the F 2 blacks gave higher ratios which could be considered wide deviates 

 from 15:1. Assuming, from the appearance of a dihybrid ratio in F 2 , 

 that two factors can produce black, it would be expected that in F 3 the 

 whites would breed true, that in every 15 blacks 7 would remain black 

 and 8 would segregate, 4 giving monohybrid ratios (3:1) and 4 giving 

 dihybrid ratios (15:1). The results gave 17:11:9 (or :11, if the two 

 families with higher ratios are included) =7:4.5:3.7 (or:4.5), whereas 

 7:4:4 was expected. 



Among eight brown varieties of wheat, he found seven that gave 

 monohybrid ratios when crossed with white, and one that gave a dihy- 



