Il8 GENETICS 



both. There are thus 4 different phaenotypes. In Mendel's 

 experiment with peas, in which the two pairs of characters 

 were (i) yellow and green; (2) round and wrinkled; in 

 Fi the proportions were 9 that were yellow and round, 3 

 that were yellow and wrinkled, 3 that were round and 

 green, and i that was green and wrinkled. These propor- 

 tions hold generally when there are two pairs of characters 

 connected with different pairs of autosomes. 



It may be observed that the proportions of the indi- 

 viduals of different constitution or genotype in F2, de- 

 scended from a cross between parents that differ in respect 

 to two pairs of autosomal characters (so that the parents 

 are AABB and aabb), can be found directly from the pro- 

 portions for a single pair of characters. In F2, for the 

 single pairs the proportions are AA -j- 2Aa -f- aA, and 

 BB + 2Bb -f- bb, respectively. If now we multiply together 

 algebraically these two polynomials, we obtain the relative 

 proportions for the different combinations produced when 

 the two pairs are together. These proportions are the fol- 

 lowing : 



AABB + 2AaBB + aaBB + 2AABb + 4AaBb + 



(I) (7) (3) (6) (5) 



2aaBb + AAbb + 2Aabb + aabb 



(9) (2) (8) (4) 



Examination will show that this is the same set of pro- 

 portions shown in table 2 on the preceding page. To bring 

 this out, the same numbers employed in table 2 are placed 

 in parenthesis beneath each combination. 



Certain other relations among the nine different types 

 are important, since they hold for all cases of two pairs of 

 characters that are dependent upon different pairs of auto- 

 somes. These are the following: 



I. There are four combinations (Nos. i, 2, 3, 4), con- 

 stituting one-fourth of all the zygotes, that are homozy- 



