16 APPLICATION OF PRINCIPLES OF HEREDITY TO BREEDING. 



cell organ, and that r and P pertain to the Mendelian mate of this 

 organ. Since most Mendelian character pairs consist of determiners 

 one of which represents the presence of something and the other 

 the absence of the same thing, we shall, in general, use for such pairs 

 of characters in hybrids symbols consisting of a capital letter and 

 the corresponding small letter, the capital letter standing for presence 

 of the character and the small letter for its absence. Thus, in the 

 cross between red and white peas, since the difference between 

 these varieties consists in the presence of red color in one and its 

 absence in the other, we represent the hybrid as Rr. Since the 

 hybrid itself is red in this instance, this formula is logical; it would 

 naturally be red because of the presence of R. But, as previously 

 stated, there are cases in which the absence of a character is domi- 

 nant in the hybrid between races one of which has the character and 

 the other does not. Thus the hybrid between polled and horned 

 cattle is polled. Here the formula for the horn determiner in the 

 pure horned breed would be HH; in the pure polled breed, M; and 

 in the hybrid, Hli. But since the determiner H does not succeed 

 in producing horns in the hybrid and the hybrid therefore has the 

 appearance of its polled parent we may write the forniula for the 

 hybrid as {H)lij to show these facts. Similarly, the hybrid between 

 bearded and smooth wheat would be represented by 



Cases like the purple hybrid primrose are so rare that we do not 

 need to use any particular symbol to indicate that the hybrid is unlike 

 either parent. 



The question why these characters, horns in cattle and beards in 

 wheat, do not develop when represented by only one active deter- 

 miner is an interesting one, and is very ably discussed by Doctor 

 Shull in the July, 1909, number of the American Naturalist. The 

 fact probably is that in these hybrids the determiners H and B are 

 not latent, but that single determiners are not able to produce that 

 chemical condition in the cell which is necessary for the develop- 

 ment of these characters. In pure horned cattle and pure bearded 

 wheat, where there are two active determiners for each of these 

 characters, the proper condition for the development of these char- 

 acters is brought about. 



In general, a hybrid produces three types of progeny with ref- 

 erence to each pair of characters in which its parents differ. The 

 hybrid between red and white varieties of peas produces two kinds 

 of pollen, which we may designate as R pollen and r pollen. It pro- 

 duces two corresponding types of ovules. On the average, half the 

 R ovules are fertilized by R pollen, so that one-fourth of the progeny 

 of such a hybrid is of the type RR or pure red. Likewise, half the r 

 ovules are fertilized by r pollen, giving rr individuals, which consti- 



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