18 APPLICATION OF PRINCIPLES OF HEHEDITY TO BREEDING. 



LAW OF RECOMBINATION. 



The third and most important principle discovered by Mendel" is 

 the fact that, generally speaking, when two or more ''pairs" of char- 

 acters are present in the same hybrid these pairs are independent of 

 each other, so that one member of a given pair may be transmitted 

 with either member of another pair. The results of this important 

 discovery are shown in Table I, w^hich illustrates the cross between 

 Polled Durham and Hereford cattle. 



As is well known. Polled Durham cattle have colored faces and no 

 horns, while Herefords have horns and white faces. The white face 

 of the Hereford seems to be due to the presence of a determiner which 

 controls the distribution of color over the body. We thus represent 

 white face by W and colored face by w, that is, absence of white face. 

 As before, the poll character is represented by h and the horn char- 

 acter by H. White face is dominant to colored face in this cross. 

 The complete formulae for these two pairs of characters in the body 

 cells are, therefore — 



In pure Hereford cattle, HHWW. 

 In Polled Durham cattle, hhww. 

 In the cross, {H)hWw. 



The cross has the white face but no visible horns, though it may 

 have scurs. 



The squares in the upper part of Table I represent germ mother 

 cells dividing in the reduction division. In this division each pair of 

 characters is separated. Thus, the pair Hli, both members of which 

 have been present in every cell of the body of the hybrid, is here 

 separated, H going to one daughter cell and Ti to the other. In the 

 cross here under consideration we have a second pair of allelomorphs, 

 namely, Ww. When a given mother cell divides, the two pairs of 

 allelomorphs may be arranged as in the left-hand square at the top 

 of Table I, in wdiich case // and w go together into one daughter cell, 

 while li and ^¥ go into the other. Such a division gives two kinds of 

 gametes, the formulae for which are, respectively, IIw and liW} Or 

 the two pairs of allelomorphs may be arranged as in the right-hand 

 square of Table I, in which case H and W go to the same daughter 

 cell, while li and w go to the other, giving two kinds of gametes having 

 the respective formulae // W and Jiw. There are, in all, therefore, four 



a The first is the so-called "law of dominance," though it is hardly entitled to rank 

 as a law; the second is the law of segregation of character pairs. 



&The gametic formula Hw does not represent a pair of determiners. It represents 

 two determiners, one of which is from one pair and the other from another pair. We 

 do not have pairs of determiners in gametes, i. e., in reproductive cells. The pairs 

 separate in the reduction division, and a gamete never has both members of the same 

 pair. 



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