LAW OF RECOMBIKATION. 



19 



kinds of gametes that a hybrid individual of the type here under con- 

 sideration can produce, namely, Hw, 7iW, HW, and Jiw. In the first 

 of these four types of gametes, namely, Hw, we find horns being trans- 

 mitted with colored face; in the third, HW, horns and white face are 

 transmitted together. Likewise, in the second type, Ji W, we have the 

 poll character and white face together, while in type four, 7iw, we have 

 the poll character and colored face. 



Since in the reduction division either of the two possible arrange- 

 ments of the two pairs of allelomorphs is just as likely to occur as the 

 other, one of them will occur in about half the cells and the other in 

 the other half. We thus get all four types of gametes in equal num- 

 bers in every hybrid animal of this character. In the male this is 

 actually realized, for millions of gametes are produced. But in the 

 female only a few reproductive cells are formed, but these few are as 

 likely to be of one type as another. Hence, on the average for a large 

 number of such females, the four types of gametes will occur equally 

 often. In the middle part of Table I we have all the possible, and 

 equally probable, unions that can occur between the gametes of the 

 two sexes. Thus the Hw gametes of the female are offered four kinds 

 of sperm in equal numbers. Hence, on the average one-fourth of these 

 Hw ovules will be fertilized by Hw sperm, giving individuals of the 

 next generation of the type HHww. Another fourth will meet liW 

 sperm, giving individuals of the type {H)liWw, and so on. 



Table I. — Cross between Polled Durham and Hereford cattle and its results. 



Reduction division as itj 

 occurs in the cells of I 

 the first-generation hy- j 

 brid. J 

 The four types of repro-i 

 ductive cells produced 

 by first-generation hy-[ 

 brids. J 

 Or simply Hw, hW, HW, hiv 



The sixteen possible, and equally probable, matings to produce second-generation 

 hybrids are as follows: 



Gametes of male. 





Hw 



hW 



HW 



hw 



Hw 



1 HHww 



2 (H) hWw 



3 HHWw 



4 (H) hww 



hW 



5 (J?) hWw 



6 hhWW 



7 (H)hWW 



8 hhWw 



HW 



9 HHWw 



10 (H) hWW 



11 HHWW 



12 (H) hWw 



hw 



13 {H)hww 



14 hhWw 



15 (H) hWw 



16 hhww 



165 



