EFFECTS OF INBREEDING AND CROSSBREEDING. 43 



(C2) the true breeding lines of course remain tlie same, while the 

 remaining portion gives rise to a population wath unchanged total 

 composition, but with a correlation of +.50 between brothers and 

 sisters. There is thus no difference in the percentage of heteroz5^gosis 

 in Cl and C2, both being just halfway between CO and the ancestral 

 inbred families. From this point the percentage declines as if from 

 a random-bred stock halfway between the inbreds and the original 

 random-breds. The percentage of heterozygosis in the later genera- 

 tions is about 75 per cent of its value in the same generation, starting 

 from random-bred stock. Thus about 4 per cent of the original 

 vigor of heterozygosis should be left after 15 generations of brother- 

 sister mating beginning with random-bred stock, but only 3 per cent 

 after 15 generations of such mating, following a first cross between 

 inbred lines. 



In our actual experiments only a limited number of families were 

 used in making the crosses. This of course makes no difference in 

 the average of the first cross (CO), provided that the particular inbred 

 lines used are typical. By the use of selected inbred lines, on the 

 other hand, it should be possible to produce a first cross superior 

 to the random-bred stock. 



The rate of decline on inbreeding the first cross in case an indefi- 

 nitely large number of families is involved is of course merely the 

 average of the results in particular cases. Thus the number of 

 families used makes no difference in our conclusions as to experiments 

 Cl and C2. 



Whatever the number of families, crosses among the crossbreds in 

 which no family is used twice, as in experiments CA, AC, and CC, are 

 equivalent to random mating among an indefinitely large number 

 of families. Thus the total composition and the percentage of 

 heterozygosis should be the same in CA, AC, and CC as in CO. As 

 already noted, however, the effects of renewed inbreeding are 

 different. 



It is only when we come to consider the effects of random mating, 

 resumed after crossing, that we must take account of the number 

 of families which form the foundation of the new stock. Random 

 mating of stock derived from a small number of homozygous lines 

 involves an appreciable amount of inbreeding and thus should give 

 results intermediate between experiments such as CO, CC, CA, and 

 AC, in which inbreeding is avoided, and Cl, in which there is brother- 

 sister mating. In the extreme case in which only two families are 

 used, random mating is of course the same as brother-sister mating 

 for one generation. There comes to be only half as much heterozy- 

 gosis as in the original stock from which the two parental families 

 were derived. The vigor of the new random breds should thus be 

 halfway between that of the original stock and of the inbreds. 



