EFFECTS OF INBREEDING AND CROSSBREEDING. 
(C2) the true breeding lines of course remain the same, while the 
remaining portion gives rise to a population with unchanged total 
composition, but with a correlation of +.50 between brothers and 
sisters. There is thus no difference in the percentage of heterozygosis 
in C1 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 
C1 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 asin 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 C1, 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. 
