EFFECTS OF INBREEDING AND CROSSBREEDING. 39 
effects. It is logical that there should be such a relation. The 
chances are much greater that any mutation will be injurious than 
beneficial, on the principle that anything done at random to a com- 
plex mechanism will probably damage it. Even if dominant and 
recessive mutations occur with equal frequency, the latter should 
accumulate more rapidly, since they can be carried along out of the 
range of natural selection, while injurious dominant mutations will 
tend to be eliminated at once. 
Thus logically we should expect to find that recessive factors would 
more frequently be deleterious than dominant ones, and study of the 
known factors shows that such a situation actually exists. Given the 
Mendelian mechanism of heredity, and this more or less perfect 
correlation between recessiveness and detrimental effect, and all of 
the long-known effects of inbreeding—the frequent appearance of 
abnormalities, the usual deterioration in size, fertility, and constitu- 
tional vigor in the early generations, the absence of such decline in 
any one or all of these 
respects in particular 
cases, and the fixa- 
tion of type and pre- 
potency attained in 
later generations— 
are the consequences 
to be expected. 
MATHEMATICAL CON- 
SIDERATION. 
The primary effect of EA ES ea ae 
of inbreeding on this AGA OSE 
. Fig. 24.—The decrease in heterozygosis in successive generations of 
theor y is the auto- inbreeding according to various systems of mating. 
matic increase in ho- 
mozygosis. Jennings (1912) showed that with self-fertilization the 
percentage of heterozygotes is halved in each successive generation. 
The decrease following brother-sister mating was worked out by Fish 
(1914) and Pearl (1914). Various other systems, such as continued 
mating of parent with offspring, were given by Jennings (1916, 1917). 
A method of calculating more remote systems has been given by the 
writer in a previous paper (1921). Figure 24 shows the decline in 
heterozygosis under various systems, starting from a random-bred 
stock. 
In Figure 24 the random-bred stock is represented as being 50 per 
cent heterozygous, which implies that dominant and recessive factors 
are equally numerous. It is easy to show, however, that the rate of 
decline is the same regardless of the ratio of recessive to total factors. 
The general formula for a random-bred population is 274A +2zy 
