EFFECTS OF INBREEDING AND CROSSBEEEDING. 



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 ^0% 

 cases, and the fixa- 

 tion of type and pre- 

 potency attained in 

 later generations — 

 are the consequences 

 to be expected. 



MATHEMATICAL CON- 

 SIDERATION. 



e a /o 



The primary effect 

 of inbreeding on this 



, . 5^ Fig. 24. — The decrease in heterozygosis in successive generations of 



tneory is tne 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 x^AA^2xy 



