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THE AMERICAN NATURALIST [Vol. XL VIII 



tinued brother X sister mating in a Mendelian population. To 

 this we may now proceed. 



The Distribution of a Mendelian Population in Successive 

 Generations with Continued Brother X Sister 

 Mating 



Let us start with a population composed entirely of complete 

 heterozygotes. We shall consider a single character pair, A 

 denoting the dominant character, and a the recessive. The com- 

 plete heterozygote individual will then be Aa, and will produce 

 in equal numbers A and a gametes. 



In making an analysis of the effect of inbreeding on the popu- 

 lation it will be necessary to deal not merely with the distribu- 

 tion of individuals in each generation, but also with the distribu- 

 tion of families of the several types. Each mating will produce 

 an array of families, as well as an array of individuals. The 

 standard family throughout this discussion is taken as including 

 32 individuals, of which 16 are males and 16 females. It is 

 further assumed that there is no sex-linkage of characters, and 

 that in any family there will be an equal number of brothers and 

 sisters of each zygotic constitution represented. One family of 

 16 pairs of brothers and sisters will make 16 matings and pro- 

 duce 16 families of 32 individuals each. This constant rate of 

 fertility is assumed throughout the discussion. 



Every mating made is of a brother with his sister. 



With so much by way of preliminary definition of the limita- 

 tions of this investigation, let us proceed to the actual analysis. 



First Generation 

 Constitution of the Population. — By hypothesis all individuals 

 are Aa. 



Proportion of Homozygotes in this Generation. — per cent, 

 of the whole population. 



Matings to Produce the Second Generation. — Start with one 

 brother X sister pair of individuals from this population. The 

 mating will be Aa X Aa. This will produce one family, 8AA 

 + 8Aa + 8aA + 8aa, 



Second Generation 

 Constitution of the Popidation.—8AA-{-8Aa-\-8Aa-\-8aa. 

 Proportion of Homozygntts in this Generation. — 50 per cent, 

 of the whole population. 



