2o8 HEREDITY AND EUGENICS 



to eliminate a dominant or a recessive character. 

 He finds that in a Mendehan population in which the 

 numbers tend to double in each generation, and in 

 which a dominant character has twice the viability 

 of the corresponding recessive, then the recessive will 

 be eliminated in the eleventh generation. On the 

 other hand, if the recessive is twice as viable as the 

 dominant, then the latter will be eliminated in eight 

 generations. Hence, other things being equal, the 

 elimination of a deleterious dominant character is 

 more rapid than of a recessive. 



The subject of the Mendelian proportions in a 

 mixed population was first considered by Pearson 

 (1904). He showed that with random mating of two 

 forms A A and a a and their progen}^, the formula 

 AA -\- 2 Ka-\- 2 aa will apply to the proportions in every 

 later generation — i.e., the population will remain 

 stable. Hard}^ (1908) pointed out the same thing. 

 Pearl (191 3, 1914) has worked out formulae for differ- 

 ent types of inbreeding, and determined coefiicients 

 for different degrees of relationship among inbred 

 pedigrees. Jennings (191 6) has elaborated eight}"- 

 two formulae, from which can be calculated, in many 

 cases directly, the results of various systems of 

 breeding in a Mendelian population. The results 

 vary, of course, not only according to the system of 

 breeding followed, but also according to the com- 

 position of the population at the beginning. The 

 systems of breeding analysed include random mating, 

 assortative mating, self- fertilisation, and various 

 systems of inbreeding, and from the formulae obtained 

 the relative proportions of the various t3^pes in any 

 generation may be determined. 



With random mating the resulting population 

 generally remains stable, but with inbreeding or 

 assortative mating it may alter progressively in a given 

 direction. Inbreeding wall also, of course, gradually 



