THE PROBLEM OF INBREEDING 149 



Starting, by hypothesis, with all individuals of 

 the population heterozygous, there will be 



etc. 



These results may be put in the form of a general 

 formula, by means of which the constitution of 

 any generation may be written down from a 

 knowledge of the preceding generation; that is, 

 from a knowledge of the n — 1th generation the 

 nth generation may be at once written down. 



This general formula may be developed as follows. 

 A single character pair will be considered, A denot- 

 ing the dominant character and a the recessive. 

 Equal fertility for all matings is assumed, the num- 

 ber of individuals per family being taken as 2 s, of 

 which s are males and s are females. One family 

 will then make s matings and produce s families 

 in the next generation. Each mating is, by hy- 

 pothesis, of a brother with his sister. 



Starting as before with a pair from a population 

 in which all individuals are of constitution ^a, there 



