THE PROBLEM OF INBREEDING 149 



Starting, by hypothesis, with all individuals of 

 the population heterozygous, there will be 



AFTER THE INDICATED NUMBERS OF 



GENERATIONS OF CONTINUED THE FOLLOWING PERCENTAGE OF 



BROTHER X SISTER MATING, HOMOZYGOTES. 



1 50.00 



2 50.00 



3 62.50 



4 68.75 



5 75.0 



6 79.69 



7 83.59 



8 86.72 



9 89.26 

 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 Aa, there 



