114 MODES OF RESEARCH IN GENETICS 



great-great-great-grandparents, instead of the 

 possible 4096. He may have had fewer than 

 2048, but Zi = 50 tells us that he could not have 

 had more. Similarly, Zi = 75 indicates that since 

 c and d, the grandsire and granddam of x, were 

 brother and sister, x cannot have in any earlier 

 ancestral generation more than 25 per cent of the 

 theoretically possible number of ancestors for 

 that generation. And so on for the other values 

 of Z. 



In the limiting case of the closest inbreeding 

 possible the successive Z's will have the values 

 given in the table on the opposite page. 



From this table it is apparent that while the 

 narrowing or exclusion of the possible different 

 source lines of descent proceeds very rapidly in 

 the first few generations of brother X sister breed- 

 ing, only relatively little change is made by further 

 generations of this sort of breeding. Thus in 

 seven generations of brother X sister breeding all 

 but about 1.5 per cent of the potentially different 

 ancestral *' blood lines" will have been eliminated. 

 After 16 generations of this sort of breeding (a 

 number easily attainable in ordinary breeding 

 experiments) an individual so bred can by no 

 chance possess more than yoVo ^^ one per cent 

 of the different lines of ancestral descent which are 

 theoretically possible. This table strongly sug- 

 gests that if, in an experiment to test the influence 

 of inbreeding, no particular effect is observed 



