VIII] THE CASE OF PAPILIO POLYTES 95 



depend upon two things, (1) the proportion of domi- 

 nants existing in the population before the process of 

 selection began, and (2) the intensity of the selection 

 process itself. Suppose, for example, that we started 

 with a population consisting of pure dominants, hetero- 

 zygotes, and recessives in the ratio 1:4:4. Since 

 these figiures satisfy the equation pr = q^, such a popu- 

 lation mating at random within itself is in a state of 

 stable equihbrium. Now let us suppose that the 

 dominant form (including of course the heterozygotes) 

 is endowed with a selection advantage over the re- 

 cessives of 10%, or in other words that the relative 

 proportion of the recessives who survive to breed is 

 only 90% of the proportion of dominants that sur- 

 vive^. It is clear that the proportion of dominants 

 must gradually increase and that of the recessives 

 diminish. 



At what rate will this change in the population take 

 place? Mr Norton has worked this out (see App. I) 

 and has shewn that at the end of 12 generations the 

 proportions of pure dominants, heterozygotes, and re- 

 cessives will be 1:2:1. The population wiU have 

 reached another position of equilibrium, but the pro- 

 portion of recessives from being four-ninths of the 



^ If for example there were 5000 dominants and 4000 recessives, 

 and if only half of the population survives to mate, then we should 

 be left with 2500 dominants and 2000 recessives as parents of the next 

 generation. But if there were also a 10 % selective disadvantage 

 working against the recessives, their numbers would be further reduced 

 from 2000 to 1800 and the proportion of dominants to recessives would 

 be changed from 5 : 4 to 25 : 18. 



