HALDANE ON SELECTION 



247 



999 generations would be needed to reduce 

 the proportion to one in one million, and 

 we need not therefore be surprised that 

 recessive sports still occur in most of our 

 domestic breeds of animals. 



For the case where selection is not very 

 intense, the author has simplified the 

 general recurring equation to the form 



Un 



kn = tt n — uq + log e — • Then starting 



from or working toward a standard 

 population containing Z5 per cent reces- 



done in Table I, so that we may use this 

 table to run forward and backward from 

 a standard population of 75 per cent 

 dominants and 2.5 per cent recessives,and 

 determine the change in the per cent of 

 recessives for any number of generations. 

 Table z has been set up from the same 

 equation except that values of kn are 

 tabulated against the percentages of the 

 favored type. These two tables are very 

 convenient for the solution of various 

 actual examples in selection. 



Effect of slow selection 



TABLE 1 



on an a-i 



'■utosomal Mendelian character 



kn (number of generations X k~)... 

 Per cent of recessives when dom- 

 inants are favored 



Per cent of recessives when reces- 



— 1000 



— 100 



-50 



—10 



-15 



99.9998 



— 10 

 99-975 



sives are favored 



O.OOOI 



0.0105 



0.0417 



0.1773 



0.4115 



1.036 



-9 

 99-933 



1.2.54 



-8 

 99.82. 

 i-545 



-7 

 99.50 

 1.940 



-6 

 98.68 

 2-497 



-5 

 96.50 



3.308 



-4-5 

 94.38 



-4 

 91.14 



4-537 



-3-5 

 86.36 



-3 

 79-71 

 6.518 



~*"5 



—2. 



-1-5 



— 1 



-0.5 







0.5 



1 



J -5 



71.2.4 



61.53 

 9.718 



50.68 



n. n 



40.98 

 15.30 



31.05 

 19-53 



15.0 

 15.0 



J9-53 

 31.05 



15.30 

 40.98 



EL. II 



50.68 



1 



9.718 

 61.53 



2-5 



71-2-4 



3 

 6.518 



79-71 



3-5 

 86.36 



4 



4-537 

 91.14 



4-5 



94.38 



5 



3.308 

 96.50 



6 



2-497 

 98.68 



7 



1.940 

 99.50 



8 



9 



10 



*5 



10 



50 



100 



1000 





1-545 



99. 8z 



1.2.54 

 99-933 



1.036 

 99-975 



0.4115 

 99.9998 



0.1773 



0.0417 



0.0105 



O.OOOI 





sives, for which uo = 1, we have kn = 

 u n + log.eUn— 1. This equation gives to 

 a sufficiently exact degree of approxi- 

 mation the relationship between n the 

 number of generations, k the intensity of 

 selection, and u n . Since making k nega- 

 tive gives the effect of a selection that 

 favors the recessives at the expense of the 

 dominants, we can use this equation and 

 the equation y n = (1 -f- &n) -2 to compute 

 for different values of kn the proportion of 

 recessives when either dominants or reces- 

 sives are favored. This the author has 



CASE C: FAMILIAL SELECTION OF A SIMPLE 

 MENDELIAN CHARACTER 



This is a case of a factor A, whose 

 presence gives an embryo possessing it an 

 advantage measured by k over those 

 members of the same family which do not 

 possess it. For this case the law used in 

 the preceding section does not hold. 



If the family has both parents in 

 common, as in mammals, and we let vhe 

 population consist of f n AA:xq n Aa:r n aa, 

 where p n + z# n + r n = unity, then in a 



