x 5° 



THE QUARTERLY REVIEW OF BIOLOGY 



If k = i, the elimination is vastly slower 

 than when selection occurs in both sexes. 

 If k is small, the selection of the homo- 

 zygotes proceeds as in the case of slow 

 selection on an autosomal Mendelian 

 character, while the heterozygous sex 

 changes rather more slowly. 



CASE I : SELECTION OF A SEX-LINKED 



CHARACTER IN THE HETEROZYGOUS 



SEX ONLY 



In certain cases, sex-linked factors 

 appear only or mainly in the heterozygous 

 sex. For example, in Drosofhila melano- 

 gaster ' 'eosin" eye-color is far more marked 

 in the male than in the female, and the 

 sex-linked fertility factor L 2 postulated 

 by Pearl (n) in poultry can show only in 

 the female sex. Under these conditions 

 we find that for complete selection, k = 

 — co ? the number of dominants is halved 

 in each generation after the second. If 

 the recessives are eliminated and k = i, 

 the proportion of recessives is halved in 

 each generation. If the selection is slow, 

 kn = 3 logttn and the selection of the 

 heterozygous sex proceeds along the 

 logistic curve but at one-third the rate 

 of an autosomal Mendelian character, 

 while the selection in the homozygous 

 sex is slightly faster. 



CASE j: CERTATION, OR GAMETIC SELECTION 

 OF AN AUTOSOMAL CHARACTER 



Gametes or gametophytes may be 

 selected according to what factors they 

 carry, and while such selection may be 

 wide, it is more likely to be among the 

 gametes of the same individual. Con- 

 sidering the gametes of one gender to be 

 affected by selection, we find that for 

 complete selection if all the dominant- 

 carrying gametes are eliminated, k — 

 -co, the proportion of dominants is 

 halved in each generation . If all recessive 

 carriers are eliminated, no recessive 



zygotes appear and the proportion of 

 heterozygotes is halved in each genera- 

 tion. If selection is slow, 



and 



ktt = 1 log e «n 



Jn = (l + 0~ 2 



A comparison of the results of complete 

 selection for the more important cases is 

 given in Table 3 . Selection is supposed to 

 begin on a population in equilibrium, 

 containing equal numbers of dominants 

 and recessives of the sex considered. The 

 author comments on this table as 

 follows: "It is worth noting that in the 

 case of sex-linked characters, and auto- 

 somal recessives when selection is gametic, 

 individuals of types which have wholly 

 disappeared reappear if selection ceases. 

 With many types of heredity dominants 

 are eliminated in one or two generations, 

 and where this is not the case they 

 generally decrease more rapidly than 

 recessives." 



The rate of slow selection has been 

 determined less rigorously than in the 

 case of rapid selection, but the effect of the 

 approximation is slight. Table 4 shows 

 the effect of slow selection in the various 

 cases considered, the rate of selection in 

 this case being one in a thousand, that is, 

 a thousand of the type considered survive 

 for every 999 of the other. 



A consideration of all of the cases dealt 

 with in this paper shows that selection is 

 most rapid when amphimixis is avoided 

 by one means or another. Moreover, 

 selection is ineffective on recessive 

 characters when these are rare, except 

 in the case of sex-linked factors, when 

 it is effective in the homozygous sex 

 and in gametic selection. It seems, 

 therefore, very doubtful whether natural 

 selection in random mating organisms can 

 cause the spread of autosomal recessive 



