2. 5 X 



THE QUARTERLY REVIEW OF BIOLOGY 



populations whose characters are deter- 

 mined by incompletely dominant, multiple 

 or polyploid factors, and for the equilibria 

 attained in certain of the cases. For a 

 multiple autosomal recessive character, 

 selection is shown to be lower than in the 

 case of a character determined by one 



tained in the cases of multiple sex-linked 

 recessive characters and multiple auto- 

 somal dominant characters, selection 

 being slower in the multiple case. 



For the case of linkage between the 

 autosomal factors, the proportions of the 

 various types of gametes are shown to 



TABLE 4 



Generations required {or a given change with various types of slow selection 

 k = o.ooi 











CHANGE IN PERCENTAGE 



DOMINANT 



TYPE OF SELECTION 



SEX 











FACTOR FAVORED 

















O.OOI-I 



1-50 



50-99 



99-99.999 



Non-amphi- 



Bisexual racial 



Both 



6,92.1 



4,592- 



4,592- 



6,911 



mictic 















Autosomal 



Bisexual racial 



Both 



6,910 



4,819 



11,664 



309,780 



Autosomal 



(Unisexual racial 1 

 [Bisexual familial/ 



Both 



13,841 



9,638 



2-3,32-8 



619,560 



Autosomal 



Bisexual familialf 



Both 



9,2.17 



6,4x5 



I5?? 2 - 2 - 



413,040 



Autosomal* 



Bisexual racial 



o* 



13,831 



8,819 



6,157 



7,111 



Sex-linked 



Bisexual racial 



/Homozygous 

 \Heterozygous 



6,916 

 6,92.8 



4,668 

 5,164 



5,593 

 11,070 



10,106 

 10,693 



Sex-linked 



Bisexual familial 



/Homozygous 

 [Heterozygous 



2-0,753 

 2.0,768 



13,785 



14,987 



13,785 

 24,332- 



2-0,753 

 41,450 



Sex-linked 



Racial of homozygous sex 



/Homozygous 

 [Heterozygous 



10,380 

 10,391 



7,2.2.8 



8,378 



17,496 

 !53» 8 93 



464,670 

 149,860,377 



Sex-linked 



Racial of heterozygous sex 



/Homozygous 

 [Heterozygous 



2.0,746 

 2-0,753 



13,2.2.8 

 13,785 



9,2-36 

 13,785 



10,668 

 2-0,753 



Autosomal 



Unisexual gametic 



Both 



13,831 



8,819 



6,157 



7,111 



Autosomal 



Unisexual gametic} 



Both 



17 , 661 



17,638 



11,314 



14,114 



Sex-linked 



Gametic of homozygous sex 



/Homozygous 

 [Heterozygous 



I °,373 

 10,377 



6,619 

 6,892. 



4,618 

 6,891 



5,334 

 10,377 



Sex-linked 



Gametic of homozygous sex} 



/Homozygous 

 [Heterozygous 



2- ,746 

 2-0,753 



13,2.2.8 

 13,785 



9,136 

 13.785 



10,668 

 2-o,753 



* Dominant in o", recessive in 9 . 



t The families have only one parent in common. 



} In heterozygous individuals gametes are replaced (as zygotes in familial selection). 



The effect of selection on recessive characters may be found by inverting the order of the four numerical 

 columns. Thus 309,780 generations are needed for an autosomal recessive to increase from 0.001 per cent 

 to 1 per cent, 11,664 generations to increase from 1 per cent to 50 per cent, and so on. 



factor alone, although when the domi- 

 nants are very rare or when one of the 

 multiple factors greatly outweighs the 

 rest, it proceeds at about the same rate 

 in the two cases. Selection is slowest for 

 the multiple case when the factors are of 

 equal weight. Similar results are ob- 



approach asymptotically those which 

 would be reached in one generation 

 without linkage. 



Part IV (5) deals with the question of 

 overlapping generations, and in it the 

 author first takes up and demonstrates the 

 theorem previously given by Lotka (13) 



