Mutation and Selection — Mating and Heterosis 



233 



an offspring of this sib will receive this allele 

 is Yi. The frequency of both events occurring 

 is, therefore, %. The frequency is also Y^ for 

 these events to occur through the female half- 

 sib, so that the frequency of a given allele 

 becoming homozygous from a half-sib mat- 



mg IS K X Ya, or Ke- 



Since the other allele in 



the common parent could, in this way, also 

 become homozygous Ke of the time, the 

 combined chance of homozygosity for half- 

 sib matings is )i. So, Y?, of heterozygous 

 genes become homozygous due to this type 

 of inbreeding. 



The amount by which heterozygosity is re- 

 duced because of inbreeding is called the 

 inbreeding coefficient, F. In the case of 

 cousin marriage, F is Yk- The values of F 

 for more complicated pedigrees can also be 

 worked out. 



We have seen that all forms of inbreeding 

 increase homozygosity. Let us now calculate 

 the consequence of cousin marriage upon the 

 frequency of phenylketonuria. The fre- 

 quency of heterozygotes per 10,000 people is 

 198 (see p. 231). Cousin marriage would re- 

 duce heterozygosity by Y\6, or 12 individuals, 

 of which six would be normal {AA) and six 

 affected {aa). Since random mating would 

 produce one affected individual per 10,000, 

 cousin marriages would bring the total num- 

 ber of affected homozygotes in this popula- 

 tion to seven (six from inbreeding, plus one 

 from random breeding). Accordingly, there 



is a sevenfold greater chance for phenylke- 

 tonuric children from cousin marriages as 

 from marriages between unrelated parents. 



An additional example can be given, of the 

 increased risk of defect as a consequence of 

 cousin marriages. In a Japanese population 

 (Figure 27-3), congenital malformations, 

 stillbirths, and infant deaths are 24 48 

 per cent higher in cousin marriages than 

 when parents are unrelated. Since defects 

 such as these are known to be due, in some 

 cases, to recessive genes in homozygous 

 condition, these data support the view that 

 homozygosis resulting from inbreeding can 

 produce detrimental results. The fact that 

 inbreeding produces homozygosis, and that 

 homozygosis can lead to the appearance of 

 defects, does not automatically mean that 

 inbreeding is disadvantageous under all cir- 

 cumstances. For, while many individuals 

 become homozygous for detrimental genes 

 as a result of inbreeding, just as many be- 

 come homozygous for the normal alleles. 

 The success of self-fertilizing species is testi- 

 mony to the advantage of homozygosity at 

 least in these species. 



In populations that normally cross-ferti- 

 lize, however, inbreeding usually results in a 

 loss of vigor. This loss of vigor is directly 

 connected to homozygosis. In what way is 

 it theoretically possible to explain the adap- 

 tive superiority of heterozygotes, which is 



usually known as heterosis or hybrid vigorl 



FIGURE 27-3. Increased risk of genetic defect witli cousin marriages. 

 {Data from Hiroshima and Nagasaki.) 



Frequency from Increase in Frequency Per cent 

 Unrelated Parents with Cousin Marriage Increase 



CONGENITAL 

 MALFORMATION 



.011 



.005 



48 



STILLBIRTHS 



.025 



.006 



24 



INFANT DEATHS 



.023 



.008 



34 



