The Gene Pool; Equilibrium Factors 



207 



by others which decrease it, so that X% 

 homozygosis remains constant generation 

 after generation. Consider what happens in 

 another portion of this population which 

 happens to practice self-fertilization for one 

 generation. Since this segment of the pop- 

 ulation already shows X% homozygosis, its 

 offspring will also have X% homozygosis. 

 But, if this segment is Z% heterozygous, 

 after self-fertilization the offspring will have 

 only V-2 Z% heterozygosis, and, therefore, 

 will show a total homozygosis of X% + % 

 Z% . In other words, each generation of self- 

 fertilization makes half of all heterozygous 

 genes homozygous, and, in a normally ran- 

 dom-mating population, the effect of self- 

 fertilization is to increase the random-mating 

 frequency of homozygosis by y 2 the fre- 

 quency of heterozygosis. 



How much is homozygosity increased in 

 brother-sister (sib) matings? The chance 

 that a particular gene in the father is present 

 in the male sib is y 2 , and the chance that 

 the male sib's child receives this is similarly 

 ] {>; the chance for the occurrence of both 

 events is %. The chance that the female 

 sib receives and transmits this same gene to 

 her child is also %. Therefore, the chance 

 that the child of the sib mating receives two 

 representatives of this same allele is l / 4 times 

 % j or it has ] \ 6 chance of being homozygous 

 for this gene. Since the child has an equal 

 chance to become a homozygote for the 

 other allele in his grandfather and for each 

 of the two alleles in his grandmother, this 

 gives him 4 times y 16 or a 25% chance of 

 homozygosis. In other words, sib matings 

 cause % of the heterozygous genes to be- 

 come homozygous. This chance of homo- 

 zygosis from sib mating is in addition to 

 the chance of homozygosis from mating at 

 random. 



Matings between individuals who have 

 one parent in common are called half-sib 

 matings. In this case, the frequency with 



which a given allele in the common parent 

 passes to the male half-sib is y 2 , and the 

 frequency with which an offspring of this 

 sib receives this allele is l / 2 ', the chance of 

 both events occurring is, therefore, %. The 

 chance is also r 4 for these events to occur 

 through the female half-sib, so that the 

 chance of a given allele becoming homo- 

 zygous from a half-sib mating is y 4 times 

 y 4 , or y 16 . Since the other allele in the 

 common parent could, in this way, also be- 

 come homozygous y 16 of the time, the com- 

 bined additional chance of homozygosity for 

 half-sib matings is 1 £, or, in other words, 

 y 8 of the heterozygous genes become homo- 

 zygous because of this type of inbreeding. 



The amount by which heterozygosity is 

 reduced because of inbreeding is called the 

 inbreeding coefficient, F. In a similar man- 

 ner we can determine that in the case of 

 cousin marriage, F is V lr> . The values of F 

 for more complicated pedigrees can be 

 worked out accordingly. 



All forms of inbreeding increase homozy- 

 gosity. Let us calculate the consequence of 

 cousin marriage upon the frequency of 

 phenylketonuria. Its frequency of hetero- 

 zygotes per 10,000 people is 198 (see p. 

 206). Cousin marriage reduces heterozy- 

 gosity by y 16 , or by twelve individuals, of 

 which half of them are expected to be nor- 

 mal (A A) and half affected {ad). Since 

 random mating produces one affected indi- 

 vidual per 10,000, cousin marriages bring 

 the total number of affected homozygotes 

 in this population to seven (six from in- 

 breeding, one from random breeding). Ac- 

 cordingly, there is a sevenfold greater chance 

 for phenylketonuric children from cousin 

 marriages than from marriages between un- 

 related parents. 



Another example of how cousin marriages 

 increase the risk of defect comes from a 

 study which found that in a Japanese pop- 

 ulation (Figure 15-5) congenital malforma- 



