232 



CHAPTER 27 



breeding pattern is generally true in animals 

 and in human beings, also. The genetic re- 

 sult is the production of more homozygotes 

 than would occur by chance matings. 



The second departure from random mating 

 involves inbreeding, the tendency for mates to 

 be more closely related in descent than they 

 would be, were selection of mates made at 

 random in the population. What is the effect 

 of inbreeding when carried out for a single 

 generation? We can estimate this by study- 

 ing what happens to the genes that are hetero- 

 zygous in the parent generation. There 

 are various degrees of inbreeding, the closest 

 form being self-fertilization, which occurs in 

 many plants. In self-fertilization, the het- 

 erozygote for a given pair of genes, Aa, pro- 

 duces progeny one half of which are homozy- 

 gotes, so that heterozygosity is reduced by 

 one half with respect to this pair of heterozy- 

 gous genes. The decrease in heterozygosity 

 due to self-fertilization can be expressed in 

 general, as follows: the chance that an off- 

 spring will receive a particular allele in the 

 male gamete is }2 and the chance it will re- 

 ceive the same allele in the female gamete is 

 y.. The chance the offspring will be a homo- 

 zygote for that allele, therefore, is %. But 

 there is an equal chance the offspring will 

 become homozygous for the other allele, so 

 that there is a total chance of 50% for homo- 

 zygosis attributed to this type of inbreeding. 

 If all members of the population self-fertilize, 

 then in each successive generation, half of 

 the genes that were heterozygous become 

 homozygous. 



Suppose, in a portion of a population that 

 mates at random, X% of the progeny are 

 homozygotes. These come from matings 

 between two heterozygotes, between two 

 homozygotes for the same or for different 

 alleles, and between a homozygote and a 

 heterozygote. If the gene pool is at equilib- 

 rium, the matings that tend to increase 

 homozygosis are counterbalanced 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. Insofar 

 as these self-fertilizing individuals are con- 

 cerned, since they themselves already show 

 X% homozygosis, their offspring will also 

 have X% for this reason. But, if they show 

 Z% heterozygosis, their offspring will have 

 only }2Z% heterozygosis, and will show a 

 total homozygosis of X + %Z%. In other 

 words, each generation of self-fertilization 

 makes half of all heterozygous genes homozy- 

 gous, and the effect of self-fertilization, in a 

 normally random mating population, is to 

 increase the random mating rate of homozy- 

 gosis by ^2 of the rate of heterozygosis. 



By how much is homozygosity increased 

 in brother-sister (sib) matingsl The chance 

 that a particular gene in the male sib's father 

 is present in the male sib is )^, and the chance 

 that the male sib's child will receive this is 

 Yi. The chance for the occurrence of both 

 events is Vi. The chance that the female sib re- 

 ceives and transmits this same gene to her child 

 is also M. The chance that the child of the 

 sib mating will receive two of this same allele 

 is M X M, or Ke, which is its chance of being 

 homozygous for this gene. Since the child 

 would have an equal chance to become a 

 homozygote for the other allele in his grand- 

 father and for each of the two alleles in his 

 grandmother, this gives him 4 X Ke, or a 

 25% chance of homozygosis. In other words, 

 sib matings will cause K of heterozygous 

 genes to become homozygous. As discussed 

 above, this chance of homozygosis is addi- 

 tional to the chance of homozygosis which 

 obtains for genes in the randomly mating 

 portion of the population and which also 

 obtains for sib matings. 



Matings between individuals who have 

 one parent in common are called half-sib 

 matings. In this case, the frequency that a 

 given allele in the common parent will pass 

 to the male half-sib is K, and the frequency 



