3.10Gene Pool as a Population

Different individuals have different genotypes, but certain interesting behaviors can be seen when observing a population. For example, if the frequencies of the alleles T1 and T2 at the locus T in the Japanese population are p and q (p + q = 1), respectively, and if the population is very large and mating occurs randomly, genetic composition T1T1 in an individual selected from the population has the probability of p2. The probability of T1T2 or T2T2 is 2pq or q2, respectively (Table 3-1). This is called the Hardy–Weinberg principle.

Table 3-1 Illustration of the Hardy–Weinberg Principle

Let us look at another example. The frequencies of the genes for blood types in the human population is A = 0.22, B = 0.16, and O = 0.62. If the abovementioned principle is applied, then the distribution of blood types can be calculated. Therefore, the frequencies obtained by calculating (0.22A + 0.16B + 0.62O)2 are [A] = AA + AO = 0.32, [B] = BB + BO = 0.22, [AB] = 0.07, and [O] = 0.39. These frequencies are almost completely consistent with those for the distribution of blood types worldwide. Thus, based on the distribution of ABO blood types, it can be concluded that human mating is quite random.


Genetic Diseases and Probability

(1) Tay–Sachs is a disease inherited as a recessive trait. It occurs at a rate of approximately 1 in 3600 births in Jewish populations. This disease occurs because of the deficiency of a glycan-degrading enzyme called hexosaminidase A and is incurable usually resulting in death by age 5. It is a recessive trait, and accordingly, both parents are heterozygous at the genetic locus of hexosaminidase A and do not exhibit the phenotypes. In Fig. 3-3, if the heterozygous probability is considered as 1/x, then the probability of developing the disease is (1/x)∙(1/x)∙(1/4) = 1/3600 and therefore 1/x = 1/30. In other words, the gene responsible for the inherited disease afflicting 1 in 3600 individuals is present in 1 among 30 individuals. Then, can you calculate the heterozygous probability of the gene for deafness that occurs in 1 among 100 Japanese individuals?
(2) An example of cousin marriage is shown in Column Fig. 3-2. If one of the ancestors, A through D individuals, is heterozygous, (in this example, the gene possessed by B is marked with a red dot), the probability of having a homozygous child in cousin marriage is shown in the figure as (1/2)∙(1/2)∙(1/2)∙(1/2)∙(1/4)∙4 = 1/16. Thus, if the probability that the gene of the common ancestor is homozygous is higher than 1/16, then such individuals are not permitted to marry in Japan. Let’s confirm that this value is certainly higher than 1/16 in the case of half brother-sister marriage.
(3) As per Column Fig. 3-2, if the common ancestor has one pathological gene, when transmitted to offspring, this number is divided by two. These genes are also known to accumulate in the next generation. A recessive trait is frequently expressed in consanguineous marriage because a single pathological gene is duplicated with high probability.

Column Figure 3-2 Cousin Marriage and Recessive Trait

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