# The hereditary form of diabetes is due to the recessive autosomal gene. A survey of the population of a large isolated island showed that

The hereditary form of diabetes is due to the recessive autosomal gene. A survey of the population of a large isolated island showed that 1% of people living on this island suffer from congenital diabetes. What proportion (%) among the healthy population of the island are heterozygous carriers of this disease?

We introduce the notation of genes:
A – normal carbohydrate metabolism;
a – congenital diabetes mellitus.
– Let p be the frequency of the dominant allele in a given population, and q be the frequency of the recessive allele.
Then p + q = 1 (or 100%).
The trait under investigation is autosomal, i.e. male and female gametes carrying the allele A are formed in people inhabiting the island with the same frequency (probability) – p. Sperm and egg cells carrying the allele a are formed with a frequency (probability) of q. A random fusion of gametes leads to the appearance of descendants of three genotypic classes: AA, Aa and aa.
Since gametes A are formed with a frequency p, gametes a with a frequency q, the proportion of people with the AA genotype is p2, the Aa genotype is 2pq, and the aa genotype is q2.
– The condition says that the proportion of people suffering from a congenital form of diabetes is 0.01 (or 1%), i.e. q2 = 0.01. Therefore, q = √ ¯ 0.01 = 0.1 (or 10%). Then p = 1 – 0.1 = 0.9 (or 90%).
The healthy population of the island is 0.99 (or 99%).
Moreover, the carriers of the disease (Aa) are: 2pq = 2 × 0.9 × 0.1 = 0.18 (or 18%).
This means that the proportion of carriers among the healthy population is 0.18: 0.99 × 100% ≈ 18.2%.
Answer: the proportion of carriers of the congenital form of diabetes among the healthy population of the island is 18.2%.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.