ABO blood type is examined in a Taiwanese population, and allele frequencies are determined. In the population, f (Iᴬ) = 0.30, f (Iᴮ) = 0.15, and f (i) = 0.55.f. Assuming Hardy–Weinberg conditions apply, what are the frequencies of genotypes, and what are the blood group frequencies in this population?

Verified step by step guidance

1. Step 1: Recall the Hardy-Weinberg equilibrium principle, which states that genotype frequencies in a population can be calculated using the formula p² + 2pq + q² = 1, where p and q are the allele frequencies. Here, the three alleles are Iᴬ, Iᴮ, and i, so we will extend this principle to include all combinations of these alleles.
2. Step 2: Write down the allele frequencies provided: f(Iᴬ) = 0.30, f(Iᴮ) = 0.15, and f(i) = 0.55. These frequencies represent p, q, and r, respectively, for the three-allele system.
3. Step 3: Calculate the expected genotype frequencies under Hardy-Weinberg equilibrium. The genotypes and their frequencies are as follows: f(IᴬIᴬ) = p², f(IᴬIᴮ) = 2pq, f(Iᴬi) = 2pr, f(IᴮIᴮ) = q², f(Iᴮi) = 2qr, and f(ii) = r². Substitute the values of p, q, and r into these formulas.
4. Step 4: Determine the blood group frequencies by grouping genotypes that correspond to the same blood type. Blood type A includes genotypes IᴬIᴬ and Iᴬi, blood type B includes genotypes IᴮIᴮ and Iᴮi, blood type AB includes genotype IᴬIᴮ, and blood type O includes genotype ii. Add the frequencies of the genotypes within each blood group.
5. Step 5: Verify that the sum of all genotype frequencies equals 1 (p² + 2pq + 2pr + q² + 2qr + r² = 1) to ensure the calculations are consistent with Hardy-Weinberg equilibrium.

Key Concepts

Hardy-Weinberg Principle

The Hardy-Weinberg Principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. This principle provides a mathematical framework to predict the expected frequencies of genotypes based on allele frequencies, assuming conditions such as random mating, no mutation, no migration, and no selection are met.

Allele Frequency

Allele frequency refers to how often a particular allele appears in a population compared to other alleles for the same gene. In the context of the ABO blood type, the frequencies of alleles Iᴬ, Iᴮ, and i are given, which can be used to calculate the expected frequencies of the corresponding genotypes under Hardy-Weinberg equilibrium.

Genotype Frequency

Genotype frequency is the proportion of a specific genotype among all individuals in a population. For the ABO blood types, the genotype frequencies can be calculated using the allele frequencies and the Hardy-Weinberg equations, which allow for the determination of how many individuals are expected to have each blood type based on the alleles present.