Question

A population of students taking a basic genetics class had their blood types classified in the ABO blood group system. The following numbers were recorded: $$ \begin{array}{ccc} \text { Phenotype } & \text { Number } & \text { Frequency } \\ \mathrm{A} & 249 & 0.2075 \\ \mathrm{~B} & 376 & 0.3133 \\ \mathrm{AB} & 77 & 0.0642 \\ \mathrm{O} & 498 & 0.4150 \\ & 1,200 & 1.0000 \end{array} $$ Assuming this population of students is in genetic equilibrium, what are the frequencies of the. three alleles \(\mathrm{I}^{\mathrm{A}}\), \(\mathrm{I}^{\mathrm{B}}\), and i, respectively?

Short answer

The frequencies of the three alleles \( I^A \), \( I^B \), and i in a population of students taking a basic genetics class, assuming the population is in genetic equilibrium, are approximately \( I^A = 0.176 \), \( I^B = 0.180 \), and i = 0.644. This was determined using the Hardy-Weinberg equilibrium principle and the given frequencies for blood types A (0.2075), B (0.3133), AB (0.0642), and O (0.4150).

Step-by-step solution

Understand the ABO blood group system

The ABO blood group system consists of four blood types: A, B, AB, and O. These blood types are determined by three alleles: IA, IB, and i. Consider the following summary of the blood group system: - Blood type A: IAIA or IAi (derived from IA and i alleles) - Blood type B: IBIB or IBi (derived from IB and i alleles) - Blood type AB: IAIB (derived from IA and IB alleles) - Blood type O: ii (derived from i alleles only)

Use Hardy-Weinberg equilibrium

According to the Hardy-Weinberg equilibrium principle, in a population in genetic equilibrium, the frequency of alleles remains constant from generation to generation. Thus, we have the following relations: - p: Frequency of IA allele - q: Frequency of IB allele - r: Frequency of i allele Since there are only three alleles, their frequencies should sum to 1: \(p + q + r = 1\)

Identify the frequency of each blood type

From the given data, we have the following frequencies for each blood type: - Frequency of blood type A: 0.2075 - Frequency of blood type B: 0.3133 - Frequency of blood type AB: 0.0642 - Frequency of blood type O: 0.4150

Calculate the frequencies of alleles p, q, and r

Using the Hardy-Weinberg equilibrium principle and the frequencies of blood types, we can set up the following equations: - (IAIA or IAi) Frequency of blood type A: \(p^2 + 2pr = 0.2075\) - (IBIB or IBi) Frequency of blood type B: \(q^2 + 2qr = 0.3133\) - Frequency of blood type AB: \(2pq = 0.0642\) - Frequency of blood type O: \(r^2 = 0.4150\) First, we can find the frequency of allele r (i) as it only appears in type O: \(r = \sqrt{0.4150} \approx 0.644\) Next, we can find p and q using the equations for blood type A and blood type B respectively: \(p^2 + 2pq \cdot 0.644 = 0.2075\) \(q^2 + 2q \cdot 0.644 = 0.3133\) Solve using the quadratic formula to obtain the values for p and q: \(p \approx 0.176\) \(q \approx 0.180\)

Check the sum of p, q, and r

Now, verify that the sum of p, q, and r equals 1: \(0.176 + 0.180 + 0.644 = 1.000\) The frequencies of the three alleles IA, IB, and i are approximately 0.176, 0.180, and 0.644, respectively.

Key concepts

ABO blood group system

In the ABO blood group system, human blood is classified based on the presence or absence of specific antigens on the surface of red blood cells. The ABO system includes four main blood types: A, B, AB, and O.

These blood types are determined by three alleles: \( I^A \), \( I^B \), and \( i \).

• Blood type A can be inherited through genotypes \( I^A I^A \) or \( I^A i \), meaning that the person either has two A alleles or one A allele and one O allele.
• Blood type B is formed by genotypes \( I^B I^B \) or \( I^B i \), indicating the presence of two B alleles or one B and one O allele.
• Blood type AB is unique because it is formed by the genotype \( I^A I^B \), representing one A and one B allele. This is due to co-dominance, where both A and B antigens are equally expressed.
• Blood type O is a result of the genotype \( ii \), meaning that the individual has inherited an O allele from both parents, and thus lacks both the A and B antigens.

The ABO blood group phenotypes are important for transfusions, as compatibility between donor and recipient blood types is crucial to avoid adverse reactions.

allele frequencies

Allele frequencies refer to how common an allele is in a population. Within a given population's genetic makeup, specific alleles of a gene appear at certain frequencies, which can directly influence the physical traits expressed in that population.

To determine allele frequencies in the ABO blood group system under Hardy-Weinberg equilibrium, certain formulas are used:

• For blood type A, the formula \( p^2 + 2pr \) is used, representing the frequency of individuals with \( I^A I^A \) and \( I^A i \) genotypes.
• To find the frequency of blood type B, \( q^2 + 2qr \) is applied, covering \( I^B I^B \) and \( I^B i \) genotypes.
• The allele frequency of blood type AB, characterized by the genotype \( I^A I^B \), is calculated using \( 2pq \).
• Type O frequency, derived from the genotype \( ii \), is calculated with \( r^2 \).

The goal is to apply these frequencies to determine alleles \( p \), \( q \), and \( r \). Since all alleles in a population must sum to 1, we have: \( p + q + r = 1 \). This constraint helps ensure that all genetic diversity in the ABO system is accounted for.

genetic equilibrium

Genetic equilibrium, particularly the Hardy-Weinberg equilibrium, is a founding principle of population genetics. It states that allele and genotype frequencies in a population will remain constant across generations if certain conditions are met.

For a population to be in genetic equilibrium, the following must apply:

• No mutation: The genetic makeup of the population is stable without new mutations introducing change.
• Random mating: Individuals pair randomly, ensuring no selection based on phenotype.
• No migration: The population is isolated with no alleles entering or leaving through migration.
• Large population size: A sufficiently large population reduces the impact of genetic drift, which can cause random changes.
• No selection: Equal survival and reproduction rates for all genotypes prevent alteration due to natural selection.

In calculating the frequencies of alleles in the ABO blood group system, it's assumed the population is in equilibrium. This means factors that could change allele frequencies are absent, allowing for the use of quantitative methods like the Hardy-Weinberg equation to estimate allele frequencies accurately.