A sample of 500 field mice contains 225 individuals that are D₁D₁, 175 that are D₁D₂, and 100 that are D₂D₂.
What are the frequencies of D₁ and D₂ in this sample?

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to calculate the allele frequencies of D₁ and D₂ in the population. Allele frequency is the proportion of a specific allele in the population, and it can be calculated using the genotype counts provided.
2. Step 2: Recall the formula for allele frequency. For allele D₁, the frequency is calculated as: \( f(D₁) = \frac{2 \times \text{count of D₁D₁} + \text{count of D₁D₂}}{2 \times \text{total individuals}} \). Similarly, for allele D₂: \( f(D₂) = \frac{2 \times \text{count of D₂D₂} + \text{count of D₁D₂}}{2 \times \text{total individuals}} \).
3. Step 3: Substitute the genotype counts into the formulas. For D₁, use the counts: 225 for D₁D₁ and 175 for D₁D₂. For D₂, use the counts: 100 for D₂D₂ and 175 for D₁D₂. The total number of individuals is 500.
4. Step 4: Perform the calculations step by step. For D₁, calculate \( 2 \times 225 + 175 \) and divide by \( 2 \times 500 \). For D₂, calculate \( 2 \times 100 + 175 \) and divide by \( 2 \times 500 \).
5. Step 5: Verify that the sum of the allele frequencies equals 1. This ensures the calculations are correct, as the total frequency of all alleles in a population must equal 1.

Key Concepts

Genotype Frequencies

Genotype frequencies refer to the proportion of different genotypes within a population. In this case, the genotypes D₁D₁, D₁D₂, and D₂D₂ represent different combinations of alleles for a specific gene. Understanding these frequencies is essential for calculating allele frequencies, as they provide the necessary data on how many individuals possess each genotype.

Allele Frequencies

Allele frequencies indicate how common an allele is in a population. They are calculated by dividing the number of copies of a specific allele by the total number of alleles for that gene in the population. In this scenario, the frequencies of alleles D₁ and D₂ can be derived from the genotype frequencies, allowing for insights into genetic diversity and population structure.

Hardy-Weinberg Principle

The Hardy-Weinberg Principle provides a mathematical framework for understanding genetic variation in a population at equilibrium. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle is useful for predicting expected genotype frequencies based on allele frequencies, which can help in analyzing the given data on field mice.