In a population of rabbits, f(C₁) = 0.70 and f(C₂) = 0.30. The alleles exhibit an incomplete dominance relationship in which C₁C₁ produces black rabbits, C₁C₂ produces tan-colored rabbits, and C₂C₂ produces rabbits with white fur. If the assumptions of the Hardy–Weinberg principle apply to the rabbit population, what are the expected frequencies of black, tan, and white rabbits?

Verified step by step guidance

1. Step 1: Recall the Hardy-Weinberg principle, which states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. The equation for genotype frequencies is p² + 2pq + q² = 1, where p and q are the frequencies of two alleles in the population.
2. Step 2: Identify the allele frequencies given in the problem. Here, f(C₁) = 0.70 (p) and f(C₂) = 0.30 (q). These represent the frequencies of the two alleles in the population.
3. Step 3: Calculate the expected frequency of the homozygous genotype C₁C₁ (black rabbits) using the formula p². This is done by squaring the frequency of the C₁ allele: p² = (0.70)².
4. Step 4: Calculate the expected frequency of the heterozygous genotype C₁C₂ (tan-colored rabbits) using the formula 2pq. This is done by multiplying 2 by the frequency of C₁ (p) and the frequency of C₂ (q): 2pq = 2 × 0.70 × 0.30.
5. Step 5: Calculate the expected frequency of the homozygous genotype C₂C₂ (white rabbits) using the formula q². This is done by squaring the frequency of the C₂ allele: q² = (0.30)².

Key Concepts

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical model 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 assumes no mutation, migration, selection, or genetic drift, allowing for the prediction of expected genotype frequencies based on allele frequencies.

Incomplete Dominance

Incomplete dominance is a genetic scenario where neither allele is completely dominant over the other, resulting in a phenotype that is a blend of both. In the case of the rabbit population, the heterozygous genotype (C₁C₂) produces a distinct tan color, while homozygous genotypes produce black (C₁C₁) and white (C₂C₂) rabbits. This concept is crucial for understanding how different allele combinations affect phenotypic expression.

Genotype Frequencies

Genotype frequencies refer to the proportion of different genotypes within a population. In the context of the Hardy-Weinberg principle, these frequencies can be calculated using the allele frequencies. For the rabbit population, the expected frequencies of black, tan, and white rabbits can be derived from the allele frequencies (f(C₁) and f(C₂)) and the genotypic ratios that result from incomplete dominance.