USA Biology Olympiad (USABO) Practice Exam

In a population of laboratory rats, if 49% have black fur and the rest are agouti, what percent is likely heterozygous for the fur trait?

1. 21%

2. 35%

3. 42%

4. 56%

The correct answer is: 42%

To understand the percentage of the population likely heterozygous for the fur trait, we can apply the Hardy-Weinberg principle. This principle helps predict genotypic frequencies in a population that is in equilibrium with respect to certain conditions. Given that 49% of the rats have black fur, we can denote the frequency of the black fur phenotype as 0.49. Since black fur is typically dominant over agouti fur, we can assume that this phenotype arises from both homozygous dominant (BB) and heterozygous (Bb) individuals. The agouti phenotype (bb) comprises the rest of the population, which is 51% (100% - 49%). In a population in Hardy-Weinberg equilibrium, the frequencies of the genotypes can be defined as: - p^2 for homozygous dominant (BB) - 2pq for heterozygous (Bb) - q^2 for homozygous recessive (bb) Here, we denote: - p = frequency of the dominant allele (B) - q = frequency of the recessive allele (b) Since homozygous recessive rats correspond to the agouti phenotype, we know that q^2 is 0.51