The ability to taste the bitter compound phenylthiocarbamide (PTC) is an autosomal dominant trait. The inability to taste PTC is a recessive condition. In a sample of 500 people, 360 have the ability to taste PTC and 140 do not. Calculate the frequency of the recessive allele.

Verified step by step guidance

1. Step 1: Understand the problem. The ability to taste PTC is controlled by an autosomal dominant allele (T), while the inability to taste PTC is controlled by a recessive allele (t). We are tasked with calculating the frequency of the recessive allele (t) in the population.
2. Step 2: Use the Hardy-Weinberg principle to calculate allele frequencies. The Hardy-Weinberg equation is: $p2+\; 2pq\; +\; q2=\; 1$, where p is the frequency of the dominant allele (T) and q is the frequency of the recessive allele (t). Additionally, $p\; +\; q\; =\; 1$.
3. Step 3: Identify the proportion of individuals who are homozygous recessive (q²). These individuals cannot taste PTC. From the problem, 140 out of 500 people are unable to taste PTC. Calculate q² as .
4. Step 4: Solve for q, the frequency of the recessive allele. Since $q\; =\; ext\{sqrt\}(q2)$, take the square root of the value obtained for q².
5. Step 5: Verify your understanding. Once q is calculated, you can also determine p (the frequency of the dominant allele) using $p\; =\; 1\; -\; q$. This ensures the Hardy-Weinberg equilibrium is satisfied.

Key Concepts

Autosomal Dominance and Recessiveness

Autosomal dominance refers to a pattern of inheritance where only one copy of a dominant allele is needed for the trait to be expressed. In contrast, a recessive trait requires two copies of the recessive allele for expression. In this case, the ability to taste PTC is dominant, while the inability to taste it is recessive.

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical framework for understanding allele frequencies 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 essential for calculating allele frequencies, including the recessive allele frequency in the given population.

Allele Frequency Calculation

Allele frequency is the proportion of a specific allele among all allele copies in a population. To calculate the frequency of the recessive allele, we can use the number of individuals expressing the recessive phenotype and apply the Hardy-Weinberg equation. In this scenario, knowing the total number of individuals and the number of tasters allows us to derive the frequency of the recessive allele responsible for the inability to taste PTC.