Textbook Question
Consider rare disorders in a population caused by an autosomal recessive mutation. From the frequencies of the disorder in the population given, calculate the percentage of heterozygous carriers:
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21. Population Genetics
Hardy Weinberg
2:25 minutesProblem 10c
Textbook Question
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 each genotype.
Verified step by step guidance1
Step 1: Define the alleles and genotypes. Let 'T' represent the dominant allele for the ability to taste PTC, and 't' represent the recessive allele for the inability to taste PTC. The genotypes are TT (homozygous dominant), Tt (heterozygous), and tt (homozygous recessive).
Step 2: Use the Hardy-Weinberg principle to model the population. The Hardy-Weinberg equation is p² + 2pq + q² = 1, where p is the frequency of the dominant allele (T), q is the frequency of the recessive allele (t), p² represents the frequency of TT, 2pq represents the frequency of Tt, and q² represents the frequency of tt.
Step 3: Calculate q², the frequency of the homozygous recessive genotype (tt). Since 140 out of 500 people cannot taste PTC, the frequency of the recessive phenotype is 140/500 = 0.28. This is equal to q².
Step 4: Solve for q, the frequency of the recessive allele. Take the square root of q² to find q. Use the equation q = √(q²).
Step 5: Calculate p, the frequency of the dominant allele. Use the relationship p + q = 1 to solve for p. Then, calculate the frequencies of each genotype: p² for TT, 2pq for Tt, and q² for tt. These represent the proportions of the population with each genotype.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Autosomal Dominance and Recessiveness
In genetics, traits can be classified as dominant or recessive based on how they are expressed in an organism. An autosomal dominant trait, like the ability to taste PTC, requires only one copy of the dominant allele for expression, while a recessive trait requires two copies of the recessive allele. This distinction is crucial for understanding inheritance patterns and predicting genotype frequencies in a population.
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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 essential for calculating genotype frequencies based on observed phenotypic ratios, as it allows for predictions about genetic diversity.
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Genotype Frequency Calculation
Genotype frequency refers to the proportion of different genotypes in a population. To calculate these frequencies, one can use the observed phenotypic data along with the principles of inheritance. For the PTC tasting trait, knowing the number of tasters and non-tasters allows for the application of the Hardy-Weinberg equations to derive the frequencies of the homozygous dominant, heterozygous, and homozygous recessive genotypes.
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