Ch. 20 - Population Genetics and Evolution at the Population, Species, and Molecular Levels

Sanders - Genetic Analysis: An Integrated Approach 3rd Edition

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Sanders 3rd Edition

Ch. 20 - Population Genetics and Evolution at the Population, Species, and Molecular Levels

문제 32c

20장, 문제 32c

The frequency of an autosomal recessive condition is 0.001 (1 in 1000) in a population.
Assuming individuals mate at random, what is the chance that two heterozygous individuals will mate?

검증된 단계별 안내

Understand the problem: The condition is autosomal recessive, meaning two copies of the recessive allele are required for an individual to express the condition. The frequency of the condition in the population is given as 0.001. We are tasked with finding the probability that two heterozygous individuals (carriers) will mate, assuming random mating.

Use the Hardy-Weinberg principle to determine the allele frequencies. Let the frequency of the recessive allele (q) be the square root of the frequency of the condition, since the condition is expressed in individuals with genotype q². Calculate q as \( q = \sqrt{0.001} \).

Determine the frequency of the dominant allele (p) using the Hardy-Weinberg equation \( p + q = 1 \). Solve for \( p \) as \( p = 1 - q \).

Calculate the frequency of heterozygous individuals (carriers) in the population using the Hardy-Weinberg equation for heterozygotes: \( 2pq \). This represents the proportion of individuals in the population who are heterozygous.

To find the probability that two heterozygous individuals will mate, multiply the frequency of heterozygous individuals (\( 2pq \)) by itself: \( (2pq) \times (2pq) \). This gives the probability of two carriers mating under random mating conditions.

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Hardy-Weinberg Principle

The Hardy-Weinberg Principle describes the genetic equilibrium in a population, stating that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. It provides a mathematical framework to calculate the expected frequencies of genotypes based on allele frequencies, which is essential for understanding how traits are inherited in a population.

Genotype Frequencies

Genotype frequencies refer to the proportion of different genotypes in a population. For an autosomal recessive condition, the frequency of the recessive genotype (homozygous recessive) can be calculated using the square of the allele frequency. In this case, if the frequency of the recessive allele is represented as 'q', then the frequency of heterozygous individuals (carriers) is represented as '2pq', where 'p' is the frequency of the dominant allele.

Heterozygous Individuals

Heterozygous individuals carry two different alleles for a particular gene, one dominant and one recessive. In the context of an autosomal recessive condition, these individuals do not express the condition but can pass the recessive allele to their offspring. Understanding the proportion of heterozygous individuals in a population is crucial for predicting the likelihood of mating between two carriers and the potential for offspring to inherit the recessive condition.

The frequency of an autosomal recessive condition is 0.001 (1 in 1000) in a population. Assuming individuals mate at random, what is the chance that two heterozygous individuals will mate?