Assume that a recessive autosomal disorder occurs in 1 of 10,000 individuals (0.0001) in the general population and that in this population about 2 percent (0.02) of the individuals are carriers for the disorder. Estimate the probability of this disorder occurring in the offspring of a marriage between first cousins. Compare this probability to the population at large.

검증된 단계별 안내

Identify the key parameters given: the frequency of affected individuals (q^2) is 0.0001, and the carrier frequency (2pq) is 0.02 in the general population. Here, q is the frequency of the recessive allele, and p is the frequency of the normal allele.

Calculate the allele frequencies p and q using the Hardy-Weinberg equilibrium equations: \(q^2 = 0.0001\) and \(2pq = 0.02\). From \(q^2\), find \(q = \sqrt{0.0001}\), then use \(2pq = 0.02\) to solve for \(p\).

Determine the probability that first cousins both carry the recessive allele inherited from a common ancestor. Since first cousins share about 1/8 of their genes identical by descent, calculate the increased probability that both are carriers due to consanguinity.

Calculate the probability that two first cousins, both carriers, will have an affected child. For autosomal recessive inheritance, this is \(\frac{1}{4}\) if both parents are carriers.

Compare the probability of affected offspring from first cousin marriage to the baseline population risk (0.0001) by multiplying the increased carrier probability by \(\frac{1}{4}\) and then comparing this value to the population frequency.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Autosomal Recessive Inheritance

Autosomal recessive disorders require two copies of a mutant allele for the disease to manifest. Carriers have one normal and one mutant allele but are typically unaffected. When both parents are carriers, there is a 25% chance their child will inherit the disorder. Understanding this inheritance pattern is essential for calculating disease risk in offspring.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle relates allele frequencies to genotype frequencies in a population at equilibrium. It allows estimation of carrier frequency (2pq) and affected frequency (q²) from disease prevalence. This concept helps interpret the given population data and estimate probabilities of genotypes in the general population.

Consanguinity and Increased Genetic Risk

Consanguineous marriages, such as between first cousins, increase the probability that both parents share alleles inherited from a common ancestor. This raises the chance of offspring inheriting two copies of a recessive allele, increasing disease risk compared to unrelated parents. Calculating this increased risk requires understanding pedigree relationships and inbreeding coefficients.