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.

Verified step by step guidance

1. span>Step 1: Understand the genetic relationship between first cousins. First cousins share a set of grandparents, which means they have a higher chance of inheriting the same alleles from their common ancestors compared to unrelated individuals.
2. span>Step 2: Use the Hardy-Weinberg principle to understand the population genetics. The frequency of the recessive allele (q) can be estimated from the disorder's occurrence rate, which is given as 0.0001. Since q^2 = 0.0001, solve for q.
3. span>Step 3: Calculate the carrier frequency (2pq) in the general population. Given that about 2 percent (0.02) of the individuals are carriers, use this information to verify the value of p (frequency of the dominant allele) and q.
4. span>Step 4: Determine the probability of the disorder occurring in the offspring of first cousins. Since both parents are first cousins, calculate the probability that both are carriers and then the probability that they pass on the recessive allele to their offspring.
5. span>Step 5: Compare the calculated probability for first cousins to the general population probability. This involves comparing the probability of the disorder in offspring of first cousins to the 0.0001 probability in the general population.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive inheritance refers to a pattern where two copies of a mutated gene (one from each parent) are necessary for an individual to express a recessive disorder. Carriers, who possess one normal and one mutated gene, do not show symptoms but can pass the mutated gene to their offspring. This concept is crucial for understanding how the disorder can manifest in children of parents who are both carriers.

Carrier Frequency

Carrier frequency is the proportion of individuals in a population who carry one copy of a recessive allele for a genetic disorder. In this case, with a carrier frequency of 2 percent, it indicates that 2 out of every 100 individuals are carriers. This statistic is essential for estimating the likelihood of two carriers mating and having an affected child, especially in consanguineous relationships like first cousins.

Inbreeding and Genetic Risk

Inbreeding, or mating between closely related individuals, increases the probability that both parents carry the same recessive allele, thereby raising the risk of offspring inheriting the disorder. In the case of first cousins, the genetic relatedness is higher than that of unrelated individuals, which can significantly elevate the risk of recessive disorders manifesting in their children compared to the general population.