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. (a) 0.0064 (b) 0.000081 (c) 0.09 (d) 0.01 (e) 0.10

Short answer

Question: Calculate the percentage of heterozygous carriers for each disorder frequency using the Hardy-Weinberg equilibrium formula. Disorder frequencies: (a) 0.0064 (b) 0.000081 (c) 0.09 (d) 0.01 (e) 0.10

Step-by-step solution

Calculate the frequency of the recessive allele (q)

For each disorder frequency provided, calculate the frequency of the recessive allele by taking the square root of the disorder frequency. For example, for (a) 0.0064, the frequency of the recessive allele (q) is sqrt(0.0064) = 0.08.

Calculate the frequency of the dominant allele (p)

Using the Hardy-Weinberg equilibrium formula, we know that p + q = 1. So subtract q from 1 to find p. For example, for (a) 0.0064, p = 1 - 0.08 = 0.92.

Calculate the frequency of the heterozygous carriers (2pq)

Multiply 2 by the dominant allele frequency (p) and the recessive allele frequency (q) to find the frequency of the heterozygous carriers. For example, for (a) 0.0064, the frequency of heterozygous carriers is 2(0.92)(0.08) = 0.1472.

Convert the frequency of the heterozygous carriers to percentage

Multiply the obtained frequency of the heterozygous carriers by 100 to convert it into a percentage. For example, for (a) 0.0064, the percentage of heterozygous carriers is 0.1472 × 100 = 14.72%. Repeat the above steps for each of the other disorder frequencies to find the percentage of heterozygous carriers for each case: (b) 0.000081 (c) 0.09 (d) 0.01 (e) 0.10

Key concepts

Hardy-Weinberg Equilibrium

One of the basic principles in population genetics is the Hardy-Weinberg equilibrium. It describes a model where the allele frequencies in a sexually reproducing population remain constant from one generation to the next, given that certain assumptions are met. These assumptions include a large breeding population, random mating, no mutation, no immigration or emigration, and no natural selection. In such an idealized system, the equilibrium provides a mathematical relationship between allele frequencies and genotype frequencies for a particular gene locus.

Recessive Allele Frequency

When tackling problems related to genetic disorders, especially those that are autosomal recessive, understanding how to calculate the recessive allele frequency is key. The recessive allele frequency, often represented by the variable q, signifies the proportion of alleles in the population that are recessive. To find this frequency, the square root of the disorder's prevalence in the population is taken. This step helps establish the basis for further calculations related to carrier percentages and the prevalence of the dominant allele in the population. The concept hinges upon the notion that the frequency of individuals with the recessive disorder (homozygous recessive genotype) is equal to q^2.

Heterozygous Carrier Percentage

Heterozygous carriers of an autosomal recessive disorder carry one copy of the normal allele and one copy of the mutant allele, but do not show symptoms of the disorder. The Hardy-Weinberg formula is used to calculate this carrier state percentage through the expression 2pq, where p represents the frequency of the dominant allele and q is the recessive allele frequency. The result shows the proportion of the population that is a carrier for a specific recessive genetic disorder. To convey this value as a percentage, simply multiply by 100. This calculation is crucial for understanding the potential impact of genetic disorders within a population, even when the disorders themselves are rare.

Genetics Disorder Frequency

The frequency of a genetic disorder within a population is an important measure for geneticists and healthcare professionals. It gives insight into how common a specific disorder is and can further indicate the burden it may place on the population. The disorder frequency, particularly for autosomal recessive conditions, can be found by squaring the recessive allele frequency (q^2). This calculation follows from the Hardy-Weinberg principle and reflects the proportion of individuals who are homozygous for the recessive allele (and thus affected by the condition). Understanding this frequency helps in planning healthcare resources and may guide genetic counseling efforts.