Epidemiologic data on the population in the previous problem reveal that before the application of modern medical treatment, natural selection played a major role in shaping the frequencies of alleles. Heterozygous individuals have the highest relative fitness, and in comparison with heterozygotes, those who are βᴬβᴬ have a relative fitness of 82%, but only about 32% of those with SCD survived to reproduce. What are the estimated equilibrium frequencies of βᴬ and βˢ in this population?

Verified step by step guidance

1. Define the variables: Let p represent the frequency of the βᴬ allele and q represent the frequency of the βˢ allele. Since these are the only two alleles in the population, p + q = 1.
2. Understand the fitness values: The relative fitness of βᴬβᴬ individuals is 0.82, the relative fitness of βᴬβˢ (heterozygotes) is 1 (highest fitness), and the relative fitness of βˢβˢ individuals is 0.32.
3. Set up the equilibrium condition: At equilibrium, the change in allele frequencies due to selection is zero. This can be expressed using the equation for balancing selection: \( p^2 \cdot w_{AA} + 2pq \cdot w_{AS} + q^2 \cdot w_{SS} = 1 \), where \( w_{AA}, w_{AS}, \) and \( w_{SS} \) are the fitness values for βᴬβᴬ, βᴬβˢ, and βˢβˢ, respectively.
4. Substitute the fitness values into the equation: Replace \( w_{AA} \) with 0.82, \( w_{AS} \) with 1, and \( w_{SS} \) with 0.32. The equation becomes \( p^2 \cdot 0.82 + 2pq \cdot 1 + q^2 \cdot 0.32 = 1 \).
5. Solve for the equilibrium frequencies: Use the relationship \( q = 1 - p \) to substitute for q in the equation. This will give a quadratic equation in terms of p. Solve this quadratic equation to find the equilibrium frequencies of p (βᴬ) and q (βˢ).

Key Concepts

Natural Selection

Natural selection is a fundamental mechanism of evolution where individuals with traits better suited to their environment tend to survive and reproduce more than those with less advantageous traits. In the context of genetics, this process can influence allele frequencies in a population, favoring alleles that confer higher fitness, such as those found in heterozygous individuals.

Heterozygote Advantage

Heterozygote advantage occurs when individuals with two different alleles for a particular gene (heterozygotes) have a higher fitness than those with two identical alleles (homozygotes). This phenomenon can maintain genetic diversity within a population, as seen in the case of sickle cell disease (SCD), where heterozygous individuals are more likely to survive malaria, thus promoting the frequency of both alleles.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is a principle that describes the genetic variation in a population that is not evolving. It provides a mathematical framework to estimate allele frequencies under certain conditions, such as no selection, mutation, migration, or genetic drift. In this scenario, understanding how to apply this principle can help estimate the equilibrium frequencies of the alleles βᴬ and βˢ based on the given fitness values.