In the mouse, Mus musculus, survival in agricultural fields that are regularly sprayed with a herbicide is determined by the genotype for a detoxification enzyme encoded by a gene with two alleles, F and S. The relative fitness values for the genotypes areGenotype Relative fitnessFF 0.72FS 1.00SS 0.45Calculate the equilibrium frequencies of the alleles.

Verified step by step guidance

1. Step 1: Understand the concept of equilibrium frequencies. In population genetics, equilibrium frequencies of alleles are determined by balancing selection pressures, such as relative fitness values, acting on different genotypes. This problem involves calculating equilibrium frequencies under heterozygote advantage (overdominance).
2. Step 2: Use the formula for equilibrium allele frequencies under heterozygote advantage. The equilibrium frequency of allele F (p) and allele S (q) can be calculated using the relative fitness values (w) of the genotypes. The formula is: \( p = \frac{w_{SS} - w_{FS}}{w_{SS} + w_{FF} - 2w_{FS}} \) and \( q = 1 - p \).
3. Step 3: Substitute the given relative fitness values into the formula. From the problem, \( w_{FF} = 0.72 \), \( w_{FS} = 1.00 \), and \( w_{SS} = 0.45 \). Plug these values into the formula for \( p \).
4. Step 4: Simplify the numerator and denominator of the formula for \( p \). Perform the subtraction and addition operations as indicated in the formula to isolate \( p \).
5. Step 5: Once \( p \) is calculated, determine \( q \) using the relationship \( q = 1 - p \). This ensures that the sum of allele frequencies equals 1, as required by population genetics principles.

Key Concepts

Genotype and Alleles

A genotype refers to the genetic constitution of an organism, specifically the alleles present at a given locus. In this case, the alleles F and S represent different versions of a gene that encodes a detoxification enzyme. Understanding how these alleles interact to form genotypes (FF, FS, SS) is crucial for analyzing their fitness in the context of natural selection.

Relative Fitness

Relative fitness is a measure of the reproductive success of a genotype compared to others in the population. It indicates how well a genotype can survive and reproduce in a given environment. In this scenario, the relative fitness values (0.72 for FF, 1.00 for FS, and 0.45 for SS) help determine which genotypes are more advantageous in agricultural fields treated with herbicides.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is a principle that describes the genetic variation in a population that remains constant from one generation to the next in the absence of evolutionary influences. It provides a mathematical framework to calculate allele frequencies based on genotype frequencies. In this question, it can be applied to find the equilibrium frequencies of alleles F and S based on their relative fitness values.