Ch. 20 - Population Genetics and Evolution at the Population, Species, and Molecular Levels

Sanders - Genetic Analysis: An Integrated Approach 3rd Edition

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Sanders 3rd Edition

Ch. 20 - Population Genetics and Evolution at the Population, Species, and Molecular Levels

Problem 24b

Chapter 20, Problem 24b

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 are

Calculate the equilibrium frequencies of the alleles.

Verified step by step guidance

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).

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 \( q = 1 - p \).

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 \( p \).

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 \( p \).

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Textbook Question

Tay–Sachs disease is an autosomal recessive neurological disorder that is fatal in infancy. Despite its invariably lethal effect, Tay–Sachs disease occurs at very high frequency in some Central and Eastern European (Ashkenazi) Jewish populations. In certain Ashkenazi populations, 1 in 750 infants has Tay–Sachs disease. Population biologists believe the high frequency is a consequence of genetic bottlenecks caused by pogroms (genocide) that have reduced the population multiple times in the past several hundred years. Assuming mating occurs at random in this population, what is the probability a couple are both carriers of Tay–Sachs disease?

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Textbook Question

Cystic fibrosis (CF) is the most common autosomal recessive disorder in certain Caucasian populations. In some populations, approximately 1 in 2000 children have CF. Determine the frequency of CF carriers in this population.

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Textbook Question

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 are

Why will this pattern of natural selection result in a stable equilibrium of frequencies of F and S?

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Textbook Question

In a population of flowers growing in a meadow, C₁ and C₂ are autosomal codominant alleles that control flower color. The alleles are polymorphic in the population, with f(C₁) = 0.80 and f(C₂) = 0.20. Flowers that are C₁C₁ are yellow, orange flowers are C₁C₂, and C₂C₂ flowers are red. A storm blows a new species of hungry insects into the meadow, and they begin to eat yellow and orange flowers but not red flowers. The predation exerts strong natural selection on the flower population, resulting in relative fitness values of C₁C₁ = 0.30, C₁C₂ = 0.60, and C₂C₂ = 1.0.

Assuming the population begins in H-W equilibrium, what are the allele frequencies after one generation of natural selection?

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Textbook Question

In a population of flowers growing in a meadow, C₁ and C₂ are autosomal codominant alleles that control flower color. The alleles are polymorphic in the population, with f (C₁) = 0.80 and f (C₂) = 0.20. Flowers that are C₁C₁ are yellow, orange flowers are C₁C₂, and C₂C₂ flowers are red. A storm blows a new species of hungry insects into the meadow, and they begin to eat yellow and orange flowers but not red flowers. The predation exerts strong natural selection on the flower population, resulting in relative fitness values of C₁C₁ = 0.30, C₁C₂= 0.60, and C₂C₂ = 1.0.

Assuming random mating takes place among survivors, what are the genotype frequencies in the second generation?

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Textbook Question

If predation continues, what are the allele frequencies when the second generation mates?

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