Genetic Analysis 20.1 predicts the number of individuals expected to have the blood group genotypes MM, MN, and NN. Perform a chi-square analysis using the number of people observed and expected in each blood-type category, and state whether the sample is in H-W equilibrium.
Table of contents
- 1. Introduction to Genetics51m
- 2. Mendel's Laws of Inheritance3h 37m
- 3. Extensions to Mendelian Inheritance2h 41m
- 4. Genetic Mapping and Linkage2h 28m
- 5. Genetics of Bacteria and Viruses1h 21m
- 6. Chromosomal Variation1h 48m
- 7. DNA and Chromosome Structure56m
- 8. DNA Replication1h 10m
- 9. Mitosis and Meiosis1h 34m
- 10. Transcription1h 0m
- 11. Translation58m
- 12. Gene Regulation in Prokaryotes1h 19m
- 13. Gene Regulation in Eukaryotes44m
- 14. Genetic Control of Development44m
- 15. Genomes and Genomics1h 50m
- 16. Transposable Elements47m
- 17. Mutation, Repair, and Recombination1h 6m
- 18. Molecular Genetic Tools19m
- 19. Cancer Genetics29m
- 20. Quantitative Genetics1h 26m
- 21. Population Genetics50m
- 22. Evolutionary Genetics29m
21. Population Genetics
Hardy Weinberg
Problem 20
Textbook Question
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?

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.
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.
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.
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 \( p^2 \cdot 0.82 + 2pq \cdot 1 + q^2 \cdot 0.32 = 1 \).
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).

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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Natural Selection
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.
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Hardy Weinberg
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.
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