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
- Genetic Cloning
  9m
- Methods for Analyzing DNA
  9m
19. Cancer Genetics29m
- Overview of Cancer
  21m
- Cancer Mutations
  7m
20. Quantitative Genetics1h 26m
21. Population Genetics50m
- Hardy Weinberg
  19m
- Allelic Frequency Changes
  31m
22. Evolutionary Genetics29m

21. Population Genetics

Hardy Weinberg

Genetics

21. Population Genetics

Hardy Weinberg

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2:07 minutes

Problem 11

Textbook Question

If the initial allele frequencies are p = 0.5 and q = 0.5 and allele a is a lethal recessive, what will be the frequencies after 1, 5, 10, 25, 100, and 1000 generations?

Verified step by step guidance

Step 1: Understand the problem. The allele frequencies p and q represent the frequencies of dominant (A) and recessive (a) alleles, respectively. Since allele a is lethal in the homozygous recessive state (aa), individuals with genotype aa will not survive to reproduce. This affects the allele frequencies over generations.

Step 2: Recall the Hardy-Weinberg principle. The genotype frequencies in a population can be calculated as p² (AA), 2pq (Aa), and q² (aa). However, since aa individuals do not survive, the q² frequency will be removed from the population, and the remaining frequencies will need to be normalized to sum to 1.

Step 3: Calculate the surviving genotype frequencies after one generation. The surviving frequencies are p² (AA) and 2pq (Aa). Normalize these frequencies by dividing each by the sum of p² + 2pq to ensure the total equals 1.

Step 4: Update allele frequencies for the next generation. The frequency of allele A (p) will be the sum of contributions from AA and Aa genotypes, while the frequency of allele a (q) will come only from the heterozygous Aa genotype. Use the formulas: p' = (p² + pq) / (p² + 2pq) and q' = pq / (p² + 2pq).

Step 5: Repeat the process iteratively for 5, 10, 25, 100, and 1000 generations. At each step, recalculate the genotype frequencies, normalize them, and update the allele frequencies. Observe how q (frequency of allele a) decreases over time due to the lethal recessive effect.

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Key Concepts

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

Allele Frequencies

Allele frequencies represent the proportion of different alleles of a gene in a population. In this case, p and q denote the frequencies of two alleles, where p is the frequency of the dominant allele and q is the frequency of the recessive allele. Understanding how these frequencies change over generations is crucial for predicting genetic variation and evolutionary dynamics.

Lethal Recessive Alleles

A lethal recessive allele is one that can cause death when an individual carries two copies of it (homozygous recessive). In this scenario, allele 'a' is lethal, meaning individuals with the genotype 'aa' will not survive to reproduce. This significantly impacts allele frequencies over generations, as the frequency of the lethal allele will decrease due to natural selection against it.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle provides a mathematical framework for understanding allele frequencies in a population under ideal conditions. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. However, the presence of a lethal recessive allele disrupts this equilibrium, necessitating calculations to determine how frequencies will change over time.

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Textbook Question

Consider a population in which the frequency of allele A is p = 0.7 and the frequency of allele a is q = 0.3 and where the alleles are codominant. What will be the allele frequencies after one generation if the following occurs?

w_AA= 1, w_Aa= 0.99, w_aa= 0.98

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Textbook Question

w_AA= 1, w_Aa= 0.95, w_aa= 0.9

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Textbook Question

Consider a population in which the frequency of allele A is p=0.7 and the frequency of allele a is q=0.3 and where the alleles are codominant. What will be the allele frequencies after one generation if the following occurs?

wAA=1, wAa=0.9, waa=0.8

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Textbook Question

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