Understanding the Hardy-Weinberg principle is crucial for grasping the fundamentals of population genetics. This worksheet provides a series of practice problems designed to solidify your understanding of this important concept. We'll delve into the calculations and interpretations, ensuring you can confidently apply the Hardy-Weinberg equilibrium to various scenarios.
What is the Hardy-Weinberg Equilibrium?
The Hardy-Weinberg principle states that the genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors. When mating is random in a large population with no disruptive circumstances, the law predicts that both genotype and allele frequencies will remain constant because they are in equilibrium.
This equilibrium is maintained under five key assumptions:
- No Mutation: No new alleles are generated.
- Random Mating: Individuals mate randomly, without preference for certain genotypes.
- No Gene Flow: No migration of individuals into or out of the population.
- Infinite Population Size: The population is large enough to prevent random fluctuations in allele frequencies (genetic drift).
- No Natural Selection: All genotypes have equal survival and reproductive rates.
Key Equations:
- p + q = 1: Where 'p' represents the frequency of the dominant allele (e.g., A) and 'q' represents the frequency of the recessive allele (e.g., a).
- p² + 2pq + q² = 1: Where p² represents the frequency of the homozygous dominant genotype (AA), 2pq represents the frequency of the heterozygous genotype (Aa), and q² represents the frequency of the homozygous recessive genotype (aa).
Practice Problems:
Let's work through some examples to apply these equations. Remember to clearly define your variables and show your work.
Problem 1: Simple Allele and Genotype Frequency Calculation
In a population of 1000 butterflies, 160 have white wings (recessive phenotype, aa). Calculate:
a) The frequency of the recessive allele (q). b) The frequency of the dominant allele (p). c) The frequency of heterozygous butterflies (Aa). d) The number of homozygous dominant butterflies (AA).
Solution:
a) q² = 160/1000 = 0.16 => q = √0.16 = 0.4
b) p = 1 - q = 1 - 0.4 = 0.6
c) 2pq = 2 * 0.6 * 0.4 = 0.48. Therefore, 480 butterflies are heterozygous.
d) p² = 0.6² = 0.36. Therefore, 360 butterflies are homozygous dominant.
Problem 2: Analyzing a Population in Disequilibrium
A population of 500 wildflowers has the following genotype frequencies: AA = 100, Aa = 200, aa = 200. Is this population in Hardy-Weinberg equilibrium? Explain your answer and show your calculations.
Solution:
First, calculate the allele frequencies:
p = (2 * 100 + 200) / (2 * 500) = 0.4 (from AA and Aa genotypes) q = (2 * 200 + 200) / (2 * 500) = 0.6 (from Aa and aa genotypes)
Next, calculate the expected genotype frequencies under Hardy-Weinberg:
p² = 0.4² = 0.16 2pq = 2 * 0.4 * 0.6 = 0.48 q² = 0.6² = 0.36
Compare the observed and expected genotype frequencies. Significant deviations indicate the population is not in equilibrium. In this case there is a significant difference, suggesting factors like selection, genetic drift, or non-random mating are influencing the population.
Problem 3: Predicting Future Generations
A large population of beetles is in Hardy-Weinberg equilibrium. The frequency of the recessive allele for green coloration (g) is 0.2. If no disturbing factors occur, what will be the frequency of green beetles (gg) in the next generation?
Solution:
The frequency of green beetles (gg) is represented by q². Since q = 0.2, q² = 0.2² = 0.04. Therefore, 4% of the beetles in the next generation will be green.
Challenge Problem:
A population of snails shows variation in shell color. Brown (B) is dominant to yellow (b). You observe 84 brown snails and 16 yellow snails. However, you suspect that non-random mating is occurring, favoring brown snails. Explain how you would investigate whether this population is truly deviating from Hardy-Weinberg equilibrium due to non-random mating.
(This challenge problem requires a more in-depth analysis, focusing on the comparison between observed and expected genotype frequencies and the interpretation of any deviations in the context of non-random mating.)
This worksheet provides a foundation for understanding the Hardy-Weinberg principle. By working through these problems, you can improve your ability to analyze population genetics data and identify potential evolutionary forces at play. Remember to always clearly state your assumptions and show all calculations.
