Hardy-weinberg Practice Problems With Answers

Mastering Hardy-Weinberg Equilibrium: Practice Problems and Solutions

The Hardy-Weinberg principle is a cornerstone of population genetics. It describes the theoretical conditions under which allele and genotype frequencies in a population remain constant from generation to generation. Understanding this principle is crucial for comprehending evolutionary processes, as deviations from Hardy-Weinberg equilibrium often indicate that evolutionary forces are at play. This article provides a comprehensive guide to Hardy-Weinberg problems, complete with detailed explanations and solutions to help you master this fundamental concept.

Understanding the Hardy-Weinberg Principle

The principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of certain evolutionary influences. These influences, often referred to as the five conditions for Hardy-Weinberg equilibrium, are:

1. No mutation: Mutation introduces new alleles into the population, altering allele frequencies.
2. Random mating: Non-random mating, such as assortative mating (mating based on similar phenotypes), can alter genotype frequencies.
3. No gene flow: Gene flow, the movement of alleles between populations, can change allele frequencies.
4. No genetic drift: Genetic drift, the random fluctuation of allele frequencies due to chance events, is more pronounced in smaller populations and can significantly alter allele frequencies.
5. No natural selection: Natural selection favors certain alleles over others, leading to changes in allele frequencies.

The Hardy-Weinberg equation itself is relatively simple:

p² + 2pq + q² = 1

Where:

• p represents the frequency of the dominant allele.
• q represents the frequency of the recessive allele.
• p² represents the frequency of the homozygous dominant genotype.
• 2pq represents the frequency of the heterozygous genotype.
• q² represents the frequency of the homozygous recessive genotype.

Furthermore, p + q = 1. This equation reflects the fact that all alleles in the population must add up to 100% (or 1).

Practice Problems with Detailed Solutions

Let's work through several practice problems to solidify your understanding of the Hardy-Weinberg principle. Each problem will demonstrate different applications of the equation and highlight common pitfalls to avoid.

Problem 1: Calculating Allele and Genotype Frequencies

In a population of 1000 wildflowers, 160 individuals exhibit white flowers (recessive phenotype). Assuming the population is in Hardy-Weinberg equilibrium, calculate the allele frequencies (p and q) and the genotype frequencies (p², 2pq, and q²).

Solution:

1. Find q²: Since white flowers represent the homozygous recessive phenotype, q² = 160/1000 = 0.16.

2. Find q: Take the square root of q²: q = √0.16 = 0.4. This represents the frequency of the recessive allele.

3. Find p: Since p + q = 1, p = 1 - q = 1 - 0.4 = 0.6. This represents the frequency of the dominant allele.

4. Calculate genotype frequencies:

   • p² (homozygous dominant) = (0.6)² = 0.36
   • 2pq (heterozygous) = 2 * 0.6 * 0.4 = 0.48
   • q² (homozygous recessive) = (0.4)² = 0.16

Therefore, the genotype frequencies are: 36% homozygous dominant, 48% heterozygous, and 16% homozygous recessive.

Problem 2: Predicting Phenotype Frequencies

A population of beetles has two alleles for color: brown (B) and green (b). The allele frequency of the brown allele (B) is 0.7. If the population is in Hardy-Weinberg equilibrium, what proportion of the beetles will have green colored bodies (recessive phenotype)?

Solution:

1. Find q: Since p + q = 1 and p = 0.7, then q = 1 - 0.7 = 0.3. This is the frequency of the green allele (b).

2. Find q²: The frequency of the homozygous recessive genotype (bb), which results in green beetles, is q² = (0.3)² = 0.09.

Therefore, 9% of the beetles will have green bodies.

Problem 3: Detecting Deviations from Hardy-Weinberg Equilibrium

A population of butterflies has two alleles for wing color: blue (B) and white (b). A survey of 1000 butterflies reveals the following genotype frequencies: BB = 490, Bb = 420, bb = 90. Is this population in Hardy-Weinberg equilibrium?

Solution:

1. Calculate observed allele frequencies:

   • Number of B alleles = (2 * 490) + 420 = 1400
   • Number of b alleles = (2 * 90) + 420 = 600
   • Total alleles = 2000
   • p (observed) = 1400/2000 = 0.7
   • q (observed) = 600/2000 = 0.3

2. Calculate expected genotype frequencies under Hardy-Weinberg:

   • p² = (0.7)² = 0.49
   • 2pq = 2 * 0.7 * 0.3 = 0.42
   • q² = (0.3)² = 0.09

3. Compare observed and expected frequencies: The observed and expected frequencies are reasonably close, suggesting the population is approximately in Hardy-Weinberg equilibrium. However, a statistical test (like a chi-square test) would be needed to confirm this conclusively. Minor deviations can occur by chance, especially in smaller populations.

Problem 4: A More Complex Scenario

In a large population of snails, shell color is determined by two alleles: brown (B) and yellow (b). Brown is dominant to yellow. If 36% of the snails have yellow shells, what percentage of the snails are heterozygous for shell color? Assume the population is in Hardy-Weinberg equilibrium.

Solution:

1. Find q²: Yellow shells represent the homozygous recessive genotype (bb), so q² = 0.36.

2. Find q: Take the square root of q²: q = √0.36 = 0.6.

3. Find p: Since p + q = 1, p = 1 - 0.6 = 0.4.

4. Find 2pq: The frequency of heterozygous snails (Bb) is 2pq = 2 * 0.4 * 0.6 = 0.48.

Therefore, 48% of the snails are heterozygous for shell color.

Problem 5: Understanding Selection Pressure

Imagine a population of birds where beak size is determined by a single gene with two alleles: large beak (L) and small beak (l). Birds with large beaks are better able to crack tough seeds, providing a selective advantage. If the frequency of the large beak allele (L) is 0.8 in one generation, and the relative fitness of the LL, Ll, and ll genotypes are 1.0, 0.8, and 0.6 respectively, calculate the allele frequencies in the next generation. This problem goes beyond simple Hardy-Weinberg, illustrating how selection alters allele frequencies. (Note: Solving this requires understanding selection coefficients, which is beyond the scope of basic Hardy-Weinberg problems but illustrates a potential extension.)

Solution: (This problem requires iterative calculations using fitness values and will not be fully solved here due to its complexity, exceeding the scope of basic Hardy-Weinberg problems)

This problem demonstrates that selection pressures cause deviations from Hardy-Weinberg equilibrium. The relative fitness values are used to calculate the expected number of each genotype in the next generation. These numbers are then used to recalculate the allele frequencies. This process would be repeated over multiple generations to see how allele frequencies change over time under selection. This often requires advanced calculations and sometimes simulations.

Frequently Asked Questions (FAQ)

Q: What are the limitations of the Hardy-Weinberg principle?

A: The Hardy-Weinberg principle is a theoretical model. In reality, few populations meet all five conditions for equilibrium. It serves as a baseline against which to compare real-world populations and identify the evolutionary forces at play.

Q: Can Hardy-Weinberg equilibrium be used for traits with more than two alleles?

A: Yes, the principles can be extended to traits with multiple alleles. However, the equations become more complex.

Q: How can I test if a population is in Hardy-Weinberg equilibrium?

A: A chi-square test is often used to compare observed genotype frequencies with those expected under Hardy-Weinberg equilibrium. A statistically significant difference indicates that the population is not in equilibrium.

Q: Why is the Hardy-Weinberg principle important?

A: The Hardy-Weinberg principle is a fundamental concept in evolutionary biology. It provides a null hypothesis – a baseline – for understanding how and why allele and genotype frequencies change in populations over time. Deviations from equilibrium reveal the action of evolutionary forces such as mutation, selection, drift, and gene flow.

Conclusion

The Hardy-Weinberg principle is a powerful tool for understanding population genetics. By practicing problems and understanding the underlying assumptions, you can apply this principle to analyze real-world populations and gain valuable insights into evolutionary processes. Remember that while the idealized conditions of Hardy-Weinberg are rarely met perfectly in nature, the principle serves as a crucial benchmark for evaluating the impact of evolutionary forces on allele and genotype frequencies. Mastering these problems allows you to move beyond simply applying the formula and truly grasp the implications of this fundamental concept in evolutionary biology.