Ap Biology Hardy Weinberg Practice Problems

Population genetics is a cornerstone of evolutionary biology, providing a mathematical framework for understanding how allele frequencies change over time. At the heart of this framework lies the Hardy-Weinberg principle, a fundamental concept that describes the conditions under which genetic variation in a population remains constant from one generation to the next. This article provides a comprehensive guide to solving AP Biology Hardy-Weinberg practice problems, covering the principle's assumptions, equations, and applications with detailed examples.

Understanding the Hardy-Weinberg Principle

The Hardy-Weinberg principle, named after Godfrey Harold Hardy and Wilhelm Weinberg, states that in a large, randomly mating population, the allele and genotype frequencies will remain constant from generation to generation in the absence of other evolutionary influences. These influences include:

• Mutation: The rate of new mutations must be negligible.
• Natural Selection: All genotypes must have equal survival and reproductive rates.
• Gene Flow: There should be no migration of individuals into or out of the population.
• Genetic Drift: The population must be large enough to avoid random changes in allele frequencies due to chance.
• Random Mating: Individuals must mate randomly, without any preference for certain genotypes.

When these conditions are met, the population is said to be in Hardy-Weinberg equilibrium, and the allele and genotype frequencies can be predicted using two equations:

1. Allele Frequency Equation: p + q = 1
2. Genotype Frequency Equation: p² + 2pq + q² = 1

Where:

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

Step-by-Step Approach to Solving Hardy-Weinberg Problems

Solving Hardy-Weinberg problems involves a systematic approach to identify given information, determine what needs to be calculated, and apply the equations correctly. Follow these steps to tackle any Hardy-Weinberg problem effectively.

Step 1: Read and Understand the Problem

Carefully read the problem statement to identify the known quantities and what you are asked to find. Look for keywords such as "frequency," "percentage," "population," and "generation." Determine which information corresponds to allele frequencies (p and q) and which corresponds to genotype frequencies (p², 2pq, and q²).

Step 2: Identify the Known Values

Typically, Hardy-Weinberg problems provide the frequency of the homozygous recessive genotype (q²) or the frequency of individuals expressing the recessive phenotype. From this, you can calculate q, the frequency of the recessive allele. Sometimes, the problem may give you the frequency of the dominant phenotype or the frequency of one of the alleles directly.

Step 3: Calculate q (if necessary)

If you are given the frequency of the homozygous recessive genotype (q²), calculate q by taking the square root of q²:

q = √q²

Step 4: Calculate p

Use the allele frequency equation (p + q = 1) to find p, the frequency of the dominant allele:

p = 1 - q

Step 5: Calculate Genotype Frequencies

Using the values of p and q obtained in the previous steps, calculate the frequencies of the genotypes:

• Frequency of homozygous dominant genotype: p²
• Frequency of heterozygous genotype: 2pq
• Frequency of homozygous recessive genotype: q² (this may already be given)

Step 6: Check Your Work

Make sure that the sum of the genotype frequencies equals 1 (p² + 2pq + q² = 1). This step is crucial to ensure that your calculations are correct.

Step 7: Answer the Question

Once you have calculated all the necessary frequencies, make sure you answer the specific question asked in the problem. For example, the problem might ask for the number of heterozygous individuals in a population, given the total population size.

Example Problems with Detailed Solutions

Let's walk through several example problems to illustrate how to apply the Hardy-Weinberg principle.

Problem 1: Cystic Fibrosis

Cystic fibrosis is an autosomal recessive disorder. In a population of 10,000 people, 4% are affected by cystic fibrosis. Calculate the frequency of the recessive allele, the frequency of the dominant allele, and the percentage of heterozygous individuals in the population.

Solution:

1. Known Value: Frequency of affected individuals (homozygous recessive, q²) = 4% = 0.04
2. Calculate q: q = √q² = √0.04 = 0.2
3. Calculate p: p = 1 - q = 1 - 0.2 = 0.8
4. Calculate Genotype Frequencies:
   • Frequency of homozygous dominant genotype: p² = (0.8)² = 0.64
   • Frequency of heterozygous genotype: 2pq = 2 * 0.8 * 0.2 = 0.32
   • Frequency of homozygous recessive genotype: q² = 0.04 (given)
5. Check Work: p² + 2pq + q² = 0.64 + 0.32 + 0.04 = 1
6. Answer the Question:
   • Frequency of the recessive allele: q = 0.2
   • Frequency of the dominant allele: p = 0.8
   • Percentage of heterozygous individuals: 2pq = 0.32 = 32%

Problem 2: Phenylketonuria (PKU)

Phenylketonuria (PKU) is an autosomal recessive metabolic disorder that results in decreased metabolism of the amino acid phenylalanine. In the United States, about 1 in 10,000 babies is born with PKU. What is the frequency of the recessive allele in the population? What is the frequency of carriers (heterozygous individuals) in the population?

Solution:

1. Known Value: Frequency of affected individuals (homozygous recessive, q²) = 1/10,000 = 0.0001
2. Calculate q: q = √q² = √0.0001 = 0.01
3. Calculate p: p = 1 - q = 1 - 0.01 = 0.99
4. Calculate Genotype Frequencies:
   • Frequency of homozygous dominant genotype: p² = (0.99)² = 0.9801
   • Frequency of heterozygous genotype: 2pq = 2 * 0.99 * 0.01 = 0.0198
   • Frequency of homozygous recessive genotype: q² = 0.0001 (given)
5. Check Work: p² + 2pq + q² = 0.9801 + 0.0198 + 0.0001 = 1
6. Answer the Question:
   • Frequency of the recessive allele: q = 0.01
   • Frequency of carriers (heterozygous individuals): 2pq = 0.0198 = 1.98%

Problem 3: Widow's Peak

Having a widow's peak (a V-shaped hairline) is a dominant trait. In a population of 1,000 individuals, 360 lack a widow's peak. Calculate the frequency of each allele and the number of individuals who are heterozygous for this trait.

Solution:

1. Known Value: Frequency of individuals lacking a widow's peak (homozygous recessive, q²) = 360/1000 = 0.36
2. Calculate q: q = √q² = √0.36 = 0.6
3. Calculate p: p = 1 - q = 1 - 0.6 = 0.4
4. Calculate Genotype Frequencies:
   • Frequency of homozygous dominant genotype: p² = (0.4)² = 0.16
   • Frequency of heterozygous genotype: 2pq = 2 * 0.4 * 0.6 = 0.48
   • Frequency of homozygous recessive genotype: q² = 0.36 (given)
5. Check Work: p² + 2pq + q² = 0.16 + 0.48 + 0.36 = 1
6. Answer the Question:
   • Frequency of the dominant allele: p = 0.4
   • Frequency of the recessive allele: q = 0.6
   • Number of heterozygous individuals: 2pq * total population = 0.48 * 1000 = 480 individuals

Problem 4: Tongue Rolling

The ability to roll one's tongue is a dominant trait. In a population of 500 people, 125 cannot roll their tongues. Assuming Hardy-Weinberg equilibrium, what percentage of the population is homozygous dominant for tongue rolling?

Solution:

1. Known Value: Frequency of individuals who cannot roll their tongues (homozygous recessive, q²) = 125/500 = 0.25
2. Calculate q: q = √q² = √0.25 = 0.5
3. Calculate p: p = 1 - q = 1 - 0.5 = 0.5
4. Calculate Genotype Frequencies:
   • Frequency of homozygous dominant genotype: p² = (0.5)² = 0.25
   • Frequency of heterozygous genotype: 2pq = 2 * 0.5 * 0.5 = 0.5
   • Frequency of homozygous recessive genotype: q² = 0.25 (given)
5. Check Work: p² + 2pq + q² = 0.25 + 0.5 + 0.25 = 1
6. Answer the Question:
   • Percentage of the population that is homozygous dominant for tongue rolling: p² = 0.25 = 25%

Problem 5: MN Blood Group

In a sample of human blood, the MN blood group is determined by two alleles, M and N. A sample of 500 individuals showed the following genotypic distribution:

• MM: 140
• MN: 280
• NN: 80

Calculate the frequencies of the M and N alleles.

Solution:

1. Calculate the number of M alleles:
   • Each MM individual has 2 M alleles, so 140 MM individuals have 140 * 2 = 280 M alleles.
   • Each MN individual has 1 M allele, so 280 MN individuals have 280 * 1 = 280 M alleles.
   • Total number of M alleles = 280 + 280 = 560
2. Calculate the number of N alleles:
   • Each NN individual has 2 N alleles, so 80 NN individuals have 80 * 2 = 160 N alleles.
   • Each MN individual has 1 N allele, so 280 MN individuals have 280 * 1 = 280 N alleles.
   • Total number of N alleles = 160 + 280 = 440
3. Calculate the total number of alleles:
   • Total number of alleles in the population = 500 individuals * 2 alleles/individual = 1000 alleles
4. Calculate the frequency of the M allele (p):
   • p = (number of M alleles) / (total number of alleles) = 560 / 1000 = 0.56
5. Calculate the frequency of the N allele (q):
   • q = (number of N alleles) / (total number of alleles) = 440 / 1000 = 0.44
6. Check Work: p + q = 0.56 + 0.44 = 1
7. Answer the Question:
   • Frequency of the M allele: p = 0.56
   • Frequency of the N allele: q = 0.44

Common Mistakes to Avoid

When solving Hardy-Weinberg problems, it is essential to avoid common mistakes that can lead to incorrect answers.

• Confusing Allele and Genotype Frequencies: Always distinguish between allele frequencies (p and q) and genotype frequencies (p², 2pq, and q²).
• Incorrectly Calculating q: Make sure to take the square root of q² to find q.
• Not Checking Your Work: Always verify that the sum of genotype frequencies equals 1.
• Misinterpreting the Question: Ensure that you answer the specific question asked in the problem.
• Assuming Hardy-Weinberg Equilibrium: The Hardy-Weinberg principle applies only when the population is in equilibrium. If the problem indicates that the population is not in equilibrium, the equations cannot be used.

Advanced Applications and Extensions

While the basic Hardy-Weinberg principle provides a foundation for understanding population genetics, more advanced applications can explore deviations from equilibrium and analyze the effects of evolutionary forces.

• Testing for Hardy-Weinberg Equilibrium: Chi-square tests can be used to determine if a population is in Hardy-Weinberg equilibrium by comparing observed genotype frequencies to expected frequencies.
• Analyzing the Effects of Natural Selection: By comparing allele frequencies over multiple generations, the effects of natural selection can be quantified.
• Modeling Gene Flow: The impact of migration on allele frequencies can be modeled using extensions of the Hardy-Weinberg principle.
• Studying Genetic Drift: The effects of genetic drift, especially in small populations, can be simulated and analyzed.

The Significance of the Hardy-Weinberg Principle

The Hardy-Weinberg principle is a cornerstone of population genetics and evolutionary biology for several reasons:

• Null Hypothesis: It provides a null hypothesis for testing whether evolution is occurring in a population. If allele and genotype frequencies deviate significantly from Hardy-Weinberg expectations, it suggests that evolutionary forces are at play.
• Baseline for Comparison: It serves as a baseline for comparing the genetic structure of different populations.
• Understanding Genetic Variation: It helps in understanding the amount of genetic variation present in a population and how it is maintained.
• Predicting Genetic Disorders: It can be used to predict the frequency of genetic disorders in populations.

Conclusion

Mastering the Hardy-Weinberg principle is essential for success in AP Biology and for understanding the fundamental principles of population genetics. By following a step-by-step approach, practicing with example problems, and avoiding common mistakes, you can confidently solve Hardy-Weinberg problems and apply this knowledge to a wide range of biological contexts. The Hardy-Weinberg principle not only provides a mathematical framework for studying evolution but also serves as a powerful tool for understanding the genetic structure of populations and the forces that shape them.