# AP Biology : Understanding Hardy-Weinberg Assumptions and Calculations

## Example Questions

### Example Question #11 : Population Genetics

Which of the following is a Hardy-Weinberg assumption?

Gene flow between populations

Natural selection is in operation

High rate of mutation

Random mating

Random mating

Explanation:

Random mating is one of the five Hardy-Weinberg assumptions that help maintain equilibrium. If random mating occurs, in tandem with the other assumptions, we can reasonably assume that there will not be a shift in allele frequencies or distributions.

The other Hardy-Weinberg assumptions are that natural selection does not occur, mutation does not occur, genetic drift (gene flow) does not occur, and that the population size is large.

### Example Question #12 : Population Genetics

Which of the following is not a Hardy-Weinberg assumption?

Random mating occurs

Mutation frequencies are high

Natural selection is not in operation

The population is large

Mutation frequencies are high

Explanation:

One of the five main assumptions is that mutations are negligible. This makes sense because, if a population is in Hardy-Weinberg equilibrium, evolution is not occurring. A low rate of mutations would help keep a population in equilibrium.

The five assumptions of Hardy-Weinberg equilibrium are a large population size, no natural selection, no mutation rate, no genetic drift, and random mating.

### Example Question #13 : Population Genetics

A population is in Hardy-Weinberg equilibrium. The gene of interest has two alleles, with 16% of the population portraying the features of the recessive phenotype. What percentage of the population is heterozygous?

Explanation:

Using the Hardy-Weinberg equilibrium equations, you can determine the answer.

The value of gives us the frequency of the dominant allele, while the value of gives us the frequency of the recessive allele. The second equation corresponds to genotypes. is the homozygous dominant frequency, is the heterozygous frequency, and is the homozygous recessive frequency.

16% of the population shows the recessive phenotype, and therefore must carry the homozygous recessive genotype. We can use this information to solve for the recessive allele frequency.

We can use the value of and the first Hardy-Weinberg equation to solve for .

Knowing both  and , you can use the second equation to find the percent of heterozygous organisms in the population.

### Example Question #14 : Population Genetics

A variety of grapes possesses a gene that generally determines the size of fruit produced. In a population of 200 plants, 194 show the dominant phenotype.

Based on the Hardy-Weinberg principles, what is the expected frequency of the dominant allele in this population?

Explanation:

The Hardy-Weinberg equations can be used to determine the expected frequency of genes and genotypes within a population, provided that only Mendelian segregation and recombination of alleles are at work. This is calculated mathematically using the equations:

We are told that 194 plants in a population of 200 demonstrate the dominant phenotype. This means that the sum of the homozygous dominant and heterozygous individuals is represented by the 194 plants described.

So, 97% of the plants show the dominant phenotype. This means that 3% must show the recessive phenotype.

Using this, we can find the frequency of the recessive allele, , and subsequently the dominant allele, .

### Example Question #11 : Understanding Hardy Weinberg Assumptions And Calculations

A person carrying two recessive alleles of a specific gene has a greater likelihood of developing lung cancer. The frequency of the dominant allele in a population is eighty-seven percent.

Based on the Hardy-Weinberg principle, what is the expected frequency of homozygous recessive genotype in this population?

Explanation:

The Hardy-Weinberg equations can be used to determine the expected frequency of genes and genotypes within a population, provided that only Mendelian segregation and recombination of alleles are at work. This is calculated mathematically using the equations:

Let's start with what we know and how it relates to these equations. We are told that the dominant allele frequency () is 87%, and then asked to find the frequency of homozygous recessive individuals ().

Known:

Unknown:

Use the second Hardy-Weinberg equation to solve for .

Square this value for find the frequency of homozygous individuals.

### Example Question #16 : Population Genetics

Hearing loss is caused by the inheritance of different genetic alleles: GM and GJ. The expected frequency of a GM allele is 90% in a given population.

Based on the Hardy-Weinberg principle, what is the expected frequency of genotype GMGJ in the next generation of this population?

Explanation:

The Hardy-Weinberg equations can be used to determine the expected frequency of genes and genotypes within a population, provided that only Mendelian segregation and recombination of alleles are at work. This is calculated mathematically using the equations:

In this example, the expected frequency to be solved for is the heterozygote GMGJ that is represented by the  component of the equation. We are told the frequency of the GM allele in the population, allowing us to solve for the frequency of the GJ allele. It is not necessary to know which allele is dominant and which is recessive in this particular question since we are dealing only with genotypes (phenotype is irrelevant).

Using these values, we can calculate the value of .

### Example Question #11 : Understanding Hardy Weinberg Assumptions And Calculations

A population of beetles exists in which black coloration is dominant to white. If there are 36 white beetles in a population of 100 beetles, what is the dominant allele frequency?

Unable to determine from the given information

Explanation:

There are multiple ways to solve this problem, but the easiest is to use the Hardy-Weinberg equations:

We are told the frequency of white beetles in the population. Using this value, we can find the recessive allele frequency. is equivalent to the homozygous recessive genotype frequency.

Use this value to solve for the dominant allele frequency.

### Example Question #12 : Understanding Hardy Weinberg Assumptions And Calculations

In a given population of snails, spiral shells are dominant to round shells. If 36% of the population is homozygous for the spiral shell allele, what percentage of the population is heterozygous?

Explanation:

We can use the Hardy-Weinberg equations to solve this problem.

We know that spiral shells are dominant, and that 36% of the population is homozygous for the spiral allele. This tells us that 36% of the population is homozygous dominant. The  term corresponds to the homozygous dominant percentage.

is the dominant allele frequency. Now we can solve for , the recessive allele frequency.

The term  will give us the frequency of heterozygotes.

48% of the population is heterozygous.

### Example Question #11 : Understanding Hardy Weinberg Assumptions And Calculations

If four percent of the population is homozygous recessive for the trait that carries dimples (recessive), what is the fractional frequency of the dominant allele?

Explanation:

Using the Hardy-Weinberg law to solve for allele frequency in populations, you can solve for the answer using the following two equations.

p is the fractional frequency of the dominant allele, q is the fractional frequency of the recessive allele, and q2 is the fraction of the population that is homozygous recessive. q2 is given in the question to be 0.04 (or 4%).

### Example Question #11 : Population Genetics

Which of the following is not a Hardy-Weinberg assumption?

Population size is large enough to prevent random drift

There is no mutation

There is no natural selection

There is no migration

There is nonrandom mating