AP Biology - Population Genetics

1

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.

$p^{2}+2pq+q^{2}=1$

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%).

$q^{2}= 0.04 \rightarrow q=0.2$

$0.2 + p=1 \rightarrow p=0.8$

2

A population of snails is originally in Hardy-Weinberg equilibrium. The snails come in two different colors: red, the dominant phenotype, and white, the recessive phenotype. The original population has a dominant allele frequency of $\small 0.6$ and a recessive allele frequency of $\small 0.4$ . A new predator is introduced to the habitat that is particularly fond of the red snails. After a few years the dominant allele frequency has been reduced to $\small 0.2$ .

What is the recessive allele frequency after the introduction of this predator?

Explanation

Most of the information in the question is actually superfluous because we are given the final dominant allele frequency. The dominant allele frequency corresponds to the variable $\small p$ in the Hardy-Weinberg equations.

The question tells us that the dominant allele frequency after introduction of the predator is $\small 0.2$ . Use this value in the first Hardy-Weinberg equation to solve for the recessive allele frequency, $\small q$ .

3

Which of the following is a Hardy-Weinberg assumption?

Random mating

Natural selection is in operation

High rate of mutation

Gene flow between populations

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.

4

A population of snails is in Hardy-Weinberg equilibrium. The snails come in two different colors: red, the dominant phenotype, and white, the recessive phenotype. There are sixteen homozygous dominant, forty-eight heterozygous, and thirty-six homozygous recessive snails.

What are the allele frequencies for this population?

$p=0.4\ \text{and}\ q=0.6$

$p=1.0\ \text{and}\ q=0.0$

$p=0.35\ \text{and}\ q=0.65$

$p=0.2\ \text{and}\ q=0.8$

Explanation

We can solve this question using the Hardy-Weinberg equations:

In the second equation, $\small p^2$ corresponds to the frequency of homozygous dominant individuals, $\small 2pq$ corresponds to the heterozygous frequency, and $\small q^2$ corresponds to the frequency of homozygous recessive individuals. We are given enough information to find each of these values from the question.

$p^2=\frac{#homo_D}{#total}=\frac{16}{16+48+36}=0.16$

$2pq=\frac{#hetero}{#total}=\frac{48}{16+48+36}=0.48$

$q^2=\frac{#homo_R}{#total}=\frac{36}{16+48+36}=0.36$

We can find the values of $\small p$ and $\small q$ by taking the square root of their squares.

$\begin{matrix} p^2=0.16 & q^2=0.36\ \sqrt{p^2}=\sqrt{0.16}& \sqrt{q^2}=\sqrt{0.36}\ p=0.4& q=0.6 \end{matrix}$

5

A population of snails is in Hardy-Weinberg equilibrium. The snails come in two different colors: red, the dominant phenotype, and white, the recessive phenotype. There are sixteen homozygous dominant, forty-eight heterozygous, and thirty-six homozygous recessive snails.

What are the allele frequencies for this population?

$p=0.4\ \text{and}\ q=0.6$

$p=1.0\ \text{and}\ q=0.0$

$p=0.35\ \text{and}\ q=0.65$

$p=0.2\ \text{and}\ q=0.8$

Explanation

We can solve this question using the Hardy-Weinberg equations:

In the second equation, $\small p^2$ corresponds to the frequency of homozygous dominant individuals, $\small 2pq$ corresponds to the heterozygous frequency, and $\small q^2$ corresponds to the frequency of homozygous recessive individuals. We are given enough information to find each of these values from the question.

$p^2=\frac{#homo_D}{#total}=\frac{16}{16+48+36}=0.16$

$2pq=\frac{#hetero}{#total}=\frac{48}{16+48+36}=0.48$

$q^2=\frac{#homo_R}{#total}=\frac{36}{16+48+36}=0.36$

We can find the values of $\small p$ and $\small q$ by taking the square root of their squares.

$\begin{matrix} p^2=0.16 & q^2=0.36\ \sqrt{p^2}=\sqrt{0.16}& \sqrt{q^2}=\sqrt{0.36}\ p=0.4& q=0.6 \end{matrix}$

6

Which of the following is a Hardy-Weinberg assumption?

Random mating

Natural selection is in operation

High rate of mutation

Gene flow between populations

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.

7

A population of snails is originally in Hardy-Weinberg equilibrium. The snails come in two different colors: red, the dominant phenotype, and white, the recessive phenotype. The original population has a dominant allele frequency of $\small 0.6$ and a recessive allele frequency of $\small 0.4$ . A new predator is introduced to the habitat that is particularly fond of the red snails. After a few years the dominant allele frequency has been reduced to $\small 0.2$ .

What is the recessive allele frequency after the introduction of this predator?

Explanation

Most of the information in the question is actually superfluous because we are given the final dominant allele frequency. The dominant allele frequency corresponds to the variable $\small p$ in the Hardy-Weinberg equations.

The question tells us that the dominant allele frequency after introduction of the predator is $\small 0.2$ . Use this value in the first Hardy-Weinberg equation to solve for the recessive allele frequency, $\small q$ .

8

A population of snails is in Hardy-Weinberg equilibrium. The snails come in two different colors: red, the dominant phenotype, and white, the recessive phenotype. The population consists of sixty-four red snails and thirty-six white snails.

Assuming that the population is in Hardy-Weinberg equilibrium, what is the value of $\small q$ ?

Explanation

We can solve this question using the Hardy-Weinberg equations:

$\small q$ is equal to the recessive allele frequency, while $\small q^2$ in the second Hardy-Weinberg equation corresponds to the frequency of the recessive phenotype.

The question tells us the number of dominant red snails and the number of recessive white snails. Using these values, we can find the frequency of the recessive phenotype.

$q^2=\frac{#white}{#total}=\frac{36}{64+36}$

From here, take the square root to find the value of $\small q$ .

$\sqrt{q^2}=\sqrt{0.36}$

9

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.

$p^{2}+2pq+q^{2}=1$

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%).

$q^{2}= 0.04 \rightarrow q=0.2$

$0.2 + p=1 \rightarrow p=0.8$

10

A population of snails is in Hardy-Weinberg equilibrium. The snails come in two different colors: red, the dominant phenotype, and white, the recessive phenotype. The population consists of sixty-four red snails and thirty-six white snails.

Assuming that the population is in Hardy-Weinberg equilibrium, what is the value of $\small q$ ?

Explanation

We can solve this question using the Hardy-Weinberg equations:

$\small q$ is equal to the recessive allele frequency, while $\small q^2$ in the second Hardy-Weinberg equation corresponds to the frequency of the recessive phenotype.

The question tells us the number of dominant red snails and the number of recessive white snails. Using these values, we can find the frequency of the recessive phenotype.

$q^2=\frac{#white}{#total}=\frac{36}{64+36}$

From here, take the square root to find the value of $\small q$ .

$\sqrt{q^2}=\sqrt{0.36}$

Population Genetics

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