Question

1. you have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. using that 36%, calculate the following:

a. the frequency of the \a\ allele: ________
b. the frequency of the \a\ allele: ________
c. the frequency of the \aa\ genotype: ________
d. the frequency of the \aa\ genotype: ________
e. the frequency of the \aa\ genotype: ________

1. in a population of fruit flies, 250 are homozygous dominant for red eyes and 500 are heterozygous for red eye. the remaining 250 flies have white eyes. given this information, calculate the following:

a. the frequency of the dominant allele: ________
b. the frequency of the recessive allele: ________
c. the frequency of the homozygous dominant genotype: ________
d. the frequency of the heterozygous genotype: ________
e. the frequency of the homozygous recessive genotype: ________

1. brown fur is dominant to white fur in mice. in a population of mice, 74% have brown fur and 26% have white fur. based on these facts, calculate the following:

a. the frequency of the dominant allele: ________
b. the frequency of the recessive allele: ________
c. the percentage of mice that are homozygous dominant: ________
d. the percentage of mice that are heterozygous: ________
e. the percentage of mice that are homozygous recessive: ________

Explanation:

Step1: Recall Hardy - Weinberg equations

$p + q=1$, $p^{2}+2pq + q^{2}=1$, where $p$ is the frequency of the dominant allele, $q$ is the frequency of the recessive allele, $p^{2}$ is the frequency of the homozygous dominant genotype, $2pq$ is the frequency of the heterozygous genotype, and $q^{2}$ is the frequency of the homozygous recessive genotype.

Question 1

Step2: Calculate the frequency of the "a" allele

Given $q^{2}=0.36$, then $q=\sqrt{0.36}=0.6$.

Step3: Calculate the frequency of the "A" allele

Since $p + q = 1$, and $q = 0.6$, then $p=1 - q=1 - 0.6 = 0.4$.

Step4: Calculate the frequency of the "AA" genotype

$p^{2}=(0.4)^{2}=0.16$.

Step5: Calculate the frequency of the "Aa" genotype

$2pq=2\times0.4\times0.6 = 0.48$.

Step6: Given frequency of "aa" genotype

$q^{2}=0.36$ (already given).

Question 2

Step7: Calculate the total number of individuals

The total number of fruit - flies $N=250 + 500+250 = 1000$.

Step8: Calculate the number of alleles

The total number of alleles is $2N = 2000$.
The number of dominant alleles from homozygous dominant individuals is $2\times250 = 500$, and from heterozygous individuals is $500$. So the total number of dominant alleles $=500 + 500=1000$. The number of recessive alleles from heterozygous individuals is $500$ and from homozygous recessive individuals is $2\times250 = 500$. So the total number of recessive alleles $=500+500 = 1000$.
The frequency of the dominant allele $p=\frac{1000}{2000}=0.5$.
The frequency of the recessive allele $q=\frac{1000}{2000}=0.5$.

Step9: Calculate the genotype frequencies

The frequency of the homozygous dominant genotype $p^{2}=(0.5)^{2}=0.25$.
The frequency of the heterozygous genotype $2pq=2\times0.5\times0.5 = 0.5$.
The frequency of the homozygous recessive genotype $q^{2}=(0.5)^{2}=0.25$.

Question 3

Step10: Calculate the frequency of the recessive allele

Given that the frequency of white - furred mice (homozygous recessive) is $q^{2}=0.26$, then $q=\sqrt{0.26}\approx0.51$.

Step11: Calculate the frequency of the dominant allele

Since $p + q = 1$, then $p=1 - q=1 - 0.51 = 0.49$.

Step12: Calculate the percentage of homozygous dominant mice

$p^{2}=(0.49)^{2}\approx0.24$.

Step13: Calculate the percentage of heterozygous mice

$2pq=2\times0.49\times0.51\approx0.50$.

Step14: Given percentage of homozygous recessive mice

$q^{2}=0.26$ (already given).

Answer:

Question 1

a. $0.4$
b. $0.6$
c. $0.16$
d. $0.48$
e. $0.36$

Question 2

a. $0.5$
b. $0.5$
c. $0.25$
d. $0.5$
e. $0.25$

Question 3

a. $0.49$
b. $0.51$
c. $24\%$
d. $50\%$
e. $26\%$