Question

1. in humans, tongue rolling is dominant to non - rolling. in a population of 1000 individuals, 910 can roll their tongues while 90 cannot. 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 the population that is homozygous dominant:
d. the percentage of the population that is heterozygous:
e. the percentage of the population that is homozygous recessive:

1. within a population of butterflies, the color brown (b) is dominant over the color white (b) and 40% of all butterflies are white. given this simple information, calculate the following:

a. the frequency of the dominant allele:
b. the frequency of the recessive allele:
c. the percentage of the \bb\ genotype:
d. the percentage of the \bb\ genotype:
e. the percentage of the \bb\ genotype:

1. approximately 1% of a given human population is lactose intolerant, a recessive condition. based on this simple fact, calculate the following:

a. the frequency of the dominant allele:
b. the frequency of the recessive allele:
c. the percentage of the population that is homozygous dominant:
d. the percentage of the population that is heterozygous:
e. the percentage of the population that is homozygous recessive:

1. a pangorian trait which results from simple mendelian inheritance is antenna shape. corkscrew antennae (a) are dominant over straight antennae (a). when the entire pangorian population was screened (all 9,904 of them), 3,565 had corkscrew, while the rest had straight antennae.

a. the frequency of the dominant allele:
b. the frequency of the recessive allele:
c. the percentage of the population that is homozygous dominant:
d. the percentage of the population that is heterozygous:
e. the percentage of the population that is homozygous recessive:

Explanation:

Step1: Recall Hardy - Weinberg equilibrium equations

$p + q=1$ and $p^{2}+2pq + q^{2}=1$, 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 4

a. The frequency of the dominant allele

Step1: Find the frequency of the homozygous recessive genotype

The number of non - rollers (homozygous recessive) is 90 out of 1000. So $q^{2}=\frac{90}{1000}=0.09$.

Step2: Calculate the frequency of the recessive allele $q$

$q=\sqrt{q^{2}}=\sqrt{0.09} = 0.3$.

Step3: Calculate the frequency of the dominant allele $p$

Since $p + q = 1$, then $p=1 - q=1 - 0.3=0.7$.

b. The frequency of the recessive allele

We already found that $q = 0.3$.

c. The percentage of the population that is homozygous dominant

$p^{2}=(0.7)^{2}=0.49$, so the percentage is $49\%$.

d. The percentage of the population that is heterozygous

$2pq=2\times0.7\times0.3 = 0.42$, so the percentage is $42\%$.

e. The percentage of the population that is homozygous recessive

$q^{2}=0.09$, so the percentage is $9\%$.

Question 5

a. The frequency of the dominant allele

Step1: Find the frequency of the homozygous recessive genotype

The frequency of white butterflies (homozygous recessive) is $q^{2}=0.4$.

Step2: Calculate the frequency of the recessive allele $q$

$q=\sqrt{q^{2}}=\sqrt{0.4}\approx0.632$.

Step3: Calculate the frequency of the dominant allele $p$

Since $p + q = 1$, then $p=1 - q=1 - 0.632 = 0.368$.

b. The frequency of the recessive allele

$q\approx0.632$.

c. The percentage of the "BB" genotype

$p^{2}=(0.368)^{2}\approx0.135$, so the percentage is $13.5\%$.

d. The percentage of the "Bb" genotype

$2pq=2\times0.368\times0.632\approx0.465$, so the percentage is $46.5\%$.

e. The percentage of the "bb" genotype

$q^{2}=0.4$, so the percentage is $40\%$.

Question 6

a. The frequency of the dominant allele

Step1: Find the frequency of the homozygous recessive genotype

The frequency of lactose - intolerant individuals (homozygous recessive) is $q^{2}=0.01$.

Step2: Calculate the frequency of the recessive allele $q$

$q=\sqrt{q^{2}}=\sqrt{0.01}=0.1$.

Step3: Calculate the frequency of the dominant allele $p$

Since $p + q = 1$, then $p=1 - q=1 - 0.1 = 0.9$.

b. The frequency of the recessive allele

$q = 0.1$.

c. The percentage of the population that is homozygous dominant

$p^{2}=(0.9)^{2}=0.81$, so the percentage is $81\%$.

d. The percentage of the population that is heterozygous

$2pq=2\times0.9\times0.1=0.18$, so the percentage is $18\%$.

e. The percentage of the population that is homozygous recessive

$q^{2}=0.01$, so the percentage is $1\%$.

Question 7

a. The frequency of the dominant allele

Step1: Find the number of homozygous recessive individuals

The number of individuals with straight antennae is $9904−3565 = 6339$.
The frequency of the homozygous recessive genotype $q^{2}=\frac{6339}{9904}\approx0.64$.

Step2: Calculate the frequency of the recessive allele $q$

$q=\sqrt{q^{2}}=\sqrt{0.64}=0.8$.

Step3: Calculate the frequency of the dominant allele $p$

Since $p + q = 1$, then $p=1 - q=1 - 0.8 = 0.2$.

b. The frequency of the recessive allele

$q = 0.8$.

c. The percentage of the population that is homozygous dominant

$p^{2}=(0.2)^{2}=0.04$, so the percentage is $4\%$.

d. The percentage of the population that is heterozygous

$2pq=2\times0.2\times0.8 = 0.32$, so the percentage is $32\%$.

e. The percentage of the population that is homozygous recessive

$q^{2}=0.64$, so the percentage is $64\%$.

Answer:

Question 4:
a. $0.7$
b. $0.3$
c. $49\%$
d. $42\%$
e. $9\%$
Question 5:
a. $0.368$
b. $0.632$
c. $13.5\%$
d. $46.5\%$
e. $40\%$
Question 6:
a. $0.9$
b. $0.1$
c. $81\%$
d. $18\%$
e. $1\%$
Question 7:
a. $0.2$
b. $0.8$
c. $4\%$
d. $32\%$
e. $64\%$