Question

Jon Snow, born Aegon Targaryen, is the son of Lyanna Stark and Thaegar Targaryen, the late Prince of Dragonstone. Jon finds a runt of a dire wolf litter, an albino, which had crawled away from its mother's corpse. Jon names the dire wolf, Ghost. Jon is interested in the population genetics of this unique albino species in Westeros. Jon’s research study of a population of dire wolves indicates that they weigh 150 pounds and are about 5 feet long. The dire wolf fur color is grey (dominant) or white (recessive). Assume the population is in Hardy-Weinberg equilibrium. Jon observed 65 white dire wolves in a total population of 215 during his study.

a. Calculate the frequency of the homozygous recessive genotype?

b. Calculate the frequency of the grey allele in the population?

c. How many of the animals were heterozygous?

On a second trip, he observed 2,500 dire wolves.

a. How many do you think will be white assuming Hardy-Weinberg equilibrium?

b. How many of the grey animals are homozygous for the dominant allele?

c. How many do you think will be grey assuming Hardy-Weinberg equilibrium?

2. In a population of dire wolves that are mating randomly,11 percent of the dire wolves have red eyes (red is an autosomal recessive (a) trait) and 89 percent have yellow eyes (the normal color A). Assume the population is in Hardy-Weinberg equilibrium.

a. Calculate the allelic frequencies of A and a?

b. Calculate the genotypic frequencies of A / A and A / a?

Answer 1

Hardy Weinberg equation for genotype frequency is :-

p2 + 2pq + q2 = 1

For allele frequency it is :-

p + q = 1

We will be using these two equations to solve our questions.

Question a)

Homozygous recessive phenotype frequency.

The formula is :- Number of homozygous / Total population

White wolves = 65, Total population = 215

Thus, 65/215 = 0.30

The frequency of Homozygous recessive genotype is 0.30

Question b)

Frequency of Grey allele.

Now Since Grey is dominant over white, Grey population consist of Homozygous Dominant as well as heterozygous. So we can not find value of p2. Instead we have to find q2 and then q value.

Allele frequency formula is p+q = 1 so if we know q, we can find p too.

In the first question, we found q2 value as White is recessive and recessive allele is q.

So to find q :-

q2 = 0.30

q =√0.30 (We reverse it on the other side of the equation)

q = 0.54

So q is 0.54

p + q = 1

p + 0.54 = 1

p = 1 - 0.54

p = 0.46

Allele frequency for grey allele in the population is 0.46

Question c) How many animals are heterozygous

So heterozygous in the equation is denoted by 2pq. If we know the 2pq (frequency) we can multiply the frequency with total population and we will get the number of heterozygous. So :-

2 (0.54)(0.46) = 0.49

So heterozygous frequency is 0.49. Now heterozygous population is :-

Heterozygous frequency * total population

0.49 * 215 = ~105

There are 105 heterozygous wolves in the population.

For the Second part where population is now 2500 wolves :-

Question a) How many will be white :-

White genotype frequency from first question is 0.30.

So if we multiply it by total population, we will get the population of white wolves.

0.30 * 2500 = 750

There will be 750 white wolves

Question b) Homozygous Dominant

In the first portion of the question, we found the the value of p was 0.46. (p is used for dominant allele)

Then p2 will be (0.46)2 = 0.2116

Now if we multiply it by 2500, we will get the number of homozygous dominant wolves.

0.2116 * 2500 = 529

There are 529 Grey wolves which are homozygous.

Question c) How many will be grey

So, there are only 2 colors in the population. Grey and white wolves. We have the number of White wolves from the part a of this question.

There are 750 white wolves. The rest will be Grey.

So total wolves are 2500. Then :-

2500 - 750 = 1750

There are total of 1750 wolves which are grey (This includes both homozygous grey and Heterozygous Grey)

Now for the Red and Yellow eyed wolves :-

Question a)

So 11% are Red and 89% are yellow.

Red is recessive, so it's homozygous while Yellow is a sum of both Homozygous as well as heterozygous.

Now Red is 11% which mean 11/100 = 0.11

So q2 is 0.11.

Then value of q will be :-

q2 = 0.11

q = √0.11

q = 0.33

So value of q is 0.33

p + q = 1

p + 0.33 = 1

p = 1 - 0.33

p = 0.67

So p was for dominant and q for recessive. Thus

Allele frequency of A is 0.67

Allele frequency of a is 0.33

Question b)

Calculate genotypic frequency of A/A and A/a

Now A/A is homozygous dominant and Homozygous dominant genotype is q2​​​​​​

So, value of A is 0.67. Then,

(0.67)2 = 0.4489

Genotype frequency of A/A is 0.4489

For frequency of A/a. It is heterozygous and for heterozygous, formula is 2pq

p is 0.67 and q is 0.33.

Then,

2 (0.67)(0.33) = 0.4422

Thus the frequency of A/a genotype is 0.4422