Problem B: Prairie Dog Population Genetics (20 Points) A relatively stable popul

Question

Problem B: Prairie Dog Population Genetics (20 Points)

A relatively stable population of Black-footed Prairie Dogs (70,000 individuals) lives in a national park in Saskatchewan, Canada. These creatures have various tones of brown fur, but may have brown or auburn tails. Furthermore, tails may be of solid color (brown or auburn) or be tipped with white or black fur. Three alleles for tail coloration exist in this population. These alleles include:

Allele

Trait

Notes of Phenotype and Relationship to Other Alleles

T

White tip

Tail has white fur at tip. Completely dominant over t; Codominant with T*

t

Black tip

Tail has black fur at tip. Codominant with T*; recessive to T.

T*

Auburn tail

Background tail color is auburn when T* is present. Codominant with T or t.

The frequency of the (T) allele in this population is 0.28, and the frequency of the (t) is 0.4.  

Answer each of the following. Show all of your work/calculations. Cite your rationale if appropriate.

1. List and describe all the possible genotypes and their respective phenotypes for this gene system in the population.

2. Using the Hardy-Weinberg theorem, calculate the probable frequency of animals with the following phenotypes in this population:

• White tipped tails

• Black tipped auburn tails

3. What is the expected combined frequency of individuals carrying the TT, TT* and Tt genotypes in this population?

4. How many (number, not percentage) of the prairie dogs would you expect to have black tipped, auburn tails? Explain.

5. In a different population of 10,000 prairie dogs (South Dakota, USA), only the T and t alleles are found. If this group included only 400 animals with black tipped, brown tails, what is the probable number (not frequency) of individuals that are homozygous dominant (TT) in this herd?

Allele

Trait

Notes of Phenotype and Relationship to Other Alleles

T

White tip

Tail has white fur at tip. Completely dominant over t; Codominant with T*

t

Black tip

Tail has black fur at tip. Codominant with T*; recessive to T.

T*

Auburn tail

Background tail color is auburn when T* is present. Codominant with T or t.

Explanation / Answer

2. According to the Hardy-Weinberg theorem, p=q=r+1 where p,q,and r are the allelic frequencies. Therefore,

0.28+0.4+T* = 1 ie, frequency of T*= 0.32

So, frequency of White tipped tails = TT + Tt = (0.28)2 + (0.28)(0.4)

                                                             0.0784 + 0.112 = 0.1904

frequency of Black tipped auburn tails = T*t = (0.32)(0.4) = 0.128

3.frequency of individuals carrying the TT, TT* and Tt genotypes in this population

TT = (0.28)(0.28) = 0.784

TT* = (0.28)(0.32) = 0.112

Tt = (0.28)(0.4) = 0.0896

4. number of the prairie dogs with black tipped, auburn tails

Blach tip means t and Auburn tail means T*. So frequnecy is T*t ie, (0.32)(0.4) = 0.128

Therefore their number is (70,000)(0.128) = 8960

5.

Here, the total number       = 10,000

Let T be the dominant and t be the recessive alleles and TT is dominat allele frequency and tt recessive allele frequency.

Number of Black tipped, brown tailed (tt) = 400

Here we have only two allels. So , Hardy-Weinberg equation will be p2+q2 = 1

= p2+q2+2pq = 1

q2 = 400/10,000 = 1/25 q = 1/5 therefore, p = 1-q = 1-1/5 = 4/5 [p2 = 16/25]

So, the number of individuals that are homozygous dominant (TT) =(10,000/25)16 = 6400

1. p q r T t T* T TT(white) Tt(white) TT*(white,auburn) t Tt(white) tt(Black) T*t(Black,auburn) T* T*T(white,auburn) T*t(Black,auburn) T*T*(auburn)

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