Problem B: Prairie Dog Population Genetics A relatively stable population of Bla

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Problem B: Prairie Dog Population Genetics
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:

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

1. The possible genotypes and their respective phenotypes for this gene system in the
population are

Genotypes - TT, Tt, T*T, T*t, tt, T*T*

Phenotypes - TT White tip, Tt White tip, T*T white tipped auburn tail, T*t black tipped auburn tails, tt black tip, T*T* auburn tail

2. The probable frequency of animals with the following
phenotypes in this population:
• White-tipped tails (TT, Tt)
• Black tipped auburn tails ( T*t)

The frequency of the (T) allele in this population is 0.28, and the frequency of the (t) is 0.4. This is the case of codominance so we use formula p + q + r = 1

Here p2 = TT, q2 = tt

So, White tipped,

TT = p2 = 0.28 X 0.28 = 0.78

Tt = 2pq = 2 X 0.28 X 0.4 = 0.224

Black tipped, tt = 0.4 X 0.4 = 0.16

If p + q+ r = 1

So, (0.28) + (0.4) + r = 1

Now, r = 0.32 or T* = 0.32

Black tipped auburn tail, T*t = 0.32 X 0.4 = 0.13

3. Expected combined frequency of individuals carrying the expected combined frequency of individuals carrying the TT, TT* and Tt genotypes in this population TT, TT* and Tt genotypes in this population should be equal to 1.

4. number of the prairie dogs we expect to have black tipped, auburn tails should be i.e. T*t =

0. 32X 0.4 = 0. 12 So, 0.12 X 70000 = 8400.

5. 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, the probable number of individuals that are homozygous dominant (TT) in this herd is -

tt = 400/10000 So, tt = 0.04 and t = 0.2 = q

T = p = 1 - q = 1 - 0.2 = 0.8 or TT = 0.8 X 0.8 = 0.64 or no. of individuals = 0.64 X 10000 = 6400

2pq = 2 X 0.8 X 0.2 = 0.32.

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