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