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ID: 62168 • Letter: I

Question

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1. Answer the following questions

(a –d) given the following information.

Please show your mathematical equations used and your work for full credit, highlight your final answer:

Suppose we have one locus with two alleles with the following absolute viabilities

and initial allele frequencies.

Absolute viability:

AA = 0.95

AB = 0.95

BB = 0.65

Initial allele frequency:

Frequency A (p) = 0.2

Frequency of B (q) = 0.8

a. What are the relative fitnesses of the genotypes?

b. What is the average fitness in the population?

c. Assuming a general selection model what will the frequency of both alleles A and B be after one generation of selection?

d. What will the percent (%) change in the allele frequency of A be after one generation of selection?

Will it be an increase or decrease change?

2. In wild Soay Sheep horn size is largely determined by a single gene with two alleles. Let us assume for simplicity that sheep with the dominant allele, H+, have large horns and sheep with recessive allele, Hs, have short horns. Below is a table showing the relative reproductive success of individuals with the following genotypes. Assume relative reproductive success is our measure of relative fitness of genotypes.

Answer the following question (a-e).

Relative Reproductive Success:

H+H+ is 1

H+Hs is 1

HsHs is 0.60

a. What is the selection coefficient (s) value against the recessive allele (Hs)?

b. What type (mode) of selection is occurring at this locus AND what is the relationship of the relative fitnesses of the genotypes?

c. You want to model selection at this locus to determine the rate at which the advantageous allele frequency will change after selection. What is the proper equation to use to determine the allele (H+) frequency change after one generation of selection?

d. Assume before selection the initial allele frequencies are H+=0.1 and Hs=0.9. What will the change in H+ frequency be after one generation of selection against the Hs allele? Show your mathematical work and highlight your final answer.

e. Draw a predicted graph of the rate of change for H+ AND Hs over say 600 generations. I am interested in if you can (a) label your axes correctly, (b) indicate the initial allele frequencies correctly, and (c) show the predicted trend lines for the change in allele frequencies over generations. You should make one graph with two lines (one for H+ and one for Hs). Label your lines as H+ and Hs, This eans you do not need to perform any math to make your plots.)

Explanation / Answer

1) a) Relative fitness= survival rate of the genotype or average fitness/ maximum survival rate or maximum fitness

Relative fitness of AA= 95/95=1; Average fitness of AA= 95%; means on an average 95% individuals survive to reproductive age.

Relative fitness of AB= 95/95=1; Average fitness = 95%

Relative fitness of BB= 65/95=0.68; Average fitness= 65%

Genotype

Genotype frequency

P2=0.2*0.2=0.04

2pq= 2*0.2*0.8=0.32

q^2=0.8*0.8= 0.64

Fitness

0.68

Changed frequency after one generation

0.04*1=0.04

0.32*1= 0.32

0.64*0.68= 0.44

Frequency of allele A after 1st generation = (0.04/0.80) + (1/2* 0.32/0.80) = 0.05+0.2= 0.25

Frequency of allele B after 1st generation = (0.44/0.80) + (1/2 * 0.32/0.80) = 0.55 + 0.2= 0.75

d) percent change in allele frequency of A after one generation = (0.25-0.2/0.2) *100 = 0.05 *100 / 0.2 = 25%