1. Lab 5: Selection

2. Goals for Lab 5:
Use the basic selection model to calculate expected changes in allele and genotype frequencies.
Demonstrate the effects of different types of selection on mean population fitness.
Explore the interactions between selection and dominance.

3. Relative fitness (ω)
Average number of surviving progeny of one genotype compared to a competitive genotype.
Survival rate = “N” after selection / “N” before selection.
Genotype with highest survival rate has ω = 1.
Assumes equal fecundity for all genotypes.
Genotype
A1A1
A1A2
A2A2
N(before)
100
N(after) 80 56 40
Survival rate
0.8
0.56
0.4
Rel. fitness (ω) 1
0.56/0.8
= 0.7
0.4/0.8
= 0.5

4. Mean fitness (ω) and genotype frequency after selection
Sum
A1A1
A1A2
A2A2
Relative fitness
ω11
ω12
ω22
Genotype frequency before selection
P = p2
H = 2pq
Q = q2 1
Genotype frequency  Relative fitness
P(ω11)
H(ω12)
Q(ω22) ω
Genotype frequency after selection
P(ω11)/ω
= (P’)
H(ω12)/ω
= (H’)
Q(ω22)/ω
= (Q’)
ω = (100/300)(1) + (100/300)(0.7) + (100/300)(0.5) = 0.733
P’ = (100/300)(1)/ = 0.45

5. Fitness in terms of s and h
Genotype
A1A1
A1A2
A2A2
Relative fitness
ω11
ω12
ω22
Fitness in terms of s and h 1
1 – hs
1 – s
s = selection coefficient
h = heterozygous effect

6. Heterozygous effect h = 0 -- A1 dominant, A2 recessive
0 < h < 1 -- incomplete dominance
h = additivity
h < overdominance
h > underdominance

7. Change in allele frequency after selection

8. Change in allele frequency after selection

9. Problem 1. A complete census of a population of a cold-intolerant plant revealed the following numbers for genotypes A1A1, A1A2, and A2A2 before and after a severe spring frost (but before sexual reproduction):   
Calculate the relative fitness for each of the three genotypes. Remember that the fitness values should be calculated relative to the genotype with the highest survival rate, whose fitness is set to 1 (e.g., if the highest survival rate is 0.9, the fitness of the genotype that has this survival rate will be 1, whereas the fitness of a genotype with survival rate of 0.6 will be 0.6/0.9  0.67).
What is the mean fitness of this population? How do you expect the mean fitness to change in response to selection, and why?
Based on the values calculated in a), calculate the values of h and s. What type of selection has occurred? (Consult your lecture notes.)
If the surviving individuals mate at random, what will be the genotype frequencies in the next generation (i.e., assuming no other evolutionary forces intervene)? (question e) on manual)
Calculate the change in the frequency of allele A2 as a result of the frost:
Based on the genotype frequencies calculated in d).
Using the formula for ∆q as a function of p, q, h, and s.
What are the assumptions of the calculation in e)? What is your biological interpretation of this result?
Genotype
A1A1
A1A2
A2A2
Before
150
300
After
120
225
105

10. Problem 2. Assume that a population has two alleles A1 and A2, with frequencies of p = 0.8 and q = 0.2, respectively. Using the general equations for changes in allele frequencies, explore the relative effects of dominance and the selection coefficient by calculating ∆p and ∆q and the fitness of each genotype. You should perform the calculations for at least five different scenarios, using a range of values of each parameter.
What do you think is going to happen with the frequencies of A1 and A2 in each of these cases over the long term?
Rank the cases from greatest to smallest allele frequency change and explain what determines the different magnitudes of change. Be sure to include an evaluation of the relative importance of dominance and the selection coefficient.
What are the implications of the relative effects of h and s from an evolutionary standpoint? In your answer, consider that most mutations that affect fitness usually have deleterious effects, and few are fully dominant.

11. Populus
Simulation program that can be used as a ‘time machine’ for prediction of evolutionary and demographic aspects of population dynamics. Example: Use Populus to evaluate the changes of allele frequencies, genotype frequencies, and mean fitness after 10 generations of selection in a population where:
p = 0.7
q = 0.3
h = 0.3
s = 0.05

12. Populus
p = 0.7
q = 0.3
h = 0.3
s = 0.05

13. Populus
p = 0.7
q = 0.3
h = 0.3
s = 0.05

14. Problem 3. Use Populus to determine the allele frequencies for A1 and A2 for all 5 cases from Problem 2 after 50 generations. Include the values of the final allele frequencies and a graph for the change of p over time in your report, but also look at the graphs showing the changes of genotype frequencies over time and the graphs showing ∆p and for different values of p.
Which cases show the fastest change in allele and genotype frequencies, and why?
What is the general trend for and why?

15. Heterozygote advantage (overdominance)
Genotype
A1A1
A1A2
A2A2
Fitness
ω11
ω12
ω22
Fitness in terms of s and h
1 – s1 1
1 – s2
Where, s1 and s2 are the selection disadvantages of A1A1 and A2A2 with respect to A1A2.

16. Heterozygote advantage (overdominance)

17. Problem 4. To describe overdominance (i. e
Problem 4. To describe overdominance (i.e., advantage of heterozygotes over all homozygotes), a more convenient way to express the fitness coefficients of the genotypes at a locus with two alleles is:
(where s1 and s2 are the selection disadvantages of A1A1 and A2A2 with respect to A1A2).   
Genotype
A1A1
A1A2
A2A2
Fitness
ω11
ω12
ω22
Fitness in terms of s and h
1 – s1 1
1 – s2
If p = 0.65, q = 0.35, s1 = 0.13, and s2 = 0.19, calculate the equilibrium frequency of A2 (consult your lecture notes).
Use Populus to verify the result of a). Does qeq depend on the initial allele frequencies p and q (show graphs and data for at least 3 starting values of p; make sure you run the program for enough generations to see the equilibrium allele frequency)? How do you explain this result?
When will the population reach its maximum mean fitness? How might a population be perturbed from this state? What would cause the population to return to maximum mean fitness?
GRADUATE STUDENTS ONLY: Is this equilibrium stable or unstable and why (Hint: Take a look at the graph showing ∆p vs p in Populus)? What causes a population to reach a stable equilibrium? Provide a specific example of a trait and selection regime that would result in a stable equilibrium. This may be hypothetical or based on the literature.