Transcript Lab 5: Selection - West Virginia University

Lab 5: Selection
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
Nbefore
Nafter
Survival rate
Rel. fitness
(ω)
A1A1
A1A2
A2A2
100
80
0.8
100
56
0.56
100
40
0.4
1
0.56/0.8 0.4 /0.8
= 0.7
= 0.5
Mean Fitness(ω) and Genotype frequency
after selection
Genotype
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 Q(ω22)/ ω
= (H’)
= (Q’)
1
ω
= (100/300)(1) + (100/300)(0.7) + (100/300)(0.5) = 0.733
P’
= {(100/300)(1)}/ 0.733 = 0.45.
Fitness in terms of ‘s’ and
‘h’
Genotype
Fitness
Fitness in terms
of s and h
A1A1
ω11
A1A2
ω12
A2A2
ω22
1
1 – hs
1–s
22  0.5  1  s  0.5  s  0.5
1- 0.7 1- 0.7
w12 = 0.7 Þ1- hs = 0.7 Þ h =
=
= 0.4
s
0.5
Change in allele frequency
after selection
pqs[ ph  q(1  h)]
p 
2
1  2 pqhs q s
 pqs[ ph  q(1  h)]
q 
2
1  2 pqhs q s
q  p
Change in allele frequency after
selection
q  q'q
N 12
N 22 
2
q
N
N '12
N '22 
2
q' 
N'
Heterozygous Effect
h = 0, A1 dominant, A2 recessive
h = 1, A2 dominant, A1 recessive
0 < h < 1, incomplete dominance
h = 0.5, additivity
h < 0, overdominance
h > 1, underdominance
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):( 20 minutes)
Number before selection
Number after selection
A1A1
150
120
Genotype
A1A2
300
225
A2A2
150
105
a. Calculate the relative fitness for each of the three genotypes.
b. What is the mean fitness of this population? How do you expect it to change in
response to selection?
c. Based on the values calculated in a), calculate the values of h and s. What type
of selection has occurred?
d. 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)?
e. Calculate the change in the frequency of allele A2 as a result of the frost:
i. Based on the genotype frequencies calculated in d).
ii. Using the formula for ∆q as a function of p, q, h, and s.
f. What are the assumptions of the calculation in e)? What is your biological
interpretation of this result?
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 Δp and Δq and the fitness of each genotype. You should perform the
calculations for at least 5 different scenarios, using a range of values of each
parameter.
a.) What do you think is going to happen with the frequencies of A1 and A2 in each of
these cases in the long term?
b.) 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.
c.) What are the implications of the relative effects of h and s from an evolutionary
standpoint? In your answer, consider that most mutations that afffect fitness usually
have deleterious effects, and few are fully dominant.
Case
1
2
3
4
5
6
h
0
0.3
0.5
1
0.5
0
s
0.2
0.2
0.2
0.2
0.5
1
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 with
the p=0.7 and q= 0.3, but with h = 0.3 and s =
0.05.
Populus
Populus
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.
a.) Which cases show the fastest change in allele and genotype
frequencies, and why?
b.) What is the general trend for  and why?
Heterozygote advantage
(Overdominance)
Fitness
Fitness in terms
of s and h
A1A1
ω11
Genotype
A1A2
ω12
A2A2
ω22
1 – s1
1
1 – s2
Where, s1 and s2 are the selection disadvantages
of A1A1 and A2A2 with respect to A1A2.
Heterozygote advantage
(Overdominance)
pq( s1 p  s 2 q)
q 
2
2
1  s1 p  s 2 q
s1
qeq 
s1  s 2
Problem 4:(25 minutes)
a) If p = 0.65, q = 0.35, s1 = 0.13, and s2 = 0.19, calculate
the equilibrium frequency of A2.
b) Use Populus to verify the result of (a). Does qeq depend
on the initial allele frequencies p and q? How do you
explain this result?
c) 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?
d) GRAD STUDENTS ONLY: Is this equilibrium stable or
unstable and why? 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.