Transcript Lab 5: Selection

Lab 5: Selection
Goals for Lab 5:
1. Use the basic selection model to calculate expected
changes in allele and genotype frequencies.
2. Demonstrate the effects of different types of
selection on mean population fitness.
3. Explore the interactions between selection and
dominance.
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
N(before)
N(after)
Survival rate
A1A1
A1A2
A2A2
100
80
0.8
Rel. fitness (ω)
1
100
56
0.56
0.56/0.8
= 0.7
100
40
0.4
0.4/0.8
= 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
= (H’)
Q(ω22)/ω
= (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
Relative fitness
Fitness in terms
of s and h
A1A1
ω11
A1A2
ω12
A2A2
ω22
1
1 – hs
1–s
s = selection coefficient
h = heterozygous effect
Heterozygous effect
h=0
h=1
0<h<1
h = 0.5
h<0
h>1
-------
A1 dominant, A2 recessive
A2 dominant, A1 recessive
incomplete dominance
additivity
overdominance
underdominance
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'
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):
a) 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).
Genotype
A1A1 A1A2 A2A2
b) What is the mean fitness of this population? How do you expect the
mean fitness to change in response to selection, and why?
B
e
f
150
c) Based on the values calculated in a), calculate the values of h and s.
o
What type of selection has occurred? (Consult your lecture notes.)
r
e
d) If the surviving individuals mate at random, what will be the genotype
A
frequencies in the next generation (i.e., assuming no other evolutionary
f
forces intervene)? (question e) on manual)
t 120
e
e) Calculate the change in the frequency of allele A2 as a result of the frost: r
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?
300
150
225
105
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.
a) What do you think is going to happen with the frequencies of A1 and A2 in each
of these cases over 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 affect fitness
usually have deleterious effects, and few are fully dominant.
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
Populus
p = 0.7
q = 0.3
h = 0.3
s = 0.05
Populus
p = 0.7
q = 0.3
h = 0.3
s = 0.05
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. 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:
Fitness
(where s1 and s2 are the selection
disadvantages of A1A1 and A2A2 with
respect to A1A2).
Fitness in
terms of s
and h
Genotype
A1A1
A1A2
A2A2
ω11
ω12
ω22
1 – s1
1
1 – s2
a) If p = 0.65, q = 0.35, s1 = 0.13, and s2 = 0.19, calculate the equilibrium frequency of A2 (consult
your lecture notes).
b) 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?
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) 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.