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One-locus diploid modelGoals:
Predict the outcome of selection: when will it result in fixation, when in polymorphism
Understand the effect of dominance on the rate of evolution
Back to the Foré
Genotype MM MV VV
juvenile 31 72 37adult 4 23 3
If selection continues to act in the same way, what will be the outcome?
One-locus diploid model
Selection acts in the diploid phase
random mating, no migration, and no mutationlarge population
Model conditions:allele frequencies
initial genotype frequencies
After selection?
p[t]
q[t]
p[t]q[t]
Genotype frequencies after selection
f’(AA)
f’(Aa)
f’(aa)
aaAaAA
AA
WqpqWWp
Wp22
2
2
aaAaAA
Aa
WqpqWWp
pqW22 2
2
aaAaAA
aa
WqpqWWp
Wq22
2
2
Allele frequencies after selection
f’(A) =
f’(a) =
aaAaAA
AaAA
WqpqWWp
pqWWp22
2
2
aaAaAA
aaAa
WqpqWWp
WqpqW22
2
2
aaAaAA
AA
WqpqWWp
Wp22
2
2
aaAaAA
Aa
WqpqWWp
pqW22 2
2
aaAaAA
aa
WqpqWWp
Wq22
2
2
f’(AA) =
f’(Aa) =
f’(aa) =
100%
100%
50%
50%
One-locus diploid model
p(t+1) = p(t)2WAA + p(t)q(t)Waa
p(t)2WAA + 2p(t)q(t)WAa + q(t)2Waa
One-locus diploid modelForms of selection
Directional Selection: Favoring allele A
Favoring allele a
Heterozygote advantage
Heterozygote disadvantage
(Which forms of selection were present in the haploid selection model?)
Directional selection
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
Directional selection: terms
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
WAA = 1
WAa = 1 + hs
Waa = 1 + s
s:
h:
Dominance
DominanceImagine two alleles fighting over
the phenotype (in this case, fitness(: where does the
heterozygote end up?
WAA
1
Waa
1 + s
WAa
1 + s/2
DominanceImagine two alleles fighting over
the phenotype (in this case, fitness(: where does the
heterozygote end up?
WAA
1
Waa
1 + s
WAa
=
DominanceImagine two alleles fighting over
the phenotype (in this case, fitness(: where does the
heterozygote end up?
WAA
1
Waa
1 + s
WAa
1 + hs
DominanceImagine two alleles fighting over
the phenotype (in this case, fitness(: where does the
heterozygote end up?
WAA
1
Waa
1 + s
WAa
1 + hs
DominanceImagine two alleles fighting over
the phenotype (in this case, fitness(: where does the
heterozygote end up?
WAA
=
1
Waa
1 + s
WAa
Dominance example
Sickle cell anemia:HH = healthy red blood cellsHh = sickle cell traithh = sickle cell anemia
Describe the dominance of H for:blood oxygen capacity? malaria resistance?
Dominance and selection
p(t+1) = p(t)2WAA + p(t)q(t)WAa
p(t)2WAA + 2p(t)q(t)WAa + q(t)2Waa
If A is dominant and rare:
If A is dominant and common:
Selection against a common allele
If WAA
< WAa
< Waa
, selection favors the a allele
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
Heterozygote advantage
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
WAa > Waa; WAa > WAA
WAa = 1; Waa = 0.9; WAA= 0.8
Heterozygote disadvantageHeterozygote disadvantage
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
WAa < Waa; WAa < WAA
WAa = 0.9; Waa = 1.0; WAA= 0.95
Equilibria
aaAaAA
AaAA
WqpqWWp
pqWWptptp
22
2
2)1()(
What are the equilibria?
Behaviour at polymorphic equilibrium
One-locus diploid modelExamples: Sickle-cell anemia
One-locus diploid modelExamples: Sickle-cell anemia
For the Nigerian population studied:
WHH = 0.88 WHh = 1
Whh = 0.14What is the expected equilibrium
frequency of the non-mutant allele (H)?
Readings and questions
References: Mead, S., M. P. H. Stumpf, et al. 2003. Balancing selection at the
prion protein gene consistent with prehistoric kurulike epidemics. Science 300: 640-643.
Reading: Freeman and Herron, chapter 6 (chapter 5)
Questions:1. What are the relative fitnesses for the three Foré
genotypes? (Use the juvenile data to estimate genotype frequencies prior to selection). What is the expected outcome of selection? Explain.
2. Imagine that a population experienced malaria but lacked the sickle-cell allele. Using the Nigerian fitness data, sketch the evolution of the population if a new sickle cell mutation arose in the population.
3. You have identified a locus that influences survival in sparrows. The relative fitnesses for each genotype are: WAA = 1.0; WAa = 0.9; Waa = 0.6. Describe the relationship between the two alleles in terms of dominance.
