one-locus diploid model

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.