how do we explain the patterns of variation observed in DNA sequences?

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how do we explain the patterns of variation observed in DNA sequences? how do we detect selection by comparing silent site substitutions to replacement substitutions? how do we detect selection by comparing fixed differences between species to polymorphisms within species? how do we detect selection by using hitchhiking?

Goal: understand the logic behind key tests.

Molecular evolution:

Neutralist vs. selectionist view

Are most substitutions due to drift or natural selection?

“Neutralist” vs. “selectionist”Agree that:

Most mutations are deleterious and are removed.

Some mutations are favourable and are fixed.Dispute:

Are most replacement mutations that fix beneficial or neutral?Is observed polymorphism due to selection or drift?

Reminder: substitution vs. polymorphism

What happen after a mutation changes a nucleotide in a locus

Polymorphism: mutant allele is one of several present in population

Substitution: the mutant allele fixes in the population. (New mutations at other nucleotides may occur later.)

Substitution schematicIndividual 1 2 3 4 5 6 7

Time 0: aaat aaat aaat aaat aaat aaat aaatTime 10: aaat aaat aaat aaat acat aaat aaatTime 20: aaat aaat acat aaat acat acat acatTime 30: acat acat acat acat acat acat acatTime 40: acat acat actt acat acat acat acat

Times 10-29: polymorphismTime 30: mutation fixed -> substitutionTime 40: new mutation: polymorphism

Reminder: substitution rates for neutral mutations

Most neutral mutations are lostOnly 1 out of 2N fixMost that are lost go quickly (< 20

generations for population sizes from 100 - 2000)

Most replacement mutations are lost since deleterious: rate of loss is faster than neutral

Data in favor of neutrality

• Substitutions in DNA appear to be clock-like

Figure 6.21

Drift model pseudocodePopulation with 2N – 1 copies of allele A, 1 of allele aFor each generation, draw from prior generation alleles.

-> generate a random number. If less than f(A), new allele = A. Otherwise, allele = a.-> repeat until 2N alleles drawn

Check to see outcome of drift->If a is lost, start over.->If a has fixed, note the number of years->Otherwise, next year with the new allele frequencies

Repeat 100x per population sizeTest populations of 100, 500, 1000, 1500, and 2000

Times to fix for neutral alleles(Only 1/2N fix: how long do they take?)

0 500 1000 1500 2000

Population size

Estimated formula: fixation time = 4.07 * N – 57

Theoretical formula: fixation time = 4N

Puzzle for neutrality

• Rates of substitution are clock-like per year, not per generation.

Actual patternrabbits

elephants

Expected pattern

rabbits

elephants

Revised theory: the nearly – neutral theory

Figure 6.22

Can we distinguish selection from drift using sequence data?

• Compare two species: infer where substitutions have occurred.

• Silent site substitutions should be neutral (dS)• Non-synonymous substitutions are expected to

be deleterious (usually) (dN)• so, expect < 1

Translation: rate of non-synonymous (dN) is less than the rate of synonymous substitutions (dS)

and inferences about selection

< 1: replacements are deleterious

= 1: replacements are neutral

> 1: replacements are beneficial

What happens to fixation time with selection? Model pseudocode

Population with 2N – 1 copies of allele A, 1 of allele aWA = 1 + s; Wa = 1For each generation, draw from prior generation alleles.

-> generate a random number. If greater than f(A), new alleel = a. Otherwise, test fitness: if random < WA, new allele = A. -> repeat until 2N alleles drawn

Check to see outcome of drift->If a is lost, start over.->If a has fixed, note the number of years->Otherwise, next year with the new allele frequencies

Repeat 100x per fitnessTest populations of 100

Time to fix favourable allele

Ne = 100 (black line: estimated time to fixation = 2 ln(2N) / |s|

0200400600800

10001200

0 0.01 0.02 0.03 0.04 0.05

Selection coefficient

Time to fix: neutral vs. favourable

0 500 1000 1500 2000

Population size

Simulation results: black – neutral mutations; red – favourable mutations

Time to fixation: drift is slowNeutral:

New mutations per generation: 2NeuProbability of fixing a new mutation: 1 / 2Ne

Fixations per generation: = 2Neu * 1 / 2Ne = uTime to fix: 4Ne

Favored by selectionNew mutations per generation: 2Neu (but how many favourable??)Favored mutation probability of fixing: 2|s|Fixations per generation: 2Neu * 2|s| * prob. favourableTime to fix: 2 ln (2Ne) / |s|

2 ln (2Ne) / |s| << 4NeShorter time to fixation

Derivations of these results are tough! See Kimura (1962) and Kimutra and Ohta (1969).

Time to fixation: favourable and neutral

dN / dS data: BRCA1

Figure 6.21

Molecular evidence of selection II: McDonald-Kreitman Test

is very conservative: many selective events may be missed.

Example: immunoglobins.

= 0.37 overall

We suspect selection favoring new combinations at key sites. Antigen recognition sites:

Evidence of selection II: McDonald-Kreitman test

McDonald-Kreitman test III

If evolution of protein is neutral, the percentage of mutations that alter amino acids should be the same along any branch

If all mutations are neutral, all should have the same probability of persisting

So: dN / dS among polymorphisms should be the same as within fixed differences

McDonald-Kreitman logic• Silent sites

- always neutral- fix slowly- contribute to polymorphism

• Replacement sites– mainly unfavourable– if neutral, fix at same rate as silent and contribute to

polymorphism– proportion of replacement mutations that are neutral

determines dN / dS for polymorphism– if favourable, fix quickly and do not contribute to

polymorphism: higher dN / dS for fixed differences, lower rate for polymorphism

Time to fixation: favourable and neutral

Polymorphism and fixation

Silent Replacement

Neutral

Deleterious

1 / 2N neutral mutations fix

Polymorphism and fixation

Silent Replacement

Neutral

Deleterious

Favourable

1 / 2N neutral mutations fix

- slow

Neutral Favourable

2|s| fix

dN / dS for neutral and favourable

Neutral

Polymorphism

Fixation

Favourable

poly dSdN

fixed=

poly dSdN

fixed<

McDonald-Kreitman hypotheses

H0: All mutations are neutral.

Then, dN / dS for polymorphic sites should equal dN / dS for fixed differences

H1: replacements are favoured. Favoured mutations fix rapidly, so dN / dS for polymorphic < dN / dS fixed

Example of MK test: ADH in Drosophilia

Compare sequences of D. simulans and D. yakuba for ADH (alcohol dehydrogenase)

Fixed differences

Polymorphic sites

Replacement 7 2

Silent 17 42

% fixed 7 / 24 = 29% 2 / 44 = 5%

Significance? Use χ2 test for independence

Evidence of selection III: selective sweeps

• Imagine a new mutation that is strongly favored (e.g. insecticide resistance in mosquitoes)

Detecting selection using linkage: G6PD in humans

Natural history:• Located on X chromosome• encodes glucose-6-phosphate dehydrogenase • Red blood cells lack mitochondria• Glycolysis only• NADPH only via pentose-phosphate shunt –

requires G6PD• NADPH needed for glutathione, which protects

against oxidation

G6PD and malaria

• Malaria (Plasmodium falciparum) infects red blood cells

• Has limited G6PD function typically (but can produce the enzyme)

• Uses NADPH from red blood cell• In G6PD deficient individuals?

G6PD mutants

• Different mutants result in different levels of enzymatic activity

• Severe mutants result in destruction of red blood cells and anemia

• Most common mutant: G6PD-202A• Usually mild effects: may increase risk of

miscarriage

• Prediction: G6PD and malaria?

Frequency of G6PD deficiency

Has G6PD-202A been selected?

• 14 markers up to 413,000 bp from G6PD• LD? • Long distance LD implies strong, recent

selection

Has G6PD-202A been selected?Li

libriu

kb from core region

Fig 7.14

Alternative hypothesis: drift caused linkage disequilibrium

Allele frequency

G6PD-202A

Figure 7.14b

Detecting selection II: CCR532

Detecting selection II: CCR5Δ32

• Stephens (1998) found strong disequilibrium between CCR5-Δ32 and nearby markers

• Implies recent origin (< 2000 years): recombination breaks down linkage

• Implies selected

Detecting selection II: CCR5Δ32

• But: new data – November 2005.

• Better map:

Detecting selection: summary

• Several approaches to detecting selection– dN / dS– McDonald-Kreitman test– using hitchhiking

Challenges of each method?

Other uses of molecular data: the coalescent

Any two alleles in a population share a common ancestor in the last generation

1 / 2Ne

Therefore, going backwards in time, the expected time to find the common ancestor is 1 / (1 / 2Ne) = 2Ne

Coalescent II

Coalescent and sequences

Imagine that you have two sequences at a locus.

They shared a common ancestor 2Ne generations ago.

They accumulate mutations at rate u per generation per basepair.

2Ne generations / lineage * 2 lineages * u = 4Neu differences per basepair between the

two sequences.

Coalescent example

We sequence 1000 base pairs from two sequences, and find 16 base pair differences, how large is the population/

Assume u = 2 x 10-8.4Neu * 1000 = 16; 8 x 10-5 * Ne = 16;

Ne * 10-5 = 2; Ne = 200,000

Neutral theory as a null model

Additional readingsEyre-Walker (2006) The genomic rate of adaptive evolution. Trends in

Ecology and Evolution 29:569-575. (Well-written review)Gillespie (2004). Population genetics: a concise guide. John Hopkins:

Baltimore, MD. (Very short, clear, but dense!)Graur and Li (2000) Fundamentals of molecular evolution. Sinauer:

Sunderland, MA. (Very clear)Kimura (1962) On the probability of fixation of mutant genes in

populations. Genetics 47:713-719. (If you really want the derivation)Kimura and Ohta (1969) The average number of generations until

fixation of a mutant gene in a finite population. Genetics 61:763-771. (If you really want the derivation)

Sabeti et al (2006) The case for selection at CCR5-32. PLoS Biology 3:1963-1969.

Questions: 1. Explain why clock-like rates of substitutions per year did not fit with the neutral theory.

See posted molecular evolution practice questions: highly recommended!

how do we explain the patterns of variation observed in DNA sequences?

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