Intro to population genetics

Shamil Sunyaev

Broad Institute of M.I.T. and Harvard

Forces responsible for genetic change

Mutation

Selection s

NeDrift

Population structure FST

Mutations

Mutation rate in humans and flies

~102 per nt changes genome

2.5x10-8 (Nachman & Crowell) 1.8x10-8 (Kondrashov)

Other events: indels (10-9)

repeat extensions/contractions (10-5)

large events (?)

NGS estimates ~1.2X10-8 per nt changes genome

Mutation rate is variable along the genome

Regional variation of mutation rate

Context dependence of mutation rate

Replication fidelity DNA damage DNA repair CpG deamination

Genetic drift

Drift is a random change of allele

frequencies

Drift depends on population size

Demographic history

Selection

12

NeutralDeleterious Advantageous

New

mutation

Functional

Nonfunctional

Selection indicates functional mutations, whether or

not the tested trait is under selection

Selective effect of mutation

Most functional mutations are deleterious

Methods of mathematical

population genetics

Dynamic of allelic substitution

time

0

1

Mathematically, allele frequency change in a population

follows a one-dimensional random walk

Diffusion approximation

Random walk that does not jump long distances can be

approximated by a diffusion process

¶f x, p,t( )¶t

= -¶Mf x, p,t( )

¶x+

1

2

¶2Vf x, p,t( )¶x2

Coalescent theory

Instead of modeling a population, we can model our sample

Time goes backwards !

t

Natural selection in protein

coding regions

Effect of new missense mutations

Computer simulations

time

¶f x, p,t( )¶t

= -¶Mf x, p,t( )

¶x+

1

2

¶2Vf x, p,t( )¶x2

Demographic history

Natural selection

• Can we find additional evidence in sequence data?

• Is there any information beyond frequency? Can we

tell alleles under selection from neutral alleles if they

are of the same frequency?

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Maruyama effect (1974): at any frequency advantageous ,

or deleterious alleles are younger than neutral alleles

Frequency x

Frequency 0%

Time

At a given frequency deleterious and

advantageous alleles are younger than

neutral

Longer trajectory: 6 jumps

Shorter trajectory: 4 jumps

Frequency 0%

Frequency x

Time

Intuition: shorter trajectories require

fewer lucky jumps

time

allele

frequencyNeutrals: equal time at each frequency

Selecteds: faster through higher frequencies

Idea: low accumulation of mutations at linked

sites indicates selection

Diffusion theory: deleterious alleles pass

fast through higher frequencies

10

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−25 −20 −15 −10 −5 0

0.0

0.1

0.2

0.3

0.4

0.5

selection coefficient 2Ns

mean age (2N generations)

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Population frequency

7%

5%

3%

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0 5 10 15 20

0.000

0.005

0.010

0.015

0.020

Intermediate allele frequency (%)

mean sojourn time (2N generations)

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Selection coefficient (2Ns)

0 (neutral)

−2 (weakly deleterious)

−10 (deleterious)

3%

*"

−0.20 −0.15 −0.10 −0.05 0.00

05

10

15

time (generations before present, in 2N units)

population frequency (%)

Allele

neutral

deleterious

+"

""

""

Figur e 1. Simulat ion and t heor et ical r esul t s for al lel ic age and sojour n t imes. a. Example

t rajectories for a neutral and deleterious allele with current populat ion frequencies 3% (indicated by an

arrow). The shaded areas indicate sojourn t imes at frequencies above 5%. b. Mean ages for neutral and

deleterious alleles at a given populat ion frequency (lines show theoret ical predict ions, dots show

simulat ion results with standard error bars). The graph shows that deleterious alleles at a given

frequency are younger than neutral alleles, and that the e↵ect is greater for more st rongly selectedalleles. c. Mean sojourn t imes for neut ral and deleterious alleles. Vert ical line denotes the current

populat ion frequency of the variant (3%). Mean sojourn t imes have been computed in bins of 1%. Line

connects theoret ical predict ions for each frequency bin. Dots show simulat ion results. The graph

illust rates that deleterious alleles spend much less t ime than neutral alleles at higher populat ion

frequencies in the past even if they have the same current frequency.

Neighborhood clock

(fuzzy clock)

29

Neighborhood clock is consistent

with Maruyama-effect expectations

Data: pilot Genome of Netherlands dataset