population genetics A brief introduction towasabiapp.org/vbox/data/ngg2016/popgen/Day 2 - Session 2- Populat… · Population genetics Definition - studies distributions & changes

A brief introduction to population genetics

529053 Evolutionary Genomics Ari Löytynoja / [email protected]

Population genetics

Definition- studies distributions & changes of allele frequencies in populations over time- effects considered:

- natural selection, genetic drift, mutation and gene flow- recombination, population subdivision and population structure

- allows inferring past events as well as predicting future

History- fundamental work by Haldane, Wright and Fisher on first half of 20th century- recent development: coalescent theory by Kingman in 1980’s

- suitable for SNPs data- computationally highly efficient


Population genetics basics: Allele

Allele- one of alternative forms of a gene or same genetic locus

- used to be visible gene product (e.g. blond vs. red hair)

- now typically a SNP (e.g. rs1805007(C) vs. rs1805007(T))

rs1805007 = C rs1805007 = T
















Alleles in a “genetic locus” do not need to be functional

- in many studies we are interested in neutral variation

- rs1805007 associated e.g. with ‘Skin sensitivity to sun’, ‘Hair color’, ‘Non-melanoma skin cancer’, ‘Freckles’

Genome provides millions of variable loci, majority of those neutral

Inferring presence of function for a locus/allele is of special interest



Population modelTheoretical models assume a simplified population model

Most commonly used model is Wright-Fisher model. It assumes:

- haploid population

- no sex

- constant population size

Wright-Fisher model (WFM) can be generalised:

- diploid population

- panmictic, random mating

- variable population size

WFM gives a good approximation for more complex populations


Population genetics basics: Wright-Fisher model

Wright-Fisher modelEvolution of an idealised population: generation 1

1




21




32




103




10


Population genetics basics: Ne

Population sizeOne central parameter in population genetics is population size

Abbreviated as N

Population size defines

- how quickly variation is lost (forwards)

- how much frequencies change per generation (now)

- how quickly sample coalesces to MRCA (backwards)

Population size is measured in ’units’ of WFM population

- known as effective population size, Ne

- can be very different from census population size

- some violations of WFM can be corrected for


Population genetics basics: Ne and Drift

- loss of variation

- change of allele frequencies

Known as genetic drift



- loss of variation

- change of allele frequencies

Known as genetic drift



Genetic driftAt every locus, variation is eventually lost and one allele becomes fixed

- in non-neutral loci, selection affects chances of fixation

- variation is lost much more rapidly in small populations

- in small populations genetic drift prevails selection and even harmful alleles may get fixed

Variation once lost is lost forever

- population bottleneck reduces variation and population

- recovery cannot bring it back

- new variation is created by mutations


Population genetics basics: Coalescent

Coalescence time

- small populations coalesce faster, more recent MRCA

- conversely: Ne can be defined by coalescence time

MRCA

N = 20 N = 100


Coalescence of two lineages

Probability of coalescence on generation r before present follows

geometric distribution: [1 − 1/(2N)]r −1 [1/(2N)]

- its mean is 1/p or 1/[1/2N)] or 2N

- for 2N=20, expected time for two random lineages to coalesce is 40 generations

For large N, coalescence process follows exponential distribution


Coalescence of many lineages

For n lineages, coalescence rate is [n(n − 1)/2][1/(2N)]

- for 2N = 20, rate and expected time to next event are:

- when n is large, coalescent events happen quickly

- last event (n = 2) is expected to take at least half of total time

lineages coalescent rate generations

5 0.5 2

4 0.3 3.3

3 0.15 6.7

2 0.05 20

total 32


Coalescence of many lineages

Expected coalescence times have large variance, tree shapes differ

- expected genetic diversity is affected by tree structure


Coalescence and Site frequency spectrum

Bamshad and Wooding, NRG, 2003

Vertical branches are evolutionary time, mutations random

- tree shapes have expected distribution of allele frequencies

- for many loci this is called site frequency spectrum- with outgroup, ancestral and derived allele can be inferred


Site frequency spectrum, DAF and MAF

SFS: also known as allele frequency spectrum

- if ancestral sate known, derived allele frequency (DAF)

- if not, minor allele frequency (MAF) or folded SFS

One of the most widely used summary statistics

- at neutral sites, reflects population history- at non-neutral sites, reflects selection pressure


Coalescence with non-constant population size

Increasing population size Decreasing population size

few coalescent events in large phase many coalescent events in small phase


Coalescence with non-constant population size

Population increase and decrease affect the expected tree shape

- mutations are random so tree shape affects expected SFS

Nielsen and Slatkin, 2013


Coalescence and Site frequency spectrum

Bamshad and Wooding, NRG, 2003


Site frequency spectrum and Demography

Evidence for bottleneck in human EUR and ASN populations

- quick coalescent & deep branches → deficit of low frequencies

Keinan et al, NG, 2007


Site frequency spectrum and Selection

Selection affects fitness and thus AF

posi

tive

nega

tive

negative selection

syn sites_ 3’UTR_ cons 3’UTR_

nonsyn sites_ cons miRNA_

Increase in low frequencies alleles due to negative selection

Chen and Rajewsky, NG, 2006


Derived allele frequencies and annotation liftover


Derived allele frequencies

We will look at DAF of

1. different populations

2. different genomic regions

The latter requires annotation that we lift-over from threespined

Documents

population genetics A brief introduction towasabiapp.org/vbox/data/ngg2016/popgen/Day 2 - Session 2- Populat… · Population genetics Definition - studies distributions & changes