Lecture 23: Causes and Consequences of Linkage

DisequilibriumNovember 16, 2012

Last Time Signatures of selection based on

synonymous and nonsynonymous substitutions

Multiple loci and independent segregation

Estimating linkage disequilibrium

Today

Recombination and LD

Drift and LD

Mutation and LD

Selection and LD

Hitchhiking and selective sweeps

Effects of recombination rate on LD Decline in LD over time

with different theoretical recombination rates (c)

Even with independent segregation (c=0.5), multiple generations required to break up allelic associations

0DeD ctt

Where t is time (in generations) ande is base of natural log (2.718)

LD varies substantially across human genome

NATURE|Vol 437|27 October 2005

Average r2 for pairs of SNP separated by 30 kb in 1 Mb windows

LD affected by location relative to telomeres and centromeres, chromosome length, GC content, sequence polymorphism, and repeat composition

Highest and lowest levels of LD found in gene-rich regions

Human HapMap Project and Whole Genome Scans

LD structure of human Chromosome 19 (www.hapmap.org)

1 common SNP genotyped every 700 bp for 270 individuals (3.4 million SNP)

9.2 million SNP in total

NATURE|Vol 437|27 October 2005

LD in the Poplar Genome

5

3

1

132

2

4

1

2

LD declines rapidly with distance

LD higher in genes than in genome as a whole

Loci separated by kilobases still in LD!

Distance (kb)0 5 10 15 20

r 2

0.0

0.1

0.2

0.3

0.4

0.5

Genomewide (core of range) Genes (core of range)

Recombination Across Poplar Chromosomes

Substantial variation in recombination rate

Related to repeat composition, methylation, and distance from centromere

Recombination rate varies among individuals Rate is often higher in females than males

Rate varies among individuals within males and females

Variation in recombination rate in the MHC region (3.3 Mb in human sperm donors

Genetic Drift and LD

Begin with highly diverse haplotype pool

Drift leads to chance increase of certain haplotypes

Generates nonrandom association between alleles at different loci (LD)

Genetic Drift and LD

Why doesn’t recombination reduce LD in this situation?

Expected Gamete Frequencies: Double Homozygote

A1B1

A1B1

NonRecombinantRecombinantRecombinantNonRecombinant

A1B1 A1B1A1B1

Meiosis

A1B1

Expected Gamete Frequencies: Double Heterozygote

A2

A1B1

B2

A1B1

Meiosis

A2B2A1B2 A2B1NonRecombinantRecombinantRecombinantNonRecombinant

LD is partially a function of recombination rate

Expected proportions of gametes produced by various genotypes over two generations

Where c is the recombination rateand D0 is the initial amount of LD

Double heterozygote is only case where recombination matters

Effect of Drift on LD Drift and recombination will have opposing effects

on LD Where r2 is the squared correlation coefficient for alleles at two loci, Ne is effective population size, and c is recombination rate

4Nec is “population recombination rate”,

Expression approaches 0 for large populations or high recombination rates

Combined effects of Drift and Recombination

LD declines as a function of population recombination rate (Ner in this figure, same as Nec)

Effects of chance fluctuation of gamete frequencies

How should inbreeding affect linkage disequilibrium?

Mutation and LD: High mutation rates

Allelic associations are masked by high mutation rates, so LD is decreased

Gamete Pool with Low Mutation

Gamete Pool with High Mutation

LD and neutral markers

Low LD is the EXPECTED condition unless other factors are acting

If LD is low, neutral markers represent very small segment of the genome in most cases

In most parts of the genome, LD declines to background levels within 1 kb in most cases (though this varies by organism and population)

Care must be taken in drawing conclusions about selection based on population structure derived from neutral markers

Selection and Linkage Disequilibrium (LD)

Selection can create LD between unlinked loci

Epistasis: two or more loci interact with each other nonadditively

Phenotype depends on alleles at multiple loci

D

Change in D over time due to epistatic interactions between loci with directional selection

Why does D decline after generation 15 in this scenario?

),min( 1221max qpqpD for D > 0

Epistasis and LD

Begin with highly diverse haplotype pool

Directional selection leads to increase of certain haplotype combinations

Generates nonrandom association between alleles at different loci (LD)

Recombination vs Polymorphism in Poplar

Nucleotide diversity (π) is positively correlated with population recombination rate (4Nec)

(R2=0.38)

LG VII

Position (Mb)

0 2 4 6 8 10 12 14

Rat

e

0.000

0.001

0.002

0.003

0.004

0.005

0.006

4Nec

Recombination vs Polymorphism

Recombination rate varies substantially across Drosophila genome

Nucleotide diversity is positively correlated with recombination rate Hartl and Clark 2007

Why is polymorphism reduced in areas of low recombination?

(or why is polymorphism enhanced in areas of high recombination)

Selection and LD Selection affects target loci as well as loci in LD

Hitchhiking: neutral alleles increase in frequency because of selective advantage of allele at another locus in LD

Selective Sweep: selectively advantageous allele increases in frequency and changes frequency of variants in LD

Background Selection: selection against detrimental mutants also removes alleles at neutral loci in LD

Hill-Robertson Effect: directional selection at one locus affects outcome of selection at another locus in LD

http://medinfo.ufl.edu/

Selective Sweep in Plasmodium Pyrimethamine used to treat malaria parasite (Plasmodium falciparum)

Parasite developed resistance at locus dhfr, which rapidly became fixed in population (6 years on Thai border)

Microsatellite variation wiped out in vicinity of dhfr

Selective Sweep

Positive selection leads to increase of a particular allele, and all linked loci

Results in enhanced LD in region of selected polymorphism

Accentuated in rapidly expanding population

Derived Alleles and Selective Sweeps

Recent, incomplete selective sweeps are expected to leave a molecular signature of

•High frequency of derived alleles

•Strong geographic differentiation

•Elevated LDACAA AA

A C

chimp Africans Europeans

LD Provides evidence of recent selection Regions under recent selection experience selective sweep, show high LD locally

Patterns of LD in human genome provide signature of selection

A statistic based on length of haplotypes and frequency of “derived alleles” reveals regions under selection (“iHS” statistic)

Selective sweep for lactase enzyme in Europeans after domestication of dairy cows

Voight et al. 2006 Plos Biology 4: 446-458

Some factors that affect LD Factor Effect

Recombination rate Higher recombination lowers LD

Genetic Drift Increases LD

Inbreeding Increases LD

Mutation rate High mutation rate decreases overall LD

Epistasis Increases LD

Selection Locally increased LD