NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab -...
Transcript of NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab -...
![Page 1: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/1.jpg)
Recombina*on and Linkage Disequilibrium (LD)
![Page 2: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/2.jpg)
A B
a B
A b
a b
½ (1-‐r)
½ (1-‐r)
½ r
½ r
r = recombina*on frac*on probability of an odd Number of crossovers occur Between our markers
A B
a b
0 <r< ½
![Page 3: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/3.jpg)
If independent the expected
frequency of gametes (haplotypes)
pA X pB
pa X pb
pA X pb
pa X pB
Define “D” DAB = pAB - pApB Dab = pab - papb DAb = pAb - pApb DaB = paB - papB
pAB = frequency of AB pab = frequency of ab pAb = frequency of Ab paB = frequency of aB
Linkage disequilibrium: The non-random association of alleles at different sites in the genome in a population.
The covariance of A and B.
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Define “D” DAB = pAB - pApB Dab = pab - papb DAb = pAb - pApb DaB = paB - papB
Linkage disequilibrium: The non-random association of alleles at different sites in the genome.
DAB = - DAb DAB = Dab and DAb = DaB (so, knowing DAB is enough - call this “D”) If O = E, then D = 0 If D >0 (or D<0) then there is “linkage disequilibrium (LD)” Note: you can also write pAB= pApB+D
![Page 5: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/5.jpg)
![Page 6: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/6.jpg)
Decay of LD in a very large boring randomly ma*ng popula*on
Dt = (1- r)t Do
With inbreeding coefficient f replace r with r(1-‐f)
![Page 7: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/7.jpg)
linkage disequilibrium How does LD change over time due to recombination?
Dt = (1- r)t Do
Note: more distant markers recombine more!
So eventually recombination leads to D=0. Even with free recombination (r=0.5), it isnt instantaneous however.
![Page 8: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/8.jpg)
What creates LD
• Muta*onal origin • Gene*c driN (and Hitchhiking) • Epista*c selec*on* • Assorta*ve ma*ng.
– Inbreeding – Popula*on structure and admixture – Assorta*ve ma*ng by phenotype*
• *only for specific markers
![Page 9: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/9.jpg)
Population structure can increase LD if allele frequencies differ among populations
Countervailing forces that increase LD
Pretty pictures courtesy of P. Andolfatto (Princeton)
![Page 10: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/10.jpg)
![Page 11: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/11.jpg)
LD between Neand
erthal alleles in
mod
ern hu
man pop
ula*
ons
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Evolu*on by gene*c driN • Evolu*on by Gene*c driN: a change in allele frequency because individuals carry the allele by chance produce more / less offspring in any given genera*on. *
• *in sexual popula*ons….
• Gene*c driN can affect selected alleles but only if they are very weakly selected (except when they are rare).
• A neutral allele: An allele with no effect on fitness from other alleles at that locus.
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• Neutral polymorphism/alleles:
• Only 2% of our genome encodes for proteins • Changes outside exons may be completely neutral if they do not disrupt regulatory sites.
• Examples of poten*ally neutral alleles: • A synonymous change in a codon. • A non-‐synonymous change that replaces one amino-‐acid with a func*onally similar one.
• A non-‐synonymous change which produces a large change in a phenotype on which selec*on no longer acts.
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How much of gene*c divergence between species is neutral.
• ~36 million subs*tu*ons have occurred since human and chimp last shared a common ancestor.
• How many of these subs*tu*ons fix due to selec*on?
• How much of polymorphism is neutral?
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Why is there so much polymorphism? • The paradox of varia*on in popula*on gene*cs: Selec*on quickly fixes alleles that are beneficial so why is there so much gene*c polymorphism within natural popula*ons?
Three explana*ons: • Balancing selec*on • Muta*on-‐selec*on balance • Muta*on-‐gene*c driN balance (Neutral theory).
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Neutral theory of molecular evolu*on
• Kimura 1968; King and Jukes 1969 • Claimed: • Most new muta*ons are deleterious and are lost immediately • Most of the observed molecular polymorphism and subs*tu*ons are neutral Claimed that this is consistent with: -‐High levels of gene*c polymorphism -‐The molecular clock
![Page 17: NEW Lecture 5 - WordPress.comDefine “D” D AB = p AB - p Ap B D ab = p ab - p ap b D Ab = p Ab - p Ap b D aB = p aB - p ap B Linkage disequilibrium: The non-random association of](https://reader035.fdocuments.in/reader035/viewer/2022081601/5fc89fdd811bfe273d0bbebb/html5/thumbnails/17.jpg)
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• The rate of gene*c driN is higher in smaller popula*ons Allele frequencies do driN in very large popula*ons but at a very slow rate.
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Loss of heterozygosity • In the absence of new muta*ons, alleles driN to either
loss or fixa*on. Thus the amount of heterozygosity within the popula*on decreases a rate inversely propor*onal to popula*on size
Heterozygosity decreases on a time-scale proportional to2N generations
Ht � H0e� t
2N
Heterozygosity = Frac*on of sites that are heterozygous
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Loss of heterozygosity
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GenerationsPast Present
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Muta*on-‐driN equilibrium (MDE)
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Muta*on-‐driN equilibrium (MDE) • Varia*on lost by driN = varia*on introduced by muta*on
• Ne = effec*ve popula*on size, µ = muta*on rate to new neutral alleles At MDE, heterozygosity = H = 4 Neµ
Muta*on-‐driN equilibrium (MDE)
The rate of gene*c driN is slower in larger popula*ons and the input of new muta*ons is higher. Large popula*ons have a higher level of neutral polymorphism
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Neutral theory of molecular evolu*on • Kimura 1968; King and Jukes 1969 • Claim: Most of the observed molecular polymorphism is neutral
Consistent with Neutral theory Levels of gene*c variability within Popula*ons (i.e. heterozygosity) are high and are broadly correlated with popula*on size