203.343 Advanced Genetics and Genomics Lecture 3 July 20th 2015 Olin Silander
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203.343 Advanced Genetics
and Genomics
Lecture 3
July 20th 2015
Olin Silander
Gene Linkage and Linkage Disequilibrium
Gene Linkage and Linkage Disequilibrium
Describe the coalescent and the neutral model of evolution
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
Two alleles:
a 40%A 60%
AA Aa aa ? ? ?
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
Two alleles:
a 40%A 60%
a
40%
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
Two alleles:
a 40%A 60%
a
40%
a
40%
aa 16%
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
Two alleles:
a 40%A 60%
a
40%
a
40%
aa 16%
A
40%
a
60%
Aa 48%
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
Two alleles:
a 40%A 60%
a
40%
a
40%
aa16%
A
40%
a
60%
A
60%
A
60%
Aa 48%
AA 36%
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
What are the assumptions of HWE?
(1) diploid (2) non-overlapping generations (3) sexual reproduction (4) random mating (5) infinite population size(6) no selection
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
What are the assumptions of HWE?
infinite population size
aa 16%
Aa 48%
AA 36%
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
What are the assumptions of HWE?
finite population size (drift)
aa 16%
Aa 48%
AA 36%
30% 40% 30%
infinite population size
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibrium
What are the assumptions of HWE?
finite population size (drift)
aa 16%
Aa 48%
AA 36%
30% 40% 30%
selection13%10%
77%
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibriumTwo alleles
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibriumTwo alleles
LinkageTwo alleles, two loci
Gene Linkage and Linkage Disequilibrium
Hardy Weinberg equilibriumTwo alleles
LinkageTwo alleles, two loci
A
B
A
b
a
b
a
B
Gene Linkage and Linkage Disequilibrium
LinkageTwo alleles, two loci
A
B
A
b
a
b
a
B
A 60%a 40%B 80%b 20%
Gene Linkage and Linkage Disequilibrium
A
B
A
b
a
b
a
B
48% 12% 8% 32%
LinkageTwo alleles, two lociA 60%
a 40%B 80%b 20%
Gene Linkage and Linkage Disequilibrium
A
B
A
b
a
b
a
B
48% 12% 8% 32%
Linkage equilibrium
LinkageTwo alleles, two lociA 60%
a 40%B 80%b 20%
Gene Linkage and Linkage Disequilibrium
A
B
A
b
a
b
a
B
60% 0% 20% 20%
Linkage disequilibrium
LinkageTwo alleles, two lociA 60%
a 40%B 80%b 20%
Gene Linkage and Linkage Disequilibrium
A 60%a 40%B 80%b 20%
Linkage disequilibrium
LinkageTwo alleles, two loci
fAB = 0.60 fAb = 0 faB = 0.20 fab = 0.20
Gene Linkage and Linkage Disequilibrium
A 60%a 40%B 80%b 20%
Linkage equilibrium
Linkage disequilibrium
LinkageTwo alleles, two loci
fAB = 0.48 faB = 0.32 fAb = 0.12 fab = 0.08
fAB = 0.60 fab = 0.20fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
A 60%a 40%B 80%b 20%
Linkage equilibrium
Linkage disequilibrium
LinkageTwo alleles, two loci
fAB = 0.48 faB = 0.32 fAb = 0.12 fab = 0.08
fAB - fAfB = 0
fAB = 0.60 fab = 0.20fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
A 60%a 40%B 80%b 20%
Linkage equilibrium
Linkage disequilibrium
LinkageTwo alleles, two loci
fAB = 0.48 faB = 0.32 fAb = 0.12 fab = 0.08
fAB - fAfB = 0
fAB - fAfB = ?
fAB = 0.60 fab = 0.20fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
A 60%a 40%B 80%b 20%
Linkage disequilibrium
LinkageTwo alleles, two loci
fAB = 0.60 fab = 0.20
fAB - fAfB = DQuantify LD
fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
A 60%a 40%B 80%b 20%
LinkageTwo alleles, two loci
fAB - fAfB = DQuantify LD
Gene Linkage and Linkage Disequilibrium
Linkage equilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = D = 0
fAB - fAfB = DQuantify LD
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
Linkage disequilibrium
fAB = 0.60 fab = 0.20
fAB - fAfB = DQuantify LD
fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = D = 0.12Linkage disequilibrium
fAB = 0.60 fab = 0.20
fAB - fAfB = DQuantify LD
fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
What is the maximum value of D?
fAB - fAfB = D = 0.12Linkage disequilibrium
fAB = 0.60 fab = 0.20
fAB - fAfB = DQuantify LD
fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = DQuantify LD
D’: scaled to be between 0 and 1
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = DQuantify LD
if D > 0 D’ =
min(fAfb, fafB )D
if D < 0 D’ =
max(-fAfB, -fafb )D
D’: scaled to be between 0 and 1
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = DQuantify LD
if D > 0 D’ =
min(fAfb, fafB )D
if D < 0 D’ =
max(-fAfB, -fafb )D
D’: scaled to be between 0 and 1
fAB - fAfB = D = 0.12Linkage disequilibrium
fAB = 0.60 fab = 0.20fAb = 0 faB = 0.20
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = DQuantify LD
if D > 0 D’ =
min(fAfb, fafB )D
if D < 0 D’ =
max(-fAfB, -fafb )D
D’: scaled to be between 0 and 1
fAB - fAfB = D = ?Linkage disequilibrium
fAB = 0.55 fab = 0.15fAb = 0.05 faB = 0.25
Gene Linkage and Linkage Disequilibrium
Quantifying LDA 60%a 40%B 80%b 20%
fAB - fAfB = DQuantify LD
if D > 0 D’ =
min(fAfb, fafB )D
if D < 0 D’ =
max(-fAfB, -fafb )D
D’: scaled to be between 0 and 1
fAB - fAfB = D = 0.07Linkage disequilibrium
fAB = 0.55 fab = 0.15fAb = 0.05 faB = 0.25
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locAA
locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=0
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=00.05 - 0.5 x 0.5=-0.2
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=00.05 - 0.5 x 0.5=-0.2
fAb - fAfb = D0.45 - 0.5 x 0.5=0.2
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=00.05 - 0.5 x 0.5=-0.2
0.45 - 0.5 x 0.5=0.2
fab - fafb = D0.05 - 0.5 x 0.5=-0.2
faB - fafB = D0.45 - 0.5 x 0.5=0.2
fAB - fAfB = D
fAb - fAfb = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=00.05 - 0.5 x 0.5=-0.2
The choice of alleles does not matter the absolute value of D is always the same
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=00.05 - 0.5 x 0.5=-0.2
fAB - fAfB = D
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locA locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
A aA T==locus A
B b==locus B
C A
0.25 - 0.5 x 0.5=00.05 - 0.5 x 0.5=-0.2
fAB - fAfB = D
if D < 0 D’ =
max(-fAfB, -fafb )D
D’ = 0.8
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locAA
locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
population 2: if we see an A
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locAA
locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
population 2: if we see an A
90% chance there is an A at locus 2
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locAA
locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
population 2: if we see an A
90% chance there is an A at locus 2
r
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
population 2population 1
Gene Linkage and Linkage Disequilibrium
Quantifying LD Ind. locAA
locB1 A A2 A A3 A A4 A A5 A A6 A A7 A C8 A A9 A A10 A A11 T C12 T C13 T C14 T A15 T C16 T C17 T C18 T C19 T C20 T C
population 2: if we see an A
90% chance there is an A at locus 2
r =
Ind. locAA
locB1 A C2 A A3 A C4 A C5 A C6 A A7 A A8 A A9 A C10 A A11 T C12 T C13 T C14 T A15 T A16 T A17 T A18 T A19 T C20 T C
population 2population 1
D√ fAfBfafb
Gene Linkage and Linkage Disequilibrium
Quantifying LD
r = D√ fAfBfafb
A 60%a 40%B 80%b 20%
if D > 0 D’ =
min(fAfb, fafB )D
if D < 0 D’ = max(-fAfB, -fafb )
D
D = fAB - fAfB =
Linkage disequilibrium
D’
fAB = 0.55 fab = 0.15fAb = 0.05 faB = 0.25
= =
Gene Linkage and Linkage Disequilibrium
Quantifying LD
r = D√ fAfBfafb
A 60%a 40%B 80%b 20%
if D > 0 D’ =
min(fAfb, fafB )D
if D < 0 D’ = max(-fAfB, -fafb )
D
D = fAB - fAfB = 0.07
Linkage disequilibrium
D’
fAB = 0.55 fab = 0.15fAb = 0.05 faB = 0.25
= 0.07/0.12 = 0.070.196
Gene Linkage and Linkage Disequilibrium
Quantifying LD
locus 1
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20
Gene Linkage and Linkage Disequilibrium
Quantifying LD
AA AA A AA AA AA ATTT TTTT T
locus 1A
T
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20
Gene Linkage and Linkage Disequilibrium
Quantifying LD
AA AA A AA AA AA ATTT TTTT T
locus 1A
T
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20C CC C CCC CCTTT TTTT T
T
C
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20
locus 2
C C C
Gene Linkage and Linkage Disequilibrium
Quantifying LD
AA AA A AA AA AA ATTT TTTT T
locus 1A
T
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20C CC C CCC CCTTT TTTT T
T
C
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20
locus 2
Both loci have the same demographic history
C C C
Complete linkage disequilibrium
Gene Linkage and Linkage Disequilibrium
Quantifying LD
AA AA A AA AA AA ATTT TTTT T
locus 1A
T
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20C CC C CCC CCTTT TTTT T
T
C
123 456 7 8910 1112 13 14 1516 17181920
locus 2
Both loci have the same demographic history
C C C
Complete linkage disequilibrium
Gene Linkage and Linkage Disequilibrium
Quantifying LD
AA AA A AA AA AA ATTT TTTT T
locus 1A
T
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20C CC C CCC CCTTT TTTT T
T
C
123 456 7 8910 1112 13 14 1516 17181920
locus 2
Both loci have different demographic histories
C C C
Partial linkage disequilibrium
Gene Linkage and Linkage Disequilibrium
Quantifying LD
D non-random associations
between AB alleles
D’ D normalized by allele frequencies
r correlation (D normalized
by allele frequencies)
Gene Linkage and Linkage Disequilibrium
Why do different loci have different demographic histories?
Gene Linkage and Linkage Disequilibrium
Why do different loci have different demographic histories?
Recombination
Gene Linkage and Linkage Disequilibrium
Why do different loci have different demographic histories?
Recombination
Gene Linkage and Linkage Disequilibrium
Why do different loci have the same demographic histories?
Gene Linkage and Linkage Disequilibrium
Why do different loci have the same demographic histories?
selectionpopulation size (bottleneck)
(lack of) recombination
population admixture (migration)
Gene Linkage and Linkage Disequilibrium
Why do different loci have the same demographic histories?
selectionpopulation size (bottleneck)
(lack of) recombination
population admixture (migration)