Fst, selection index

FST & Some Selection Index
유전체역학 2017
김진섭
GSPH, SNU
November 22, 2017
김진섭 (GSPH, SNU) FST & Some Selection Index November 22, 2017 1 / 65

Fst
Contents
1 Fst
Wright’s F-statistics
Cockerham’s θ-statistics
2 Selection Index
EHH
iHS
xp-EHH
3 Practice

Fst Wright’s F-statistics
3 types of Heterozygosity[4]
Individual, Subpopulation, Total Population
1 HI = 1
n
n
i=1
ˆHi
2 HS = 1
n
n
i=1 2pi qi
3 HT = 2¯p¯q
( ˆHi : observed heterozygosity in ith subpopulation, 2pi qi : average
heterozygosity in ith subpopulation, 2¯p¯q: average heterozygosity of total
population)
Locus 별로 값 구한다.

Wright’s F-statistics[4]
1 FIS = HS −HI
HS
2 FST = HT −HS
HT
3 FIT = HT −HI
HT
Example
FST = 0 → Subpopulation의 eﬀect없다!! 차이 없다.
FST = 1 → Subpopulation별로 차이가 크다.
Simple relation
1 − FIT = (1 − FIS )(1 − FST )

http://academic.reed.edu/biology/professors/srenn/pages/
research/2011_students/sean/SM_thesis.html

http://www.johnderbyshire.com/Miscellaneous/Other/Fst.jpg

FST inference[5]
Convenient measure of genetic diﬀerentiation.
Most widely used descriptive statistics in population and
evolutionary genetics.
Natural selection in particular subpopulation.

Problem in estimation
HT = 2¯p¯q
1 Subpopulation마다 sample수가 다르면??
2 Ex: SASIA 1000명, Oceania 100명..
3 제대로 된 ¯p 추정이 아님.

Fst Cockerham’s θ-statistics
ANOVA approach[1, 5]
θ =
σP
σT
(σP: variance due to population, σT : total variance)

Wright’s FST = Cockerham’s θ
실제 계산은 대부분 θ

θ inference
Population > 2
대세와 다른 population이 있다!!
어떤 population인지는 말 안해준다.
Pairwise FST
2 population만 가지고 계산.
상대적인 비교.

Figure. FST calculated for each SNP between Tibetan and Han populations[6]

Figure. Inter-population pairwise comparisons of FST statistics
http://academic.reed.edu/biology/professors/srenn/pages/
research/2011_students/sean/SM_thesis.html

Selection Index
Contents
1 Fst
2 Selection Index
EHH
iHS
xp-EHH
3 Practice

Selection Index
특정 인구집단에 특정 haplotype이 많냐??
Example: Erik Corona’s slide - Next slide

Selection Index
Population Genetics
Glucose
HAPLOTYPES
GATTACAGATTACA 22%
AATTACAGATTAAA 3%
GACTACAGATTACC 19%
GATTACCTATTAAC 24%
AACTACAGATTACC 16%
GATTACAGACTACA 7%
AATTACAGATTACA 9%
Lactase + H2O

Selection Index
Population Genetics
Lactase + H2O
Glucose
HAPLOTYPES
GATTACAGATTACA 22%
AATTACAGATTAAA 3%
GACTACAGATTACC 19%
GATTACCTATTAAC 24%
AACTACAGATTACC 16%
GATTACAGACTACA 7%
AATTACAGATTACA 9%

Selection Index
Population Genetics
Lactase + H2O
Glucose
HAPLOTYPES
GATTACAGATTACA 22%
AATTACAGATTAAA 3%
GACTACAGATTACC 19%
GATTACCTATTAAC 24%
AACTACAGATTACC 16%
GATTACAGACTACA 7%
AATTACAGATTACA 9%
AATTGCAGATTACA <1%

Selection Index
Population Genetics
Lactase + H2O
Glucose
HAPLOTYPES
GATTACAGATTACA 21% -1%
AATTACAGATTAAA 3%
GACTACAGATTACC 19%
GATTACCTATTAAC 24%
AACTACAGATTACC 16%
GATTACAGACTACA 7%
AATTACAGATTACA 8% -1%
AATTGCAGATTACA 2% +2%

Selection Index
Population Genetics
Lactase + H2O
Glucose
HAPLOTYPES
AATTACAGATTAAA 3%
GACTACAGATTACC 19%
GATTACCTATTAAC 23% -1%
AACTACAGATTACC 15% -1%
GATTACAGACTACA 7%

Selection Index
Population Genetics
Lactase + H2O
Glucose
HAPLOTYPES
AATTACAGATTAAA 3%
GACTACAGATTACC 19%
GATTACCTATTAAC 23% -1%
AACTACAGATTACC 15% -1%
GATTACAGACTACA 6% -1%

Selection Index EHH
EHH: Sabeti, Reich et al. (2002)[7]
Extended Haplotype Homozygosity
Random으로 2개 haplotype 뽑았을 때 그것이 같을 확률은??
0 → haplotype이 다 다르다.
1 → haplotype이 모두 같다.
관심있는 haplotype을 Core라 한다.
EHHt =
s
i=1
eti
2
ct
2
(t: core haplotype, c: the number of samples of a particular core
haplotype, e: the number of samples of a particular extended haplotype, s:
the number of unique extended haplotype)

Selection Index EHH
How can we detect Pos. Sel.?
AATTACAGATTACA 50 people have this
GATTACAGATTACA 50 people have this
---- 50 KB ----

Selection Index EHH
50 KB + 20 KB = 70 KB__
AATTACAGATTACA AACACGC 10
AATTACAGATTACA ATGATAG 8
AATTACAGATTACA AACCCAG 7
AATTACAGATTACA CTGACAG 5
AATTACAGATTACA CAGACAG 3
AATTACAGATTACA AACACAG 6
AATTACAGATTACA CACACAG 4
AATTACAGATTACA CACCCAG 7
GATTACAGATTACA CACATAG 24
GATTACAGATTACA CACACAG 26
How can we detect Pos. Sel.?

Selection Index EHH
Extended Haplotype Homozygosity (EHH)

Selection Index EHH
( (3
2
5
2
7
2
8
2)+
10
2)+( )+( )+ )+( )+6
2( )+4
2( )7
2
)50
2(
(

Selection Index EHH
)+
10
2( )+ 8
2( )+7
2( )+5
2( )+3
2( )+6
2( )+4
2( )7
2(
)50
2(
0.121

Selection Index EHH
EHH Drops Over Genetic Distance
EHH drops off quickly over
genetic distance
Starts with 1
Ends at 0
Every hap block will
eventually be unique

Selection Index EHH
EHH What It Is & What It Isn’t
Detects over‐representation of a haplotype
This will raise the p(two haps are homozygous)
Does NOT detect if a haplotype spread quickly
Low recombination != spread quickly

Selection Index EHH
Compare EHH Scores
)+24
2( )26
2(
)50
2(
0.121
0.490
Low Recombination
Over Represented

Selection Index EHH
Can EHH Detect Pos. Sel.?

Selection Index EHH
Relative EHH
Detects over‐representation of a haplotype
Low recombination
This will raise the p(two haps are homozygous)
Does detect if a haplotype spread quickly
Other haplotype blocks are controls!
Recombination cold‐spot / hot‐spot agnostic
Low score if both alleles are assoc. w/ high or
low recombination

Selection Index EHH
0.121
0.490
0.490
0.121
= 4.05REHH =

Selection Index EHH
REHH: Problem #1
We get a different REHH value at different genetic
distance cutoffs
AATTACAGATTACA 50
GATTACAGATTACA 50
---- 50 KB ----
REHH = 1.0
---------- 70 KB ---------
REHH = 4.05

Selection Index EHH
Which REHH value to use?
Extend to the right
AGTTACAGATTACAAACACGC
AAATACAGATTACAATGATAG
AATTACAGATTACAAACCCAG
AATTTCAGATTACACTGACAG
AATTAAAGATTACACAGACAG
AATTACCGATTACAAACACAG
AATTACAAATTACACACACAG
AATTACAGGTTACACACCCAG
GATTACAGATTACACACATAG
GATTACAGATTACACACACAG
---------- 70 KB ---------
REHH = 4.05

Selection Index EHH
…ACAGATTACAGTTACAGATTACAAACACGC…
…ACAGATTACAAATACAGATTACAATGATAG…
…ACAGATTACAATTACAGATTACAAACCCAG…
…ACAGATTACAATTTCAGATTACACTGACAG…
…ACAGATTACAATTAAAGATTACACAGACAG…
…ACAGATTACAATTACCGATTACAAACACAG…
…ACAGATTACAATTACAAATTACACACACAG…
…ACAGATTACAATTACAGTTACACACCCAG…
…TACAGATTAGATTACAGATTACACACATAG
…TACAGATTAGATTACAGATTACACACACAG
---------- 70 KB ---------
REHH = 4.05
Extend to the right

Selection Index EHH
Extend to the right
---------- 70 KB ---------
REHH = 4.05

Selection Index EHH
Extend to the left
---------- 70 KB ---------
REHH = 4.05

Selection Index EHH
REHH: Problem #2
REHH score is heavily
biased by allele
frequencies
Must normalize
P(REHH | Allele Freq.)

Selection Index EHH
REHH: Problem #3
Not possible to detect
selection in high
frequency alleles
Solution requires a X‐
population approach
(discussed later)

Selection Index EHH
Leaves a lot to be desired
Picking the maximum is arbitrary
Why not the mean REHH score?
Biased by allele frequency
ln(REHH | allele freq) ~ norm dist.
Still widely used and published with
REHH Overview

Selection Index EHH
Site-speciﬁc EHH[9]
두 allele의 EHH값의 대략적인 평균(weight: squared allele frequencies)
Focal SNP의 대략적인 EHH크기

Selection Index iHS
iHS: sabeti(2007)[8]
모든 위치에 대해 적분!!!!해서 비교

Selection Index iHS
Integrated Haplotype Score (iHS)
Unstandardized iHS =
EHH
y x
y = bwd distance
x = fwd distance
EHHD = derived allele
EHHA = ancestral allele

Selection Index iHS
…ACAGATTACAATTACAGTTACAACACCCAG…
+ 0.5 = 1.20.7
4.0 + 4.4 = 8.4
Unstandardized iHS
ln(8.4/3.2) = 0.419

Selection Index iHS
iHS Characteristics
As both alleles have the same AUC, iHS zero
Large negative values indicate selection of allele in the
denominator
Large positive values indicate selection of allele in the
numerator
Still heavily biased by allele frequency!
Z‐score normalization

Selection Index iHS
Unstandardized iHS ‐ E(iHS | Allele Frequency)
SD(iHS | Allele Frequency)
E(iHS | Allele Freq.): Estimated from empirical distribution
SD(iHS | Allele Freq.): Estimated from empirical distribution
= iHS

Selection Index iHS
iHS Overview
iHS and REHH are EHH based methods to detect
positive selection
iHS outperforms REHH in specific allele frequencies
They don’t completely outperform each other

Selection Index iHS
iHS: Problem #1
Still can’t detect selection in high frequency (old)
alleles
Relatively High EHH values
are not present high
frequency (old) alleles!
Use a reference population
If pos. sel. didn’t take place
in ref. population, EHH is
high

Selection Index xp-EHH
xp-EHH: sabeti(2007)[8]
Population 별, 같은 allele별 integreted EHH를 비교!!

Cross Population EHH (XP‐EHH)
Same allele but diff population
AATTACAGATTACA CACATAG 20
0.5
XP‐EHH = ln(3.3/0.5) = 1.89 Z‐score Norn
Integrate EHH over distance from allele
Calculated for fwd/rev sides independently
Integrate until EHH = 0.04 in e.a. population
3.3

REHH and iHS are more or less complementary
e.a. is better at detecting pos. sel. at diff freqs.
XP‐EHH
Can detect pos. sel. in high freq. alleles
Susceptible to population variation in
recombination rate
Overview

Final Verdict: REHH vs iHS vs XP‐EHH
REHH
iHS test
XP‐EHH

Rsb[9]
Population끼리 비교하는 또다른 지표.
Population별로만 비교.
Locus별로 두 allele의 integrated EHH의 average: iES
Locus의 대략적인 selection정도를 population끼리 비교.

Practice
Contents
1 Fst
2 Selection Index
EHH
iHS
xp-EHH
3 Practice

Practice
FST
hierfstat[3]
PER3 gene in HGDP(Human Genome Diversity Panel): 289 SNPs &
7 population
EHH, iHS
rehh[2]
패키지 자체 제공 예제

Practice
Reference I
[1] Cockerham, C. C. (1969). Variance of gene frequencies. Evolution, pages 72–84.
[2] Gautier, M. and Vitalis, R. (2012). rehh: an r package to detect footprints of selection in genome-wide snp data from
haplotype structure. Bioinformatics, 28(8):1176–1177.
[3] Goudet, J. (2005). Hierfstat, a package for r to compute and test hierarchical f-statistics. Molecular Ecology Notes,
5(1):184–186.
[4] Hamilton, M. (2011). Population genetics. John Wiley & Sons.
[5] Holsinger, K. E. and Weir, B. S. (2009). Genetics in geographically structured populations: defining, estimating and
interpreting fst. Nature Reviews Genetics, 10(9):639–650.
[6] Huerta-Sánchez, E., Jin, X., Bianba, Z., Peter, B. M., Vinckenbosch, N., Liang, Y., Yi, X., He, M., Somel, M., Ni, P., et al.
(2014). Altitude adaptation in tibetans caused by introgression of denisovan-like dna. Nature, 512(7513):194–197.
[7] Sabeti, P. C., Reich, D. E., Higgins, J. M., Levine, H. Z., Richter, D. J., Schaffner, S. F., Gabriel, S. B., Platko, J. V.,
Patterson, N. J., McDonald, G. J., et al. (2002). Detecting recent positive selection in the human genome from haplotype
structure. Nature, 419(6909):832–837.
[8] Sabeti, P. C., Varilly, P., Fry, B., Lohmueller, J., Hostetter, E., Cotsapas, C., Xie, X., Byrne, E. H., McCarroll, S. A.,
Gaudet, R., et al. (2007). Genome-wide detection and characterization of positive selection in human populations. Nature,
449(7164):913–918.
[9] Tang, K., Thornton, K. R., and Stoneking, M. (2007). A new approach for using genome scans to detect recent positive
selection in the human genome. PLoS biology, 5(7):e171.

Practice
END
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Fst, selection index

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Fst, selection index