Selection index population_genetics

FST & Some Selection Index진화, 인구집단 유전학과 건강 2014

김진섭

GSPH, SNU

October 29, 2014

김진섭 (GSPH, SNU) FST & Some Selection Index October 29, 2014 1 / 65

Fst

Contents

1 Fst

Wright’s F -statisticsCockerham’s θ-statistics

2 Selection IndexEHHiHSxp-EHH

3 Practice


Fst Wright’s F -statistics

3 types of Heterozygosity[4]

Individual, Subpopulation, Total Population

1 HI = 1n

∑ni=1 Hi

2 HS = 1n

∑ni=1 2piqi

3 HT = 2pq

(Hi : observed heterozygosity in ith subpopulation, 2piqi : averageheterozygosity in ith subpopulation, 2pq: average heterozygosity of totalpopulation)Locus 별로 값 구한다.



Wright’s F -statistics[4]

1 FIS = HS−HIHS

2 FST = HT−HSHT

3 FIT = HT−HIHT

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



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


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


FST inference[5]

Convenient measure of genetic differentiation.

Most widely used descriptive statistics in population andevolutionary genetics.

Natural selection in particular subpopulation.



Problem in estimation

HT = 2pq

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 =σPσT

(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.html김진섭 (GSPH, SNU) FST & Some Selection Index October 29, 2014 14 / 65



Selection Index

Contents

1 Fst



3 Practice


Selection Index

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


Selection Index

Population Genetics

Glucose

HAPLOTYPESGATTACAGATTACA 22%AATTACAGATTAAA 3%GACTACAGATTACC 19%GATTACCTATTAAC 24%AACTACAGATTACC 16%GATTACAGACTACA 7%AATTACAGATTACA 9%

Lactase + H2O


Selection Index

Population Genetics

Lactase + H2O

Glucose



Selection Index

Population Genetics

Lactase + H2O

Glucose


AATTGCAGATTACA <1%


Selection Index

Population Genetics

Lactase + H2O

Glucose


AATTGCAGATTACA <1%


Selection Index

Population Genetics

Lactase + H2O

Glucose

HAPLOTYPESGATTACAGATTACA 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

HAPLOTYPESGATTACAGATTACA 21% -1%AATTACAGATTAAA 3%GACTACAGATTACC 19%GATTACCTATTAAC 23% -1%AACTACAGATTACC 15% -1%GATTACAGACTACA 7%AATTACAGATTACA 7% -2%



Selection Index

Population Genetics

Lactase + H2O

Glucose

HAPLOTYPESGATTACAGATTACA 20% -2%AATTACAGATTAAA 3%GACTACAGATTACC 19%GATTACCTATTAAC 23% -1%AACTACAGATTACC 15% -1%GATTACAGACTACA 6% -1%AATTACAGATTACA 5% -4%



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 =

∑si=1

(eti2

)(ct2

)(t: core haplotype, c : the number of samples of a particular corehaplotype, 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 thisGATTACAGATTACA 50 people have this---- 50 KB ----


Selection Index EHH

50 KB + 20 KB = 70 KB__AATTACAGATTACA AACACGC 10AATTACAGATTACA ATGATAG 8 AATTACAGATTACA AACCCAG 7AATTACAGATTACA CTGACAG 5AATTACAGATTACA CAGACAG 3 AATTACAGATTACA AACACAG 6 AATTACAGATTACA CACACAG 4AATTACAGATTACA CACCCAG 7

GATTACAGATTACA CACATAG 24 GATTACAGATTACA CACACAG 26

How can we detect Pos. Sel.?


Selection Index EHH

Extended Haplotype Homozygosity (EHH)

AATTACAGATTACA AACACGC 10AATTACAGATTACA ATGATAG 8 AATTACAGATTACA AACCCAG 7AATTACAGATTACA CTGACAG 5AATTACAGATTACA CAGACAG 3 AATTACAGATTACA AACACAG 6 AATTACAGATTACA CACACAG 4AATTACAGATTACA CACCCAG 7



Selection Index EHH

( (32

52

72

82)+




102)+( )+( )+ )+( )+6

2( )+42( )72

)502(

(


Selection Index EHH

)+




102( )+ 8

2( )+72( )+5

2( )+32( )+6

2( )+42( )72(

)502(

0.121


Selection Index EHH

EHH Drops Over Genetic Distance

EHH drops off quickly over genetic distanceStarts with 1Ends at 0

Every hap block will eventually be unique


Selection Index EHH



EHH What It Is & What It Isn’tDetects 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

AATTACAGATTACA AACACGC 22AATTACAGATTACA ATGATAG 28



Selection Index EHH

Compare EHH ScoresAATTACAGATTACA AACACGC 10AATTACAGATTACA ATGATAG 8 AATTACAGATTACA AACCCAG 7AATTACAGATTACA CTGACAG 5AATTACAGATTACA CAGACAG 3 AATTACAGATTACA AACACAG 6 AATTACAGATTACA CACACAG 4AATTACAGATTACA CACCCAG 7


)+242( )262(

)502(

0.121

0.490

Low RecombinationOver Represented


Selection Index EHH

Can EHH Detect Pos. Sel.?


Selection Index EHH

Relative EHH

Detects over‐representation of a haplotypeLow recombinationThis will raise the p(two haps are homozygous)

Does detect if a haplotype spread quicklyOther haplotype blocks are controls!

Recombination cold‐spot / hot‐spot agnosticLow score if both alleles are assoc. w/ high or low recombination

AATTACAGATTACA AACACGC 22AATTACAGATTACA ATGATAG 28



Selection Index EHH




0.121

0.490

0.4900.121

= 4.05REHH =


Selection Index EHH

REHH: Problem #1

We get a different REHH value at different genetic distance cutoffs

AATTACAGATTACA 50GATTACAGATTACA 50---- 50 KB ----

REHH = 1.0


GATTACAGATTACA CACATAG 24 GATTACAGATTACA CACACAG 26---------- 70 KB ---------

REHH = 4.05


Selection Index EHH

Which REHH value to use?

Extend to the right

AGTTACAGATTACAAACACGCAAATACAGATTACAATGATAG AATTACAGATTACAAACCCAGAATTTCAGATTACACTGACAGAATTAAAGATTACACAGACAG AATTACCGATTACAAACACAG AATTACAAATTACACACACAGAATTACAGGTTACACACCCAG

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



REHH = 4.05


Selection Index EHH


Extend to the right



REHH = 4.05


Selection Index EHH


Extend to the right



REHH = 4.05


Selection Index EHH


Extend to the right



REHH = 4.05


Selection Index EHH


Extend to the left



REHH = 4.05


Selection Index EHH


Extend to the left



REHH = 4.05


Selection Index EHH


Extend to the left



REHH = 4.05


Selection Index EHH

REHH: Problem #2

REHH score is heavily biased by allele frequenciesMust normalize

P(REHH | Allele Freq.)


Selection Index EHH

REHH: Problem #3

Not possible to detect selection in high frequency allelesSolution requires a X‐population approach (discussed later)


Selection Index EHH

Leaves a lot to be desiredPicking 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 distancex = fwd distanceEHHD = derived alleleEHHA = ancestral allele


Selection Index iHS

…ACAGATTACAGTTACAGATTACAAACACGC……ACAGATTACAAATACAGATTACAATGATAG… …ACAGATTACAATTACAGATTACAAACCCAG……ACAGATTACAATTTCAGATTACACTGACAG……ACAGATTACAATTAAAGATTACACAGACAG… …ACAGATTACAATTACCGATTACAAACACAG… …ACAGATTACAATTACAAATTACACACACAG……ACAGATTACAATTACAGTTACAACACCCAG…

…TACAGATTAGATTACAGATTACACACATAG …TACAGATTAGATTACAGATTACACACACAG

+ 0.5 = 1.20.7

4.0 + 4.4 = 8.4

Unstandardized iHSln(8.4/3.2) = 0.419



Selection Index iHS

iHS Characteristics

As both alleles have the same AUC, iHS zeroLarge negative values indicate selection of allele in the denominatorLarge positive values indicate selection of allele in the numeratorStill 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 distributionSD(iHS | Allele Freq.): Estimated from empirical distribution


= iHS


Selection Index iHS

iHS Overview

iHS and REHH are EHH based methods to detect positive selectioniHS outperforms REHH in specific allele frequencies

They don’t completely outperform each other


Selection Index iHS

iHS: Problem #1Still 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 populationAATTACAGATTACA CACATAG 20 AATTACAGATTACA CACACAG 30

0.5

XP‐EHH = ln(3.3/0.5) = 1.89 Z‐score Norn

Integrate EHH over distance from alleleCalculated for fwd/rev sides independentlyIntegrate until EHH = 0.04 in e.a. population

3.3



REHH and iHS are more or less complementarye.a. is better at detecting pos. sel. at diff freqs.

XP‐EHHCan detect pos. sel. in high freq. allelesSusceptible to population variation in recombination rate

Overview



Final Verdict: REHH vs iHS vs XP‐EHH

REHHiHS testXP‐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



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 fromhaplotype 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 andinterpreting fst. Nature Reviews Genetics, 10(9):639–650.

[6] Huerta-Sanchez, 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 haplotypestructure. 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 positiveselection in the human genome. PLoS biology, 5(7):e171.


Practice

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