遺伝的多様性、集団構造と環境適応 genetic diversity...

遺伝的多様性、集団構造と環境適応

2019.5.29 生物配列統計学（Sequence Statistics and Mathematical Biology）

Genetic diversity,population structure and environmental adaptation

• Genetic diversity• A fundamental source of biodiversity• Correlates with fitness of individuals and populations • Poor understanding of determinants of the variation

• Population structure• Environmental adaptation of species• Evolution of species• Precise estimation needed

Why important?

Alleles at a locus: 遺伝子座と対立遺伝子

A random mating population

locus (loci)

male female

��

microsatellites（CA repeats）

single nucleotide polymorphism (SNP)

DNA

Large

Smallheterozygote

8

56

3

7

（CA）8 （CA）5 （CA）3 （CA）7（CA）6 （CA）6

Allele size（bp）

Microsatellite allele sizes defined by electrophoresis

個体1 個体2 個体3

homozygote

Capillary electrophoresis

Microsatellite genotypes, allele frequencies and genetic diversity (Pacific herring)

Locus（遺伝子座）個体

6AK1, 113151 122132 157162 113120 2162366AK2, 117147 114132 138157 113120 2142206AK3, 117117 122130 157162 113134 2242306AK4, 151159 122122 151157 113113 2162306AK5, 112117 107122 157166 113120 2022206AK6, 112131 120136 162164 113120 1962266AK7, 141167 120128 157168 120124 1982066AK8, 117125 120122 157162 113113 204230

0.00.10.20.30.4 Before2005

0.00.10.20.30.4

2006

0.00.10.20.30.4

2007

0.00.10.20.30.4

microsatellite alleles (Cha123)

After2014

2005

2007

2008

2013

OB (尾駮沼) MY (宮古湾)

Data: Kitada, Yoshikai, Fujita, Hamasaki, Nakamichi, Kishino (2017). Conserv. Genet. 18, 423-437.

松島湾

宮古湾13宮古湾08宮古湾07

宮古湾放流05宮古湾05尾駮沼14尾駮沼07尾駮沼06尾駮沼05

噴火湾

湧洞沼07湧洞沼03厚岸湖13厚岸湖06

厚岸湖放流03厚岸湖03

能取湖

サロマ湖

石狩湾

0.0 0.4 0.8Observed heterozygosity

23 samples (4,617 fish) were collected from nine spawning grounds in the spawning season during 2003 –2014.

homozygote

ℎ 1 𝑝

281 SNP genotypes: Atlantic herringLimborg et al. (2012). Molec. Ecol. 21, 3686-3703.

Allles 001, 002 heterozygotes

Bothnian_Bay, 002002 001002 001001 001002 001002 002002 001001 002002 001002 002002002002 001002 002002 001002 002002 001002 001001 002002 002002 001002002002 001002 001002 001002 002002 001002 002002 001002 002002 002002002002 001001 001002 001001 001002 002002 001002 002002 001001 001002001002 001001 000000 001001 001001 002002 002002 001001 002002 001002001002 001002 000000 001001 002002 001002 001002 001002 001001 001002001002 002002 002002 001002 001002 001002 002002 001001 001001 001001001002 002002 001002 002002 002002 001002 001002 002002 001002 001002002002 002002 002002 001001 001002 002002 001001 001002 001001 002002002002 001002 001002 001001 002002 002002 001001 001002 002002 002002001001 002002 001001 001002 002002 002002 002002 001001 002002 001002002002 002002 002002 002002 002002 001002 001002 002002 002002 002002001002 001002 001002 002002 002002 001001 001001 002002 002002 001001002002 001001 002002 001002 001002 002002 001001 001002 002002 002002002002 002002 001002 001001 002002 002002 001002 001002 001001 002002001002 002002 001001 002002 001002 002002 002002 001002 001001 002002002002 002002 002002 002002 001002 002002 002002 001001 001001 001002001001 002002 002002 001001 001002 001002 001002 002002 002002 002002001002 002002 002002 001002 002002 002002 002002 001002 001001 002002001002 001002 001001 001002 002002 001001 001002 002002 001001 002002001002 002002 002002 001001 002002 001002 002002 001002 002002 002002002002 001001 001002 001002 001001 001001 002002 002002 002002 002002001002 001002 002002 001001 002002 002002 001002 001002 001001 001001002002 001002 001002 001002 001002 001002 002002 002002 001001 001002002002 002002 001001 002002 002002 002002 002002 001002 001002 001001002002 001001 001002 001001 001002 001002 001001 001001 002002 002002001002 002002 001001 002002 001002

Bothnian_Bay, 001002 002002 001001 002002 001001 001002 002002 002002 001002 002002002002 001002 002002 002002 002002 002002 001002 002002 001002 001001

個体 SNP

Spring-spawning herring (n=607) were sampled in the spawning season during 1999-2009.

SNP allele frequencies and genetic diversity (Atlantic herring)

BBCNSCLSECGFGDHBICEIRSKATLIM

SHLNOR

GRRF

RUGSKAWIR

HSP 70

0.0 0.4 0.8Allle frequency


SHLNOR

GRRF

RUGSKAWIR

Cha_1025.1-149



SHLNOR

GRRF

RUGSKAWIR

　Cha_15984.1-275 (Hba)



SHLNOR

GRRF

RUGSKAWIR

Cha_1513.1-91(cat)



SHLNOR

GRRF

RUGSKAWIR

HSP 70

0.0 0.4 0.8Heterozygosity


SHLNOR

GRRF

RUGSKAWIR

Cha_1025.1-149



SHLNOR

GRRF

RUGSKAWIR

　Cha_15984.1-275 (Hba)



SHLNOR

GRRF

RUGSKAWIR

Cha_1513.1-91(cat)


allele frequencies

heterozygosity

Environmental gradients in the North Atlantic and the Baltic Sea

5 6 7 8 9 10 11 12

5

10

15

20

25

30

35

KAT

LIM

RFRUG

SKA

BB

GFGDHB

GR

CNSSHL CLSECIRS

WIRICENOR

Mean annual SST

Mea

n an

nual

SSS

http://ocean.dmi.dk/models/hbm.uk.php

Seto Inland SeaMean depth 38mMax depth 105m

Data Limborg et al. (2012). Molec. Ecol. 21, 3686-3703.

Atlantic herring population structure in the NE Atlantic/Baltic

265 neutral SNPs 281 all SNPs

Rosenberg, N. A., Pritchard, J. K., Weber, J. L., Cann, H. M., Kidd, K. K., Zhivotovsky, L. A., & Feldman, M. W. (2002). Genetic structure of human populations. science, 298(5602), 2381-2385.

52 populations (377 microsatellite loci, n=1,056)

Human population structure

STRUCTURE: Bayesian clustering

Pritchard, Stephens, Donnelly (2000) Genetics 155, 945-959.

( ) ( ) ( 1)

( ) ( ) ( )

Step1. Sample , from Pr( , | , ).Step2. Sample from Pr( | , , ).Step2. Update using a Metropolis-Hasting step.

s s s

s s s

P Q P Q X ZZ Z X P Q

MCMC algorithm (s=1, 2,…)

Priors

Goal : Sample from the joint posterior distribution

Pr( | )X K Most likely K

Assumption : HWE in putative original populationsData : multi-locus genotypes

Pr( , , , , | , )P Q Z X K

MCMC

A mixed populationi

1 K

i

Pr( ) 1/iz k K

1

1 2

~ Dir( ,..., )... 1

k m

m

p

𝑞 𝑞 , ⋯ , 𝑞

𝑞 𝑖 ~𝐷𝑖𝑟 𝛼, … , 𝛼 , 𝛼 ∈ 0,10

Hardy-Weinberg equilibrium (HWE)

A1 (p) A2 (q)

A1(p)

A1A1(p×p)

A1A2(p×q)

A2(q)

A1A2(p×q)

A2A2(q×q)

female

male

Genotype frequencies

2 2 22 ( ) 1p pq q p q

A random mating population Allele and genotype frequencies are expected to be stable in a HWE population without

• Natural selection• Mutation• Non-random mating• Migration• Genetic drift

Putative ancestry population

FST, 1

FST, 2

FST, 6

STRUCTURE F-model: linked loci and correlated allele frequencies

Falush, Stephens, Pritchard (2003) Genetics 164, 1567-1587. ST, ST, ST,

1 2ST, ST, ST,

1 1 1~ Dir( , ,..., )k k k

k A A Amk k k

F F Fp p p p

F F F

ST

ST

ST ST

1/ ( 1)11 1

FF

F F

1

1 2

~ Dir( ,..., )... 1

A m

m

p

PA

𝑞 𝑞 , ⋯ , 𝑞


Assumption : HWE in putative original populationsData : multi-locus genotypes

MCMC

P r 𝑃, 𝑄, 𝑍, 𝐹 , 𝛼, 𝜆|𝑋, 𝐾

𝑞 𝑖 ~𝐷𝑖𝑟 𝛼, … , 𝛼 ,

Wright’s island model and FST（Fixation index）

Sewall Green Wright 1889.12.16‐ 1988.3.3

Wright, S., 1931 Evolution in mendelian populations. Genetics 16: 97–158.

Wright, S., 1951 The genetical structure of populations. Ann. Eugen. 15: 323–354.

𝑓 𝑝Γ 4𝑁𝑚

Γ 4𝑁𝑚𝑝 Γ 4𝑁𝑚 1 𝑝 𝑝 1 𝑝

allele frequencies of populations at a biallelic locus (a beta distribution)

multiple loci (a Dirichlet distribution)

𝐹1

4𝑁𝑚 11

𝜃 1

4Nm

Prior for allele frequencies

ST

1

11

1

( )( | )( )

1/ ( 1)

i

m

imiii

m

ii

global

p

F

p α 11

1

( | ) ...!... !

mxxm

m

nL p px x

p x

Likelihood of allele counts

distribution of pmultinomial (binomial)

Conjugate prior for the allele frequency

Histogram of rbeta(5000, 1, 1)

rbeta(5000, 1, 1)

Freq

uenc

y

0.0 0.2 0.4 0.6 0.8 1.0

010

2030

4050

6070

~ beta(1,1)kp

Dirichlet (beta)

1

1 2

~ Dir( ,..., )... 1

A m

m

p

1

1 2

~ Dir( ,..., )... 1

k m

m

p

STRUCTURE

Atlantic herring population structure

LOCPRIOR given information of sampling sites (1,…,18)

STRUCTURE

Data: Neutral marker set (265 SNPs)

Limborg et al. (2012). Molec. Ecol. 21, 3686-3703.

18 sampling sites

STRUCTURE: LOCPRIOR for high gene flow species

Hubisz, Falush, Stephens, Pritchard (2009) Molecular Ecology Resources 9, 1322-1332.

Given the location information as integer (l=1, 2, …, S).

Pr( | )ii l kz k

. 1 2~ Dir( , ,..., )l Kr r r

~ unif (0, ),~ Dir(1,...,1)

MAXrr

Informativeness of location information

A small r estimate (r<1.0) indicates that the location information is informative.


STPr( , , , , , | , 1,..., )S,P Q Z F X Kr

1 k K

li

1~ ( ,..., )i l lKq Dir

( ) ~ unif (0, 10)gk MAX

( )~ gamma( ,1/ )glk kr r

Global value of α forthe k cluster

Sampling location (l=1,…, S)

MCMC: STRUCTURE_LOCPRIOR (Atlantic herring, K=3)Burn‐in 100,000MCMC 500,000

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

0.5

SNP

glob

al F

st Cha_1025.1-149

Cha_15389.3‐101 (Hsp70)

Cha_15984.1‐275 (Hba)

Cha_2884.1‐367

1513.1.91 (Cat)

locus‐F S

T(EBF

ST)

Detecting loci influenced by selection

BAYSCAN (2008)

𝐩𝐢𝐣~Dir 𝜃 𝑝 , . . . , 𝜃 𝑝 ,

𝜃1

𝐹ST1 at locus 𝑖 population 𝑗.

𝐩 ~Dir 1, . . . , 1

Ancestry population

FST, 1

FST, 2

FST, J

𝐩𝐢

𝐩𝐢𝐣

Estimates the probability that a locus is influenced by selection

ST

ST

1log log1

ij

jijij

iFF

π 𝐩 𝐩, 𝛉 𝐿 𝜋 𝐩𝐢𝐣|𝐩𝐢, 𝛉𝐢𝐣

K: num. alleles

Foll & Gaggiotti (2008) Genetics 180, 977-993.

𝐿 𝑎 ,…, 𝑎 |𝜃 , 𝑝 ,…, 𝑝∏

𝐴𝜋 𝐩|𝐩, 𝛂, 𝛃 𝜋 𝛼

𝜋 𝐩|𝐩, 𝛂 with 𝛼 0, 𝛃 𝑞 𝛼

To accept to add with probability min (1,A)𝛼

P 𝛼 number of times 𝛼 included in the model

Posterior odds𝑃 𝛼

1 𝑃 𝛼

MCMC

Or to delete 𝛼 with probability min (1,1/A)

PO(posterior odds)

Among 281 loci, 16 outlier were found (265 were neutral).

Outlier loci of Atlantic herring populations (BAYSCAN)

105

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

0.5

SNP

glob

al F

st Cha_1025.1-149

Cha_15389.3‐101 (Hsp70)

Cha_15984.1‐275 (Hba)

Cha_2884.1‐367

locus‐FST

1513.1.91 (Cat)


5% 1%

BAYENV (2010) Coop, Witonski, Rienzo, Pritchard (2010) Genetics 185, 1411-1423.

𝑥 𝑔 𝜃 0 if 𝜃 0 𝜃 0 𝜃 1 1 𝜃 1

Ancestry population of allele frequencies

𝜀 ~Beta 1,1

𝑥Ω

MCMC

BFPr Model 1|𝐧𝐥, 𝐦𝐥Pr Model 0|𝐧𝐥, 𝐦𝐥

Estimates the probability that a locus is influenced by environmental variables

l: locus

𝑃 𝜃 |Ω, 𝜀 ~𝑁 𝜀 , 𝜀 1 𝜀 Ω

Null model (Model 0)

Ω~inverse Wishart

Ω A single draw of Ω after burn-in

𝑃 𝜃 , Ω, 𝛆𝐥|𝐧 , 𝐦 ∝ 𝑃 𝐧 , 𝐦 |𝑥 𝑔 𝜃𝑃 𝜃 |Ω, 𝛆𝐥 𝑃 Ω 𝑃 𝛆𝐥 Observed allele count (1 and 2)

Joint posterior of the parameters

Alternative model (Model 1)

( | , , ) ~ ( , 1 ) ), (l l l l lP NY Y

𝑃 𝜃 , Ω, 𝛆𝐥, 𝛃|𝐧 , 𝐦 ∝ 𝑃 𝐧 , 𝐦 |𝑥 𝑔 𝜃𝑃 𝜃 |Ω, 𝛆𝐥, 𝛃 𝑃 Ω 𝑃 𝛆𝐥 𝑃 𝛃

𝑃 𝛽 ~Unif 𝛽 , 𝛽


Detecting environment-linked loci (BAYENV)

• The first two columns left of the SNP names show all detected outliers where * and ** denote outliers with P < 0.05 or 0.01 for the ARLEQUIN analysis. BAYESCAN outliers were detected with false discovery rates of 5% (*) and 1% (**).

• Statistical inference of correlations between SNPs and landscape parameters are given for relationships with log10(BF) = 1.5–2.0 (*) and log10(BF) > 2.0 (**).

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

0.5

SNP

glob

al F

st Cha_1025.1-149

Cha_15389.3‐101 (Hsp70)

Cha_15984.1‐275 (Hba)

Cha_2884.1‐367

locus‐FST

1513.1.91 (Cat)

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

0.5

SNP

glob

al F

st Cha_1025.1-149

Cha_15389.3‐101 (Hsp70)

Cha_15984.1‐275 (Hba)

Cha_2884.1‐367

locus‐FST

1513.1.91 (Cat)

Salinity, SST and allele frequenciesPS

U

浸透圧調整

5 10 15 20 25 30 35

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

KAT

LIM

RF

RUG

SKA

BB

GF

GD

HB

GR

CNSSHLCLSECIRSWIRICENOR

Mean annual sea surface salinity (PSU)

Cha

_153

60.2

-279

(Hsp

70) a

llle fr

eque

ncy

5 6 7 8 9 10 11 12

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

KAT

LIM

RF

RUG

SKA

BB

GF

GD

HB

GR

CNSSHL CLSECIRS WIRICENOR

Mean annual sea surface temperature

Cha

_153

60.2

-279

(Hsp

70) a

llle fr

eque

ncy

HSP70 呼吸？

5 6 7 8 9 10 11 120.65

0.70

0.75

0.80

0.85

0.90

0.95

KAT

LIM

RF

RUG

SKA

BB

GF

GD

HBGR

CNS

SHL

CLS

ECIRS

WIR

ICENOR


Cha

_151

05.2

-341

(Cat

) allle

freq

uenc

y

5 10 15 20 25 30 350.65

0.70

0.75

0.80

0.85

0.90

0.95

KAT

LIM

RF

RUG

SKA

BB

GF

GD

HBGR

CNS

SHL

CLS

ECIRS

WIR

ICENOR


Cha

_151

05.2

-341

(Cat

) allle

freq

uenc

y

Cat酸素運搬

5 10 15 20 25 30 35

0.0

0.1

0.2

0.3

0.4

0.5

0.6

KAT LIM

RF

RUG

SKA

BBGFGD

HB

GR

CNS

SHLCLSEC

IRSWIRICENOR


Cha

_159

84.1

-275

(Hba

) allle

freq

uenc

y

5 6 7 8 9 10 11 12

0.0

0.1

0.2

0.3

0.4

0.5

0.6

KATLIM

RF

RUG

SKA

BBGF GD

HB

GR

CNS

SHLCLSEC

IRSWIR

ICENOR


Cha

_159

84.1

-275

(Hba

) allle

freq

uenc

y

Hba

SST

5 6 7 8 9 10 11 12

0.4

0.6

0.8

1.0

KATLIMRF

RUG

SKA

BB

GF

GD

HB

GR

CNS

SHL

CLSECIRSWIR

ICE

NOR


Cha

_102

5.1-

149

allle

freq

uenc

y

5 10 15 20 25 30 35

0.4

0.6

0.8

1.0

KAT LIMRF

RUG

SKA

BB

GF

GD

HB

GR

CNS

SHL

CLSECIRSWIR

ICE

NOR


Cha

_102

5.1-

149

allle

freq

uenc

y

Cha_1025.1-149

STT S

T

H HFH

全多様度集団内多様度集団間多様度

全多様度全多様度

( )2S

1 1

2

11

1

r mij

i j

within

H pr

p

2

( )T

1 1

2

1

11

1

m rij

j i

m

jj

H pr

p

GST measuring population divergence (= FST)

r: number of populationsm： number of alleles

Nei, M. (1973). Analysis of gene diversity in subdivided populations. PNAS, 70, 3321-3323.

STglobalF

STpairF

Pairwise FST population structure (281 SNPs)

Kitada, Nakamichi, Kishino (2017) Molecular Ecology Resources. 17, 1210-1222.

FinePop

global FST=0.0128 (WC)

c.f. global FST=0.0413 (WC) for Atlantic salmon

Precise estimation of pairwise FST is difficult particularly in high gene flow species

Kitada, Kitakado, Kishino (2007) Genetics 177, 861-873.

1~ Dir( , ..., )k mp

1 1ˆ ˆ~ Dir( , ..., )

posteriork

m m

pn n

STpair T S

T

H HFH

Dirichlet-multinomial marginal likelihood

Kitada, Hayashi, Kishino (2000) Genetics 156, 2063-2079.

EBFST

Performance of pairwise FST estimators


𝐹ST 𝛽 𝐷 𝛽 𝑇 𝛽 𝑆 𝛽 𝐷 𝑇 𝛽 𝐷 𝑆 𝛽 𝑇 𝑆 𝛽 𝐷 𝑇 𝑆

TIC 2 maximum log likelihood 2 trace 𝐴 𝐵


FinePop

trace 𝐴 𝐵𝜎𝑠

𝜎 : variance of parameters𝑠 : variance of parameters assuming 𝑖𝑖𝑑

𝐴 𝐵

𝜎𝑠

⋯𝜎 𝜎

𝑠⋮ ⋱ ⋮

𝜎 𝜎𝑠

⋯𝜎𝑠

Salinity and geographical distance explained 60% variation of population structure

iid bootstrap

Lamichhaney et al. (2017). doi/10.1073/pnas.1617728114.

ST 0.026globalF

among 26 Atlantic herring populations

NW Atlantic

NE Atlantic/Baltic

n=1,837, ~1.2 million SNPs

* autumn-spawning

Lamichhaney et al. (2017).doi/10.1073/pnas.1617728114. TSHR thyroid-stimulating hormone receptor甲状腺刺激ホルモン受容体SOX11, CALM1 photoperiodic regulation ofreproduction in birds and mammals生殖の光周期調節ESR2A estrogen receptor beta 2 雌性ホルモンHERPUD2 homocysteine-responsive endoplasmic reticulum-resident ubiquitin-like domain member 2

America, NW Atlantic Europe, NE Atlantic/Baltic

P=10‐50

* autumn-spawning

TSHR pop structure

遺伝的多様性、集団構造と環境適応 genetic diversity...

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