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2017/11/18 13:00-14:45

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Pictured by Dr. Satoshi Niikura

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šÙ

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Ɨ'ǨȓQTLșɉȳɂɕȥ

• şƖȂȌȓȖȕrĖǯǨšÙǾǪȁǤəšÙˆŰɠċɚ

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țȯȫȟɗȫɎɕšÙ

• ƌŲÿĮȂYȋȖȕ]ĦɖķŁșĜºĒǤǽǞDNAɉɗȡɗtiǿŘĎit

iƖȃƗ'ǨȓǞƗƌzšəȋǷȄSNPɚșã:

• ×Ä7ȂȌȓȖȕæǠȁŸųrĖǩšÙˆŰǿȁȕəšÙˆŰɠ˜ɚ

• ƌŲÿȧɒȤȫɎɕȐŋĦƅĥȂǣȕķŁȁȀșùĒǾǪȕǟ

ȋǷǞǵȖȓķŁǾOƟǮȖǷÈ{ȃȶɗȰșÓGùĒǾǪȕəÍĩƖȃIJĸɚ

• ×ÄȂȒǺǽȄǞƮš1™ǾȃšÙǩǾǪȕ

ATCGAG TAGACT

TATACG

ATCGAG TAGACT

TATACG

ATCGAG TAGACA

TATACG

ATCGAG TAGACT

TATACG

ATCGAG TAGACT

TATACG

ATCGAG TAGACT

TATACG

ATCGAG TAGACA

TATACG

ATCGAG TAGACA

TATACG

ATCGAG TAGACT

TATACG

ATCGAG TAGACA

TATACG

7

nkti

(single nucleotide polymorphisms: SNPs)

šÙǩ

țȯȫȟɗȫɎɕšÙȈȃƆșµǤǷ

GeneChip Rice 44K SNP Genotyping Array

• 44,100 SNPs (10kbñȂ1 SNP)

QTLšÙ

ŠÂȃşșƏǯǞ ǵȃ¢șšÙ

ďēɠ şƖȃƈǤəŒ ȃƈǤɚȄ;ǨǺ

ǽȏǞŧļȁDNA

tiəȫɉȫɉɚ

ȋǾŝ;ǬȓȖ ȁǨǺǷ

š1™ǩ ǤǞ×Ä"ȔȂÍƖǩǨǨȕ š1™ǩƮǤǞƏșŖǥ¦ŜǩȁǤ

ǷǸǯǞƌĚŌÎȃƈǤȂȒȕ-ƛ¨ǩđǰÌǤ

ȦȽɊɔȜȸ țȯȫȟɗȫɎɕ

šÙəGWASɚ

tÂȃ)!ə]Ħɚș ǵȃȋȋšÙ

ďēɠ ]ĦƖȂŝȓȖ

ȕŧļȁDNAt

iəȫɉȫɉɚǩ ŝ;ǬȓȖȕȒǥ ȂȁǺǷ

Morrell et al. (2012) Nature Review Genetics 13:85

£Øȃ

QTL

šÙ

vs.

țȯȫȟɗȫɎɕšÙ

țȯȫȟɗȫɎɕšÙȃ@ăǿéă

țȯȫȟɗȫɎɕšÙȄǞƌŲÿȂYȋȖȕtæȁr

ĖȃšÙȂƊǯǽǤȕ

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‚i

țɐɑȃů†Ǯ Ʈ

¦Ŝȁɉɗȡɗ Š t

Ə€Ƭȃ¦Ŝ¨ Ŝ Ŝ

š1™ Ʈ

ȶȪȜɕǮȖǷɉȳ ɂɕȥƟb

ŐȂYes No

ƌĚŌÎȃƈǤ ȂˆDZȕ«P¨

‰ u

ƂƓ–ŗə

linkage disequilibrium: LD

ɚ

Ĥ3əDy ʼnɚȃÜŒ!

tÂȃ Ǿ đǰǷľ½Ǧ

Ď]ĦȃÜ Œ!

–ŗəŽǤɚ

–ŗəƉǤɚ

ÜŒ!Ɩȃ½ǦȂȒȔǞ–ŗȄŷƠȂ%{ǯǽ 11

ƂƓ–ŗə

linkage disequilibrium: LD

ɚ

Ĥ3əDy ʼnɚȃÜŒ!

tÂȃ Ǿ đǰǷľ½Ǧ

Ď]ĦȃÜ Œ!

Maƌzã:ȃMď

MaƌzəQTLɚ

ŘĎi

ĜºĚ țȯȫȟɗȫɎɕ

əƌĚ¿Əɚ

܌!

(Modified from Balding 2006)

əĜºŠ‡ǾǪȁǤɚ

ǭȃțȯȫȟɗȫɎɕșã:DZȕǭǿǾǞMaƌz

ȃŽ.ȂǣȕSNPɉɗȡɗșĪǪëȎȕ

Ǥ ƣĊī¨

(ƂƓ–ŗ)

SNP

ɉɗȡɗ

ǤƖºĚ țȯȫȟɗȫɎɕ

œǤƖºĚ țȯȫȟɗȫɎɕ

œǤ ƣĊī¨ (ƂƓ–ŗ)

SNP

ɉɗȡɗ

13

ƂƓ–ŗǿǵȃ·ç

(Rafalski 2002ȒȔÀrɚ

ǜB ǜb

ǜA pAB pAb pA

ǜa paB pab pa

pB pb

r

2

₌

D

2

p

A

p

a

p

B

p

b

(ǜǜș1,ǜǜș0ǿǯǷǿǪȃ

ĝƗ'Âȃ)

D

=

p

_AB

−

p

_A

p

_B

=

p

_AB

p

_ab

−

p

_Ab

p

_aB

r2= 0.25 2

0.5×0.5×0.5×0.5 =1

ABǩĊīȃmVȂ Ô¡ǮȖȕABȃƧ™

€ƝȂŠ‡ǮȖǷ ABȃƧ™

r2

=0.1024 _r2=0

ƂƓ–ŗ ƂƓ–ŗ

ƌzšA

ƌzšB

14

ã:ȃ„ÌǮǿš1™ȃȷɒɗȸȠɃ

•

ƂƓ–ŗȃĥ™ǩ

Ʈ

ǤmV

ȄǞ

ŠÂ

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ȡɗǾțȯȫȟɗȫɎɕș

ã:ǾǪȕǩǞ

š1™Ȅ

Ǥ

•

ƂƓ–ŗȃĥ™ǩ

ǤmV

ȄǞ

š1™ȄƮ

Ǥ

ǩǞã:ȂȄ

tÂ

ȃ

ɉɗȡɗș¦ŜǿDZȕ

(Rafalski 2002ȒȔÀr)

15

âĈĦȂȒȕ

LD

ȃĥ™ȃƈǤ

Gupta et al. (2005)ȒȔÀr

Əæ› ƿƾȃijc

ȫɓȜȻȹȭȹ Ŏï¨ ƷƹƵljǃ

Ȝȼ Ŏï¨ ƶƵƵƳƷƵƵljǃ

ȠȠɊȣ Ŏï¨ ƶƵƳƷƵDŽǀ

ȧɊȣ Ŏï¨ ƶƵƳƷƵDŽǀ

ȯɑȢɊ Ŏï¨ ƻƱƸDŽǀ

ȱȜȭ Ŏï¨ ƼƱƹƵljǃ

ȷȝɌɓȧȫ ï¨ ƵƴƹƳƺƴƵljǃ

ȠȝȫɍȝȷȝɁəǁǍǏǓǂǕƱǐǎǏǒDŽdžƲ ï¨ ɤƶƵƵƳƷƵƵǃǎ

ȵɗȱɉȴəNJǍǃNJǍNJNJǕƱǎLjnjdžƲ ï¨ ƶƵƵƳƶƹƵƵǃǎ

ŐȂǞ

• Ŏï¨ ɢ ï¨

• ƟbȩȜȭ u ɡ ‰

əÓGȁ½Ǧəľ½Ǧǩđǰȕ½ǦɚȄǞɅȵɓºV™Ȃ%{DZȕɚ

×ÄȂȒȕ

LD

ȃĥ™ȃƈǤ

(Zhu et al. 2007)

àjĦȐàj]ĦǾȄǞDyʼnGÚǞƋ²ȂȒȕɇȷɑȼȳȤǞü Â;řȃèȃŠȁǮǨȓǞƑđĦȐfØ]ĦȂòȉǽƮǤƂ Ɠ–ŗəLDɚǩŝȓȖȕmVǩtǤ

ĉȂǞŽ]ĦǨȓȁȕȒǥȁƌŲÿȧɒȤȫɎɕǾȄǞǵȃ/XǩƮǤ

→ ×ÄșǥȋǫƋȇǭǿǾǞLDșŬÃDZȕǭǿȏǾǪȕ

Ʈ ↑ ƂƓ–ŗ ↓ 17

țȯȫȟɗȫɎɕȃã:ɠ

ȡȵȨɐɗȶɗȰȃmV

ɉɗȡɗ ė‚ ´±¨ ė‚ «P¨

AA

ɛɛ

ɞ

aa

ɝ

ɟ

ǭǭǾȄǞŎï¨ȃmVșňǦǽǤȕ _†

țȯȫȟɗȫɎɕǩǣȕmVɠ

$ǦȅǞ´±¨ȃ]ĦǾȄǞ

ɉɗȡɗƌziAAȃƧ™

ǩǞaaȂòȉǽƮǫȁȔǞ«P

¨ȃ]ĦǾȄǞǵȃžȂȁȕ

«P¨ǿ´±¨ȃƖǾȀȃĥ™Ƨ™ȃ‘ǩǣȖȅ ǡțȯȫȟɗȫɎɕǩǣȕǢǿ>ÅǾǪȕȃǸȗǥǨɣ

ŁţĚãɠ$ǦȅǞχ2_{ãȐFisherȃìĢĢčãəFisher’s exact testɚ}

18

χ

2

_{ãȂȒȕĊī¨ã}

ė‚´±¨(R) ė‚«P¨(S)

AA f11 (11) f12 (4) f1. (15) aa f21 (3) f22 (7) f2. (10) f.1 (14) f.2 (11) n (25)

ė‚´±¨ǾǣȕĢč p(R) = f.1 / n = 14 / 25 = 0.56

ė‚«P¨ǾǣȕĢč p(S) = f.2 / n = 11 / 25 = 0.44

ɉɗȡɗǩAAǾǣȕĢč p(AA) = f1. / n = 15 / 25 = 0.60

ɉɗȡɗǩaaǾǣȕĢč p(aa) = f2. / n = 10 / 25 = 0.40

ȏǯǞė‚«P¨ǿɉɗȡɗƌziǩĊīȁȓǞ

UȮɑȃÔ¡™ÂȄUĢčȃħȂłÂșǨǬǷȏȃǿȁȕ ↓

RǨǻAA nǖp(R) ǖp(AA) = 25 ǖ0.56 ǖ0.60 = 8.4 RǨǻaa nǖp(R) ǖp(aa) = 25 ǖ0.56 ǖ0.40 = 5.6 SǨǻAA nǖp(S) ǖp(AA) = 25 ǖ0.44 ǖ0.60 = 6.6 SǨǻaa nǖp(S) ǖp(aa) = 25 ǖ0.44 ǖ0.40 = 4.4

χ2

= (obs−exp) 2

exp

∑

=(11−8.4)

2

8.4 + (3−5.6)2

5.6 + (4−6.6)2

6.6 + (7−4.4)2

4.4 =4.57

“ąŪȃȏǿǾŎē™(r-1)(c-1)ȃχ2_{;’ərȄŖÂǞcȄ=Âɚ}

5%óĀǾÓªəĊīǾȁǤɚ

χ0.01 2

(1)=6.63>χ2

=4.57>χ0.05 2

(1)=3.84

ǭȃÇ÷ȄǞ™ÂȃŠ ȁǤə5ÕþɚȮɑǩǣ ȕmVȄìĢǾǣȕ ǭǿǩĠȓȖǽǤ ȕɘɘ ;CŘ 19 ɉɗȡɗȃGÚ

țȯȫȟɗȫɎɕšÙ

:

ƒĚŸųȃmV

-4 -2 0 2 4 6 8

mQQ mqq QTL㑇ఏᏊᆺ

QQ qq

࣐ 勖 ࢝ 勖 㑇 ఏ Ꮚ ᆺ AA aa 40 10 10 40

-4 -2 0 2 4 6 8

₯ᅾⓗ࡞ΰྜศᕸ

-4 -2 0 2 4 6 8

࣐࣮࣮࢝ ⾲⌧ᆺศᕸ

mAA

-4 -2 0 2 4 6 8

maa

y

_i

=

u

+

β

_j

x

_ij

+

e

_i

ɉɗȡɗƌzixǿŘĎi+yȃ

ƖȃƗ'șĜŃǾ`“DZȕ

-0.2 0.2 0.6 1.0

-2 0 2 4 6 Marker genotype Phenotype

)!iǩAAȃǿǪxi=2

aaȃǿǪxi=0ǿDZȕ

xi yi n‘39&9‰>UR"O:DŠwGeGi"}Lvj XAV V JA1 ,.(64 20

K

NZGi

-3 _{-2 -1} 0 _{1 2} 3

45

50

55

x

y

y

_i

=

α

+

β

x

_i

+

ε

_i

=

y

ˆ

_i

+

ε

_i

yɠ £ŽrÂǞȋǷȄǞ§İrÂ

dependent (response) variable

$ǦȅǞOƒ

&ɠ ĊīrÂǞȋǷȄǞŪËrÂ

independent (explanatory) variable

$ǦȅǞSNPȃƌziȐŊÄóĀ

βɠ `“'Â

regression coefficient

εɠ î‘

residuals

ĜŃȃ/Ǫ

ĜŃǨȓȃƜǷȔ

yi

ˆ

y i=α+βxi

x

i

εi

αɠ <ćǞȋǷȄǞÂƦ

intercept, constant term

ĜŃȃy<ć

21

`“ɀɏɋɗȰȃţı÷ щ÷

The method of least squares

ε

_i

=

y

_i

−

(

α

+

β

x

_i

)

`“î‘ɠ

Ç\ɠ(dǞŴŒăŃƎȃ2\ɚ

SS

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=

ε

i 2

i n

∑

=

(

y

_i

−

α − β

x

_i

)

2 i

n

∑

Ç\ȃщI əщɚ:

∂SS_E

∂β =−2 (yi−α − βxi)xi i

n

∑

=0

∂SS_E

∂α =−2 (yi−α−βxi) i

n

∑

=0

a= _iyi n

∑

n−b _ixi n

∑

n=y −bx

b= ixiyi− n

∑

_ixi n

∑

_iyi n

∑

n xi 2₋ xi i n

∑

(

)

2

n i

n

∑

= i(xi−x )(yi−y ) n

∑

(xi−x )

2

i n

∑

n _ixi

n

∑

xi i n

∑

xi

2 i n

∑

# $ % % & ' ( ( a b # $ % & ' ( = yi i n

∑

xiyi i n

∑

# $ % % & ' ( ( ìŞÇĥ›

-3 _{-2 -1} 0 _{1 2} 3

45 50 55 x y yi ˆ

y i=α+βxi

x

i

εi

22

(aǿbȄαǿβȃ»+ɚ

K`“ȂȒȕšÙ

y

_i

=

u

+

β

_j

x

_ij

+

e

_i

ČĵŸș

ƒIǯǷ©l

1311

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əSNPsɚ

All materials can be downloaded from http://ricediversity.org/

K`“ ĿÚ

SNPsǩÓªȂ… əȋǮȂɉɕȾȳȰɕɣɚ

ǭȚȁȂǷǫǮȚƌzǩǣȕȃɣ

0e+00 1e+08 2e+08 3e+08

LD

ș¿ƏDZȕŜa

Ŝa GÚ

Əæ›ɠ Ŏï Ʈƿƾ

Əæ›ɠ ï ƿƾ

ķŁƖȃƌĚƜǷȔ ƿƾȃpF

Ɵbȃ;I ƿƾȃpF

ƟbȃûV ƿƾȃpF

ŎĆƋ³ǞĄƋ² ƿƾȃ®ĚpF

ƟbȩȜȭ ‰Ɵb Ǜ Ʈƿƾ

}IƋ³ ƿƾȃpF

ĪĆrĖč

ƮǤĪĆrĖč Ǜ 5!ĚȁƿƾȄ Ǟ ǯǨǯǞĪĆrĖȃ[ŻǾȄƿƾǩÍĚȂ Ʈȋȕ

ȦȽɊ9Ə= 9Ə=Ȅ®ĚȂľ½Ǧș°AǯǞŽ.Ȃ

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2

i n

∑

=

( ˆ

y

i

−

y

)

2

i n

∑

+

(

y

i

−

y

ˆ

i

)

2

i n

∑

(a) 5–Ç\

SSY

(a)

(b)

(c)

(b) `“Ǿ ŪËǮȖȕ

–Ç\ SSR

(c) î‘ȃ –Ç\

SSE

êȃȒǥȂ–Ç\ș;CǾǪȕɠ

Ŝa –Ç\ Ŏē™ –h–Ç _F+

`“

(b)

SSR 1 MSR=

SSR

MSR /MSE

î‘

(c)

SSE n - 2 MSE=

SSE/(n-2)

5!

(a)

SSY n - 1

FãȂȒȔǞ`“ȃÓª¨ãǩǾǪȕ

y

_i

y

ˆ

y

_i

yp

C(bm!am‘

62

ȃщI

J= (yi−α−βxi)

2

i=1

N

∑

əNňɚы÷ȂȒȕ`“ɀɏɋɗȰȃ»

y

_i

=

α

+

β

x

_i

+

ε

_i

ε

i

~

N

(0,

σ

2

)

ũ‘ǩ–h0Ǟ;Áσ2_{ȃìŞ;’DZȕǿňǦȕ}

y

_i

~

N

(

α

+

β

x

_i

,

σ

2

)

yȄ–h_ìŞ;’DZȕα+βxǞ;Áσ2ȃ

L=p(y1,y2,...,yN)=

exp{−(yi−α − βxi) 2_/2σ2_} 2πσ2 i=1

N

∏

=exp{− (yi−α − βxi)

2_/2σ2 i=1

N

∑

}

(2πσ2 )N 0.0 0.1 0.2 0.3 0.4

α+βx

i y_i

p(yi)=

1 2πσ2exp−

(yi−α − βxi)

2 2σ2 ' ( ) * + , ìŞ;’ȃĢ腙Ɨ W\ ˆÂ‹™ȄǞ

lnL=− 1

2σ2 (yi−α−βxi)

2

i=1

N

∑

−N

2log2πσ

2

ÑuI əы÷ɚ

∂lnL

∂β =− 1

σ2 (yi−α − βxi)xi i

n

∑

=0

∂lnL

∂α =− 1

σ2 (yi−α − βxi) i

n

∑

=0

ũ‘ǩ–h0Ǟ;Áσ2_ȃìŞ;’

Ȃ£ǥǿǪǞы÷ǿщ÷

ȃ»ɀɏɋɗȰȄŏDZȕ əũ‘ǩǞìŞ;’Ȃ£ȘȁǤm

VȄǞ¦DzǯȏŏǯȁǤɚ ₆₃