9 D 1 I - ' +8 * & P & G N ]Ö Fisheraiwata/biomet/...B P P üE× * & P & G N ]Ö:! o üjR!-4 -2 0 2 4 6 8 m QQ m qq QTL4G Ê º QQ qq Ð RÖ RÖ 4G Ê º AA aa 40 10 10 40-4 -2 0

!060310391!ɒŵxƊɓƪɏ!0560565!ɒČxƊɓ!

!

ȹȕȚɄȱɉȭȟȧ!ī8\!

ȔȪȦȘɐȦɇɎŝÖ�

2014/6/5!!!8:40-10:10!@1PƤ-ī4ũŁ}�

1!

ȔȪȦȘɐȦɇɎŝÖ!(associa5on!analysis)!ȔȪȦȘɐȦɇɎĝĦ!(associa5on!study)�

……T……C……A……G……T………………A…………A………�

•  ƈ�ŮûȇŅģĶÓǻUȂȎȍYģȇĴĻȑĎǝǶǗǮȎȋǷŜ�ǧȎȍDNApfǸŒċfpfƒǼƓ(ǡȋǗJ]ƈ�vǼß:ȑŢȃȍÄó!ɒ�Ƌ|ƥȑ¡ŖǸǨǺǝɓ!

……T……C……A……A……T………………A…………A………�……T……A……G……G……T………………A…………A………�……G……C……A……A……T………………C…………T………�……T……A……A……G……T………………A…………A………�……T……C……A……A……T………………A…………A………�……T……C……A……G……T………………A…………T………�……T……A……G……G……T………………C…………A………�

……G……C……A……G……C………………A…………T………�……T……A……A……G……C………………A…………A………�……T……C……A……G……C………………C…………T………�……T……A……A……A……C………………C…………A………�……T……C……G……G……C………………A…………T………�……G……A……A……G……C………………A…………A………�……T……C……A……A……C………………C…………A………�

YģA�

YģB�

YģC�

:�

:!:�

DNApf�

ůĖȰɐȫ�

%ǟǾǗ200Yģ�Ǽ!ē~¯¬£YģǼBR�

70/80�

23/120�

ƎĖȰɐȫ�

Œċfpf�

%ǟǾǗ200YģǼ�Ŏ�!

2!

�7>BE3=��(^U)�7>Bcg'ts�/f_(��fO'"�#2;84�8CF1m+/�

� �1-"��r\k���$nS`�

��1-"���r\k���$nS`�

� �1-"��r\(�d](uMh�

T�

��1-"��r\(�d](uMh�

C�

ÒÆǼȝɐɍɐȲ!•  ƈ�Ůû!•  ȔȪȦȘɐȦɇɎŝÖǸ�ÔǼQTLŝÖ!•  žƏ��ő!•  ȡȷɃɍȕȲȔȪȦȘɐȦɇɎĝĦɒGWASɓǸ+Ŕƈ�vȔȪȦȘɐȦɇɎĝĦ!

•  χ2ßzǻȊȍćĩ£ßz!•  FisherǼèĞĞĊßz!•  H\�;Ö!•  ƙ^áŽǻȊȍ.Ɩ£!•  ī1ģǼƁťǗī2ģǼƁťǗ.Ɩ£ĊǗ.ƕ£Ċ!•  .ĔŗĊǗÐ�.ĔŗĊ!

3!

ƈ�Ůû!•  ɖ�*Ǽƈ�vǢǜȍčąǷǗQƈ�v�ǻǠǝǶ3ģƢǼƈ�vfɒAA,!Aa,!aaɓǢǜȍjRǗ330,000żȌǼƈ�vǼĹRǬɒƈ�vfɓǢłǟȋȎȍ!

•  ǦǼȊǞǻƈ�vǼĹRǬǻȊȌč¨ǧȎȍŮûǼNŇ£ǽāƔDZǢǗ�ÄǷǗėĖǻŗRdzǰĆzǼƈ�vfȑªǻ4ȎȍǦǸǽƝ�ǻƛǨǝ!

•  ǦǼȊǞǺŜÿǡȋǗrĂǻwcǪȍǗǜȍǝǽǗƐ�ǼYģ»ŋȇĝĦƑĔǼ¨×ǸǨǶ ȋȎǰǗĆzǼƈ�vŀǼĹRǬǷǜȍ*"ȇĴĻɒ%ǟǾǗ»ŋYģǗcÔYģǗÜgÞąǼŸľƍčģǗÃ#ąǻǺȌǞȍNŇ£Ǽǜȍƍčģɓǽƈ�ĖǺǏŮûǐǸȃǺǧȎǗǮǼ´ķɏLƙɏ)wǢŐȐȎǶǝȍ!

ŅģxŴ6ɒ2005ɓgƣƤǖȊȌ»n!4!

ȬȕȢɎǼÛ�nĒ!

ū�

Pictured!by!Dr.!Satoshi!Niikura!

âǙǺÛ�ȑȆdzǰȬȕȢɎǼYģɏĴĻǢǗǮǼYģ»ŋǼéOǼ�ǷǗöŭŃǼ[tȇD�Ć£ǻRȐǬǶǗ#:ǧȎǶǣǰ� 5!

|ƥ�ƋǻďÔǪȍ;ƚƙ^ȑĎǝȍ!�ÔǼQTLŝÖ�

•  |ƥ�ƋǻďÔǪȍ;ƚƙ^ȑĎǝǶǗDNAɂɐțɐǼpfǸŒċfpfƒǼƓ(ǡȋQTLȑɂȭȼɎȠ�

•  śƒǻȃȋȎȍnĒǨǡŝÖǷǣǺǝɒŝÖ�ŬəĈɓ�•  �Ƌ|ƥȑŖǪȍǰȅǗð�£ÞąǺǹǷǽʃǢǡǡȍɒʃĖAĵɓ�•  *"ȤȕȨǼqǣǺÞąǷǽǗ�ǝajǢ¡ŖɒħƒĖAĵɓ�•  ĿǼ¶zij�Ǣ¡ǫǨȆƦǤǺǝɒŝ1�ǼƔĐɓ�

×!

6!

pâǺYģɏĴĻĬȑʵĎǝȍ!ȔȪȦȘɐȦɇɎŝÖ!

•  ƈ�ŮûĬǻUȂȎȍYģɏĴĻȑʵĎǝǶǗDNAɂɐțɐpfǸŒċfpfƒǼƓ(ǡȋǗƓƈ�v�ɒȂǰǽSNPɓȑß:�

•  ÓÁ7ǻȃȋȎȍâǙǺ�ůnĒǢŝÖ�ŬǸǺȍɒŝÖ�Ŭə�ɓ�•  ƈ�ŮûȢɋȟȦɇɎȇŅģƁĢǻǜȍĴĻǺǹȑõĎǷǣȍǘ!ȂǰǗǮȎȋĴĻǷLƙǧȎǰÅwǼȰɐȫȑÏEõĎǷǣȍɒÊħƒǼįĵɓ�

•  ÓÁǻȊdzǶǽǗƦŝ1�ǷǼŝÖǢǷǣȍ�

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!

�khpf(single!nucleo5de!polymorphisms:!SNPs)ŝÖǢ!ȔȪȦȘɐȦɇɎŝÖȀǼƂȑ°ǝǰ�

GeneChip!Rice!44K!SNP!Genotyping!Array!•  44,100!SNPs!

!(10kbíǻ1!SNP)�

Tung!et!al.!(2010)!Rice!3:205-217�8!

QTLŝÖ�

�½Ǽśȑ�ƋǨǗ!ǮǼ��ȑŝÖ�

Čďə!śƒǼƄǝɒŌǼƄǝɓǽ;ǡdzǶȆǗţĸǺDNApfɒȦɂȦɂɓȂǷŗ;ǥȋȎǺǡdzǰ�

ŝ1�Ǣ!ǝǗÓÁ#ȌǻʃǢǡǡȍ� ŝ1�ǢƦǝǗ�ƋȑŐǞ¡ŖǢǺǝ!ǰDZǨǗƈ�ĖņËǼƄǝǻȊȍ.Ɩ£ǢčǩÉǝ�

ȡȷɃɍȕȲ!ȔȪȦȘɐȦɇɎ!ŝÖɒGWASɓ�

p½Ǽ*"ɒYģɓȑ!ǮǼȂȂŝÖ!

�

Čďə!YģƒǻŗȋȎȍţĸǺDNApfɒȦɂȦɂɓǢŗ;ǥȋȎȍȊǞǻǺdzǰ�

Morrell!et!al.!(2012)!Nature!Review!Gene5cs!13:85�

�ÔǼQTLŝÖ!vs.ȔȪȦȘɐȦɇɎŝÖ!

ȔȪȦȘɐȦɇɎŝÖǼ@ÿǸåÿ!

ȔȪȦȘɐȦɇɎŝÖǽǗƈ�ŮûǻUȂȎȍpâǺnĒǼŝÖǻƆǨǶǝȍ�

10!

�ÔǼQTLŝÖ% ȔȪȦȘɐȦɇɎŝÖ%

ȔɉɊǼū�ǧ! !! Ʀ!

¡ŖǺɂɐțɐ½! �! p!

�Ƌ|ƥǼ¡Ŗ£! Ŗ! �Ŗ!

ŝ1�! !! Ʀ!

ȰȥȕɎǧȎǰɂȭȼɎȠƙ^!

�ŊǻYes! No!

ƈ�ĖņËǼƄǝǻ�Ǫȍ¦M£!

�! q!

žƏ��őɒlinkage!disequilibrium:!LDɓ�

ġ3ɒCuŃɓǼÙŌ"!

p½Ǽ�ǷčǩǰŸǟ!

ċYģǼÙŌ"!

!�

!�

!�

!�

��őɒŸǝɓ�

!�

�őɒƅǝɓ�

!�

!�

!�

ÙŌ"ƒǼ�¸ǟǻȊȌǗ��őǽųƚǻ&wǨǶ!�� 11!

žƏ��őɒlinkage!disequilibrium:!LDɓ�

ġ3ɒCuŃɓǼÙŌ"!

p½Ǽ�ǷčǩǰŸǟ!

ċYģǼÙŌ"!�¸ǟǻȊȌǗ��őǽųƚǻ&wǨǶ!��

J]ƈ�vß:ǼJČ�

J]ƈ�vɒQTLɓ!

Œċf�

ʵĖ!ȔȪȦȘɐȦɇɎ!ɒƈ�ĖºƋɓ�

ÙŌ"�

(Modified!from!Balding!2006)�

ɒʵŜ�ǷǣǺǝɓ!

ǦǼȔȪȦȘɐȦɇɎȑß:ǪȍǦǸǷǗJ]ƈ�vǼŸ/ǻǜȍSNPɂɐțɐȑĨǣçȅȍ�

�ǝ!Ɲćĩ£!

(žƏ��ő)!

SNP!ɂɐțɐ�

�ǝƒµĖ!ȔȪȦȘɐȦɇɎ�

�ǝƒµĖ!ȔȪȦȘɐȦɇɎ�

�ǝ!Ɲćĩ£!

(žƏ��ő)!

SNP!ɂɐțɐ�

13!

žƏ��őǸǮǼ²ã�

(Rafalski!2002ȊȌ»nɓ�

●B ●b

●A pAB pAb pA

●a paB pab pa

pB pb

€

r2 =D2

pA pa pB pb(●●ȑ1,●●ȑ0ǸǨǰǸǣǼ!ęƓ(½Ǽ��)!

€

D = pAB − pA pB= pAB pab − pAb paB

€

r2 =0.252

0.5 × 0.5 × 0.5 × 0.5=1

ABǢćĩǼjRǻ!Ð�ǧȎȍABǼƠ��

|ƘǻŜ�ǧȎǰ!ABǼƠ��

€

r2 = 0.1024

€

r2 = 0

žƏ��ő� žƏ�ő�

ƈ�v�A�ƈ�v�B�

14!

ß:Ǽ�ÉǧǸŝ1�ǼȱɋɐȲȚȽǖǖǖǖǖǖǖǖ�

•  žƏ��őǼĢ�ǢƦǝjRǽǗ�½ǼɂɐțɐǷȔȪȦȘɐȦɇɎȑß:ǷǣȍǢǗŝ1�ǽ!ǝǓ�

•  žƏ��őǼĢ�Ǣ!ǝjRǽǗŝ1�ǽƦǝǢǗß:ǻǽp½Ǽɂɐțɐȑ¡ŖǸǪȍǓ�

(Rafalski!2002ȊȌ»n)!

15!

ÞąģǻȊȍLDǼĢ�ǼƄǝ�

Gupta!et!al.!(2005)ȊȌ»n�

ǖ� �Ƌâ�� ƸƷǼİ_�

ȦɌȕȵȳȨȳ� ňë£� ưƲƮǂƼ

ȕȶ� ňë£� ƯƮƮƬưƮƮǂƼ

ȚȚɃȞ� ňë£� ƯƮƬưƮƽƹ

ȢɃȞ� ňë£� ƯƮƬưƮƽƹ

ȪɊȜɃ� ňë£� ƴƪƱƽƹ

ȬȕȨ� ňë£� ƵƪƲƮǂƼ

ȱȖɅɌȢȦ� �ë£� ƮƭƲƬƳƭƮǂƼ

ȚȖȦɆȖȱȖȻɒƺdžLjnjƻǎƪljLJLjNjƽƿƫ �ë£� ɝƯƮƮƬưƮƮƼLJ

ȯɐȬɂȮɒǃdžƼǃdžǃǃǎƪLJǁDžƿƫ �ë£� ƯƮƮƬƯƲƮƮƼLJ

�ŊǻǗ!•  ňë£ǖɛǖ�ë£!•  ƙ^ȤȕȨǖǖqǖɚǖ�!!ɒÏEǺ�¸ǟɒŸǟǢčǩȍ�¸ǟɓǽǗȿȯɌµR�ǻ&wǪȍɓ!16!

ÓÁǻȊȍLDǼĢ�ǼƄǝ�

(Zhu!et!al.!2007)!

ÜgģȇÜgYģǷǽǗCuŃE×ǗƇ­ǻȊȍɀȱɊȶȭȟǗù½;œǼä�Ǽ�ǺǧǡȋǗƍčģȇcÔYģǻîȁǶƦǝžƏ��őɒLDɓǢŗȋȎȍjRǢpǝ�

ĆǻǗŸ�YģǡȋǺȍȊǞǺƈ�ŮûȢɋȟȦɇɎǷǽǗǮǼ0TǢƦǝ�

→ǖÓÁȑǞȂǤƇǿǦǸǷǗLDȑŨ¾ǪȍǦǸȆǷǣȍ�

ǖǖǖƦ��ǖǖǖ↑��žƏ��ő��ǖǖǖ↓!!ǖǖǖ!�

17!

ȔȪȦȘɐȦɇɎǼß:ə!țȯȣɉɐȰɐȫǼjR!

!!ɂɐțɐ!

ē~!¯¬£!

ē~!¦M£!

!AA!

ɔɔ! ɗ!

!aa!

ɖ! ɘ!

ǦǦǷǽǗňë£ǼjRȑłǟǶǝȍ!

�ů!ȔȪȦȘɐȦɇɎǢǜȍjRə!!%ǟǾǗ¯¬£ǼYģǷǽǗɂɐțɐƈ�vfAAǼƠ�ǢǗaaǻîȁǶƦǤǺȌǗ¦M£ǼYģǷǽǗǮǼŻǻǺȍ!

¦M£Ǹ¯¬£ǼƒǷǹǼĢ�Ơ�Ǽ�ǢǜȎǾ!ǚȔȪȦȘɐȦɇɎǢǜȍǛǸ>ÂǷǣȍǼDZȏǞǡɜ!

ĻşĖßzə%ǟǾǗχ2�ßzȇFisherǼèĞĞĊßzɒFisher’s!exact!testɓ!

18!

χ2ßzǻȊȍćĩ£ßz!ē~¯¬£(R)� ē~¦M£(S)�

AA� f11!!!!!!(11)� f12!!!!!!(4)� f1.!!!!!!(15)�

aa� f21!!!!!!(3)� f22!!!!!!(7)� f2.!!!!!!(10)�

f.1!!!!!!!!(14)� f.2!!!!!!!(11)� n!!!!!!!!(25)�ē~¯¬£ǷǜȍĞĊǖƪƪƪƪƪp(R)!=!f.1!/!n!=!14!/!25!=!0.56!ē~¦M£ǷǜȍĞĊƪƪƪƪƪƪƪƪp(S)!=!f.2!/!n!=!11!/!25!=!0.44!ɂɐțɐǢAAǷǜȍĞĊƪƪƪƪp(AA)!=!f1.!/!n!=!15!/!25!=!0.60!ɂɐțɐǢaaǷǜȍĞĊƪƪƪƪƪp(aa)!=!f2.!/!n!=!10!/!25!=!0.40�

ȆǨǗē~¦M£Ǹɂɐțɐƈ�vfǢćĩǺȋǗ!QȩɊǼÐ��½ǽQĞĊǼĤǻļ½ȑǡǥǰȆǼǸǺȍǖ↓�

RǡǴAAǖǖǖǖn!×!p(R)!×!p(AA)!=!25!×!0.56!×!0.60!=!8.4!RǡǴaa!!!!!!!!!!!!n!×!p(R)!×!p(aa)!=!25!×!0.56!×!0.40!=!5.6!SǡǴAAǖǖǖǖn!×!p(S)!×!p(AA)!=!25!×!0.44!×!0.60!=!6.6!SǡǴaa!!!!!!!!!!!!n!×!p(S)!×!p(aa)!=!25!×!0.44!×!0.40!=!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

�ā�ŦǼȆǸǷňď�!(r-1)(c-1)!Ǽχ2;�ɒrǽŐ½Ǘcǽ=½ɓ�

5%ïüǷÏ¥ɒćĩǷǺǝɓ!

€

χ0.012 (1) = 6.63 > χ2 = 4.57 > χ0.05

2 (1) = 3.84

ǦǼÄóǽǗ�½Ǽ�Ǻǝɒ5ÑúɓȩɊǢǜȍjRǽ�èĞǷǜȍǦǸǢĜȋȎǶǝȍɑɑ�

;BŒ!

19!

ǰDZǨǗæǼÿǻô¥ǨȊǞɑ�

•  ƇǾȎǰȤɎȾɊɒYģɏĴĻɓǢǹǼȊǞǻǨǶƇǾȎǰȆǼǡɜ!

•  ā#ĀɒrandomɓǻƇǾȎǰȆǼǷǺǥȎǾǗǮǼǦǸȑł§ǨǰɅȰɊȑĎǝǺǥȎǾǺȋǺǝ!

20!

ɂɐțɐǼE×�

ȔȪȦȘɐȦɇɎŝÖ:!ƎĖ�ůǼjR!

-4 -2 0 2 4 6 8

mQQ mqq

QTL

QQ qq

AA

aa

40 10

10 40

-4 -2 0 2 4 6 8 -4 -2 0 2 4 6 8

mAA

-4 -2 0 2 4 6 8

maa

yi = u+β j xij + ei

ɂɐțɐƈ�vfxǸŒċf,yǼƒǼƓ(ȑĘĽǷ\�Ǫȍ!

-0.2 0.2 0.6 1.0

-20

24

6

Marker genotype

Phenotype

*"iǢAAǼǸǣxi=2!aaǼǸǣxi=0ǸǪȍ!

xi

y i

l�A�5�GoYO1wI%�#�HRqi(tXta1T!�(%p�QK'&.,��

Ve)LW$�&���LW$�/()Je(?:<6DB ���

21!ǖǖǖ0!!!!!!!!!!!!!!!!!!2!!!!!!!!�

Œċf,�

H\�;Ö!

-3 -2 -1 0 1 2 3

4550

55

x

y

€

yi =α + βxi + εi = ˆ y i + εi

yəǖ !��n½ǗȂǰǽǗ¢ĭn½!ǖǖ !dependent!(response)!variable�

%ǟǾǗLƎ�

�əǖ !ćĩn½ǗȂǰǽǗŦÈn½!ǖǖ !independent!(explanatory)!variable�

%ǟǾǗSNPǼƈ�vfȇńÁïü!

βəǖ !\�(½!ǖǖ !regression!coefficient�

εəǖ !ê�!ǖǖ !residuals�

ĘĽǼ0ǣ�

ĘĽǡȋǼƗǰȌ�

€

yi

€

ˆ y i =α + βxi

€

xi€

εi

αəǖ!<ăǗȂǰǽǗz½Ɵ!ǖǖ !intercept,!constant!term�

ĘĽǼy<ă�

22!

\�ȺɈɄɐȫǼşĮóǖÍ���ó!The!method!of!least!squares�

€

ε i = yi − (α + βxi)\�ê�ə�

ê��ÄXəƪ(`�ǗŰŌÿĽƊǼ2�Xɓ�

€

SSE = ε i2

i

n

∑ = (yi −α − βxi)2

i

n

∑ê��ÄXǼÍ�GǖɒÍ���ɓ:�

€

∂SSE∂β

= −2 (yi −α − βxi)xii

n

∑ = 0

€

∂SSE∂α

= −2 (yi −α − βxi)i

n

∑ = 0

€

a = yii

n∑ n − b xii

n∑ n = y − bx

€

b =xiyi −i

n∑ xii

n∑ yii

n∑ n

xi2 − xii

n∑( )

2

ni

n∑

=(xi − x )(yi − y )

i

n∑

(xi − x )2i

n∑

€

n xii

n∑

xii

n∑ xi

2i

n∑

#

$

% %

&

'

( ( ab#

$ % &

' ( =

yii

n∑xiyii

n∑

#

$

% %

&

'

( ( èŘÄĢ��

-3 -2 -1 0 1 2 3

4550

55

x

y

€

yi

€

ˆ y i =α + βxi

€

xi€

εi

23!

(aǸbǽαǸβǼ¶z,ɓ�

H\�ǻȊȍŝÖ�

yi = u+β j xij + ei

ĉIJ�ȑ!zƎGǨǰ¤i�

1311Ǽ�khpfɒSNPsɓ!!All!materials!can!be!downloaded!from!hkp://ricediversity.org/!�

H\�ƪĺ×�

ǜȌǸǜȋȈȍSNPsǢÏ¥ǻ…!ɒȂǧǻɂɎȸȭȫɎɜɓ!ǦȒǺǻǰǤǧȒƈ�vǢǜȍǼɜ�

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

05

1020

30

position (bp)

−log

10(p

)

LDȑºƋǪȍŖ]�Ŗ]� E×�Ÿǟ'� ƦǝŸǟ'ǖǔǖ!ƸƷ �Ƌâ�əǖňë� ƦƸƷ �Ƌâ�əǖ�ë� !ƸƷ ĴĻƒǼƈ�ĖƗǰȌ� ƸƷǼlD�ƙ^Ǽ;G� ƸƷǼlD�ƙ^Ǽ÷R� ƸƷǼlD�ňĂƇ®Ǘ�ĀƇ­� ƸƷǼ�©ĖlD�ƙ^ȤȕȨ� �ƙ^ǖǔǖƦƸƷ yzGƇ®� ƸƷǼlD�ĨĂnĒĊ�

ƦǝĨĂnĒĊǖǔǖ5"ĖǺƸƷǽ!�ǗǨǡǨǗĨĂnĒǼWŶǷǽƸƷǢ�ÊĖǻƦȂȍ�

ȡȷɃ9Ƌ=ƪ� 9Ƌ=ǽ�©ĖǻŸǟȑ«AǨǗŸ/ǻǠǥȍƸƷȑlDǧǬȍ�

ȘȼȧȫȦȧ� ƸƷȑlDǖɒƶdžƬƻƾƻLJNJƿƾƪǀƿDžƿƪƽdžDŽLJǃƿǍǺǹƫ�

ĞĊĖE×� ƸƷǽlDǗȂǰǽù��

žƏ��őɒLDɓǽǗâǙǺŖ]Ǽ�ƞȑǞǥȍ�

ɒRafalski!and!Morgante!2004ǗOraguzie!et!al.!2007)! 26!

ȔȪȦȘɐȦɇɎŝÖǼZơÿ:!;ƙ^áŽǻȊȍ.Ɩ£�

!  �…)suppose)that)a)would4be)gene7cist)set)out)to)study)the)“trait”)of)ability)to)eat)with)chops7cks)in)the)San)Francisco)popula7on)by)performing)an)associa7on)study)with)the)HLA)complex.)The)allele)HLA4A1)would)turn)out)to)be)posi7vely)associated)with)ability)to)use)chops7cks)…)because)the)allele)HLA4A1)is)more)common)among)Asians)than)Caucasians.”!!Lander!and!Schork!(1994)�HLA��Human Leukocyte Antigen

27!

ǺǭǗƙ^áŽǢ.Ɩ£ȑčǩȍǡ?�

Yģŀ!1�

Yģŀ!2�

ƑōÐ�

Çǝ� ƀǝ�

(Modified!from!Balding!2006)�28!

;ƙ^áŽǸĉIJ�ǼƓ(�

•  IndicaYģɒþŌɓǻǽĸƐǝȫȕȾǢpǤǗJaponicaYģɒĕɓǻǽ��ǼȫȕȾǢpǝ�

;ƙ^ȑł§Ǩǰ\��

yi = u+β j xij + vkqikk=1

K

∑ + ei

1.0

0.0

0.5

;vɂɐțɐ¤iȑȆǸǻBayesialȟɈȧȫɉɎȠǻȊȌǗQYģɏĴĻǼƈ�ĖņËȑ¶zɒStructureŝÖǖPritchard!et!al.!(2000)!Gene5cs!155:945–!959ɓƪ�

;ƙ^ǻȊȍŒċfǼƄǝȑVLǧǬȍ�

4YģɏĴĻǼƈ�ĖņË�

6ǴǼ;ƙ^ɒK=6ɓǻű]ǪȍȡȷɃǼBRɒŨɓȑŒǪǘ!%ǟǾǗ�ǡȋ2đėǼYģǽǗ!qi1 = 0.78, qi3 = 0.32,!ǮȎ�oǽ0�

;ƙ^ȑł§Ǩǰ\�ƪĺ×�

�ǨDZǥǗȂǨǻǺdzǰɜ�

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

05

1015

2025

position (bp)

−log

10(p

)

#ąǻȃȋȎȍƈ�áŽ�

pâ£ǢƦǤǶȆǗǹǼĴĻƒȆSǩųƚǷǜȎǾ.Ɩ£ǽčǩǺǝǘ!!ǨǡǨǗ|Ƙǽ…! ;ƙ^ǢǜdzǰȌǗ! �ĴáŽǢǜdzǰȌǪȍǘ!

→ǖ.Ɩ£ȑčǩȍJ]ǸǺȍ� 32!

;ƙ^Ǹ�ĴáŽȑł§Ǩǰ\��

ŏľƓ(ƪA ȑ!ɅȰɊǻĹȃŷȄ!

•  Yu!et!al.!(2006)!Nat.!Genet.!38:!203�

yi = u+β j xij + vkqikk=1

K

∑ +αi + ei

a ~ N(0, Aσα2 )

var(αi ) = a(i, i)σα2

*?ǻÌǤǸ�

cov(αi,αi ' ) = a(i, i ')σα2

;ƙ^Ǹ�ĴáŽȑł§Ǩǰ\�ǖĺ×�

ę�ǗȂǨǻǺdzǰɑ!→ǖƆ<ǺĻşɅȰɉɎȠǢƌŖɑ�

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

01

23

4

position (bp)

−log

10(p

)

1SNPíǻŝÖǪȍǦǸǼåÿə!�Ǽƈ�vǻȊȍ¹��

SNP�

ǜȍSNPǻɂȕȟȑšĿǨǶ!ƈ�vAɒțȘɊAɓǼj©ȑǴǣǸȅȊǞǸǨǶǝȍǼǻǗ!?Ǽƈ�vBɒțȘɊBɓǼ�ƞɒƨǣmɓǢƉƧǷ!ƈ�vǼ ĿȇE×ǢèĞǻ¶zǷǣǺǝ�

��Ǖ! �Ǖ!

țȘɊB� țȘɊA�

35!

ƈ�vA�ƈ�vB�

5ǶǼSNPsȑSÊǻŝÖǪȍ!ɅȰɉɎȠ�

SNP�

ƈ�vA�

5ǶǼj©ǻɂȕȟȑšĿǪȍǦǸǷǗ!�Ǘŕ½Ǽƈ�vɒțȘɊAǸBɓǼ ĿǸE×ȑ!

SÊǻèĞǻ¶zǪȍ!

��Ǖ! �Ǖ!

țȘɊB� țȘɊA�

36!

ƈ�vB�

ŕ½Ǽƈ�v�ȑSÊǻł§Ǩǰ\�!Bayesiann½Ƈ®�

5ȡȷɃ�ǼQTLǼE×ȑ!SÊǻɅȰɊGǪȍ�

yi = u+ β jγ j xijj=1

J

∑ + vkqikk=1

K

∑ +αi + ei

•  Iwata!et!al.!(2007)!Theor!Appl!Genet!114:1437–1449,!Iwata!et!al.!ÑĔŒƪ�

γ j =10

!"#

jđėǼSNPȑ!!!!!!ɅȰɊǻUȅȍ�

jđėǼSNPȑ!!!!!!ɅȰɊǻUȅǺǝ�γ j ~ B(1, pj )

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

0.0

0.2

0.4

0.6

0.8

1.0

position (bp)

Post

erio

r pro

b. o

f QTL

Bayesiann½Ƈ®ǖĺ×�

ę�ǗȟɉȔǻǺdzǰɑ!→ǖĻşɅȰɊȑ�sǪȍǦǸǻȊȌ!ǖǖȦȠȳɊȑÈěǻǸȌDZǬȍ�

γ jǼ��ĞĊ�

ß:ǧȎǰȼɐȟǽ…�

Chr.!3�

GS3�

63!kb�id3008333�

546!kb�

id3008127�

Chr.!5�

qSW5�

id5002699�

1.0�0.95�

66!kb�

0.88�

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

0.0

0.2

0.4

0.6

0.8

1.0

position (bp)

Post

erio

r pro

b. o

f QTL ÅĜǼƈ�v!

ǼŸ/SNPsDZdzǰ�

Q,!KǼşĮó!

•  Qə!–  StructureŝÖ!(Pritchard!et!al.!2000)!–  ¨;;ÖɒEIGENSTRAT,!Price!et!al.!2006)!– pæ2��óɒZhu!and!Yu!2009)!

•  K:!– ɂɐțɐpfǻhǵǤŸľ(½ɒLoiselle!et!al.!(1995),!Ritland!et!al.!(1996),!SPAGeDi!sotware)!

– ȔɉɊȦȗȔɉɎȠĊɒZhao!et!al.!2007ɓ!– ĴŪǡȋŸľ(½ȑşĮ!

!40!

ƆĎ%ɓȦɌȕȵȳȨȳǻǠǥȍGWAS!Atwell!et!al.!(2010)!Nature!465:!627!

ƙ^áŽȑ!ł§!

ƙ^áŽȑ!ł§ǨǺǝ!

→ǖaǷǽǗƑōƓžƈ�vǷpǤǼɂɐțɐǢß:ǧȎǰɒp;ǗpǤǢ.Ɩ£ɓ!

ÈěǺȔȪȦȘɐȦɇɎǢß:ǧȎǺǝ�ůȆǜdzǰǢǗ�ǻǽǗȟɉȔǻƓƈ�vǼ ĿǢß:ǧȎȍjRȆǜdzǰ! 41!

ȔȪȦȘɐȦɇɎŝÖǻǠǥȍ!.Ɩ£ĊǗ.ƕ£ĊǗ.ĔŗĊ!

J]ƈ�vǸǨǶ%ß:ǧȎǺǝ%

J]ƈ�vǸǨǶ%ß:ǧȎȍ%

Ò�ǽƕ£!ɒJ]ƈ�vǷǺǝɓ!

A! B!(īɔģǼƁťɓ!!

Ò�ǽƖ£!ɒJ]ƈ�vǷǜȍɓ!

C)(īɕģǼƁťɓ! D!

.Ɩ£Ċɒfalse!posi5ve!rate:!FPRɓ=!B!/!(A!+!B)!!!.ƕ£Ċɒfalse!nega5ve!rate:!FNRɓ=!C!/!(C!+!D)!!!.ĔŗĊɒfalse!discovery!rate:!FDRɓ=!B!/!(B!+!D)!

Ò�ǽƕ£ǺǼǻǗƖ£ɒJ]ƈ�vɓǸǨǶß:ǧȎȍBR�

Ò�ǽƖ£ɒJ]ƈ�vɓǺǼǻǗƕ£ǸǨǶß:ǧȎȍBR�

Ɩ£ɒJ]ƈ�vɓǸǨǶĔŗǧȎǰȆǼǼ�ǼǗȴȩɅȷɒƕ£ɓ!ǼBR�

.Ɩ£ĊǸ.ƕ£ĊǽȱɋɐȲȚȽǼƓ(ǻǜȍ!ǨǰǢdzǶ!

.ĔŗĊȑ�zǻȢɎȱɌɐɊǪȍÄóȆ³ȋȎȍ! 42!

ȕȶǼĉIJ�ǼȔȪȦȘɐȦɇɎŝÖ�

•  ȕȶ293YģɏĴĻǼĉIJ�ȑȽɐɉȘŠŹvȑĎǝǶzƎG!

•  ȔȪȦȘɐȦɇɎŝÖǼĺ×Ǘ5ț©ǻE×ǼqǣǺƈ�v�ȑß:!

•  ŻȽɐɉȘn¸ǻȊdzǶǗß:ǧȎǰƈ�v�ǼE×ȑřŚĖǻĞŤǷǣǰ�

Iwata!et!al.!(2010)!Mol!Breeding!25:203� 43!

ÆÒȳȦǼȔȪȦȘɐȦɇɎŝÖ�

•  ȳȦǼQTLŝÖǻǽƐǝ�ÎǸ�ǝbdȑ¡ŖǪȍ!

•  ǮǦǷǗÅwǼYģȑÓÁǸǨǶǗȔȪȦȘɐȦɇɎŝÖȑŐdzǰǘŒċfȰɐȫǻǽŅģǺǹȑżǩǶÅǻLƙǧȎǶǝǰȆǼȑĎǝǰǘ!

•  ȔȪȦȘɐȦɇɎŝÖǼĺ×ǗLĥÐǸƩÀē¯¬£ǻǴǝǶǗƓǪȍƈ�v�Ǣß:ǧȎǰ!

•  ß:ǧȎǰƈ�v�ȑ?ǼªìǷĞŤǨǰĺ×ǗǝǫȎȆ.Ɩ£ǷǽǺǡdzǰǘ�

Iwata!et!al.!ɒÑĔŒɓ�

DNAɂɐțɐȑĎǝǶLĥÐȇƩÀē¯¬£ȑEĊȊǤƇ­ǪȍǦǸǢNŇǸǺdzǰ�

44!

ȂǸȅ!•  ȔȪȦȘɐȦɇɎŝÖǽǗpâǺnĒȑUȄYģȇĴĻȑǮǼȂȂĎǝǶǗŒċfnĒǻƓǪȍƈ�vǼß:ȑŢȃȍÄóǷǜȍ!

•  ȔȪȦȘɐȦɇɎŝÖǻǽžƏ��őǸǝǞċŬǢJ]ƈ�vǼß:ǻ@ĎǧȎȍ!

•  žƏ��őǼĢ�ǽǗčąģȇYģŀǻȊdzǶĒǺȍ!•  žƏ��őǽǑĚǼžƏǒ�oǼŖ]ǻȊdzǶȆčǩȍǘǸǤǻǗƙ^;GǻȊȍžƏ��őǽǗȔȪȦȘɐȦɇɎŝÖǻǠǥȍ.Ɩ£ĊȑƦȅȍǼǷô¥Ǣ¡ŖǷǜȍǘ!

•  ƈ�ĖņËȑł§ǨǰȔȪȦȘɐȦɇɎŝÖǻȊȌ.Ɩ£ȑ«ǟȍǦǸǢǷǣȍ!

•  ��ǽǗDNApfŝÖǢȂǪȂǪƦEĊǻŐǟȍȊǞǻǺdzǶǝǤǘǮȎǻ�ǝǗȔȪȦȘɐȦɇɎŝÖǽǗ�ÔǼQTLŝÖǼ�ÿȑŔǞǗƌŖǺƈ�ŝÖóǸǺdzǶǝǤǸłǟȋȎȍǘ!

45!

�ſǼ�8�

•  �ſǸǝǞȊȌǽǗ3ſǗ3ǙſǼ�8ǷǪǘ!

•  žƏŝÖǗžƏd`#¨ǗQTLŝÖǻǴǝǶţǨǤŦÈǧȎǶǝȂǪ!

•  òǨǶıHǺÒǷǽǺǝǷǪǢǗXÌǼ�ǷǽǗ�Ìǻǽ�ȐȌǢǷǣǺǝÒǸǺdzǶǝȂǪ!

•  :ĄĠ:%Õ�qx:Ą�ƪ(2000/01)%

•  ISBN110:%4130602063%•  ISBN113:%97814130602068!

46!

hkp://www.amazon.co.jp/�

ȹȕȚɄȱɉȭȟȧī8\ǖ�ɋɁɐȱŧơ!

!!

1.  ǜȍňë£ǼÞąƙ^ǡȋȤɎȾɉɎȠǧȎǰ100*"ǻǴǝǶǗ2ǴǼɂɐțɐƈ�v�A,!BǻǴǝǶŨÚǨǰĺ×Ǘƈ�vfAABB,!aaBB,!AAbb,!aabbǷǜȍ*"ǢǗǮȎǯȎǗ40,!10,!10,!40*"Ŝ�ǧȎǰǘǦǼƙ^ǻǠǥȍƈ�v�ABƒǼžƏ��őǼĢ�ɒD�r2ɓȑñȅǶ�ǧǝǘ!

2.  �ǼŜ�ĺ×ǡȋǗɂɐțɐABƒǽćĩɒžƏ�őɓǷǜȍǸŞǟȍǷǨȉǞǡɜǖɂɐțɐABƒǼćĩ£ǻǴǝǶǗχ2�ßzȑĎǝǶßzǨǶ�ǧǝǘ!

47!

ɋɁɐȱǼ·:ó!

ɚ·:Ǽ�Äɛ!ɄɐɊǼÒ¿ǗȂǰǽǗPDFȇMS-WordȽșɐɂȭȱɒǷǣȎǾPDFǻǨǶ�ǧǝɓǼȽȓȕɊǸǨǶ#¨ǨǗeɄɐɊǻø�ǨǶ[email protected]!{ǻźdzǶ�ǧǝǘ!!!ɚ;Ǝɛ!Ćǻ²zǽǨȂǬȒǘ!!!ɚÐƔɛ!2014�6Î12ÆȂǷ!

48!

ɒKłɓFisherǼèĞĞĊßz!Fisher’s!exact!test!

•  �ā�ŦǢèǨǝjRǻǗŜ�ǧȎǰ�Ŭȇ“ȊȌàĪǺ”�ŬǢčǩȍĞĊȑʵĖǻşĮǪȍǘ!

•  ǮǼĞĊǢ�ǧǝjRǻǽǗ�ā�ŦǼȆǸǷǽčǩǻǤǝ�ŬǢŜ�ǧȎǰǦǸȑğǪǘǮǦǷǗ�ā�ŦȑÝIǨǶǗ�ĩ�Ŧȑ³®Ǫȍǘ!

•  ǮǼĞĊǢ�ǧǤǺǝjRǻǽǗ�ā�ŦǽÝIǧȎǺǝǘ!

49!

R� S�

AA� a� c� g�

aa� b� d� h�

e� f� n�

WŶ�½ǸȊǿ�

WŶ�½Ǣe,!f,!g,!hǻǺȍĞĊ�

€

P(e, f ,g,h) =ne"

# $ %

& ' peq f ×

ng"

# $ %

& ' rgsh =

(n!)2

e! f !g!h!peq f rgsh

ǰDZǨǗp!=!e/n,!q!=!f/n,!r!=!g/n,!s!=!h/n�

ȩɊǼ�½Ǣa,!b,!c,!dǻǺȌǗWŶ�½Ǣe,!f,!g,!hǻǺȍĞĊ�

ǜȍ;BŒǢ ȋȎȍĞĊǼşĮ�

€

P(a,b,c,d e, f ,g,h) = p(a,b,c,d,e, f ,g,h) / p(e, f ,g,h) =e! f !g!h!

n!1

a!b!c!d!

WŶ�½Ǣe,!f,!g,!hǸǺdzǰǸǣǻǗ!ȩɊǼ�½Ǣa,!b,!c,!dǻǺȍĞĊ�

€

P(a,b,c,d,e, f ,g,h) =ne"

# $ %

& ' peq f ×

ea"

# $ %

& ' rasb ×

fc"

# $ %

& ' rcsd =

n!e! f !

e!a!b!

f !c!d!

peq f rgsh

50!

€

P(B)

€

P(A∩ B)

€

P(A |B) = P(A∩ B) /P(B)

WŶ�½ȑnǟǺǝɒa,b,c,dɓǼĹȑ5Ƕłǟȍ�

11� 4�

3� 7�

R� S�

AA� 11� 4!� 15�

aa� 3!� 7!� 10�

14� 11� 25�

5ǶǼ;BŒǻǴǝǶǮǼĞĊȑşĮǨǗĞĊǢpx��ǻǺȍȆǼȑ5ǶŲǨRȐǬȍ!ɒŰØǷ±dzǰ6ǴǼ;BŒǘǦǼǸǣ�-ßzǸǺȍǦǸǻô¥ǘƜØDZǥDZǸă-ßzɓ�

€

px =14!11!15!10!

25!1

11!3!4!7!"

# $

%

& ' = 0.0367

FisherǼèĞĞĊßzǽǗşĮǢqnǺǼǷǗȢɎȼɆɐȫǻȊȍýĮȑŐǞǘ!ȢɎȼɆɐȫǼĔƃǻȊdzǶǗ�½ǼqǣǺ;BŒǷȆşĮǷǣȍȊǞǻǺdzǶǝȍǘ!Ćǻ�½Ǣ�ǺǝjRǻǽǗŸ�ǻhǵǤχ2ßzȊȌǗǦDzȋȑ$ǞǦǸǢFȅȋȎȍǘ�

5%ïüǷÏ¥�

12� 3�

2� 8�13� 2�

1� 9�

14� 1�

0� 10�

10� 5�

4� 6�

9� 6�

5� 5�8� 7�

6� 4�

7� 8�

7� 3�

6� 9�

8� 2�

5� 10�

9� 1�4� 11�

10� 0�

€

p =14!11!15!10!

25!1

11!3!4!7!+

112!2!3!8!

+1

13!1!2!9!+

114!0!1!10!

+1

5!9!10!1!+

14!10!11!0

"

# $

%

& '

= 0.0486

ǦǼ;BŒǢ ȋȎȍĞĊƪpxȑşĮǪȍ�

51!

ɒKłɓ!\�ǼÏ¥£Ǽßz�

-3 -2 -1 0 1 2 3

4550

55

-3 -2 -1 0 1 2 3

4550

55

-3 -2 -1 0 1 2 3

4550

55

€

yi

€

ˆ y i€

y

€

(yi − y )2i

n∑ = ( ˆ y i − y )2

i

n∑ + (yi − ˆ y i)

2i

n∑

(a)!5�ÄX!SSY�

(a)�

(b)�

(c)�

(b)!\�Ƿ!ŦÈǧȎȍ!�ÄXǖSSR�

(c)!ê�Ǽ!�ÄX!SSE�

æǼȊǞǻ�ÄXȑ;BǷǣȍə�

Ŗ]� �ÄX� ňď�� �e�Ä� F,�

\�!(b)�

SSR� 1� MSR!=!SSR�

MSR)/MSE�

ê�!(c)�

SSE� n!-!2� MSE!=!!SSE)/(n42)�

5"!(a)�

SSY� n!-!1�

FßzǻȊȌǗ\�ǼÏ¥£ßzǢǷǣȍ!€

yi€

y

€

ˆ y i

Zv'&/()�N� �����P,0*��P,!#�,���

52!

ǖǖǖǖǖǖǖǖǖǖǖǖǼÍ�G!

€

J = (yi −α −βxi)2

i=1

N∑

ɒKłɓÍ�óǻȊȍ\�ȺɈɄɐȫǼ¶z�

€

yi = α + βxi +ε i

€

ε i ~ N(0,σ2)

ť�Ǣ�e0Ǘ;¼σ2ǼèŘ;�ǪȍǸłǟȍ�

€

yi ~ N(α + βxi,σ2) yǽ�eα+βxǗ;¼σ2Ǽ!

èŘ;�Ǫȍ�

€

L = p(y1,y2,...,yN ) =exp{−(yi −α −βxi)

2 /2σ 2}2πσ 2

i=1

N

∏ =exp{− (yi −α −βxi)

2 /2σ 2

i=1

N∑ }

(2πσ 2)N

0.0

0.1

0.2

0.3

0.4

y

€

α + βxi

€

yi€

p(yi) =12πσ 2

exp −(yi −α −βxi)

2

2σ 2

' ( )

* + ,

èŘ;�ǼĞĊ��Ɠ½!

��ǽǗ!

�½��ǽǗ!

€

lnL = −12σ 2 (yi −α −βxi)

2

i=1

N∑ −

N2log2πσ 2

ÍqGǖɒÍ�óɓ!

€

∂ lnL∂β

= −1σ 2 (yi −α −βxi)xi

i

n

∑ = 0

€

∂ lnL∂α

= −1σ 2 (yi −α −βxi)

i

n

∑ = 0

ť�Ǣ�e0Ǘ;¼σ2ǼèŘ;�!ǻ�ǞǸǣǗÍ�óǸÍ���óǼ¶zȺɈɄɐȫǽ�ʼnǪȍ!ɒť�ǢǗèŘ;�ǻ�ȐǺǝjRǽǗ¡ǫǨȆ�ʼnǨǺǝɓ! 53!

�@�9b(['Hj�,��