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060310391 ƭĉLĜƮ ƫ 0560565 ƭ¹LĜƮ ƔźŽƠƐƥƍƁƈ Ñ12= Ùã¡ 2014/7/3 8:40.10:10 @1.Ñ4ÿëQ 1 Fig. 4. Convergent evolu0on of feeding morphology and color among East African cichlid fishes. Species from Lake Tanganyika are in the leA column; those from Lake Malawi are to the right. Each of the illustrated fishes from Lake Malawi are more closely related to one another than to any species in Lake Tanganyika. h1p://www.pnas.org/ Albertson et al. (2003) ģĀ]ĺ\Ġƭ1996Ʈ 2 ŠſƬƩƬƑ ŸƤźƪƠƪƐ ÙãLĺÙã¡ ĕ-Ćī Ćī© Ċĩâ7© ÖÚ© ĕ-đc ƘƬƐƈƐƤƍƙN 3 ŸƤźƪƠƪƐ 2ŘŠDNAƭŨŔšRNAŬƋƪƕƁăƮşŘŀ ŚĺŒŲůŠ£ĒƭĞŬŸƞƓĞŠĝ'Ʈ ŠŀşSqŏűƭIJŏűƮĜ&Ņ´Nśņű ŮŁşƀƢƍƙŵ:ŪŚŦłŔūŠ ŸƤźƪƠƪƐŌŲŔDNAƭŨŔšRNAŬƋƪƕƁ ăƮšĺŒŲůŠŀŠ¢ï¿ĺĒ¿ĺĕ-¿ ŞĥērŵÅűyŅńŰŜōŚĺfņäņĺÙã ¡wŞŝŠ ļŞùş»ŀůŲű 4
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Page 1: lecture.ecc.u-tokyo.ac.jp - z } ¥ Ñ 12 Ùã¡aiwata/biomet/...B b : ð match ® _1¯ : ð(mismatch) _−1¯ : ¢ _.2¯ u B Z :! R ` n A ^ x u H- O q n A ^ d B u e K \ _ O q! d B

!060310391!ƭĉLĜƮĶƫ!0560565!ƭ¹LĜƮ!

!

ƔźŽƠƐƥƍƁƈ!Ñ12=!Ùã¡�

2014/7/3!!!8:40.10:10!@15Ĵ.Ñ4ÿëQ�

1!

Fig.%4.%Convergent%evolu0on%of%feeding%morphology%and%color%among%East%African%cichlid%fishes.%Species%from%Lake%Tanganyika%are%in%the%leA%column;%those%from%Lake%Malawi%are%to%the%right.%Each%of%the%illustrated%fishes%from%Lake%Malawi%are%more%closely%related%to%one%another%than%to%any%species%in%Lake%Tanganyika.!

h1p://www.pnas.org/!Albertson!et#al.#(2003)!ģĀ]ĺ\Ġƭ1996Ʈ! 2!

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Page 2: lecture.ecc.u-tokyo.ac.jp - z } ¥ Ñ 12 Ùã¡aiwata/biomet/...B b : ð match ® _1¯ : ð(mismatch) _−1¯ : ¢ _.2¯ u B Z :! R ` n A ^ x u H- O q n A ^ d B u e K \ _ O q! d B

A-TGTAAACGCTA AGTGTAAT-GCTA�

ATGTAAACGCTA AGTGTAATGCTA�

ATGTAAACGCTA AGTGTAATGCTA�

�łŢĺŋŠŮŁŞĝ'ŵ§ćŏűC7ş…!

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ōńōĺ�łŢĺ6ĝ'ŠęhŞ�éşƀƢƍƙƭ.Ʈŵ�ŲűŜ!

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śšĺŀŗŔŀĺŝŠŮŁŞA®ś�Ť�łŲŢñŀŠŕųŁńƵ!

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�łŢĺ�ðƭmatchƮş1¯ĺ��ð(mismatch)ş−1¯ĺƀƢƍƙş.2¯ŵ�łŚĺ!ŒŠŮŁŞƈƃŸŵ�H-ŏűŮŁŞ�Ť�łŵĚťŋŜşŏű!

�Ť�łŠĘŀşŮŰĺ½ŞűÙãĥ�Ņ�NŌŲŚōŨŁ!

①šĺ7×1+5×(.1)=2!¯! ②šĺ10×1+1×(.1)+2×(.2)=5!¯!

ƈƃŸŵ�H-ŏű�Ť�łŵ¨Ūű! ŸƦƄƥƉƟŠpõr!5!

?ŸƤźƪƠƪƐŜ!XxŸƤźƪƠƪƐ�

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•  XxŸƤźƪƠƪƐ!– ĝ'#şXx¿ş!ĐĜ�Ņ¸ŲűC7şĺ!ĐĜ�şŘŀŚŠũŸƤźƪƠƪƐŏű!�ƮSmith.WatermanŸƦƄƥƉƟ!

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Needleman.Wunsch!algorithm!Needleman!and!Wunsch!(1970)!J!Mol!Biol!48:443�

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Needleman.Wunsch!algorithm!Needleman!and!Wunsch!(1970)!J!Mol!Biol!48:443�

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Page 3: lecture.ecc.u-tokyo.ac.jp - z } ¥ Ñ 12 Ùã¡aiwata/biomet/...B b : ð match ® _1¯ : ð(mismatch) _−1¯ : ¢ _.2¯ u B Z :! R ` n A ^ x u H- O q n A ^ d B u e K \ _ O q! d B

Needleman.Wunsch!algorithm!Needleman!and!Wunsch!(1970)!J!Mol!Biol!48:443�

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Needleman.Wunsch!algorithm!Needleman!and!Wunsch!(1970)!J!Mol!Biol!48:443�

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ATGT-C A-GTAC�

ŸƤźƪƠƪƐŠƈƃŸ!

Ɲƍƌ!4!×!1!+!ƞƈƝƍƌ!0!×!(.1)!+!ƀƢƍƙ!2!×!(.2)!=!0!

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Ɲƍƌ!2!×!1!+!ƞƈƝƍƌ!3!×!(.1)!+!ƀƢƍƙ!0!×!(.2)!=!.1!

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12!

Page 4: lecture.ecc.u-tokyo.ac.jp - z } ¥ Ñ 12 Ùã¡aiwata/biomet/...B b : ð match ® _1¯ : ð(mismatch) _−1¯ : ¢ _.2¯ u B Z :! R ` n A ^ x u H- O q n A ^ d B u e K \ _ O q! d B

ƛŸƩźƉŸƤźƪƠƪƐŜ!ƝƦƌƙƦŸƤźƪƠƪƐ�

•  2ŘŠĝ'ŵŸƤźƠƪƐŏűūŠŵƛŸƩźƉŸƤźƪƠƪƐĺ3Ř��Šĝ'ŵ8�şŸƤźƠƪƐŏűūŠŵƝƦƌƙƦŸƤźƪƠƪƐŜŀŁ!

•  óŠ£��ŵ�ŊŲŢNeedleman.WunschŸƦƄƥƉƟū)»śņűŅĺmĝ'ŠŸƤźƪƠƪƐşšO(nm)ŠúÕġŅpõŜŞű!

•  ƝƦƌƙƦŸƤźƪƠƪƐşšĺ,·¿ŸƦƄƥƉƟŅpõƭ�ƲClustal!ŸƦƄƥƉƟƮ�

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Clustal!ŸƦƄƥƉƟ�

Thompson!et!al.!(1994)!Nuc!Acid!Res!22:!4673�

2ŘŠĝ'¦şŸƤźƪƠƪŵòŀĺĝ'ĤŠĆīŵ¨Ūű!

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NJ¡Š�ÐńůįşĺŸƤźƪƠƪƐŵòŗŚŀň!1.  Hbb_Human!vs.!Hbb_Horse!2.  Hba_Human!vs.!Hba_Horse!3.  (1)!vs.!(2)!4.  (3)!vs.!Myg_Phyca!!!!!!!!!!!!!!!!!!!!!!!!!!!!:!!

ŸƤźƪƠƪƐŌŲŔĝ'êĤŠŸƤźƪƠƪƐŠƈƃŸšĺêĤŠ à7őŠa>ƈƃŸŜōŚúÕĻ!ğũ�ʼnŏűC7šĺ2¥ÀŠŮŁŞúÕŜŞűĻ!

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ÙãL!(phylogene_cs)�

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Page 5: lecture.ecc.u-tokyo.ac.jp - z } ¥ Ñ 12 Ùã¡aiwata/biomet/...B b : ð match ® _1¯ : ð(mismatch) _−1¯ : ¢ _.2¯ u B Z :! R ` n A ^ x u H- O q n A ^ d B u e K \ _ O q! d B

Ùã¡�wŠ�©şš ļĿű�

•  Ćī©!–  �NŌŲŔDAƭŨŔšŸƞƓĞƮé��Òŵĝ'ĤŠĆīŜōŚĺÙã¡ŵ�×ŏűĻƁƤƈƋù�Ŝ8ŎŸƦƄƥƉƟŅ»ŀůŲűC7ƭUPGMAƮūĿűŅĺDAé��ŵĆīŜōŔC7ĺ.ÛŞÁĘcŵĆīŜōŔƁƤƈƋù�â�Ŝ½ŞűŋŜşªtŏűĻ!

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qt� qt+1�

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1!−!λ�

λ/3�λ/3�λ/3�

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qt+1 ≅ (1− λ)2qt + 2(1− λ)(λ /3)(1− qt )

≅ (1− 2λ)qt +2λ3(1− qt )

qt+1 − qt =2λ3−8λ3qt

ēä�Ĥśìłĺ_&ŵn&dq/dtśéņ�łűŜ�

dqdt

=2λ3−8λ3q

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nVŞ�Ĥ.�ŵ!ìłű�

q =1−341− exp(−8λt 3)( )

ddx

y + P(x)y =Q(x)

⇒ y = exp(− Pdx∫ ) Qexp( Pdx∫ ) +C∫( )

2λt = −34ln 1− 4

3(1− q)

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( )

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P =141− 2exp(−4(α + β)t) + exp(−8βt)( )

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= −12ln(1− 2P −Q) − 1

4ln(1− 2Q)

20!

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Page 6: lecture.ecc.u-tokyo.ac.jp - z } ¥ Ñ 12 Ùã¡aiwata/biomet/...B b : ð match ® _1¯ : ð(mismatch) _−1¯ : ¢ _.2¯ u B Z :! R ` n A ^ x u H- O q n A ^ d B u e K \ _ O q! d B

UPGMA!(Unweighted!Pair!Group!Method!with!Arithme_c!mean)�

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Saitou!and!Nei!(1987)�

�ģŠ<ŵ�Uŏű#Ĝ�ƭinternal!branchƮŵį£�Ýŏű!

SO = LiX =1

N −1Dij

i< j∑

i=1

N

∑6OUTŠ�šĺŒŠOTUŜ�FŠOTUƭN.1�ƮŜŠĆīŠ<ŵ!úÕŏűĨşĺN.1=žŻƪƐŌŲűƭ�ģŵúÕŏűşšN.1ś*űpõŅĿűƮ�

Dij:!OTU!iŜjĤŠĆī!Lab:!ƓƬƑabĤŠ�ģ!

LXY =1

2(N − 2)(D1k +D2k ) − (N − 2)(L1X + L2X ) − 2 LiY

i=3

N

∑k=3

N

∑$ % &

' ( )

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|g#Ñ2ĺ3ĮƲƓƬƑXYĤŠĆīŵúÕŏű!Šş�&ŞĜ&!

S12 = LXY + (L1X + L2X ) + LiYi=3

N

=1

2(N − 2)(D1k +D2k ) +

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∑k=3

N

∑ =1

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12D12 +

1N − 2

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k=3

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L1X = (D12 +D1Z −D2Z ) /2L2X = (D12 +D2Z −D1Z ) /2

D1Z = D1ii=3

N∑ /(N − 2)

D2Z = D2ii=3

N∑ /(N − 2)

24!

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