Maximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002

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1 Mmm lkelhood eme of phylogey BIO 9S/ S 90B/ MH 90B/ S 90B Iodco o Bofomc pl 00

2 Ovevew of he pobblc ppoch o phylogey o k ee ccodg o he lkelhood d ee whee d e e of eqece d ee by ee wh leve fo he eqece. he mpo of by ee o eo lmo bece y ohe bchg pe c be ppomed by by ee whch ome of he bche e vey ho. Mmm lkelhood ee he ee whch gve he mmm vle of he lkelhood d ee ove ll ee opologe.

3 he lkelhood he pobbly of e of d gve ee deoed... Hee he d e e of eqece.... ee wh leve wh eqece j lef j d e he edge legh of he ee. o defe he lkelhood we eed model of evolo.e. of he mo d eleco eve h chge eqece log he edge of ee. e me h we c defe pobbly y fo cel eqece y o evolve o eqece log edge of legh. he pobbly of ee wh pecfc e of ceo ged o ode c he be clcled by mlplyg ll he evoloy pobble oe fo ech edge of he ee. oo

4 oo Fo he ee how hee he lkelhood wold be whee deoe he pobbly of occg he oo of he ee. I geel he cel eqece wll be kow d o ob he pobbly of he kow eqece fo he gve ee we eed o m ove ll he poble ceo

5 Seekg he mmm lkelhood ee Mmm lkelhood ee he ee wh opology d edge legh h mmze.... Fdg h mmm eqe ech ove ee opologe wh he ode of gme of eqece he leve pecfed; d fo ech opology ech ove ll poble legh of edge. Sce he mbe of ee gow vey lge fo moe h hlf doze eqece effce ech pocede eqed o cy o eche ove ee. Mmzg he lkelhood of edge legh c be cheved by vey of opmzo echqe.

6 obbly model of evolo o defe y he pobbly of eqece g fom cel eqece y ove edge of legh. We mke mplfyg mpo h evey e of he gve d eqece c be eed depede d deleo d eo do o occ. O eqece heefoe fom gpped lgme wh depede evolo ech e. 6

7 7 : d whch we deoe by m h deped o we c we hee cleode eqece Fo. e look poble fom fo he bo pobble dee e he lgme. whee d gple eqece wo lged.he o mpo mple h fo ove edge legh ede by hvg beg bed ede deoe he pobbly of e S S b y y y b b

8 8 Fo cleode eqece oe model h of Jke & o. he evolo model volved kowledge ochc pocee. We oly gve he el fom S:. d hee pobbly bewee wo dffee cleode. wh he me mo vey ymmec he m e e α α

9 I Jke-o model oe h whe. h me h he cleode eqlbm feqece mpled by he model e q q q q he eqlbm feqece e ed fo he oo pobble. 9

10 0 lclg he lkelhood of wo eqece ode e q We do o kow wh he oo ede w heefoe If hee e N e we c we he fll lkelhood q. N

11 Emple: he lkelhood of wo cleode eqece mg he Jke-o model he pobbly of occg boh leve of he ee By ymmey Smlly q q q q

12 6 6 e e α α Sbg he vle d gve I he emple eqece hee e 8 e whee he cleode he wo eqece e decl d e whee bo occ. he Noe h he lkelhood deped oly o he m of d. We c fd he mmm lkelhood eme of by kg devve e e α α

13 he lkelhood fo by mbe of eqece e deoe he mmede cel ode o.e. he ode he op of he edge bove. Fo ee wh leve hee e - el ode ddo. We g he el ode by wh o be he oo. h α... q α α

14 h pobbly c be comped by wokg p he ee fom he leve g lgohm of Felee 98. e k deoe he pobbly of ll he leve below ode k gve h he ede k. he we compe fom he pobble b d j c fo ll b d c whee d j e he dghe ode of k. k

15 Felee lgohm fo lkelhood Ilzo: Se Reco: ompe fo ll follow: If k lef ode If k o lef ode emo: kelhood e. k k. 0 f f Se k k k k c b j j k j c c b b j. d e he dghe ode fo ll ompe.... q

16 Ug he lkelhood fo feece Oe cdde fo he be ee he ee h mmze he lkelhood. he opology d he gme of edge legh h gve he ovell mmm of h lkelhood he deed ee. ve mll mbe of eqece y o ey o emee ll ee d we dow he lkelhood eplcly fco of he edge legh. Fo lge mbe of eqece he lkelhood c be comped by Felee lgohm. We c e dd opmze kg devve of he lkelhood wh epec o he edge legh o fd he opml edge legh. Eve wh he be opmze mmzg he lkelhood compolly demdg. 6

17 Refeece R. Db S. Eddy. Kogh d. Mcho. Bologcl eqece ly hpe 8 p Felee J. 98 "Evoloy ee fom DN eqece: mmm lkelhood ppoch" Jol of Molecl Evolo 7:

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