What is maximum Likelihood? History Features of ML method Tools used Advantages Disadvantages Evolutionary models

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1 Wha i maximum Likelihood? Hiory Feaure of ML mehod Tool ued Advanage Diadvanage Evoluionary model

2 Maximum likelihood mehod creae all he poible ree conaining he e of organim conidered, and hen ue he aiic o evaluae he mo likely ree. For a mall number of organim hi i poible, for a large number of organim he ak canno be accomplihed a he number of generaed ree i very large Therefore, heuriic are ued o elec a ube of ree o creae.

3 Likelihood mehod for phylogeny were fir inroduced by Edward and Cavalli-Sforza in 964 for he gene frequency daa. Neyman in 97 applied likelihood o he molecular equence and hi work wa exended by Kahyap and Suba in 974. Felenein(973, 98) bough he maximum likelihood frame work o he nucleoide baed phylogeneic inference.

4 In hi mehod he bae of all he equence a each ie are conidered eparaely and he loglikelihood of having hee bae are compued for a given opology by uing a paricular probabiliic model. Thi log-likelihood i added for all he ie, and he um of he log-likelihood i maximied o eimae he branch lengh of he ree. Thi procedure i repeaed for all he poible opologie, and he opology ha how he highe likehood i choen a he final ree.

5 Saiical (probabiliic ) mehod for inferring he phylogenie:. Subiuion model i choen for equence daa(alignmen) 2. Likelihood of oberving he equence daa given in he ubiuion model i obained for each opology evaluaed(parameer fiing on branch lengh) 3. Topology ha give he highe likelihood i choen a he be ree.

6 The ML mehod i available for boh nucleic acid and proein daa. Thee are he freely available ool: DNAML (only DNA daa; in he PHYLIP package) FaDNAML (only DNA daa; a faer algorihim applied o DNAML) ProML(boh DNA and proein daa) Puzzle (boh DNA and proein daa). Thi i much faer han PROTML.

7 Eimae he brnch lengh of he final ree. Mehod are uually conien. I i exended o allow diance beween he rae of raniion and ranverion. Evaluae differen ree opologie. Ue all he equence informaion.

8 ML i very CPU inenive and hu exremely low. Need long compuaion ime o conruc a ree. The reul depend on he model of he evoluion ued. Thi mehod eimae he branch lengh no opology, o i may give he wrong opology.

9 Over long ime period, he nucleoide a a given poiion remain he ame Bu periodically, hi nucleoide change (over he enire populaion) Thi i called ubiuion, i.e., replacemen of he predominan nucl. for ha poiion wih anoher predominan nucl.

10 Subiuion Marix The ubiuion marix i expreed a follow: S( ) = pr( pr( pr( A A A M A, A A 2 k,, ) ) ) pr( A 2 K A, ) K O pr( pr( A A k k M A, A k, ) ) where { A,A, K, A } Σ, for example{a,c,t, G} 2 k

11 Here he aumpion i ha he rae of evoluion i conan. The ubiuion rae of a nucleoide by a differen nucleoide i α. Subiuion probabiliy of A by G,C or T i α. Since he oal probabiliy i, ubiuion rae of A i -3 α.

12 Hence for a hor ime ε, S( ε ) 3αε αε = αε αε αε 3αε αε αε αε αε 3αε αε αε αε αε 3αε

13 For a longer ime hi reduce o, Where, = r r r r ) S(

14 Kimura model ake ino accoun boh he raniion and ranverion rae. Thi model conider rae of raniion o be α and he rae of ranverion o be β.

15 Here he ubiuion marix i a follow:

16 For a longer ime hi reduce o, Where, = r u r u u r u r S ) ( ( ) ( ) ( ) = + = = + u r e e u e β α β β

17 URL: The ArrayExpre Archive i a daabae of funcional genomic experimen including gene expreion where you can query and download daa colleced o MIAME and MINSEQE andard. Gene Expreion Ala conain a ube of curaed and re-annoaed Archive daa which can be queried for individual gene expreion under differen biological condiion acro experimen.

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19 Bioinformai Principle and Applicaion by Zhumur Ghoh and Mallick. Bioinformaic Sequence and genome analyi by David W.Moun.

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