Inferring Molecular Phylogeny

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1 Dr. Walter Salzburger he tree of life, ustav Klimt (1907) Inferring Molecular Phylogeny Inferring Molecular Phylogeny 55 Maximum Parsimony (MP): objections long branches I!! B D long branch attraction problem can lead to more support for ((,),(B,D)) than for ((,B),(,D))

2 Inferring Molecular Phylogeny 56 Maximum Likelihood (ML)! Maximum likelihood principle: preference of the explanation that makes the observed outcome the most likely (i.e. the most probable)! in phylogenetics: choosing the tree that explains best the data, i.e. the tree that makes the data at hand the most probable evolutionary outcome ( most likely tree )...!...based on a model of molecular evolution Inferring Molecular Phylogeny 57 Maximum Likelihood (ML) likelihood data LD = Pr ( D H ) hypothesis probability of obtaining the data (D) given a tree (H)! he most likely tree is the one that maximizes LD under a discrete model of molecular evolution

3 Inferring Molecular Phylogeny 58 Maximum Likelihood (ML) alignment Site axon axon B axon axon D axon E t1 y t6 B t2 x t3 z t8 D w t7 t4 E t5 tree 1 Lsite1 = Pr (,,,,,w,x,y,z 1 ) = = Pr (x) + Pr (y x,t6) + Pr ( y,t1) + Pr ( y,t2) + Pr (z x,t8) + Pr ( z,t3) + Pr (w z,t7) + Pr ( w,t4) + Pr ( w,t5) Inferring Molecular Phylogeny 59 Maximum Likelihood (ML) Ldata = Lsite1 x Lsite2 x Lsite3 x... x LsiteN = N =! L(j) j=1 values get incredibly small ln Ldata = ln Lsite1 x ln Lsite2 x ln Lsite3 x... x ln LsiteN = N = " ln L(j) j=1

4 Inferring Molecular Phylogeny 60 Maximum Likelihood (ML) Phylogenetic hypothesis B D E with branch-lengths! he three elements of ML Observed data e.g., sequence alignment model of sequence evolution Models of Molecular Evolution (c) J. orliss

5 Models of Molecular Evolution 2 Models of molecular evolution! Why do we need models of sequences evolution?! How do these models look like?! Which model is best?! How do we chose the right model? Inferring Molecular Phylogeny 3 Why? orrection for transition/transversion bias RNSIION RNSVERSION RNSVERSION RNSIION ransition mutations outnumber transversions!

6 Models of Molecular Evolution 4 Why? orrection for different base frequencies axon axon B axon axon D alignment base frequencies freq. = 14/32 = freq. = 4/32 = freq. = 2/32 = freq. = 12/32 = Here, if a mutation occurs, it is more likely that an mutates into something else than that a changes into something else... Models of Molecular Evolution 5 Why? orrection for multiple hits Sequence difference Expected difference } Observed difference multiple hit correction ime multiple hit problem due to back-mutations

7 Models of Molecular Evolution 6 How? Discrete model of molecular evolution! remember:! NJ, UPM, ME ( distance methods ): a distance is translated into a phylogenetic hypothesis! MP: each mutations counts the same* *Note: there is a possibility to weight mutations Models of Molecular Evolution 7 How? Substitution probability matrix probability that site started with and stayed P P P P Pt = P P P P P P P P P P P P probability that site started with but had a at time = t

8 Models of Molecular Evolution 8 How? Base composition vector f = [ f f f f ] equal frequencies: f = f = f = f Models of Molecular Evolution 9 How? Jukes-antor (J) model Pt =. # # # #. # # # #. # # # #. f = [!!!! ]

9 Models of Molecular Evolution 10 How? Kimura s 2 parameter model (K2P) Pt =. $ # $ $. $ # # $. $ $ # $. f = [!!!! ] Models of Molecular Evolution 11 How? Felsenstein 1981 (F81) Pt =. " # " # " # " #. " # " # " # " #. " # " # " # " #. f = [ " " " " ] Felsenstein (1981)

10 Models of Molecular Evolution 12 How? Hasegawa, Kishino and Yano (HKY) Pt =. " $ " # " $ " $. " $ " # " # " $. " $ " $ " # " $. f = [ " " " " ] Hasegawa et al. (1985) Models of Molecular Evolution 13 How? eneral (time) reversible model (R), (REV) Pt =. " a " b " c " a. " d " e " b " d. " f " c " e " f. f = [ " " " " ] six classes of substitutions: a, b, c, d, e, f Yang et al. (1994)

11 Models of Molecular Evolution 14 transition/ transversion bias Jukes-antor (J) " = " = " = " "=# varying base frequencies Kimura 2 parameter (K2P) " = " = " = " " # # Felsenstein (F81) " # " # " # " "=# varying base frequencies Hasegawa et al. (HKY) " # " # " # " " # # transition/ transversion bias eneral reversible (R) " # " # " # " six substitution classes six pairs of substitutions have different rates Models of Molecular Evolution 15 Observed Which model is the best?...the one that reflects the data best!??? J K2P R

12 Models of Molecular Evolution 16 Observed J K2P R Models of Molecular Evolution 17 hoosing the best-fitting model: likelihood ratio test likelihood ratio statistics likelihood of the null hypothesis! = log L1 - log L0 likelihood of the alternative hypothesis? values are very small!

13 Models of Molecular Evolution 18 hoosing the best-fitting model: likelihood ratio test estimate the log likelihood for the most simple model loglj estimate the log likelihood for the next complex model loglk2p calculate likelihood ratio statistics (comparison)! = loglj-loglk2p * * estimate the log likelihood for the next complex model loglhky *proceed if the more complex model is better than the more simple model Models of Molecular Evolution 19 hoosing the best-fitting model: likelihood ratio test estimate the log likelihood for the most simple model phylogenetic hypothesis estimate the log likelihood for the next complex model nested design calculate likelihood ratio statistics (comparison) estimate the log likelihood for the next complex model chi-square tests

14 Models of Molecular Evolution 20 hoosing the best-fitting model: likelihood ratio test Salzburger et al. (2002) Models of Molecular Evolution 21 gamma substitution correction shape parameter: # # = 100 # = 0.5

15 Models of Molecular Evolution 22 gamma substitution correction: examples ype of sequence shape parameter (#) nuclear genes albumin genes 1.05 insulin genes 0.40 c-myc genes 0.47 prolactin genes S-like RNs, stems 0.29 viral genes Hepatitis B virus genome 0.26 mitochondrial genes cytochrome b 0.44 control region 0.17 Page and Holmes (1998) Models of Molecular Evolution 23 invariant sites probability that a site is invariant i.e., a site has zero rate of change

16 Models of Molecular Evolution 24 hoosing the best-fitting model: Modeltest* *computer program by Posada et al. (1998) Inferring Molecular Phylogeny 61 Bootstrapping:! resampling technique used to estimate sampling error! strategy: generating pseudoreplicates from the sequence data and inferring a phylogeny for each replicate! pseudoreplicates: sampling at random with replacement! bootstrap values reflect the percentage of pseudoreplicates, in which a branch has been found

17 Inferring Molecular Phylogeny 62 Bootstrapping: original dataset axon axon B axon axon D pseudorep. 1 axon axon B axon axon D pseudorep. 2 axon axon B axon axon D pseudorep. 3 B B D D B onsensus tree axon axon B axon axon D B 67 D D Inferring Molecular Phylogeny 63 Bayesian Inference (BI) of phylogeny!...closely allied to maximum likelihood homas Bayes ( )! strategy: choosing the tree with the highest posterior probability, which is proportional to the likelihood multiplied by the prior probability (Bayes theorem)!...based on a model of molecular evolution!...confidence of the results is assessed during the analysis

18 Inferring Molecular Phylogeny 64 Bayes theorem probability of observing D given that the hypothesis holds homas Bayes ( ) prior probability of the hypothesis Pr ( H D ) = Pr ( D H ) Pr ( H ) Pr ( D ) posterior probability of the hypothesis probability of observing the data Inferring Molecular Phylogeny 65 Bayesian Inference (BI) of phylogeny Pr ( H D ) = Pr ( D H ) Pr ( H ) Pr ( D )! he optimal tree is the one that maximizes the posterior probability

19 Inferring Molecular Phylogeny 66 Metropolis-coupled Markov hain Monte arlo (MM) simulations start with a random tree X go one step and take Y parameter 2 posterior probability high low R = if R"1 Pr (Y) (Z) Pr (X) (Y) go one step and take Z X Y Z parameter 1 tree space (all possible trees) Inferring Molecular Phylogeny 66 Metropolis-coupled Markov hain Monte arlo (MM) simulations start with a random tree X go one step parameter 2 posterior probability high and take W Y low if R<1 R = Pr (Y) Pr (X) keep tree X as current tree X W Y parameter 1 tree space (all possible trees)

20 Inferring Molecular Phylogeny 67 Metropolis-coupled Markov hain Monte arlo (MM) simulations parameter 2 high local optimum posterior probability low run for many generations! parameter 1 tree space (all possible trees) Inferring Molecular Phylogeny 67 Metropolis-coupled Markov hain Monte arlo (MM) simulations global optimum parameter 2 posterior probability high local optimum low parallel chains parameter 1 tree space (all possible trees)

21 Inferring Molecular Phylogeny 68 Bayesian Inference (BI) of phylogeny MrBayes (computer program): output en!! LnL!! L!! pi()!! pi()!! pi()!! pi()! 1000! ! 1.618! ! ! ! ! 1100! ! 1.628! ! ! ! ! 1200! ! 1.628! ! ! ! ! 1300! ! 1.627! ! ! ! ! 1400! ! 1.620! ! ! ! ! 1500! ! 1.619! ! ! ! ! 1600! ! 1.621! ! ! ! ! 1700! ! 1.617! ! ! ! ! 1800! ! 1.641! ! ! ! ! 1900! ! 1.640! ! ! ! ! 2000! ! 1.630! ! ! ! ! 2100! ! 1.639! ! ! ! ! Inferring Molecular Phylogeny 69 Bayesian Inference (BI) of phylogeny burn-in stationary phase -ln likelihood enerations

22 Inferring Molecular Phylogeny 70 Bayesian Inference (BI) of phylogeny Posterior probabilities: branching order was found in 96 %of the trees branching order was found in 80% of the trees Inferring Molecular Phylogeny 71 raditional versus Bayesian approaches Holder and Lewis (2003)

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