Phylogenetic Analysis of Molecular Data
Phylogenetic Analysis of Molecular Data BOTANY 563
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This 11 page Class Notes was uploaded by Etha Kassulke on Thursday September 17, 2015. The Class Notes belongs to BOTANY 563 at University of Wisconsin - Madison taught by David Baum in Fall. Since its upload, it has received 182 views. For similar materials see /class/205320/botany-563-university-of-wisconsin-madison in Botany at University of Wisconsin - Madison.
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Date Created: 09/17/15
Parsimony Sequence evolution AGTTGTAQGTATGCCGA AGTAGTACGTATGCCIA AGT GTACGTATGCCGA AGTQGQACGTATGACIA AGTAGTACGT ATGC CIA AGTAGTAC GTATGC CGA AGTTGTACGTATGCCGA Parsimony favor the tree that can explain the data With the fewest Character state changes COMPUTATIONAL METHOD Optimality criterion Deductive method 5 PARSIMONY m g MAXIMUM LIKELIHOOD HENNIGIAN INFERENCE Ii E 5 BAYESIAN t E x g g MINIMUM EVOLUTION UPGMA o g LEAST SQUARES NEIGHBORJOINING n Data matrlx 1 1 1 1 1 1 1 123456789012 34567 AGTTGTAQGTATGCCGA AGTAGTACGTATGCCGA AGTAGTAC GTATGC CEA OWgtO AGTAGQACGTATGACEA Remove invariant characters 1111111 12345678901234567 T T g c G ID a 0 0 ha 3 55 3 CD 393 a 0 0 m lib lo 0 lib Iva These trees can be drawn Without the root There are three possible arrangements that we need to consider 0 0 Tree 1 Tree 2 0 Tree 3 These trees can be drawn Without the root Map the characters onto tree 1 Actually there are two ways to 3 map character 5 o G l 2 3 4 5 A G O T T G C G B T A A T C C G C T B A T C C T 0 1 A C A G C A T 38 gt825 K C 2 B Either way the character contributes 2 Total cost length 6 steps steps to the overall cost Map the characters onto tree 2 M ap the characters onto tree 3 H OUUgtO gt3gtDgtH QHHHN Gnome gt0004gt Haomu owgto gtgtDgtHH QHHHN 000C gt0004gt gt22 8 Total COSt 5 Total cost 6 steps The difference in tree length is all due to character 5 Parsimony informative What was the cost of 1 2 3 4 5 Tree 1 B quot O T T G C G Length 6 t 391 A A T C C G 0 A B A T C C T C A G C A T 13 Tree 3 C Length 6 Par51mony unlnformatlve Parsimon informative y Redraw tree 2 w1th root 1n place characters 0 C 0 At least two states that occur in at least two taxa m OCDCD Dgt DgtCDCCD ogtaaa nagtaa B h OW This is the correct tree R Which rooted tree is correct A O FGHED CAB How does character con ict arise 0 The tree is not divergent O ABCDE A H G ABCDEOFG B CDE 0 HGF W 0 A particular character changes more than once Homoplasy A Reversal BC D E F G G gtA Con ict between characters no tree explains all characters in the minimum number of changes owgto gtHgtHH models gtOgtOm 00094 C3gtCgtgtm How does character con ict arise 0 The tree is not divergent 0 A particular character changes more than once Homoplasy A B C D E F G G gtA GOA Parallelism Convergence OWgtO Parsimony criterion pick the tree that is shortest overall gtHgtHH Cam 1a gtOgtOm Q0004 C1gtClgtuu 0 XS H A Bayesian Phylogenetics Bayes Theorem 0 PrTreelData PrgData Tree X PrgTreeL PrData 0 PrTree Prior probability of the tree 0 PrData Prior probability of the data 7 PrDatalTree over all trees weighted by their prior probabilities PrDatalTree Likelihood of the data given the tree 0 PrTreelData Posterior probability of the tree Assuming he prior probability of wo rees ie ree opologies equal he who of heirpos enor prohahilihes equals he who of heir likelihoo scores True or false PrCTreellData Pr DatzTreel x Pr reel PrData PrCTreeZlData Pr DatzTreeZ x Pr ree2 PrData Pr reel Data mmmlx Prm pramez Dam PrData rDa1alTree2 x PrTree2 Bayes Theorem 0 PrTreelData PrgData Tree X PrgTreeL PrData Assuming he prior probability of wo rees ie ree opologies equal he who of heirpos enor prohahilihes equals he who of heir likelihoo scores True or false PrCTreellData Pr DatzTreel x Pr reel PrData PrCTreeZlData Pr DatzTreeZ x Pr ree2 PrData Pr reel Data mmmlx Prm Hangman PrData rDa1alTree2 x PrTree2 Assuming he prior probability of wo rees ie ree opologies equal he who of heirpos enor prohahilihes equals he who of heir likelihoo scores True or false PrCTreellData Pr DatzTreel x Pr reel PrData PrTree2lData Pr DatzTreeZ x Pr ree2 PrData Pr reel Data mmmlx Prm prmma rDa1alTree2 x PrTree2 PrTree2lDatz Assuming he prior probability of two trees ie tree topologies equal he mtio of theirposterior probabilities equals he mtio of their likelihood cores True or false PrTreellData Pr DatzTreel x Pr reel PrData PrTree2lData Pr DatzTreeZ x Pr ree2 PrData Pr reel Data Pr QataTreel PrTree2 lDatz PrDatalTree2 How do Bayesian and Likelihood approaches differ in their treatment of nuisance parameters Likelihood 7 Find the value of each parameter that maximizes the likelihood of the data Bayesian 7 Integrate over all possible values of each parameter weighted by the prior probability ution distrlb Like walking over tree space at a rate governed by altitude If tree topology is the parameter of interest what are some nuisance parameters that need to be accommodated in a Bayesian or Maximum Likelihood analysis 0 Branch lengths Substitution rates 0 Base frequencies 0 Rate heterogeneity parameters How does MCMC get around the problem of not being able to calculate PrData The probability of stayingleaving a tree is determined by its posterior probability relative to other nearby trees 0 The overall time spent on a tree will converge to its absolute posterior probability What happens at each step of a Bayesian phylogenetic MCMC analysis 0 A new parameter topology branch lengths substitution parameters etc is proposed 0 Whether the new parameter is accepted is governed by the metropolis hasting equation Qatari 39 x pgx 39 x P pmposingXZi x5 m1quot 1 PrDatalxi Prxi P gmposing x39 xi A A A Pr Posterior ratio Prior ratio Proposal ratio Why is the output of MCMC called a posterior distribution What does it contain 0 It contains a list of parameters in effect at a sampled set of generations after burnin The frequency of a parameter in this sample should be proportional to its posterior probability How can the posterior distribution be queried to evaluate other parameters for example the transitiontransversions ratio 0 Generate a histogram or t to a probability density function 0 Establish a credibility interval the range than encompasses say 95 of the distribution Bayesian approach PrHD PrD H x PrH PrD lsix 2six Sum PrH PrDIH How can the posterior distribution be queried to nd the posterior probability of a clade Just see the proportion of trees in the distribution that have the clade A dice example 0 A manufacturer makes regular dice and trick dice with 2 sixes 7 in equal numbers You are given a die from this manufacturer and are not allowed to look at all the sides 7 you can only look at the side that is up after a roll You roll this die 10 times and get these numbers 0 What is the probability that the die is one with two sixes Bayesian approach PrHD PrD H x PrH PrD lsix 2six Sum PrH 10 PrDIH Bayesian approach PrHD PrD H x PrH PrD lsix 2six Sum PrH 05 05 10 PrDIH Bayesian approach PrHD PrD H x PrH PrD lsix 2six Sum PrH 05 05 10 PrDIH 744E05 000123 000129 MCMC approach PgD gx at I X 11quot 1 PrDaIaix i v 1 six 2 sixes Bayesian approach PrHD PrD H x PrH PrD lsix 2six Sum PrH 05 05 10 PrDIH 165563 265463 Bayesian approach PrHD 000123 X 05 0953 000129 X 05 PrHD 000006 X 05 0047 000129 X 05 lsix 2six Sum PrH 05 05 10 PrDIH 744E05 000123 000129 MCMC approach P Daxgonesix 1 m1quot 1 PrDaIaitwosixes v 1 six 2 sixes MCMC approach PrQatgtwosixes PgDaxgtwosixes m1quot 1 PrDataione six PrDataione six V 1 six 2 sixes If you run this long enough you will spend only 47 of the time on 1 sixquot This is the PP of that hypothesis
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