Inferring phylogeny. Today s topics. Milestones of molecular evolution studies Contributions to molecular evolution

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1 Today s topics Inferring phylogeny Introduction! Distance methods! Parsimony method!"#$%&'(!)* +,-.'/01!23454(6!7!2845*0&4'9#6!:&454(6 ;<=>?@AB=C?DEF Overview of phylogenetic inferences Methodology Methods using distance data UPGMA, Neighbor-joining, minimum evolution Methods using discrete data Maximum parsimony Maximum likelihood Bayesian inference 1 2 Milestones of molecular evolution studies Genetics: Gregor Mendel ( ) Origin of species: Charles Darwin (1859) Emergence of cladistics: Willi Hennig et al. Discovery of DNA structure: James Watson & Francis Crick (1953) First comparison of amino acid sequence (insulin) among different species: Fred Sanger et al. (1955) First example of molecular systematics: Vince Sarich & Allan Wilson (1967) on human evolution Technical breakthrough in the 1990s: computer speed, methodological improvement Technical breakthrough in the 1980s: PCR, DNA sequencing, etc. The blooming of evo devo studies Contributions to molecular evolution The patterns of evolution Cladistics and phylogenetics: Willi Hennig ( ) The mechanisms The neutral theory of molecular evolution: Motoo Kimura (!"#$, ) The models and methodological concerns The uses of parsimony, maximum likelihood methods in phylogenetics: Joseph Felsenstein Genome Science and of Biology, University of Washington, Seattle 3 Nature (1968) 217: of molecular evolution 4 Reconstructing phylogeny The concepts of trees The data used to construct phylogenetic trees Morphological data Molecular data Homology of characters in data matrices Sequence alignment The basics of evolutionary trees The tree shapes Are these two trees different? 5 5 Baum et al. (2005) Science 310:

Most recent common ancestor (MRCA) Types of data Character and character types Quantitative and qualitative characters Binary and multistate characters Assumptions about character evolution

2 Most recent common ancestor (MRCA) Types of data Character and character types Quantitative and qualitative characters Binary and multistate characters Assumptions about character evolution Substitution models Step matrix Which is the MRCA of a mushroom and a sponge? Which is the MRCA of a mouse and a fern? b d Plant Molecular Evolution Distance method Evolution of DNA sequences UPGMA (Unweighted Pair Group Method using Arithmetic averages) Transformed distance method Neighbor-Joining method Minimum evolution A TCAGCCGACTGT T TCAGCCGACTGT C TCAGACGACTGT SpA SpB ACAGCCGATTGT TCAGCCGATTGT TCAGACGACTGT SpC TCAGCCGACTGT SpD TCAGACGACTGT In distance method, sequences were grouped based on their similarity, we need to measure the differences among sequences Measuring genetic distance SpA SpB SpC SpD ACAGCCGATTGT TCAGCCGATTGT TCAGCCGACTGT TCAGACGACTGT How different are the two sequences we have? The ways of measuring nucleotide substitution Simplest way Hamming distance = n/n x% SpA SpB ACAGCCGA-TGT TCAGCCGA-TGT 2/12 = 16.6% SpC TCAGCCGACTGT 1/12 = 8.3% SpD TCAGACGACTGT 11 12

Measuring differences between sequences The common ways Direct counting The probability of substitution at certain nucleotide site change from i to j.

3 Measuring differences between sequences The common ways Direct counting The probability of substitution at certain nucleotide site change from i to j. Nucleotide substitution models Jukes & Cantor(1969) s one parameter model Kimura(1980)'s two parameter model F81 (Felsenstein, 1981) HKY85 (Hasegawa et al., 1985) Generalized time reversible model (GTR) The probability of nucleotide substitution SpC SpD TCAGCCGACTGT TCAGACGACTGT In order to know the probability of the sequences to be different (p), we can calculate the probability of the sequences being the same (I (t)) first. Let s start with Jukes-Cantor model We can just use another estimator, K, the number of substitutions per site since time of divergence between the two sequences 3"t Y X 3"t Z Therefore, K = 2 x 3"t = 6"t! 8!t = "ln(1" 4 3 p) " A C " " G " " " " K =! 3 4 ln(1! 4 3 p) T Under J-C model, Example of calculation If there are 80 transitions and 20 transversions between two sequences (length=0bp), the number of substitutions per site K can be estimated: K =! 3 4 ln(1! 4 3 p) = (p=0.1) Under Kimura 2P model: K = 1 2 ln( 1 1! 2P! Q ) ln( 1 1! 2Q ) = (P=0.08, Q=0.02) where p = the observed proportions of different nucleotides between the two sequences 15 where P = the proportions of transitions and Q = the proportions of transversions. p is the proportion of total substitution Overview of Distance method UPGMA 1. Transform the data matrix into distance table OTU A B C B d AB C d AC d BC D d AD d BD d CD OTU (AB) C C d (AB)C D d (AB)D d CD where d (AB)C = (d AC + d BC )/2 and d (AB)D = (d AD + d BD )/2 2. Use this new data matrix to evaluate/ construct the tree (Page & Holme 1998) (Graur & Li 2000) 18 18

4 Example Example Felsenstein (2004) Felsenstein (2004) Example UPGMA tree Felsenstein (2004) Felsenstein (2004) True tree 3 SP1: AAACGCGCTTAGATCGCCTAACGTACAAGC 10 SP2: TATAAAGGGTAGAAAACCTAAGGATCAACG N1: AATCGCGCTTAGATCGCCTAACGTACAACG 2 3 N2: AATCGCGGGTAGATCGCCTAACGTACAACG SP3: AATCGCGGGTATTTCGCCTAACGTACATCG SP1 SP2 SP SP1 SP2 SP SP2 SP1 SP3 Neighbor-Joining (NJ) method Saitou & Nei (1987); Studier & Keppler (1988) NJ does not assume a clock and approximates the minimum evolution method

5 NJ procedure 1. For each tip, compute u i = # n j: j"i D i (n! 2) 2. Choose the i and j for which D ij -u i -u j is smallest 3. Join i and j, compute the new node (ij) to every other nodes D (ij ),k = (D ik + D jk! D ij ) 2 4. Delete tips i and j and make new table with the new node (ij) Limitation on distance methods All nucleotide sites change independently. When evolutionary rates vary from site to site, than the data set needs to be corrected The substitution rate is constant over time and in different lineages. The base composition is at equilibrium. The conditional probabilities of nucleotide substitutions are the same for all sites and do not change over time. 5. Continue till resolve the tree Discrete methods Maximum parsimony (%&'()*) Maximum likelihood (+,-./)*) Bayesian inference ( ) Others Parsimony methods The goal is to find the most parsimonious tree The criteria are to calculate the changes of character states, i.e. the evolutionary steps First, we have to know the way to evaluate a given tree A simple data matrix w/ discrete characters SpA: TCAGACGATTGTCAGACCATTG SpB: TCAGTCGACTGTCAAACCATTG SpC: TCGGTCAATTGTCAAACGATTG SpD: TCGGTCAATTGTCAAACGATTG SpA SpB SpC SpD SpA SpB SpD SpC SpA SpC SpD SpB A simple data matrix w/ discrete characters For position no. 3 SpA: TCAGACGATTGTCAGACCATTG SpB: TCAGTCGACTGTCAAACCATTG SpC: TCGGTCAATTGTCAAACGATTG SpD: TCGGTCAATTGTCAAACGATTG A A G G A A G G A G G A SpA SpB SpC SpD SpA SpB SpD SpC SpA SpC SpD SpB A A G G SpA SpB SpC SpD A to G Character change (step) = 2 Character change (step) = Character change (step) =

6 A simple data matrix w/ discrete characters For position no. 7 SpA: TCAGACGATTGTCAGACCATTG SpB: TCAGTCGACTGTCAAACCATTG SpC: TCGGTCAATTGTCAAACGATTG SpD: TCGGTCAATTGTCAAACGATTG A simple data matrix w/ discrete characters SpA: TCAGACGATTGTCAGACCATTG SpB: TCAGTCGACTGTCAAACCATTG SpC: TCGGTCAATTGTCAAACGATTG SpD: TCGGTCAATTGTCAAACGATTG G G A A G G A A G A A G SpA SpB SpC SpD SpA SpB SpD SpC SpA SpC SpD SpB G G A A G G A A G A A G SpA SpB SpC SpD SpA SpB SpD SpC SpA SpC SpD SpB G to A Character change (step) = 9 Character change (step) = 9 Character change (step) = 6 Character change (step) = 2 Character change (step) = 2 Character change (step) = Consensus trees Finding the underlying information among trees So, how many trees out there are we dealing with? (Page & Holme 1998) taxa Tree searching The number of unrooted trees: N unrooted = (2n! 5)! 2 n!3 (n! 3)! 4 taxa The number of rooted trees: N rooted = (2n! 3)! 2 n!2 (n! 2)!

7 Taxon number All possible unrooted tree number , , ,027, ,459, ,729, ,749,310, ,234,143, ,905,853,580, ,458,046,676, ,190,283,353,629, ,898,783,962,510, ,332,659,870,762,850, ,643,095,476,699,771, ,200,794,532,637,891,559, ,830,986,772,877,770,815, ,113,070,457,687,988,603,440, ,862,029,680,583,509,947,946, ,373,791,335,626,257,947,657,609,375 > etc Note Say a computer can evaluate 10 6 trees per second. If we want to evaluate all of the trees for 25 taxa, we will need x = /10 6 /60/60/24/365 = 3.17x10 15!"#$%!& We got to have some ways to approximate the true tree Ways to solve time paradigm Skip unnecessary calculation Change the tree searching ways The procedure can be simplified SpA: TCAGACGATTGTCAGACCATTG SpB: TCGGTCGACTGTCAGACCATTG SpC: TCAGTCGATTGTCA-ACGATTG SpD: TCAGTCGATTGTCA-ACGATTG SpE: TCAGTCGATCGTCA-ACGATTG Parsimonious uninformative Parsimonious informative Searching for optimal trees Exhausted search Branch-and-bound method Heuristic approach Stepwise/closest/random addition Star decomposition Branch swapping Exhausted search 41 Page & Holme (1998) Molecular evolution 41 42

Distribution of tree length Frequency distribution of lengths of 0000 random trees: mean=6528.095481 sd=65.005662 g1=-0.322317 g2=0.159848 6114.

8 Distribution of tree length Frequency distribution of lengths of 0000 random trees: mean= sd= g1= g2= / (1) (3) (24) (84) (302) (1071) # (3493) ### (9300) ######## (22649) ################# (48576) ################################# (94873) ################################################## (144323) ################################################################# (187000) ##################################################################### (199355) ##################################################### (153445) ############################### (88764) ############# (36489) ### (8865) (1266) (117) \ Data of bird ovomucoids 43 Tree-island profile: First Last First Times Island Size tree tree Score replicate hit Results of heuristic search, with random addition from random starting points Data of bird ovomucoids 44 Branch and bound searching A shortest Hamiltonian path problem Hendy & Penny (1982) first used this method for inferring phylogenies. An example - shortest Hamiltonian path (SHP) For n cities, there will be n-1 cities to come next, so there will be n! possible solution Point x y Random route: Total length= Adding by greedy manner: Length= Optimal solution: Length= Hendy, M.D. & D. Penny (1982) Mathem. Biosci. 60: Felsenstein (2004) Inferring phylogeny Felsenstein (2004) Inferring phylogeny 46 Branch-and-bound search heuristic searching for best tree #This method can greatly improve the speed of search, but it still cannot escape from the constraints of the NPhardness proof. Page & Holme (1998) Molecular evolution Felsenstein (2004) Inferring phylogeny 48 48

Heuristic approach- Branch swapping: NNIs Nearestneighbor interchanges (NNI) How greedy should we be? In a tree with n tips, there will be n-3 interior branches.

9 Heuristic approach- Branch swapping: NNIs Nearestneighbor interchanges (NNI) How greedy should we be? In a tree with n tips, there will be n-3 interior branches. In all, 2(n-3) neighbors will be examined for each tree. Should we do NNI for each of the best trees, or stop at some point, or should we start from scratch more often? Swofford et al. (1996) Molecular Systematics The space of all 15 possible unrooted trees The space of all 15 possible unrooted trees NNI is to moving in this graph Felsenstein (2004) Inferring phylogeny Felsenstein (2004) Inferring phylogeny 52 Heuristic approach- Branch swapping: TBR Tree bisection and reconnection (TBR) In a n 1 +n 2 species in the tree, there will be (2n 1-3)(2n 2-3) possible ways to reconnect the two trees. Rearrangement Browsing tree space Random starting point strategy to avoid being trapped in tree island (Maddison 1991) Parsimony ratchet Parsimony ratchet uses a re-weighted subset of characters as a starting point to browse the tree space, and tries to find as many tree islands as possible by using adjacent-tree searching method. (Nixon 1999) 53 Swofford et al. (1996) Molecular Systematics 53 Maddison, D.R. (1991) Syst. Zool. 40: Nixon, K.C. (1999) Cladistics 15:

10 Parsimony ratchet Described by Nixon (1999), and available in various programs (NONA, WINCLADA, PAUPRat, etc.). Parsimony ratchet uses a re-weighted subset of characters as a starting point to browse the tree space, and tries to find as many tree islands as possible by using adjacent-tree searching method. Parsimony ratchet procedure Generate a starting Wagner tree Randomly select a subset of character (5-25%) and add 1 weight score Performing TBR branch swapping, keep 1 tree Reset the weighting to original Performing branch swapping, keep the best tree Return to step 2, repeat the iteration (step2-6) times Nixon, K.C. (1999) Cladistics 15: Notes on parsimony ratchet It seems to improve the effectivity of tree searching It can be used with any objective function based on character data: compatibility, distance matrix, and likelihoods. The strategy can be modified Nixon, K.C. (1999) Cladistics 15: Weighted parsimony method Incorporating simple nucleotide models into MP analysis Transition vs. transversion scores The Sankoff algorithm applied to the tree C A C A G! 0!! 0!!!! 0!! 0!!!!! 0! A C G T A C G T A C G T S = min S 0 (i) A C G T A C G T Modified from Felsenstein (2004) Inferring phylogeny 60 60

11 Evaluating trees How do we know the tree we got is right? The evaluation Character properties (CI, RI) Examining how clean is the data on a given tree Confidence level of trees Comparisons between obtained trees Partition distance Kishino-Hasegawa test Distance test Likelihood ratio test Bootstrap/jackknife (internal support) Bremer support (for parsimony) Properties of characters Consistency index (CI) of each character is: character CI = m i /S i Tree CI for all characters in a specific tree: n! m i w i i=1 tree CI = n! w i s i i=1 m i ='()*+,-./i01/23)*+,45 (minimum conceivable steps) S i =06+,-./i01/+,45 w i = i01/789n:01; Properties of characters Retention index (RI) of each characters is: M character RI = i! s i M i! m i m i ='()*+,-./i01/23)*+,45 (minimum conceivable steps) M i ='()*+,-./i01/2<)*+,45 (maximum conceivable steps) S i =06+,-./i01/+, Example: calculating CI & RI Evaluating trees Taxon Taxon Taxon Taxon Taxon Tree 1 Tree 2 Taxon1 0 Taxon1 0 Taxon2 0 Taxon4 1 Taxon3 1 Taxon3 1 Taxon4 1 Taxon2 0 Taxon5 1 Taxon5 1 Character properties (CI, RI) Confidence level of trees Comparisons between obtained trees Bootstrap/jackknife (internal support) Bremer support (for parsimony) Character(1) CI=1/1=1 Character(1) RI=(2-1)/(2-1)=1 Character CI=1/2=0.5 Character RI=(2-2)/(2-1)=0 TreeCI = =1 TreeCI = =

a consensus tree based on majority rule, numbers indicates the % of supported topology. Usually only >50% branches are shown.

12 Bootstrap method Characters N A B C Taxa D E F G Bootstrap method M times replica; M=, 500, 0, or any desired number N N Make a tree Make a tree Make a tree for each replica Make a consensus tree based on majority rule, numbers indicates the % of supported topology. Usually only >50% branches are shown. Page & Holme (1998) Molecular evolution Diagram explaining the bootstrapping procedure used in phylogenetic analysis Taxa A B C D E F G Characters N Jackknife method Take out X% of characters, X=30, 50, or any number M times replica; M=, 500, 0, or any desired number Primate mtdna phylogeny MP criteria 5 Bootstrap 0 replicates N-X characters N-X characters Make a tree Make a tree Make one tree for each replica Make a consensus tree based on majority rule, numbers indicates 99 the % of supported topology Usually only >50% branches are shown Freq % ** %...**** %...*** %.** %..***** % Gorilla grouped with Homo/Pan or other primates Diagram explaining the Jackknife procedure used in phylogenetic analysis Pseudo-resampling. Bootstrapping An approximate measure of repeatability and accuracy of data. Will not correct the inconsistency caused by reconstruction method. The tree constructed in every replicate still depend on the methods you choose, therefore subject to associated problems Decay/support index Also called Bremer support (Bremer 1988, 1994; Donoghue et al. 1992) An index of support calculating the difference in tree lengths between the shortest trees that contain versus lack a specific group. Constraint trees can be generated by AutoDecay

13 Method of calculation 1. Obtain most parsimonious tree(s) (MP) Generate a strict consensus tree 2. Obtain all trees one step longer (MP + 1) Generate a strict consensus tree If branch is not supported, Decay index = 1 3. Obtain all trees one step longer (MP + 2) Generate a strict consensus tree If branch is not supported, Decay index = 2 4. Obtain all trees one step longer (MP + 3) Generate a strict consensus tree If branch is not supported, Decay index = 3 Bremer Support (decay index) the number of extra steps it takes to collapse a group example: 1 MP tree, 110 steps Haliperp HPE Arabaren AAU43231 Arabsuec ASU43227 Arabthal ATU43224 Arabsuec ASU43226 Arabthal ATH Capsrube CRU Capsrube CRU Bremer Support (decay index) 3 trees <= 111 steps Bremer Support (decay index) 3 trees <= 111 steps Haliperp HPE Arabaren AAU43231 Arabsuec ASU43227 Arabthal ATU43224 Arabsuec ASU43226 Arabthal ATH Capsrube CRU Capsrube CRU Haliperp HPE Arabaren AAU43231 Arabsuec ASU43227 Arabthal ATU43224 Arabsuec ASU43226 Arabthal ATH Capsrube CRU Capsrube CRU Bremer Support (decay index) Bremer Support (decay index) 5 trees <= 117 steps Haliperp HPE Arabaren AAU43231 Arabsuec ASU43227 Arabthal ATU43224 Can not be larger than the branch length No direct connection to branch length otherwise Quantification of support in a parsimony framework Haliperp HPE Arabaren AAU43231 Arabsuec ASU43227 Arabthal ATU43224 Arabsuec ASU43226 Arabthal ATH Arabsuec ASU43226 Arabthal ATH Capsrube CRU Capsrube CRU Capsrube CRU Capsrube CRU

Methodological concerns Effects of sampling Sampling problem Performance of phylogenetic methods under computer simulation 0 change 3 changes Makes No.

14 Methodological concerns Effects of sampling Sampling problem Performance of phylogenetic methods under computer simulation 0 change 3 changes Makes No.2 a fast evolving taxon 79 (Page & Holmes, 1998) Long branch attraction Simulation analysis Joe Felsenstein (1978, Syst. Zool. 27: ) UPGMA Parsimony Page & Holme (1998) Molecular evolution Page & Holme (1998) Molecular evolution Equal rate of evolution Unequal rate of evolution Page & Holme (1998) Molecular evolution Page & Holme (1998) Molecular evolution 84 84

Parsimony Weighted parsimony UPGMA Lake!s invariants Maximum likelihood (Jukes-Cantor) Maximum likelihood (Kimura) References of phylogenetics Graur, D. and W.-H. Li. 2000.

15 Parsimony Weighted parsimony UPGMA Lake!s invariants Maximum likelihood (Jukes-Cantor) Maximum likelihood (Kimura) References of phylogenetics Graur, D. and W.-H. Li Fundamentals of Molecular Evolution. 2nd ed., Sinauer Assoc., Sunderland, MA, USA. Hall, B. G Phylogenetic trees made easy: a how-to manual, 2nd ed. Sinauer Assoc., Sunderland, MA. Hillis, D. M., C. Moritz, and B. K. Mable (eds) Molecular systematics. Sinauer Assoc., Sunderland, MA. Page, R. D. M., and E. C. Holmes Molecular evolution - A phylogenetic approach. Blackwell Science Ltd, Oxford, the United Kingdom. Yang, Z. H Computational molecular evolution. Oxford University Press. Weighted least squares Swofford et al. (1996) Molecular Systematics

Constructing Evolutionary/Phylogenetic Trees

Constructing Evolutionary/Phylogenetic Trees 2 broad categories: istance-based methods Ultrametric Additive: UPGMA Transformed istance Neighbor-Joining Character-based Maximum Parsimony Maximum Likelihood