Phylogeny

Presented By Dr. Shazzad Hosain Asst. Prof. EECS, NSU Phylogeny What is phylogenetics? Phylogenetics is the study of evolutionary relationships among and within species. crocodiles birds lizards snakes rodents primates marsupials What is phylogenetics? crocodiles birds lizards snakes rodents primates marsupials This is an example of a phylogenetic tree. • Forensics: Did a patient’s HIV infection result from an invasive dental procedure performed by an HIV+ dentist? Applications of phylogenetics • Conservation: How much gene flow is there among local populations of island foxes off the coast of California? • Medicine: What are the evolutionary relationships among the various prion-related diseases? To be continued… Phylogenetic concepts: Interpreting a Phylogeny Sequence A Sequence B Sequence C Sequence D Sequence E Time Which sequence is most closely related to B? A, because B diverged from A more recently than from any other sequence. Physical position in tree is not meaningful! Only tree structure matters. Phylogenetic concepts: Rooted and Unrooted Trees Time A B C D Root = A B C D Root X = ? A B C D ? ? ? ? ? X Rooting and Tree Interpretation bacteria archaebacteria oak fruit fly chicken human bacteria archaea oak fruit fly chicken human bacteria archaebacteria oak fruit fly chicken human – bones – cell nuclei + cell nuclei + bones Rooting Methods Given an unrooted network of relationships among four species of Carnivora [left], outgroup rooting uses an additional taxon (the outgroup) known from independent evidence to be less closely related to any of the other species (the ingroup) than they are to each other. The root is then placed on the branch between the outgroup and the ingroup. In this case, Lynx is a feloid carnivore in a separate superfamily from the four canoid carnivores. Inclusion of Lynx in the network analysis places it on the internode.This method requires accurate information as to ingroup / outgroup relationships.   Outgroup Rooting a network of relationships How Many Trees? Unrooted trees Rooted trees # sequences # pairwise distances # trees # branches /tree # trees # branches /tree 3 4 5 6 10 30 N (assuming bifurcation only) How Many Trees? 2N - 2 (2N - 3)! 2N - 2 (N - 2)! 2N - 3 (2N - 5)! 2N - 3 (N - 3)! N (N - 1) 2 N 58 4.95 ? 1038 57 8.69 ? 1036 435 30 18 34,459,425 17 2,027,025 45 10 10 945 9 105 15 6 8 105 7 15 10 5 6 15 5 3 6 4 4 3 3 1 3 3 # branches /tree # trees # branches /tree # trees # pairwise distances # sequences Rooted trees Unrooted trees Tree Properties Root Ultrametricity All tips are an equal distance from the root. X Y a b c d e a = b + c + d + e Root Additivity Distance between any two tips equals the total branch length between them. X Y a b c d e XY = a + b + c + d + e In simple scenarios, evolutionary trees are ultrametric and phylograms are additive. Terminology External nodes: things under comparison; operational taxonomic units (OTUs) Internal nodes: ancestral units; hypothetical; goal is to group current day units Root: common ancestor of all OTUs under study. Path from root to node defines evolutionary path Unrooted: specify relationship but not evolutionary path If have an outgroup (external reason to believe certain OTU branched off first), then can root Topology: branching pattern of a tree Branch length: amount of difference that occurred along a branch Phylogeny Applications Tree of Life: Analyzing changes that have occurred in evolution of different organisms http://tolweb.org/tree/phylogeny.html Phylogenetic relationships among genes can help predict which ones might have similar functions (e.g., ortholog detection) Follow changes occurring in rapidly changing species (e.g., HIV virus) Phylogeny Packages PHYLIP, Phylogenetic inference package evolution.genetics.washington.edu/phylip.html Felsenstein Free! PAUP, phylogenetic analysis using parsimony paup.csit.fsu.edu Swofford Similarity vs. Homology Similar sequences resemble one another Homolog sequences derived from common ancestor Ortholog homologous sequences within a species Paralog homologous sequences between species Ortholog vs. Paralog Ortholog genomic variation occurs after speciation hence can be used for phylogeny of organism Paralog genetic duplication occurs before speciation hence not suitable for phylogeny of organism Homoplasy Sequence similarity NOT due to common ancestry May arise due to parallelism or convergent evolution Parallelism or parallel evolution the development of a similar trait in related, but distinct, species descending from the same ancestor, but from different clades Convergent evolution Parallel evolution Parallel evolution occurs when two species that have descended from the same ancestor remain similar over long periods of time because they independently acquire the same evolutionary adaptations. Parallel evolution occurs because genetically related species adapt to similar environmental changes in similar ways. After many years, the organisms may still resemble each other, even though they speciated in the distant past. Convergent evolution when species from different ancestors colonize the same environment, they may independently acquire the same adaptations. The evolution of species descended from different ancestors to become superficially similar because they are adapting to the same environment is called convergent evolution Divergent Evolution Phylogeny of what? Organisms Whole genome phylogeny Ribosomal RNA (surrogate for whole genome) Strains (closely related microbes) Individual genes (or gene families) Repetitive DNA sequences Metabolic pathways Secondary Structures Any discrete character(s) Human languages Microbial communities Why compute phylogenetic trees? Understand evolutionary history Map pathogen strain diversity for vaccines Assist in epidemiology Of infectious diseases Of genetic defects Aid in prediction of function of novel genes Biodiversity studies Understanding microbial ecologies Tree Building Exercises Computational Approaches to Phylogenetic Tree Computation Distance Based Methods UPGMA Neighbor joining Character State Methods Maximum Parsimony Method Maximum Likelihood Methods Tree merging Consensus trees, super-trees What data is used to build trees? Traditionally: morphological features (e.g., number of legs, beak shape, etc.) Today: Mostly molecular data (e.g., DNA and protein sequences) Data for Phylogeny Can be classified into two categories: Numerical data Distance between objects e.g., distance(man, mouse)=500, distance(man, chimp)=100 Usually derived from sequence data Discrete characters Each character has finite number of states e.g., number of legs = 1, 2, 4 DNA = {A, C, T, G} UPGMA UPGMA 2. Determine the evolutionary distances and build distance matrix - A simple example AGGCCATGAATTAAGAATAA AGCCCATGGATAAAGAGTAA AGGACATGAATTAAGAATAA AAGCCAAGAATTACGAATAA Distance Matrix In this example the evolutionary distance is expressed as the number of nucleotide differences for each sequence pair. For example, sequences 1 and 2 are 20 nucleotides in length and have four differences, corresponding to an evolutionary difference of 4/20 = 0.2. 1 2 3 4 1 - 0.2 0.05 0.15 2 - 0.25 0.4 3 - 0.2 4 - 3. Phylogenetic Tree Construction example (UPGMA algorithm) 1. Pick smallest entry Dij 2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes Dij Bear Raccoon Weasel Seal Bear - 0.26 0.34 0.29 Raccoon - 0.42 0.44 Weasel - 0.44 Seal - Bear Raccoon 0.13 0.13 UPMGA (Michener & Sokal 1957) 3. Phylogenetic Tree Construction example (UPGMA algorithm) Dij Bear Raccoon Weasel Seal Bear - 0.26 0.34 0.29 Raccoon - 0.42 0.44 Weasel - 0.44 Seal - 3. Compute new distances to the other species using arithmetic means Bear Raccoon 0.13 0.13 3. Phylogenetic Tree Construction example (UPGMA algorithm) Dij BR Weasel Seal BR - 0.38 0.365 Weasel - 0.44 Seal - 1. Pick smallest entry Dij 2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes Bear Raccoon Seal 0.13 0.1825 0.1825 3. Phylogenetic Tree Construction example (UPGMA algorithm) Dij BR Weasel Seal BR - 0.38 0.365 Weasel - 0.44 Seal - Compute new distances to the other species using arithmetic means Bear Raccoon Seal 0.13 0.1825 0.1825 3. Phylogenetic Tree Construction example (UPGMA algorithm) Dij BRS Weasel BRS - 0.4 Weasel - Pick smallest entry Dij. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes. Done! Bear Raccoon Seal Weasel 0.13 0.1825 0.2 0.2 Downside of UPGMA Assume molecular clock (assuming the evolutionary rate is approximately constant) Generates only rooted tree Trees are ultrametric Doesn’t work the following case: 37 Computational Approaches to Phylogenetic Tree Computation Distance Based Methods UPGMA Neighbor joining Character State Methods Maximum Parsimony Method Maximum Likelihood Methods Tree merging Consensus trees, super-trees Neighbor-joining method Developed in 1987 by Saitou and Nei Works in a similar fashion to UPGMA Still fast – works great for large dataset Doesn’t require the data to be ultrametric Great for largely varying evolutionary rates 39 How to construct a tree with Neighbor-joining method? Step 1: Calculate sum all distance from x and divide by (leaves – 2) Sx = (sum all Dx) / (leaves - 2) Step 2: Calculate pair with smallest M Mij = Distance ij – Si – Sj Step 3: Create a node U that joins pair with lowest Mij S1U = (Dij / 2) + (Si – Sj) / 2 40 How to construct a tree with Neighbor-joining method? Step 4: Join I and j according to S and make all other taxa in form of a star Step 5: Recalculate new distance matrix of all other taxa to U with: DxU = Dix + Djx - Dij 41 Example of Neighbor-joining A B C D E B 5 C 4 7 D 7 10 7 E 6 9 6 5 F 8 11 8 9 8 Step 1: S calculation : Sx = (sum all Dx) / (leaves - 2) S(A) = (5 + 4 + 7 + 6 + 8) / 4 = 7.5 S(B) = (5 + 7 + 10 + 9 + 11) / 4 = 10.5 S(C) = (4 + 7 + 7 + 6 + 8) / 4 = 8 S(D) = (7+ 10 + 7 + 5 + 9) / 4 = 9.5 S(E) = (6 + 9 + 6 + 5 + 8) / 4 = 8.5 S(F) = (8 + 11 + 8 + 9 + 8) / 4 = 11 42 Example of Neighbor-joining cont 1 Step 2: Calculate pair with smallest M Mij = Distance ij – Si – Sj Smallest are M(AB) = d(AB) – S(A) –S(B) = 5 – 7.5 – 10.5= -13 M(DE) = 5 – 9.5 – 8.5 = -13 A B C D E B -13 C -11.5 -11.5 D -10 -10 -10.5 E -10 -10 -10.5 -13 F -10.5 -10.5 -11 -11.5 -11.5 43 Example of Neighbor-joining cont 2 Step 3: Create a node U S1U = (Dij / 2) + (Si – Sj) / 2 U1 joins A and B: S(AU1) = d(AB) / 2 + (S(A) – S(B)) / 2 = 5 / 2 + (7.5 - 10.5) / 2 = 1 S(BU1) = d(AB) / 2 + (S(B) – S(A)) / 2 = 5 / 2 + (10.5 – 7.5) / 2 = 4 44 Example of Neighbor-joining cont 3 Step 4: Join A and B according to S, and make all other taxa in form of a star. Branches in black are unknown length and Branches in red are known length 45 Example of Neighbor-joining cont 4 Step5: Calculate new distance matrix Dxu = (Dix + Djx – Dij) / 2 d(CU) = (d(AC) + d(BC) - d(AB)) / 2 = (4 + 7 - 5) / 2 =3 d(DU) = d(AD) + d(BD) - d(AB) / 2 = 6 Same as EU and FU Then we get the new distance matrix U1 C D E C 3 D 6 7 E 5 6 5 F 7 8 9 8 46 Example of Neighbor-joining cont 5 Repeat 1 to 5 until all branches are done In this example, we will get this at the end 47 Downside of Neighbor-joining Generates only one possible tree Generates only unrooted tree 48 Computational Approaches to Phylogenetic Tree Computation Distance Based Methods UPGMA Neighbor joining Character State Methods Maximum Parsimony Method Maximum Likelihood Methods Tree merging Consensus trees, super-trees 50 Parsimony-score: Number of character-changes (mutations) along the evolutionary tree (tree containing labels on internal vertices) Example: Maximum Parsimony Method AGA AAA AAG GGA 1 1 0 2 0 0 1 0 0 1 0 1 AAA AAA AAA AGA AAA AAG GGA AAA AAA AGA Most parsimonious tree: ? Tree with minimal parsimony score Score = 4 Score = 3 Minimal Evolution Principle 51 We break the problem into two: Small parsimony: Given the topology find the best assignment to internal nodes Large parsimony: Find the topology which gives best score Large parsimony is NP-hard We’ll show solution to small parsimony (Fitch and Sankoff’s algorithms) Input to small parsimony: tree with character-state assignments to leaves Example: Small vs. Large Parsimony Aardvark Bison Chimp Dog Elephant A: CAGGTA B: CAGACA C: CGGGTA D: TGCACT E: TGCGTA 52 Fitch’s Algorithm Execute independently for each character: Bottom-up phase: Determine set of possible states for each internal node Top-down phase: Pick states for each internal node Aardvark Bison Chimp Dog Elephant 1 2 CAGGTA CAGACA CGGGTA TGCACT TGCGTA Dynamic Programming framework 53 Determine set of possible states for each internal node Initialization: Ri = {si} Do a post-order (from leaves to root) traversal of tree Determine Ri of internal node i with children j, k: Fitch’s Algorithm Bottom-up phase Parsimony-score = # union operations T CT T C T A G T AGT GT T score = 3 54 Pick states for each internal node Pick arbitrary state in Rroot for the root Do pre-order (from root to leaves) traversal of tree Determine sj of internal node j with parent i: Fitch’s Algorithm Top-down phase T CT T C T A G T AGT GT T Complexity: O(mnk) #characters #taxa/nodes #states score = 3 55 Weighted Parsimony Sankoff’s algorithm Each mutation a?b costs differently - S(a,b). Bottom-up phase: Determine Ri(s) – cost of optimal state-assignment for subtree of i, when it is assigned state s. Top-down phase: Pick optimal states for each internal node Fitch’s algorithm as special case: Ri – set of states which yield minimal-cost subtree of i Same as algorithm for optimal lifted tree alignment (Tutorial #4) 56 Determine Ri(s) for each internal node Initialization: Do a post-order (from leaves to root) traversal of tree Determine Ri of internal node i with children j, k: Sankoff’s Algorithm Bottom-up phase C T A G T T Natural generalization For non-binary trees Remember pointers s?s’ 57 Pick states for each internal node Select minimal cost character for root (s minimizing Rroot(s)) Do pre-order (from root to leaves) traversal of tree: - For internal node j, with parent i, select state that produced minimal cost at i (use pointers kept in 1st stage) Sankoff’s Algorithm Top-down phase C T A G T T Complexity: O(mnk2) #characters #taxa/nodes #states 58 Unweighted parsimony: Sankoff’s algorithm: Ri(s) - cost of optimal subtree of i, when it is assigned state s Fitch’s algorithm: Score(i) - cost of optimal state-assignment for subtree of i Ri - set of optimal state-assignment for subtree of i We need to show that: Optimal tree assigns node i with state from Ri. Fitch’s bottom-up recursive formula for Ri. is correct: Fitch’s Algorithm as special case of Sankoff’s algorithm Check for yourselves 59 Unweighted parsimony: Score(i) - cost of optimal state-assignment for subtree of i Ri - set of optimal state-assignment for subtree of i We need to show that: Optimal tree assigns node i with state from Ri. Trivially true for the root Assume (to the contrary) that in an optimal assignment, some node – j is assigned sj?Rj root i j sj?Rj ? Rj(sj) ? Score(j)+1 ? By switching from sj to some s?Rj we do not raise the parsimony-score Why is this not the case for the weighted version? Parsimony-score is integer Fitch’s Algorithm as special case of Sankoff’s algorithm Computational Approaches to Phylogenetic Tree Computation Distance Based Methods UPGMA Neighbor joining Character State Methods Maximum Parsimony Method Maximum Likelihood Methods Tree merging Consensus trees, super-trees Maximum likelihood Originally developed for statistics by Ronald Fisher between 1912 and 1922 Therefore, explicit statistical model Uses all the data Tends to outperform parsimony or distance matrix methods 61 How to construct a tree with Maximum likelihood? Step 1: Make all possible trees depending on the number of leaves Step 2: Calculate likelihood of occurring with the given data L(Tree) = probability of each tree. optimizing branch length generating tree topology Step 3: Pick the tree that have the highest likelihood. 62 Sounds really great? Num of leaves Num of possible trees 3 1 5 15 10 2027025 13 15058768725 20 8200794532637891559375 Maximum likelihood is very expensive and extremely slow to compute 63 Comparison of Methods Distance Maximum parsimony Maximum likelihood Uses only pairwise distances Uses only shared derived characters Uses all data Minimizes distance between nearest neighbors Minimizes total distance Maximizes tree likelihood given specific parameter values Very fast Slow Very slow Easily trapped in local optima Assumptions fail when evolution is rapid Highly dependent on assumed evolution model Good for generating tentative tree, or choosing among multiple trees Best option when tractable (<30 taxa, homoplasy rare) Good for very small data sets and for testing trees built using other methods Methods of evaluating trees Bootstrap: resample initial data set with one datum removed and replaced with another member Jackknife: resample initial distribution with one datum missing and not replaced MCMC: complex, but generates random numbers to produce a desired probability distribution with which to compare model Phylogeny Flowchart Difference in Methods Maximum-likelihood and parsimony methods have models of evolution Distance methods do not necessarily Useful aspect in some circumstances E.g., trees built based on whole genomes, presence or absence of genes Religious wars over which methods to use Most people now believe ML based methods are best: most sensitive at large evolutionary distances – but also most time-consuming & depend on specific model of evolution used Most commonly used packages contain software for all three methods: may want to use more than 1 to have confidence in built tree Phylip URL: http://evolution.genetics.washington.edu/phylip.html Parsimony DNApenny or Protpars Distance Compute distance measure using DNAdist or Protdist Neighbor (can use NJ or UPGMA) ML DNAml Visualising trees Treeview You can change the graphic presentation of a tree (cladogram, rectangular cladogram, radial tree, phylogram), but not change the structure of a tree http://homopan.wayne.edu/softwares/phoenix/index.html Reference Mostly from Web