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1 Tree of Life iological Sequence nalysis Chapter Phylogenetic Prediction ll organisms on Earth have a common ancestor. ll species are related. The relationship is called a phylogeny which can be represented by a phylogenetic tree. Phylogenetic analysis of shapes of teeth from different species of animals or a family of related DN/protein sequences is to infer the tree from observations upon the organisms. Phylogenetic Prediction Traditional taxonomy mainly is based on a variety of morphological characters, embryology, and the information about the geological context (stratigraphy). Molecular phylogeny is based on the similarity of DN/protein sequences. The study of nucleotide sequences of 1S rrn revealed 3 major evolutionary groups in the tree of life: acteria, Eucarya and rchaea. The Tree of Life 1
2 Homologous Genes Orthologous Refers to homologous genes located in the genomes of different organisms Genes diverged through speciation Paralogous Refers to homologous genes located in the same genome Genes diverged by gene duplication enologous Refers to homologous genes located in the genomes of different organisms Genes diverged by horizontal gene transfer Orthologous Paralogous axolotl panda lesser moose panda goshawk duck vulture alligator Tree obtained based on a set of alpha hemoglobins. myoglobin theta alpha zeta epsilon gamma beta Tree obtained by a chain of human hemoglobins delta enologous Characteristics of Tree phylogenetic tree is characterized by its topology and its branch length: Each internal node of a tree is an estimation of the ancestor of the child nodes Each leaf node corresponds to observed sequences The length of each edge indicates the amount of evolutionary divergence associated to it, defined by some measure of distance between sequences or the internal nodes Rooted and unrooted trees For a rooted full binary tree, # internal nodes = #?# of leaves -1
3 Phylogenetic tree construction methods Methods indirectly based on sequences : Distance matrices (UPGM, Fitch-Margoliash, NJ, ) Find tree that accounts for estimated evolutionary distances Methods directly based on sequences: Parsimony Find tree that requires minimum number of changes to explain the data Maximum likelihood Find tree that maximizes likelihood of data Distance Matrix Methods Convert sequence data into a set of discrete pairwise distance values, arranged into a matrix. Distance methods fit a tree to this matrix. The phylogenetic tree is constructed by using a cluster analysis method. The phylogeny makes an estimation of the distance for each pair as the sum of branch lengths in the path from one sequence to another through the tree. Tree of life p-distance I aagtcatgct II aaatcaggct III cagacagtca IV cacactgcca p-distance is the proportion of nucleotide sites at which two sequences are different. HUMN MOUSE DROSOPHLI RICE YEST This yields the pairwise p(ij) distance matrix: I II III IV I II 0.0 III IV Jukes-Cantor distance Maximum likelihood estimate of the number of substitutions between two sequences. p is described with the method p-distance. nother distance measure Distance (d) between two sequences (1, ) is computed from the pairwise alignment score: d = (1-score1/score11) (1-score1/score) For nucleotides: d = -3/4 log (1 - p 4/3) For amino acids: d = -19/0 log (1 - p 0/19) 3
4 UPGM Unweighted Pair Group Method using rithmetic vg Distance of two clusters: d ij =(Σ p Ci q Cj d pq pq )/(nm) where n, m are numbers of sequences lgorithm: UPGM Initialization: UPGM ssign each sequence i to its own cluster C i Define one leaf of T for each sequence, and place at height zero Iteration: Determine the two clusters i, j for which d ij is minimal Define a new cluster k by C k = C i C j, and define d kl for all l Define a node k with daughter nodes i and j, and place it at height d ij / dd k to the current clusters and remove i and j Termination: When only two clusters i, j remain, place the root at height d ij / UPGM 1 t 1 =t =d 1 / 4 5 t 4 =t 5 =d 45 / 8 8 t 3 =d 3 / d 8 / Molecular Clock The edge lengths in the resulting tree can be viewed as times measured by a molecular clock with a constant rate. If the distance data are derived by adding up edge lengths in a tree T with a molecular clock, then UPGM will reconstruct T correctly --- ultra-metric condition. The distances are ultrametric if i,j,k, d ij, d ik, d jk are either all equal or two are equal and the third is smaller. ut, the same rate of evolution at each point in the tree is generally not TRUE. 9 8 Neighbor Joining ssumes additivity: distance between pairs of leaves = sum of lengths of edges connecting them Does not make molecular clock assumption : modified distance matrix constructed to adjust for differences in evolution rate Produces unrooted tree Rooting trees root can be added by considering an outgroup (species known to be more distantly related). myoglobin theta alpha If the rate of evolution at every sequence position is roughly constant, root the tree at the midpoint of the longest span across the tree. If all the paralogs from most of the organisms are included in the analysis, root the tree where the paralog gene trees converge. zeta epsilon hemoglobin gamma beta delta 4
5 More on Distance Methods dvantages: easy to perform quick calculation fit for sequences having high similarity scores Disadvantages: all sites are generally equally treated (do not take into account differences of substitution rates ) the sequences are not considered as such (loss of information) not applicable to distantly divergent sequences. Parsimony ased pproaches Most widely used phylogenetic tree building algorithms llows the use of all known evolutionary information in the tree Strategy --- find a tree that explains the observed sequences with a minimal number of substitutions. Compute a cost for a given tree T Search through all trees to find the tree with the minimum cost Parsimony treats each site independently. Example of Parsimony Informative and Uninformative Sites asic step: counting the min # of changes needed at one site. Example: Site 1,, 3, 4 are not informative! Only site 5 is informative. Why? T G G T C G T T G G C T T T Sequences have to be aligned first! T T T C C G T C G T G G T G G T G T G T G G T T Informative and Uninformative Sites For a site to be informative, it must have at least two different nucleotides and at least two of the nucleotides have to be presented at least twice each. Only informative sites need to be considered. Fitch s algorithm Used for finding the minimum # of changes for a given tree ssumes: ll substitutions are equally likely Positions are independent First, post-order order traverses the tree to determine set of possible states for each internal node; then pre-order traverses the tree to pick ancestral states for internal nodes 5
6 Fitch s algorithm Example lgorithm (traditional parsimony, Fitch 191) Set C = 0 and k = n-1 Recursion: To obtain the set R k : If k is a leaf, R k = x k. Otherwise, Compute R i, R j for daughter nodes i, j of k and set R k = R i R j if the intersection is not empty, or else set R k = R i R j and increment C. Termination: Minimal cost of the tree = C. {,} {,} {} {} {} {} {} {} Can not be obtained from the method Possible Topologies For 5 species there are 105 different topologies. More generally, for any strictly bifurcating phylogeny with n species there are (n-3)!/( n- (n-)!) different topologies (rooted trees). With n=15 species there are 13,458,04,,85 different topologies. There are (n-5)!/( n-3 (n-3)!) unrooted trees. ranch and ound method for faster searches. First, use computationally fast method such as UPGM to obtain a upper bound C for the minimum number of substitutions. Then incrementally growing a tree by adding branches one at a time. If a subset of a tree requires more substitutions than C, stop growing the tree based on the subset. Update the upper bound C during the process. Other heuristic Searches ranch and ound ssessing the Trees: the bootstrap Krane & Raymer Given an alignment of sequences Generate an artificial alignment of the same size by picking columns from the alignment at random with replacement pply the parsimony algorithm to the new alignment Repeat for 1000 times The frequency with which a chosen phylogenetic feature appears is taken to be a measure of the confidence we can have in this feature
7 Disadvantages of Parsimony Methods Long computation time to construct a tree Within practical computational limits, this often leads to the generation of tens or more "equally most parsimonious trees" which make it difficult to justify the choice of a particular tree If the evolutionary clock is not constant, the procedure might generate misleading results. Krane & Raymer Maximum Likelihood Methods The maximum likelihood method assigns quantitative probabilities to mutational events, rather than merely counting them. It assigns branch lengths based on the probabilities of the mutational events. The optimal tree is the one with the highest likelihood of generating the observed data.
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