Phylogenetic Analysis Unit 16 BIOL221T: Advanced Bioinformatics for Biotechnology Irene Gabashvili, PhD

B&O, chapter 14 Bioinformatics analyses should be interpreted in evolutionary context Bioinformatics analyses should be interpreted in evolutionary context Good-quality sequence alignments important for evolutionary analysis Good-quality sequence alignments important for evolutionary analysis Common phylogenetic methods and software are different – be cautious when using and interpreting your results Common phylogenetic methods and software are different – be cautious when using and interpreting your results

Terminology and the Basics Phylogenetics is sometimes called claudistics Phylogenetics is sometimes called claudistics Clade – a set of descendants from a single ancestor (greek for branch). Clade – a set of descendants from a single ancestor (greek for branch). 3 basic assumptions: 3 basic assumptions: Any group of organism descended from a common ancestor Any group of organism descended from a common ancestor Bifurcating pattern of cladogenesis Bifurcating pattern of cladogenesis Change in characteristics occurs in lineages over time Change in characteristics occurs in lineages over time

Brief Introduction to the Theory of Evolution

Classification: Linnaeus Carl Linnaeus

Classification: Linnaeus Hierarchical systemHierarchical system –Kingdom(Rige) –Phylum(Række) –Class(Klasse) –Order(Orden) –Family(Familie) –Genus(Slægt) –Species(Art)

Classification depicted as a tree

SpeciesGenusFamilyOrderClass

Theory of evolution Charles Darwin

Phylogenetic basis of systematics Linnaeus: Linnaeus: Ordering principle is God. Darwin: Darwin: Ordering principle is shared descent from common ancestors. Today, systematics is explicitly based on phylogeny. Today, systematics is explicitly based on phylogeny.

Darwin’s four postulates I. More young are produced each generation than can survive to reproduce. II. Individuals in a population vary in their characteristics. III. Some differences among individuals are based on genetic differences. IV. Individuals with favorable characteristics have higher rates of survival and reproduction.  Evolution by means of natural selection  Presence of ”design-like” features in organisms: quite often features are there “for a reason”

Theory of evolution as the basis of biological understanding ”Nothing in biology makes sense, except in the light of evolution. Without that light it becomes a pile of sundry facts - some of them interesting or curious but making no meaningful picture as a whole” T. Dobzhansky

Phylogenetic Reconstruction: Distance Matrix Methods

Trees: terminology

Terminology Clades – monophyletic taxon Clades – monophyletic taxon Taxons – any named group of organism Taxons – any named group of organism Branches – divergence (length may indicate the degree) Branches – divergence (length may indicate the degree) Nodes – any bifurcating branch point Nodes – any bifurcating branch point

Trees: terminology

Trees: representations Three different representations of the same tree

Trees: rooted vs. unrooted A rooted tree has a single node (the root) that represents a point in time that is earlier than any other node in the tree. A rooted tree has directionality (nodes can be ordered in terms of “earlier” or “later”). In the rooted tree, distance between two nodes is represented along the time-axis only (the second axis just helps spread out the leafs) EarlyLate

Trees: rooted vs. unrooted A rooted tree has a single node (the root) that represents a point in time that is earlier than any other node in the tree. A rooted tree has directionality (nodes can be ordered in terms of “earlier” or “later”). In the rooted tree, distance between two nodes is represented along the time-axis only (the second axis just helps spread out the leafs) EarlyLate

Trees: rooted vs. unrooted A rooted tree has a single node (the root) that represents a point in time that is earlier than any other node in the tree. A rooted tree has directionality (nodes can be ordered in terms of “earlier” or “later”). In the rooted tree, distance between two nodes is represented along the time-axis only (the second axis just helps spread out the leafs) EarlyLate

Trees: rooted vs. unrooted In unrooted trees there is no directionality: we do not know if a node is earlier or later than another node Distance along branches directly represents node distance

Trees: rooted vs. unrooted In unrooted trees there is no directionality: we do not know if a node is earlier or later than another node Distance along branches directly represents node distance

Reconstructing a tree using non- contemporaneous data

Reconstructing a tree using present-day data

Data: molecular phylogeny DNA sequences DNA sequences genomic DNA genomic DNA mitochondrial DNA mitochondrial DNA chloroplast DNA chloroplast DNA Protein sequences Protein sequences Restriction site polymorphisms Restriction site polymorphisms DNA/DNA hybridization DNA/DNA hybridization Immunological cross-reaction Immunological cross-reaction

Morphology vs. molecular data African white-backed vulture (old world vulture) Andean condor (new world vulture) New and old world vultures seem to be closely related based on morphology. Molecular data indicates that old world vultures are related to birds of prey (falcons, hawks, etc.) while new world vultures are more closely related to storks Similar features presumably the result of convergent evolution

Molecular data: single-celled organisms Molecular data useful for analyzing single-celled organisms (which have only few prominent morphological features).

Distance Matrix Methods 1. Construct multiple alignment of sequences 2. Construct table listing all pairwise differences (distance matrix) 3. Construct tree from pairwise distances Gorilla : ACGTCGTA Human : ACGTTCCT Chimpanzee: ACGTTTCG GoHuCh Go-44 Hu-2 Ch- Go Hu Ch

Finding Optimal Branch Lengths S1S1S1S1 S2S2S2S2 S3S3S3S3 S4S4S4S4 S1S1S1S1- D 12 D 13 D 14 S2S2S2S2- D 23 D 24 S3S3S3S3- D 34 S4S4S4S4- Observed distance S1 S3 S2 S4 a b c d e Distance along tree D 12  d 12 = a + b + c D 13  d 13 = a + d D 14  d 14 = a + b + e D 23  d 23 = d + b + c D 24  d 24 = c + e D 34  d 34 = d + b + e Goal:

Optimal Branch Lengths: Least Squares Fit between given tree and observed distances can be expressed as “sum of squared differences”: Q =  (D ij - d ij ) 2 Find branch lengths that minimize Q - this is the optimal set of branch lengths for this tree. S1 S3 S2 S4 a b c d e Distance along tree D 12  d 12 = a + b + c D 13  d 13 = a + d D 14  d 14 = a + b + e D 23  d 23 = d + b + c D 24  d 24 = c + e D 34  d 34 = d + b + e Goal: j>i

Least Squares Optimality Criterion Search through all (or many) tree topologies Search through all (or many) tree topologies For each investigated tree, find best branch lengths using least squares criterion For each investigated tree, find best branch lengths using least squares criterion Among all investigated trees, the best tree is the one with the smallest sum of squared errors. Among all investigated trees, the best tree is the one with the smallest sum of squared errors.

Exhaustive search impossible for large data sets No. taxa No. trees , , ,027, ,459, ,729, ,749,310, ,234,143, ,905,853,580,625

Heuristic search 1. Construct initial tree; determine sum of squares 2. Construct set of “neighboring trees” by making small rearrangements of initial tree; determine sum of squares for each neighbor 3. If any of the neighboring trees are better than the initial tree, then select it/them and use as starting point for new round of rearrangements. (Possibly several neighbors are equally good) 4. Repeat steps 2+3 until you have found a tree that is better than all of its neighbors. 5. This tree is a “local optimum” (not necessarily a global optimum!)

Clustering Algorithms Starting point: Distance matrix Starting point: Distance matrix Cluster least different pair of sequences: Cluster least different pair of sequences: Tree: pair connected to common ancestral node, compute branch lengths from ancestral node to both descendants Tree: pair connected to common ancestral node, compute branch lengths from ancestral node to both descendants Distance matrix: combine two entries into one. Compute new distance matrix, by finding distance from new node to all other nodes Distance matrix: combine two entries into one. Compute new distance matrix, by finding distance from new node to all other nodes Repeat until all nodes are linked Repeat until all nodes are linked Results in only one tree, there is no measure of tree-goodness. Results in only one tree, there is no measure of tree-goodness.

Neighbor Joining Algorithm For each tip compute u i =  j D ij /(n-2) For each tip compute u i =  j D ij /(n-2) (this is essentially the average distance to all other tips, except the denominator is n-2 instead of n) Find the pair of tips, i and j, where D ij -u i -u j is smallest Find the pair of tips, i and j, where D ij -u i -u j is smallest Connect the tips i and j, forming a new ancestral node. The branch lengths from the ancestral node to i and j are: Connect the tips i and j, forming a new ancestral node. The branch lengths from the ancestral node to i and j are: v i = 0.5 D ij (u i -u j ) v j = 0.5 D ij (u j -u i ) Update the distance matrix: Compute distance between new node and each remaining tip as follows: Update the distance matrix: Compute distance between new node and each remaining tip as follows: D ij,k = (D ik +D jk -D ij )/2 Replace tips i and j by the new node which is now treated as a tip Replace tips i and j by the new node which is now treated as a tip Repeat until only two nodes remain. Repeat until only two nodes remain.

Superimposed Substitutions Actual number of evolutionary events:5 Observed number of differences:2 Distance is (almost) always underestimated ACGGTGC C T GCGGTGA

Model-based correction for superimposed substitutions Goal: try to infer the real number of evolutionary events (the real distance) based on Goal: try to infer the real number of evolutionary events (the real distance) based on 1. Observed data (sequence alignment) 2. A model of how evolution occurs

Jukes and Cantor Model Four nucleotides assumed to be equally frequent (f=0.25) All 12 substitution rates assumed to be equal Under this model the corrected distance is: D JC = x ln( x D OBS ) For instance: D OBS =0.43 => D JC =0.64 ACGT A -3     C    G    T   

Other models of evolution

Homologs Orthologs - speciation Orthologs - speciation Paralogs - duplication Paralogs - duplication Xenologs – horizontal transfer Xenologs – horizontal transfer

Clustering Algorithms Clustering algorithms use distances to calculate phylogenetic trees. These trees are based solely on the relative numbers of similarities and differences between a set of sequences. Start with a matrix of pairwise distances Start with a matrix of pairwise distances Cluster methods construct a tree by linking the least distant pairs of taxa, followed by successively more distant taxa. Cluster methods construct a tree by linking the least distant pairs of taxa, followed by successively more distant taxa.

From Multiple Sequence Alignment Best cluster: {ATCC,ATGC} Best cluster: {ATCC,ATGC} ATCCATGCTTCGTCGG ATCC0124 ATGC033 TTCG02 TCGG0 {ATCC,ATGC}TTCGTCGG {ATCC,ATGC}0½(2+3)=2.5½(4+3)=3.5 TTCG02 TCGG0 Best cluster: {TTCG,TCGG} Best cluster: {TTCG,TCGG}

Example {ATCC,ATGC}{TTCG,TCGG} 0½( )=3 {TTCG,TCGG}0 ATCC ATGC TTCG TCGG A Cladogram or a Phylogram?

Cladistic Methods Evolutionary relationships are documented by creating a branching structure, termed a phylogeny or tree, that illustrates the relationships between the sequences. Evolutionary relationships are documented by creating a branching structure, termed a phylogeny or tree, that illustrates the relationships between the sequences. Cladistic methods construct a tree (cladogram) by considering the various possible pathways of evolution and choose from among these the best possible tree. Cladistic methods construct a tree (cladogram) by considering the various possible pathways of evolution and choose from among these the best possible tree. A phylogram is a tree with branches that are proportional to evolutionary distances. A phylogram is a tree with branches that are proportional to evolutionary distances.

Hamming distance : the number of positions for which the corresponding symbols are different. The number of substitutions required to change one into the other, or the number of errors that transformed one string into the other. : the number of positions for which the corresponding symbols are different. The number of substitutions required to change one into the other, or the number of errors that transformed one string into the other.

Hamming distance The Hamming distance between and is 2. The Hamming distance between and is 2. The Hamming distance between and is 3. The Hamming distance between and is 3. The Hamming distance between "toned" and "roses" is 3. The Hamming distance between "toned" and "roses" is 3.

Levenshtein Distance A measure of the similarity between two strings: number of deletions, insertions, or substitutions A measure of the similarity between two strings: number of deletions, insertions, or substitutions For example, If s is "test" and t is "test", then LD(s,t) = 0, If s is "test" and t is "test", then LD(s,t) = 0, If s is "test" and t is "tent", then LD(s,t) = 1, because one substitution (change "s" to "n") is sufficient to transform s into t. If s is "test" and t is "tent", then LD(s,t) = 1, because one substitution (change "s" to "n") is sufficient to transform s into t. If s os “test” and t is “attempt”, LD(s,t)=4 If s os “test” and t is “attempt”, LD(s,t)=4

Levenshtein distance The Levenshtein distance algorithm has been used in: The Levenshtein distance algorithm has been used in: Spell checking Spell checking Speech recognition Speech recognition DNA analysis DNA analysis Plagiarism detection Plagiarism detection

DNA Distances Distances between pairs of DNA sequences are usually computed as the sum of all base pair differences between the two sequences. Distances between pairs of DNA sequences are usually computed as the sum of all base pair differences between the two sequences. If sequences are similar enough to be aligned If sequences are similar enough to be aligned Generally all base changes are considered equal Generally all base changes are considered equal Insertion/deletions are generally given a larger weight than replacements (gap penalties). Insertion/deletions are generally given a larger weight than replacements (gap penalties). It is also possible to correct for multiple substitutions at a single site, which is common in distant relationships and for rapidly evolving sites. It is also possible to correct for multiple substitutions at a single site, which is common in distant relationships and for rapidly evolving sites.

Phylogenetic methods (1) Distance matrix/cluster (UPGMA, NJ): Bacterial taxonomy based on morphological, chemical, biochemical and physiological chacters did not allow natural relationships to be deduced Numerical taxonomy (Sneath and Sokal, 1963, 1973) Parsimony (maximum parsomony) The taxonomy of animals shall reflect their natural relatioonships Phylogenetic Systematics (Willi Hennig 1950, 1966) Without direction (eg. Wiley 1980)

UPGMA The simplest of the distance methods is the UPGMA (Unweighted Pair Group Method using Arithmetic averages) The simplest of the distance methods is the UPGMA (Unweighted Pair Group Method using Arithmetic averages) The PHYLIP programs DNADIST and PROTDIST calculate absolute pairwise distances between a group of sequences. Then the GCG program GROWTREE uses UPGMA to build a tree. The PHYLIP programs DNADIST and PROTDIST calculate absolute pairwise distances between a group of sequences. Then the GCG program GROWTREE uses UPGMA to build a tree. Many multiple alignment programs such as PILEUP use a variant of UPGMA to create a dendrogram of DNA sequences which is then used to guide the multiple alignment algorithm. Many multiple alignment programs such as PILEUP use a variant of UPGMA to create a dendrogram of DNA sequences which is then used to guide the multiple alignment algorithm.

Neighbor Joining The Neighbor Joining method is the most popular way to build trees from distance measurements The Neighbor Joining method is the most popular way to build trees from distance measurements (Saitou and Nei 1987, Mol. Biol. Evol. 4:406) Neighbor Joining corrects the UPGMA method for its (frequently invalid) assumption that the same rate of evolution applies to each branch of a tree. Neighbor Joining corrects the UPGMA method for its (frequently invalid) assumption that the same rate of evolution applies to each branch of a tree. The distance matrix is adjusted for differences in the rate of evolution of each taxon (branch). The distance matrix is adjusted for differences in the rate of evolution of each taxon (branch). Neighbor Joining has given the best results in simulation studies and it is the most computationally efficient of the distance algorithms (N. Saitou and T. Imanishi, Mol. Biol. Evol. 6:514 (1989) Neighbor Joining has given the best results in simulation studies and it is the most computationally efficient of the distance algorithms (N. Saitou and T. Imanishi, Mol. Biol. Evol. 6:514 (1989)

Cladistic methods Cladistic methods are based on the assumption that a set of sequences evolved from a common ancestor by a process of mutation and selection without mixing (hybridization or other horizontal gene transfers). Cladistic methods are based on the assumption that a set of sequences evolved from a common ancestor by a process of mutation and selection without mixing (hybridization or other horizontal gene transfers). These methods work best if a specific tree, or at least an ancestral sequence, is already known so that comparisons can be made between a finite number of alternate trees rather than calculating all possible trees for a given set of sequences. These methods work best if a specific tree, or at least an ancestral sequence, is already known so that comparisons can be made between a finite number of alternate trees rather than calculating all possible trees for a given set of sequences.

Parsimony Parsimony is the most popular method for reconstructing ancestral relationships. Parsimony is the most popular method for reconstructing ancestral relationships. Parsimony allows the use of all known evolutionary information in building a tree Parsimony allows the use of all known evolutionary information in building a tree In contrast, distance methods compress all of the differences between pairs of sequences into a single number In contrast, distance methods compress all of the differences between pairs of sequences into a single number

Building Trees with Parsimony Parsimony involves evaluating all possible trees and giving each a score based on the number of evolutionary changes that are needed to explain the observed data. Parsimony involves evaluating all possible trees and giving each a score based on the number of evolutionary changes that are needed to explain the observed data. The best tree is the one that requires the fewest base changes for all sequences to derive from a common ancestor. The best tree is the one that requires the fewest base changes for all sequences to derive from a common ancestor.

Methods Distance-based: UPGMA, NJ, FM, ME Distance-based: UPGMA, NJ, FM, ME Other: Maximum Parsimony, ML, etc Other: Maximum Parsimony, ML, etc Neighbor Joining methods generally produce just one tree, which can help to validate a tree built with the parsimony or maximum likelihood method Neighbor Joining methods generally produce just one tree, which can help to validate a tree built with the parsimony or maximum likelihood method

Phylogenetic methods Maximum likelihood methods Phylogenies should be formulated in a probalistic framework and statistically testable. Protein and DNA sequence data are extraordinary good for phylogenetic interpreation and can ”resist” such treatment. Cavalli-Sforza and Edwards 1967 (theory) Felsenstein 1981 first practically useful algorithms.

Phylogenetic analysis. Comparison of phylogenetic methods Consistency: a phylogenetic method is consistent for an evolutionary model, if the method converges on the corrrect tree as the data becomes infinite. Efficiency: a phylogenetic method have high efficiency if it quickly converges on the correct solution as more data are applied to the problem. Robustness: a phylogenetic method is robust if converges on the correct solution with violations of the assumptions about the evolutionary model. Hillis Syst. Biol. 44, 3-16.

Phylogenetic analysis. Test of robustness. Bootstrap Purpose. To show how well supported the nodes are by the data. Performance. The original data are simulated by drawing columns randomly with replacement 100 or 1000 times. The phylogenetic analysis is repeated and the number of nodes common in all 100 or 1000 trees summarized. Example. Original data1 replicate2 replicate Species 1AGGAAAGAGGAA Species 2ACGTAACTCGTT Species 3ACGTAACTCGTT Species 4ACTTAACTCTTT Species 5CCGTCCCTCGTT linear form(2,3)4)5)1;(2,3)4)5)1;(2,3)5)4)1;

Are there Correct trees?? Despite all of these caveats, it is actually quite simple to use computer programs calculate phylogenetic trees for data sets. Despite all of these caveats, it is actually quite simple to use computer programs calculate phylogenetic trees for data sets. Provided the data are clean, outgroups are correctly specified, appropriate algorithms are chosen, no assumptions are violated, etc., can the true, correct tree be found and proven to be scientifically valid? Provided the data are clean, outgroups are correctly specified, appropriate algorithms are chosen, no assumptions are violated, etc., can the true, correct tree be found and proven to be scientifically valid? Unfortunately, it is impossible to ever conclusively state what is the "true" tree for a group of sequences (or a group of organisms); taxonomy is constantly under revision as new data is gathered (example: 80s revision of the seals and sea lions tree) Unfortunately, it is impossible to ever conclusively state what is the "true" tree for a group of sequences (or a group of organisms); taxonomy is constantly under revision as new data is gathered (example: 80s revision of the seals and sea lions tree)