Phylogenetic analysis

Phylogenetics Phylogenetics is the study of the evolutionary history of living organisms using treelike diagrams to represent pedigrees of these organisms. The tree branching patterns representing the evolutionary divergence are referred to as phylogeny. - based on Essential Bioinformatics

Studying phylogenetics http://www.agiweb.org/news/evolution/fossilrecord.html Studying phylogenetics Fossil records – morphological information, available only for certain species, data can be fragmentary, morphological traits are ambiguous, fossil record nonexistent for microorganisms Molecular data (molecular fossils) – more numerous than fossils, easier to obtain, favorite for reconstruction of the evolutionary history - hemoglobin, 1HBO

Tree of life - principal relationships among prokaryotic domains Bacteria and Archaea http://tikalon.com/blog/blog.php?article=2011/domains

DNA sequence evolution -3 mil yrs -2 mil yrs -1 mil yrs today AAGACTT TGGACTT AAGGCCT AGGGCAT TAGCCCT AGCACTT AGCGCTT AGCACAA TAGACTT TAGCCCA www.cs.utexas.edu/users/tandy/CSBtutorial.ppt

Tree terminology A B C D E Terminal nodes – taxa (taxon) Branches taxa, singular form is taxon bifurkace – rozdvojení D Ancestral node or root of the tree E Internal nodes or Divergence points (represent hypothetical ancestors of the taxa) Based on lectures by Tal Pupko

Based on lectures by Tal Pupko Monophyletic (clade) – a taxon that is derived from a single ancestral species. Polyphyletic – a taxon whose members were derived from two or more ancestors not common to all members. Paraphyletic – a taxon that excludes some members that share a common ancestor with members included in the taxon. Based on lectures by Tal Pupko

dichotomy – all branches bifurcate, vs dichotomy – all branches bifurcate, vs. polytomy – result of a taxon giving rise to more than two descendants or unresolved phylogeny (the exact order of bifurcations can not be determined exactly)

unrooted – no knowledge of a common ancestor, shows relative relationship of taxa, no direction of an evolutionary path rooted – obviously, more informative

Finding a true tree is difficult Correct reconstruction of the evolutionary history = find a correct tree topology with correct branch lengths. Number of potential tree topologies can be enormously large even with a moderate number of taxa. 𝑁 𝑅 = 2𝑛−3 ! 2 𝑛−2 𝑛−2 ! 𝑁 𝑈 = 2𝑛−5 ! 2 𝑛−3 𝑛−3 ! 6 taxa … NR=945, NU=105 10 taxa … NR=34 459 425, NU = 2 027 025 NR … number of rooted trees NU … number of unrooted trees n … number of taxa

Based on lectures by Tal Pupko Rooting the tree A B C Root D To root a tree mentally, imagine that the tree is made of string. Grab the string at the root and tug on it until the ends of the string (the taxa) fall opposite the root: Unrooted tree A B C D Root Note that in this rooted tree, taxon A is no more closely related to taxon B than it is to C or D. Rooted tree Based on lectures by Tal Pupko

Now, try it again with the root at another position: B C Root Unrooted tree D A A B C D Rooted tree Note that in this rooted tree, taxon A is most closely related to taxon B, and together they are equally distantly related to taxa C and D. Root Based on lectures by Tal Pupko

Based on lectures by Tal Pupko An unrooted, four-taxon tree theoretically can be rooted in five different places to produce five different rooted trees Rooted tree 1b A B C D 2 A C B D Rooted tree 1d C D A B 4 Rooted tree 1a B A C D 1 The unrooted tree 1: Rooted tree 1e D C A B 5 Rooted tree 1c A B C D 3 These trees show five different evolutionary relationships among the taxa! Based on lectures by Tal Pupko

Based on lectures by Tal Pupko Rooting the tree outgroup – taxa (the “outgroup”) that are known to fall outside of the group of interest (the “ingroup”). Requires some prior knowledge about the relationships among the taxa. The outgroup can either be species (e.g., birds to root a mammalian tree) or previous gene duplicates (e.g., a-globins to root b-globins). outgroup Based on lectures by Tal Pupko

Based on lectures by Tal Pupko Rooting the tree midpoint rooting approach - roots the tree at the midway point between the two most distant taxa in the tree, as determined by branch lengths. Assumes that the taxa are evolving in a clock-like manner. A B C D 10 2 3 5 d (A,D) = 10 + 3 + 5 = 18 Midpoint = 18 / 2 = 9 Based on lectures by Tal Pupko

Molecular clock This concept was proposed by Emil Zuckerkandl and Linus Pauling (1962) as well as Emanuel Margoliash (1963). This hypothesis states that for every given gene (or protein), the rate of molecular evolution is approximately constant. Pioneering study by Zuckerkandl and Pauling They observed the number of amino acid differences between human globins – β and δ (~ 6 differences), β and γ (~ 36 differences), α and β (~ 78 differences), and α and γ (~ 83 differences). They could also compare human to gorilla (both β and α globins), observing either 2 or 1 differences respectively. They knew from fossil evidence that humans and gorillas diverged from a common ancestor about 11 MYA. Using this divergence time as a calibration point, they estimated that gene duplications of the common ancestor to β and δ occurred 44 MYA; β and derived from a common ancestor 260MYA; α and β 565 MYA; and α and γ 600MYA.

Gene phylogeny vs. species phylogeny Main objective of building phylogenetic trees based on molecular sequences: reconstruct the evolutionary history of the species involved. A gene phylogeny only describes the evolution of that particular gene or encoded protein. This sequence may evolve more or less rapidly than other genes in the genome. The evolution of a particular sequence does not necessarily correlate with the evolutionary path of the species. Branching point in a species tree – the speciation event Branching point in a gene tree – which event? The two events may or may not coincide. To obtain a species phylogeny, phylogenetic trees from a variety of gene families need to be constructed to give an overall assessment of the species evolution. - answer: gene duplication event

Closest living relatives of humans? Based on lectures by Tal Pupko

Closest living relatives of humans? MYA Chimpanzees Orangutans Humans Bonobos Gorillas 14 Humans Bonobos Gorillas Orangutans Chimpanzees MYA 15-30 Mitochondrial DNA, most nuclear DNA-encoded genes, and DNA/DNA hybridization all show that bonobos and chimpanzees are related more closely to humans than either are to gorillas. The pre-molecular view was that the great apes (chimpanzees, gorillas and orangutans) formed a clade separate from humans, and that humans diverged from the apes at least 15-30 MYA.

Orangutan Gorilla Chimpanzee Human From the Tree of the Life Website, University of Arizona

Forms of tree representation phylogram – branch lengths represent the amount of evolutionary divergence cladogram – external taxa line up neatly, only the topology matters

Based on lectures by Tal Pupko Taxon A Taxon B Taxon C Taxon E Taxon D No meaning to the spacing between the taxa, or to the order in which they appear from top to bottom. This dimension either can have no scale (for ‘cladograms’), can be proportional to genetic distance or amount of change (for ‘phylograms’), or can be proportional to time (for ‘ultrametric trees’ or true evolutionary trees). ((A,(B,C)),(D,E)) = The above phylogeny as nested parentheses These say that B and C are more closely related to each other than either is to A, and that A, B, and C form a clade that is a sister group to the clade composed of D and E. If the tree has a time scale, then D and E are the most closely related. Based on lectures by Tal Pupko

Newick format linear form of nested parentheses within which taxa are separated by commas. If the tree is scaled, branch lengths are indicated immediately after the taxon name. The numbers are relative units that represent divergent times.

A consensus tree combining the nodes: strict consensus - all conflicting nodes are collapsed into polytomies majority rule – among the conflicting nodes, those that agree by more than 50% of the nodes are retained whereas the remaining nodes are collapsed into polytomies Sometimes a tree-building method may result in several equally optimal trees. A consensus tree can be built by showing the commonly resolved bifurcating portions derived from three individual inferred trees based on a majority rule. Conflicting nodes are represented by a multifurcating node in the consensus tree

Procedure Choice of molecular markers Multiple sequence alignment Choice of a model of evolution Determine a tree building method Assess tree reliability

Choice of molecular markers Nucleotide or protein sequence data? NA sequences evolve more rapidly. They can be used for studying very closely related organisms. E. g., for evolutionary analysis of different individuals within a population, noncoding regions of mtDNA are often used. Evolution of more divergent organisms – either slowly evolving NA (e.g., rRNA) or protein sequences. Deepest level (e.g., relatioships between bacteria and eukaryotes) – conserved protein sequences NA sequences: good if sequences are closely related, reveal synonymous/nonsynonymous substitutions - mtDNA … mitochondrial DNA

Positive and negative selection synonymous substitution – nucleotide changes in a sequence not resulting in amino acid sequence changes (genetic code degeneracy, 3rd codon position) nonsynonymous changes nonsynonsymous substitution rate ≫ synonymous – positive selection certain parts of the protein are undergoing active mutations that may contribute to the evolution of new function negative selection – synonymous > nonsynonymous neutral changes at the AA level, the protein sequence is critical enough that its changes are not tolerated

MSA Critical step Multiple state-of-the-art alignment programs (e.g., T-Coffee, Praline, Poa, …) should be used. The alignment results from multiple sources should be inspected and compared carefully to identify the most reasonable one. Automatic sequence alignments almost always contain errors and should be further edited or refined if necessary – manual editing! Rascal and NorMD can help to improve alignment by correcting alignment errors and removing potentially unrelated or highly divergent sequences.

Model of evolution A simple measure of the divergence of two sequences – number of substitutions in the alignment, a distance between two sequences – a proportion of substitutions If A was replaced by C: A → C or A → T → G → C? Back mutation: G → C → G. Parallel mutations – both sequences mutate into e.g., T at the same time. All of this obscures the estimation of the true evolutionary distances between sequences. This effect is known as homoplasy and must be corrected. Statistical models infer the true evolutionary distances between sequences.

Model of evolution Homplasy is corrected by substitution (evolutionary) models. There exists a lot of such models. Jukes-Cantor model 𝑑 𝐴𝐵 =− 3 4× 𝑙𝑛 1− 4 3× 𝑝 𝐴𝐵 dAB … distance, pAB … proportion of substitutions example: alignment of A and B is 20 nucleotides long, 6 pairs are different, pAB = 0.3, dAB = 0.38 Kimura model 𝑑 𝐴𝐵 =− 1 2× 𝑙𝑛 1−2 𝑝 𝑡𝑖 − 𝑝 𝑡𝑣 − 1 4×ln⁡(1−2 𝑝 𝑡𝑣 ) pti … frequency of transition, ptv … frequency of transversion - transition: Y->Y, R->R, transversion: Y->R, R->Y

Models of amino acids substitutions use the amino acid substitution matrix PAM JTT – 90s, the same methodology as PAM, but with larger protein database protein equivalents of of Jukes–Cantor and Kimura models, e.g., 𝑑=−ln⁡(1−𝑝−0.2× 𝑝 2 )

Among site variations Up to now we have assumed that different positions in a sequence are assumed to be evolving at the same rate. However, in reality is may not be true. In DNA, the rates of substitution differ for different codon positions. 3rd codon mutates much faster. In proteins, some AA change much more rarely than others owing to functional constraints. It has been shown that there are always a proportion of positions in a sequence dataset that have invariant rates and a proportion that have more variable rates. The distribution of variant sites follows a Gamma distribution pattern.

Gamma distribution

To account for site-dependent rate variation, a Gamma correction factor 𝛼 can be used. For the Jukes–Cantor model, the evolution distance can be adjusted with the following formula: 𝑑 𝐴𝐵 = (3/4)𝛼[ 1 − 4 3 × 𝑝 𝐴𝐵 − 1 𝛼 −1] For the Kimura model, the evolutionary distance becomes 𝑑 𝐴𝐵 = 𝛼 2 1 − 2 𝑝 𝑡𝑖 − 𝑝 𝑡𝑣 − 1 𝛼 − 1 2 1 − 2 𝑝 𝑡𝑣 − 1 𝛼 − 1/2]

Tree building methods Two major categories. Distance based methods. Based on the amount of dissimilarity between pairs of sequences, computed on the basis of sequence alignment. Characters based methods. Based on discrete characters, which are molecular sequences from individual taxa.

Tree building methods COMPUTATIONAL METHOD DATA TYPE Clustering algorithm Optimality criterion DATA TYPE Characters Distances Maximum parsimony (MP) Maximum likelihood (ML) UPGMA Neighbor-joining (NJ) Fitch-Margoliash (FM)

Distance based methods Calculate evolutionary distances dAB between sequences using some of the evolutionary model. Construct a distance matrix – distances between all pairs of taxa. Based on the distance scores, construct a phylogenetic tree. clustering algorithms – UPGMA, neighbor joining (NJ) optimality based – Fitch-Margoliash (FM), minimum evolution (ME)

Clustering methods UPGMA  (Unweighted Pair Group Method with Arithmetic Mean) Hierachical clustering, agglomerative, you know it as an average linkage Produces rooted tree (most phylogenetic methods produce unrooted tree). Basic assumption of the UPGMA method: all taxa evolve at a constant rate, they are equally distant from the root, implying that a molecular clock is in effect. However, real data rarely meet this assumption. Thus, UPGMA often produces erroneous tree topologies.

Neighbor joining A B C D E 2 3 4 5 B D A C E A,B C D E 2.5 4.5 3.5 3 4 5 A D C E B A,B B D A C E The Minimum Evolution (ME) criterion: in each iteration we separate the two sequences which result with the minimal sum of branch lengths

Optimality based methods Clustering methods produce a single tree. There is no criterion in judging how this tree is compared to other alternative trees. Optimality based methods have a well-defined algorithm to compare all possible tree topologies and select a tree that best fits the actual evolutionary distance matrix.

Distance based – pros and cons clustering Fast, can handle large datasets Not guaranteed to find the best tree The actual sequence information is lost when all the sequence variation is reduced to a single value. Hence, ancestral sequences at internal nodes cannot be inferred. UPGMA – assumes a constant rate of evolution of the sequences in all branches of the tree (molecular clock assumption) NJ – does not assume that the rate of evolution is the same in all branches of the tree NJ is slower but better than UPGMA exhaustive tree searching (FM) better accuracy, prohibitive for more than 12 taxa

Character based methods Also called discreet methods Based directly on the sequence characters They count mutational events accumulated on the sequences and may therefore avoid the loss of information when characters are converted to distances. Evolutionary dynamics of each character can be studied Ancestral sequences can also be inferred. The two most popular character-based approaches: maximum parsimony (MP) and maximum likelihood (ML) methods.

Maximum parsimony Based on Occam’s razor. William of Occam, 13th century. The simplest explanation is probably the correct one. This is because the simplest explanation requires the fewest assumptions and the fewest leaps of logic. A tree with the least number of substitutions is probably the best to explain the differences among the taxa under study. parsimony – setrnost

A worked example 1 2 3 4 5 6 7 8 9 A G T C To save computing time, only a small number of sites that have the richest phylogenetic information are used in tree determination. informative site – sites that have at least two different kinds of characters, each occurring at least twice

A worked example 1 2 3 4 5 6 7 8 9 A G T C To save computing time, only a small number of sites that have the richest phylogenetic information are used in tree determination. informative site – sites that have at least two different kinds of characters, each occurring at least twice

How many possible unrooted trees? 1 2 3 G A C 4 𝑁 𝑈 = 2𝑛−5 ! 2 𝑛−3 𝑛−3 ! 1 2 3 4 1 3 2 4 1 4 3 2 Tree I Tree II Tree III

GGAA G A G A G A G A G G G G 1 4 3 2 Tree I 1 2 3 4 Tree II 1 3 2 4 Tree III

GGCC G C G C G C Tree I G G G C Tree II G G Tree III

AGAG A G A A A G Tree I A G A G Tree II G G Tree III

GGA ACA GGG ACG GGA ACA I II III GGAA 1 2 GGCC AGAG Tree length 4 5 6 Tree I

Weighted parsimony The parsimony method discussed so far is unweighted because it treats all mutations as equivalent. This may be an oversimplification; mutations of some sites are known to occur less frequently than others, for example, transversions versus transitions, functionally important sites versus neutral sites. A weighting scheme takes into account the different kinds of mutations.

Weighted … transitions are weighted by 1 and transversions as 5

Branch-and-bound The parsimony method examines all possible tree topologies to find the maximally parsimonious tree. This is an exhaustive search method, expensive. N = 10 … 2 027 025 N = 20 … 2.22 × 1020 Branch-and-bound Rationale: a maximally parsimonious tree must be equal to or shorter than the distance-based tree. First build a distance tree using NJ or UPGMA. Compute the minimum number of substitutions for this tree. The resulting number defines the upper bound to which any other trees are compared. I.e., when you build a parsimonous tree, you stop growing it when its length exceeds the upper bound.

Heuristic methods When a number of taxa exceeds 20, even branch-and-bound becomes computationally unfeasible. Then, heuristic search can be applied. Both exhaustive search and branch-and-bound methods lead to the optimum tree. Heuristic search leads to the suboptimum tree (compare to BLAST which is also heuristic).

MP – pros and cons Intuitive - its assumptions are easily understood The character-based method is able to provide evolutionary information about the sequence characters, such as information regarding homoplasy and ancestral states. It tends to produce more accurate trees than the distance-based methods when sequence divergence is low because this is the circumstance when the parsimony assumption of rarity in evolutionary changes holds true. When sequence divergence is high, tree estimation by MP can be less effective, because the original parsimony assumption no longer holds. Estimation of branch lengths may also be erroneous because MP does not employ substitution models to correct for multiple substitutions.

Maximum likelihood – ML Uses probabilistic models to choose a best tree that has the highest probability (likelihood) of reproducing the observed data. ML is an exhaustive method that searches every possible tree topology and considers every position in an alignment, not just informative sites. By employing a particular substitution model that has probability values of residue substitutions, ML calculates the total likelihood of ancestral sequences evolving to internal nodes and eventually to existing sequences. It sometimes also incorporates parameters that account for rate variations across sites.

ML – pros and cons Based on well-founded statistics instead of a medieval philosophy. More robust, uses the full sequence information, not just informative sites. Employs substitution model – strength, but also weakness (choosing wrong model leads to incorrect tree). Accurately reconstructs the relationships between sequences that have been separated for a long time. Very time consuming, considerably more than MP which is itself more time consuming than clustering methods.

Phylogeny packages PHYLIP, Phylogenetic inference package evolution.genetics.washington.edu/phylip.html Felsenstein Free! PAUP, phylogenetic analysis using parsimony paup.csit.fsu.edu Swofford