Phylogenetic Analysis Unit 16

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Phylogenetic AnalysisUnit 16

• BIOL221T Advanced Bioinformatics for
  Biotechnology

Irene Gabashvili, PhD
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BO, chapter 14

• Bioinformatics analyses should be interpreted in
  evolutionary context
• Good-quality sequence alignments important for
  evolutionary analysis
• Common phylogenetic methods and software are
  different be cautious when using and
  interpreting your results

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Terminology and the Basics

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

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Brief Introduction to the Theory of Evolution
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Classification Linnaeus
Carl Linnaeus 1707-1778
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Classification Linnaeus

• Hierarchical system
• Kingdom (Rige)
• Phylum (Række)
• Class (Klasse)
• Order (Orden)
• Family (Familie)
• Genus (Slægt)
• Species (Art)

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Classification depicted as a tree
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Classification depicted as a tree
Species
Genus
Family
Order
Class
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Theory of evolution
Charles Darwin 1809-1882
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Phylogenetic basis of systematics

• Linnaeus
• Ordering principle is God.
• Darwin
• Ordering principle is shared descent from common
  ancestors.
• Today, systematics is explicitly based on
  phylogeny.

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Darwins four postulates

• More young are produced each generation than can
  survive to reproduce.
• Individuals in a population vary in their
  characteristics.
• Some differences among individuals are based on
  genetic differences.
• 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

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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
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Phylogenetic ReconstructionDistance Matrix
Methods
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Trees terminology
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Terminology

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

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Trees terminology
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Trees representations
Three different representations of the same tree
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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)

Early
Late
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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)

Early
Late
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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)

Early
Late
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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

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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

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Reconstructing a tree using non-contemporaneous
data
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Reconstructing a tree using present-day data
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Data molecular phylogeny

• DNA sequences
• genomic DNA
• mitochondrial DNA
• chloroplast DNA
• Protein sequences
• Restriction site polymorphisms
• DNA/DNA hybridization
• Immunological cross-reaction

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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
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Molecular data single-celled organisms
Molecular data useful for analyzing single-celled
organisms (which have only few prominent
morphological features).
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Distance Matrix Methods
Gorilla ACGTCGTA Human
ACGTTCCT Chimpanzee ACGTTTCG

• Construct multiple alignment of sequences
• Construct table listing all pairwise differences
  (distance matrix)
• Construct tree from pairwise distances

Ch
1
1
1
Hu
2
Go
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Finding Optimal Branch Lengths
S2
S1
a
c
b
e
d
S3
S4
Distance along tree
Observed distance
D12 ? d12 a b c D13 ? d13 a d D14 ? d14
a b e D23 ? d23 d b c D24 ? d24 c
e D34 ? d34 d b e
Goal
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Optimal Branch Lengths Least Squares
S2
S1
a
c

• Fit between given tree and observed distances can
  be expressed as sum of squared differences
• Q ?(Dij - dij)2
• Find branch lengths that minimize Q - this is the
  optimal set of branch lengths for this tree.

b
e
d
S3
S4
Distance along tree
jgti
D12 ? d12 a b c D13 ? d13 a d D14 ? d14
a b e D23 ? d23 d b c D24 ? d24 c
e D34 ? d34 d b e
Goal
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Least Squares Optimality Criterion

• Search through all (or many) tree topologies
• 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.

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Exhaustive search impossible for large data sets
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Heuristic search

• Construct initial tree determine sum of squares
• Construct set of neighboring trees by making
  small rearrangements of initial tree determine
  sum of squares for each neighbor
• 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)
• Repeat steps 23 until you have found a tree
  that is better than all of its neighbors.
• This tree is a local optimum (not necessarily a
  global optimum!)

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Clustering Algorithms

• Starting point Distance matrix
• Cluster least different pair of sequences
• 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
• Repeat until all nodes are linked
• Results in only one tree, there is no measure of
  tree-goodness.

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Neighbor Joining Algorithm

• For each tip compute ui ?j Dij/(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 Dij-ui-uj
  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
• vi 0.5 Dij 0.5 (ui-uj)
• vj 0.5 Dij 0.5 (uj-ui)
• Update the distance matrix Compute distance
  between new node and each remaining tip as
  follows
• Dij,k (DikDjk-Dij)/2
• Replace tips i and j by the new node which is now
  treated as a tip
• Repeat until only two nodes remain.

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Superimposed Substitutions

• Actual number of
• evolutionary events 5
• Observed number of
• differences 2
• Distance is (almost) always underestimated

ACGGTGC C T GCGGTGA
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Model-based correction for superimposed
substitutions

• Goal try to infer the real number of
  evolutionary events (the real distance) based on
• Observed data (sequence alignment)
• A model of how evolution occurs

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Jukes and Cantor Model

• Four nucleotides assumed to be equally frequent
  (f0.25)
• All 12 substitution rates assumed to be equal
• Under this model the corrected distance is
• DJC -0.75 x ln(1-1.33 x DOBS)
• For instance
• DOBS0.43 gt DJC0.64

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Other models of evolution
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Homologs

• Orthologs - speciation
• Paralogs - duplication
• Xenologs horizontal transfer

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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
• Cluster methods construct a tree by linking the
  least distant pairs of taxa, followed by
  successively more distant taxa.

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From Multiple Sequence Alignment

• Best cluster ATCC,ATGC

• Best cluster TTCG,TCGG

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Example
A Cladogram or a Phylogram?
1.5
1.5
0.5
0.5
1
1
ATCC ATGC TTCG TCGG
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Cladistic Methods

• 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.
• A phylogram is a tree with branches that are
  proportional to evolutionary distances.

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Hamming distance

• ltbetween two strings of equal lengthgt 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.

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Hamming distance

• The Hamming distance between 1011101 and 1001001
  is 2.
• The Hamming distance between 2143896 and 2233796
  is 3.
• The Hamming distance between "toned" and "roses"
  is 3.

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Levenshtein Distance

• 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 "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

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Levenshtein distance

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

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DNA Distances

• 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
• Generally all base changes are considered equal
• 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.

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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 Phy
logenetic Systematics (Willi Hennig 1950,
1966) Without direction (eg. Wiley 1980)
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UPGMA

• 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.
• 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.

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Neighbor Joining

• The Neighbor Joining method is the most popular
  way to build trees from distance measurements
• (Saitou and Nei 1987, Mol. Biol. Evol. 4406)
• 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).
• 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. 6514 (1989)

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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).
• 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.

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Parsimony

• Parsimony is the most popular method for
  reconstructing ancestral relationships.
• 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

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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.
• The best tree is the one that requires the fewest
  base changes for all sequences to derive from a
  common ancestor.

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Methods

• Distance-based UPGMA, NJ, FM, ME
• 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

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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.
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Phylogenetic analysis. Comparison of phylogenetic
methodsConsistency 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 1995. Syst. Biol. 44, 3-16.
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• 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 data 1 replicate 2
  replicate
• Species 1 AGGA AAGA GGAA
• Species 2 ACGT AACT CGTT
• Species 3 ACGT AACT CGTT
• Species 4 ACTT AACT CTTT
• Species 5 CCGT CCCT CGTT
• linear form (2,3)4)5)1 (2,3)4)5)1 (2,3)5)4)1

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Are there Correct trees??

• 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?
• 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)