Download Phylogenetic analysis

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.
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
Tree of life
http://tikalon.com/blog/blog.php?article=2011/domains
DNA sequence evolution
AAGACTT
AAGGCCT
AGGGCAT
AGGGCAT
-2 mil yrs
TGGACTT
TAGCCCT
TAGCCCA
-3 mil yrs
TAGACTT
AGCACTT
AGCACAA
AGCGCTT
-1 mil yrs
today
www.cs.utexas.edu/users/tandy/CSBtutorial.ppt
Tree terminology
Terminal nodes – taxa (taxon)
Branches
A
B
C
D
Ancestral node
or root of
the tree
Internal nodes or
Divergence points
(represent hypothetical
ancestors of the taxa)
E
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. 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.
2𝑛 − 3 !
𝑁𝑅 = 𝑛−2
2
𝑛−2 !
2𝑛 − 5 !
𝑁𝑈 = 𝑛−3
2
𝑛−3 !
6 taxa … NR=945, NU=105
10 taxa … NR=34 459 425, NU = 2 027 025
Rooting the tree
B
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:
C
Root
D
Unrooted tree
A
A
Note that in this rooted tree, taxon A is no
more closely related to taxon B than it is to
C or D.
B
C
D
Rooted tree
Root
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
Root
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.
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
A
The unrooted tree 1:
2
4
1
B
C
5
D
3
Rooted tree 1a
Rooted tree 1b
Rooted tree 1c
Rooted tree 1d
Rooted tree 1e
B
A
A
C
D
A
B
B
D
C
C
C
C
A
A
D
D
D
B
B
These trees show five different evolutionary relationships among the taxa!
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
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
d (A,D) = 10 + 3 + 5 = 18
Midpoint = 18 / 2 = 9
10
C
3
B
2
2
5
D
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.
Closest living relatives of humans?
Based on lectures by Tal Pupko
Closest living relatives of humans?
14
Humans
Gorillas
Chimpanzees
Chimpanzees
Bonobos
Bonobos
Gorillas
Orangutans
Orangutans
Humans
0
MYA
Mitochondrial DNA, most nuclear DNAencoded genes, and DNA/DNA hybridization
all show that bonobos and chimpanzees are
related more closely to humans than either
are to gorillas.
15-30
MYA
0
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
Taxon B
Taxon C
Taxon A
Taxon D
No meaning to the
spacing between the
taxa, or to the order in
which they appear from
top to bottom.
Taxon E
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
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
Procedure
1. Choice of molecular markers
2. Multiple sequence alignment
3. Choice of a model of evolution
4. Determine a tree building method
5. 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
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
𝑑𝐴𝐵 = − 3 4 × 𝑙𝑛 1 − 4 3 × 𝑝𝐴𝐵
• 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
𝑑𝐴𝐵 = − 1 2 × 𝑙𝑛 1 − 2𝑝𝑡𝑖 − 𝑝𝑡𝑣 − 1 4 × ln(1 − 2𝑝𝑡𝑣 )
• pti … frequency of transition, ptv … frequency of transversion
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 × 𝑝2 )
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:
𝑑𝐴𝐵 = (3/4)𝛼[ 1 −
4
×
3
𝑝𝐴𝐵
1
𝛼
−
− 1]
• For the Kimura model, the evolutionary distance becomes
𝑑𝐴𝐵
𝛼
=
2
1 − 2𝑝𝑡𝑖 −
1
−𝛼
𝑝𝑡𝑣
−
1
2
1 −
1
−𝛼
2𝑝𝑡𝑣
− 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
Characters
Maximum parsimony (MP)
Distances
DATA TYPE
Optimality criterion
Fitch-Margoliash (FM)
Clustering algorithm
Maximum likelihood (ML)
UPGMA
Neighbor-joining (NJ)
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
C
A
D
B
A
B
C
D
E
A
0
B
2
0
C
3
3
0
D
4
4
3
0
E
E
4
5
4
5
0
A,B C D E
A,B 0 2.5 4.5 3.5
C
0 3 4
D
0 5
E
0
C
A
D
A,B
B
E
The Minimum Evolution (ME) criterion:
in each iteration we separate the two
sequences which result with the minimal
sum of branch lengths
C
A
D
B
E
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.
A worked example
1
2
3
4
5
6
7
8
9
1
A
A
G
A
G
T
G
C
A
2
A
G
C
C
G
T
G
C
G
3
A
G
A
T
A
T
C
C
A
4
A
G
A
G
A
T
C
C
G
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
1
A
A
G
A
G
T
G
C
A
2
A
G
C
C
G
T
G
C
G
3
A
G
A
T
A
T
C
C
A
4
A
G
A
G
A
T
C
C
G
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
1
G
G
A
2
G
G
G
3
A
C
A
4
A
C
G
2𝑛 − 5 !
𝑁𝑈 = 𝑛−3
2
𝑛−3 !
1
3
1
2
1
3
2
4
3
4
4
2
Tree I
Tree II
Tree III
GGAA
G
A
G A
A
G
G
G
G G
Tree I
1
2
3
A
1
3
4
2
A G
Tree II
A
GG
4
1
2
3
4
A
Tree III
G
GGCC
G
C
G C
C
G
G
G
G G
Tree I
C
Tree II
C G
C
GG
C
Tree III
G
AGAG
A
A
A A
G
G
A
G
A G
Tree I
A
Tree II
G A
A
GG
G
Tree III
G
I
II
III
GGAA
1
2
2
GGCC
1
2
2
AGAG
2
1
2
Tree length
4
5
6
ACA
GGA
GGA
2
1
ACA
1
GGG
ACG
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.
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 distancebased 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