Post on 27-Dec-2015
What is phylogenetics?
Phylogenetics is the study of evolutionary relationships among and within species.
crocodiles
birds
lizards
snakesrodents
primates
marsupials
What is phylogenetics?
crocodilesbirdslizardssnakesrodentsprimatesmarsupials
This is an example of a phylogenetic tree.
• Forensics:Did a patient’s HIV infection result from an invasive dental
procedure performed by an HIV+ dentist?
Applications of phylogenetics
• Conservation:How much gene flow is there among local populations of island
foxes off the coast of California?
• Medicine:What are the evolutionary relationships among the various
prion-related diseases?
To be continued…
Phylogenetic concepts:Interpreting a Phylogeny
Sequence A
Sequence BSequence C
Sequence D
Sequence E
Time
Which sequence is most closely related to B?
A, because B diverged from A more recently than from any other sequence.
Physical position in tree is not meaningful! Only tree structure matters.
Phylogenetic concepts:Rooted and Unrooted Trees
Time
A
B
C
D
Root =
A B
C D
Root
X
=?
A B
C D
?
? ?
? ?
X
Rooting and Tree Interpretation
bacteria archaebacteria
oak
fruit fly
chickenhuman
bacteria
archaea
oak
fruit fly
chicken
human
bacteria
archaebacteria
oak
fruit fly
chicken
human
– bones
– cell nuclei
+ cell nuclei
+ bones
Rooting Methods
Given an unrooted network of relationships among four species of Carnivora [left], outgroup rooting uses an additional taxon (the outgroup) known from independent evidence to be less closely related to any of the other species (the ingroup) than they are to each other. The root is then placed on the branch between the outgroup and the ingroup. In this case, Lynx is a feloid carnivore in a separate superfamily from the four canoid carnivores. Inclusion of Lynx in the network analysis places it on the internode.This method requires accurate information as to ingroup / outgroup relationships.
Outgroup Rooting a network of relationships
How Many Trees?
Unrooted trees Rooted trees
# sequences
# pairwise distances # trees
# branches
/tree # trees# branches
/tree
3
4
5
6
10
30
N
(assuming bifurcation only)
How Many Trees?
2N - 2(2N - 3)!2N - 2 (N - 2)!
2N - 3(2N - 5)!2N - 3 (N - 3)!
N (N - 1)2
N
584.95 1038578.69 103643530
1834,459,425172,027,0254510
109459105156
8105715105
6155364
433133
# branches/tree# trees
# branches
/tree# trees# pairwise distances
# sequences
Rooted treesUnrooted trees
Tree Properties
Root
UltrametricityAll tips are an equal
distance from the root.X
Y
a
bc d
e
a = b + c + d + e
Root
AdditivityDistance between any two tips equals the total branch
length between them.
X
Ya
b
c de
XY = a + b + c + d + e
In simple scenarios, evolutionary trees are ultrametric and phylograms are additive.
Terminology• External nodes: things under comparison; operational
taxonomic units (OTUs)• Internal nodes: ancestral units; hypothetical; goal is to
group current day units• Root: common ancestor of all OTUs under study. Path
from root to node defines evolutionary path• Unrooted: specify relationship but not evolutionary path
– If have an outgroup (external reason to believe certain OTU branched off first), then can root
• Topology: branching pattern of a tree• Branch length: amount of difference that occurred along
a branch
Phylogeny Applications
• Tree of Life: Analyzing changes that have occurred in evolution of different organisms http://tolweb.org/tree/phylogeny.html
• Phylogenetic relationships among genes can help predict which ones might have similar functions (e.g., ortholog detection)
• Follow changes occurring in rapidly changing species (e.g., HIV virus)
Phylogeny Packages
• PHYLIP, Phylogenetic inference package– evolution.genetics.washington.edu/phylip.html– Felsenstein– Free!
• PAUP, phylogenetic analysis using parsimony– paup.csit.fsu.edu– Swofford
Similarity vs. Homology
• Similar– sequences resemble one another
• Homolog– sequences derived from common ancestor
• Ortholog– homologous sequences within a species
• Paralog– homologous sequences between species
Ortholog vs. Paralog
• Ortholog – genomic variation occurs after speciation – hence can be used for phylogeny of organism
• Paralog – genetic duplication occurs before speciation – hence not suitable for phylogeny of organism
Homoplasy
• Sequence similarity NOT due to common ancestry
• May arise due to parallelism or convergent evolution
• Parallelism or parallel evolution– the development of a similar trait in related, but
distinct, species descending from the same ancestor, but from different clades
• Convergent evolution
Parallel evolutionParallel evolution occurs when two species that have descended from the same ancestor remain similar over long periods of time because they independently acquire the same evolutionary adaptations. Parallel evolution occurs because genetically related species adapt to similar environmental changes in similar ways. After many years, the organisms may still resemble each other, even though they speciated in the distant past.
Convergent evolutionwhen species from different ancestors colonize the same environment, they may independently acquire the same adaptations. The evolution of species descended from different ancestors to become superficially similar because they are adapting to the same environment is called convergent evolution
Phylogeny of what?
• Organisms– Whole genome phylogeny– Ribosomal RNA (surrogate for whole genome)
• Strains (closely related microbes)• Individual genes (or gene families)• Repetitive DNA sequences• Metabolic pathways• Secondary Structures• Any discrete character(s)• Human languages• Microbial communities
Why compute phylogenetic trees?
• Understand evolutionary history• Map pathogen strain diversity for vaccines• Assist in epidemiology
– Of infectious diseases– Of genetic defects
• Aid in prediction of function of novel genes• Biodiversity studies• Understanding microbial ecologies
Computational Approaches toPhylogenetic Tree Computation
• Distance Based Methods– UPGMA– Neighbor joining
• Character State Methods– Maximum Parsimony Method– Maximum Likelihood Methods
• Tree merging– Consensus trees, super-trees
What data is used to build trees?
• Traditionally: morphological features (e.g., number of legs, beak shape, etc.)
• Today: Mostly molecular data (e.g., DNA and protein sequences)
Data for Phylogeny
• Can be classified into two categories:– Numerical data
• Distance between objects– e.g., distance(man, mouse)=500,– distance(man, chimp)=100– Usually derived from sequence data
– Discrete characters• Each character has finite number of states
– e.g., number of legs = 1, 2, 4– DNA = {A, C, T, G}
2. Determine the evolutionary distances and build
distance matrix - A simple example
1. AGGCCATGAATTAAGAATAA2. AGCCCATGGATAAAGAGTAA3. AGGACATGAATTAAGAATAA4. AAGCCAAGAATTACGAATAA
Distance Matrix
In this example the evolutionary distance is expressed as the number of nucleotide differences for each sequence pair. For example, sequences 1 and 2 are 20 nucleotides in length and have four differences, corresponding to an evolutionary difference of 4/20 = 0.2.
1 2 3 4
1 - 0.2 0.05 0.15
2 - 0.25 0.4
3 - 0.2
4 -
3. Phylogenetic Tree Construction example (UPGMA algorithm)
1. Pick smallest entry Dij
2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes
DijBear Raccoon Weasel Seal
Bear - 0.26 0.34 0.29
Raccoon - 0.42 0.44
Weasel - 0.44
Seal -
Bear Raccoon
0.13 0.13
UPMGA (Michener & Sokal 1957)
3. Phylogenetic Tree Construction example (UPGMA algorithm)
DijBear Raccoon Weasel Seal
Bear - 0.26 0.34 0.29
Raccoon - 0.42 0.44
Weasel - 0.44
Seal -
3. Compute new distances to the other species using arithmetic means
365.02
44.029.0
2
38.02
42.034.0
2
)(
)(
SRSBBRS
WRWBBRW
DDD
DDD
Bear Raccoon
0.13 0.13
3. Phylogenetic Tree Construction example (UPGMA algorithm)
DijBR Weasel Seal
BR - 0.38 0.365
Weasel - 0.44
Seal -
1. Pick smallest entry Dij
2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes
Bear Raccoon Seal
0.13
0.1825 0.1825
3. Phylogenetic Tree Construction example (UPGMA algorithm)
DijBR Weasel Seal
BR - 0.38 0.365
Weasel - 0.44
Seal -
3. Compute new distances to the other species using arithmetic means
4.03
44.042.034.0
3)(
WSWRWBBRSW
DDDD
Bear Raccoon Seal
0.13
0.1825 0.1825
3. Phylogenetic Tree Construction example (UPGMA algorithm)
DijBRS Weasel
BRS - 0.4
Weasel -
1. Pick smallest entry Dij.
2. Join the two intersecting species and assign branch lengths Dij/2 to each of the nodes.
3. Done!
Bear Raccoon Seal Weasel
0.13 0.1825
0.2 0.2
Downside of UPGMA Assume molecular clock (assuming the
evolutionary rate is approximately constant)
Generates only rooted tree Trees are ultrametric Doesn’t work the following case:
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Computational Approaches toPhylogenetic Tree Computation
• Distance Based Methods– UPGMA– Neighbor joining
• Character State Methods– Maximum Parsimony Method– Maximum Likelihood Methods
• Tree merging– Consensus trees, super-trees
Neighbor-joining method
Developed in 1987 by Saitou and Nei Works in a similar fashion to UPGMA Still fast – works great for large dataset Doesn’t require the data to be
ultrametric Great for largely varying evolutionary
rates
39
How to construct a tree with Neighbor-joining method?
Step 1: Calculate sum all distance from x and divide by
(leaves – 2) Sx = (sum all Dx) / (leaves - 2)
Step 2: Calculate pair with smallest M
Mij = Distance ij – Si – Sj Step 3:
Create a node U that joins pair with lowest Mij S1U = (Dij / 2) + (Si – Sj) / 2
40
How to construct a tree with Neighbor-joining method? Step 4:
Join I and j according to S and make all other taxa in form of a star
Step 5: Recalculate new distance matrix of all other
taxa to U with: DxU = Dix + Djx - Dij
41
Example of Neighbor-joiningA B C D E
B 5
C 4 7
D 7 10 7
E 6 9 6 5
F 8 11 8 9 8
Step 1: S calculation : Sx = (sum all Dx) / (leaves - 2)
S(A) = (5 + 4 + 7 + 6 + 8) / 4 = 7.5S(B) = (5 + 7 + 10 + 9 + 11) / 4 = 10.5S(C) = (4 + 7 + 7 + 6 + 8) / 4 = 8 S(D) = (7+ 10 + 7 + 5 + 9) / 4 = 9.5 S(E) = (6 + 9 + 6 + 5 + 8) / 4 = 8.5 S(F) = (8 + 11 + 8 + 9 + 8) / 4 = 11
42
Example of Neighbor-joining cont 1
Step 2: Calculate pair with smallest M Mij = Distance ij – Si – Sj
Smallest are M(AB) = d(AB) – S(A) –S(B) = 5 – 7.5 – 10.5= -
13 M(DE) = 5 – 9.5 – 8.5 = -13
A B C D E
B -13
C -11.5
-11.5
D -10 -10 -10.5
E -10 -10 -10.5
-13
F -10.5
-10.5
-11 -11.5
-11.5
43
Example of Neighbor-joining cont 2
Step 3: Create a node US1U = (Dij / 2) + (Si – Sj) / 2
U1 joins A and B: S(AU1) = d(AB) / 2 + (S(A) – S(B)) / 2
= 5 / 2 + (7.5 - 10.5) / 2 = 1 S(BU1) = d(AB) / 2 + (S(B) – S(A)) / 2
= 5 / 2 + (10.5 – 7.5) / 2 = 4
44
Example of Neighbor-joining cont 3
Step 4: Join A and B according to S, and make all other taxa in form of a star. Branches in black are unknown length and Branches in red are known length
45
Example of Neighbor-joining cont 4
Step5: Calculate new distance matrixDxu = (Dix + Djx – Dij) / 2 d(CU) = (d(AC) + d(BC) - d(AB)) / 2
= (4 + 7 - 5) / 2 =3 d(DU) = d(AD) + d(BD) - d(AB) / 2 = 6
Same as EU and FU Then we get the new distance matrix
U1 C D E
C 3
D 6 7
E 5 6 5
F 7 8 9 846
Example of Neighbor-joining cont 5
Repeat 1 to 5 until all branches are done In this example, we will get this at the
end
47
Computational Approaches toPhylogenetic Tree Computation
• Distance Based Methods– UPGMA– Neighbor joining
• Character State Methods– Maximum Parsimony Method– Maximum Likelihood Methods
• Tree merging– Consensus trees, super-trees
50
Parsimony-score:Number of character-changes (mutations) along the evolutionary tree
(tree containing labels on internal vertices)
Example:
Maximum Parsimony Method
AGA AAAAAG GGA
1 1 0 2
0 0
1 0 0 1
0 1AAA
AAA AAAAGAAAAAAG GGA
AAA
AAA AGA
Most parsimonious tree: Tree with minimal parsimony score
Score = 4 Score = 3
Minimal Evolution Principle
51
We break the problem into two:
1. Small parsimony: Given the topology find the best assignment to internal nodes
2. Large parsimony: Find the topology which gives best score
Large parsimony is NP-hard We’ll show solution to small parsimony (Fitch and Sankoff’s
algorithms)
Input to small parsimony: tree with character-state assignments to leaves
Example:
Small vs. Large Parsimony
AardvarkBisonChimp Dog Elephant
A: CAGGTAB: CAGACAC: CGGGTAD: TGCACTE: TGCGTA
52
Fitch’s Algorithm
Execute independently for each character:
1. Bottom-up phase: Determine set of possible states for each internal node
2. Top-down phase: Pick states for each internal node
AardvarkBisonChimp Dog Elephant
1 2
CAGGTACAGACA
CGGGTATGCACT
TGCGTA
Dynamic Programming framework
53
Determine set of possible states for each internal node
• Initialization: Ri = {si}• Do a post-order (from leaves to root) traversal of tree
– Determine Ri of internal node i with children j, k:
Fitch’s AlgorithmBottom-up phase
Parsimony-score =# union operations
T
CT
T
C T A
otherwiseRR
RRifRRR
kj
kjkj
i
G T
AGTGT
T
score = 3
54
Pick states for each internal node
• Pick arbitrary state in Rroot for the root• Do pre-order (from root to leaves) traversal of tree
– Determine sj of internal node j with parent i:
Fitch’s AlgorithmTop-down phase
T
CT
T
C T AG T
AGTGT
T
otherwiseRstatearbitrary
Rsifss
j
jii
j
Complexity: O(mnk)
#characters#taxa/nodes
#states
score = 3
55
Weighted ParsimonySankoff’s algorithm
• Each mutation a↔b costs differently - S(a,b).
1. Bottom-up phase: Determine Ri(s) – cost of optimal state-assignment for subtree of i, when it is assigned state s.
2. Top-down phase: Pick optimal states for each internal node
Fitch’s algorithm as special case:• Ri – set of states which yield minimal-cost subtree of i
Same as algorithm foroptimal lifted tree alignment
(Tutorial #4)
56
Determine Ri(s) for each internal node
• Initialization: • Do a post-order (from leaves to root) traversal of tree
– Determine Ri of internal node i with children j, k:
Sankoff’s AlgorithmBottom-up phase
C T AG T T
Natural generalizationFor non-binary trees
otherwise
ssifsR i
i
0)(
),'()'(min),'()'(min)( '' ssSsRssSsRsR ksjsi
Remember pointersss’
57
Pick states for each internal node
• Select minimal cost character for root (s minimizing Rroot(s))
• Do pre-order (from root to leaves) traversal of tree:- For internal node j, with parent i, select state that produced minimal cost at i (use pointers kept in 1st stage)
Sankoff’s AlgorithmTop-down phase
C T AG T T
Complexity: O(mnk2)
#characters#taxa/nodes
#states
),'()'(min
),'()'(min)(
'
'
ssSsR
ssSsRsR
ks
jsi
58
Unweighted parsimony:
Sankoff’s algorithm:• Ri(s) - cost of optimal subtree of i, when it is assigned state s
Fitch’s algorithm:• Score(i) - cost of optimal state-assignment for subtree of i • Ri - set of optimal state-assignment for subtree of i
We need to show that:1. Optimal tree assigns node i with state from Ri.
2. Fitch’s bottom-up recursive formula for Ri. is correct:
Fitch’s Algorithmas special case of Sankoff’s algorithm
otherwiseRR
RRifRRR
kj
kjkj
i
otherwise
baifbaS
1
0),(
Check for yourselves
59
Unweighted parsimony:
• Score(i) - cost of optimal state-assignment for subtree of i • Ri - set of optimal state-assignment for subtree of i
We need to show that:1. Optimal tree assigns node i with state from Ri.
• Trivially true for the root• Assume (to the contrary) that in an optimal assignment,
some node – j is assigned sj∉Rj
otherwise
baifbaS
1
0),(
rooti
j sj∉Rj Rj(sj) ≥ Score(j)+1
By switching from sj to some s∊Rj we do not raise the parsimony-score
Why is this not the case for the weighted version?
Parsimony-score is integer
Fitch’s Algorithmas special case of Sankoff’s algorithm
Computational Approaches toPhylogenetic Tree Computation
• Distance Based Methods– UPGMA– Neighbor joining
• Character State Methods– Maximum Parsimony Method– Maximum Likelihood Methods
• Tree merging– Consensus trees, super-trees
Maximum likelihood
Originally developed for statistics by Ronald Fisher between 1912 and 1922
Therefore, explicit statistical model Uses all the data Tends to outperform parsimony or
distance matrix methods
61
How to construct a treewith Maximum likelihood? Step 1: Make all possible trees
depending on the number of leaves Step 2: Calculate likelihood of occurring
with the given dataL(Tree) = probability of each tree.
• optimizing branch length • generating tree topology
Step 3: Pick the tree that have the highest likelihood.
62
Sounds really great?
Num of leaves
Num of possible trees
3 1
5 15
10 2027025
13 15058768725
20 8200794532637891559375
Maximum likelihood is very expensive and extremely slow to compute
63
Comparison of MethodsDistance Maximum
parsimonyMaximum likelihood
Uses only pairwise distances
Uses only shared derived characters
Uses all data
Minimizes distance between nearest neighbors
Minimizes total distance
Maximizes tree likelihood given specific parameter values
Very fast Slow Very slow
Easily trapped in local optima
Assumptions fail when evolution is rapid
Highly dependent on assumed evolution model
Good for generating tentative tree, or choosing among multiple trees
Best option when tractable (<30 taxa, homoplasy rare)
Good for very small data sets and for testing trees built using other methods
Methods of evaluating trees
• Bootstrap: resample initial data set with one datum removed and replaced with another member
• Jackknife: resample initial distribution with one datum missing and not replaced
• MCMC: complex, but generates random numbers to produce a desired probability distribution with which to compare model
Difference in Methods
• Maximum-likelihood and parsimony methods have models of evolution
• Distance methods do not necessarily– Useful aspect in some circumstances
• E.g., trees built based on whole genomes, presence or absence of genes
• Religious wars over which methods to use– Most people now believe ML based methods are best: most
sensitive at large evolutionary distances – but also most time-consuming & depend on specific model of evolution used
• Most commonly used packages contain software for all three methods: may want to use more than 1 to have confidence in built tree
Phylip
• URL: http://evolution.genetics.washington.edu/phylip.html• Parsimony
– DNApenny or Protpars
• Distance– Compute distance measure using DNAdist or Protdist– Neighbor (can use NJ or UPGMA)
• ML– DNAml
Visualising trees
• Treeview• You can change the graphic presentation of a tree (cladogram,
rectangular cladogram, radial tree, phylogram), but not change the structure of a tree
• http://homopan.wayne.edu/softwares/phoenix/index.html