Phylogenetics 101
Eddie Holmes
Center for Infectious Disease Dynamics,
Department of Biology,
The Pennsylvania State University
Fogarty International Center, National Institutes of Health
Modern Phylogenetics
Useful Textbooks & Software
Books:
• Page RDM & Holmes EC. (1998). Molecular Evolution: A Phylogenetic
Approach. Blackwell Science Ltd, Oxford.
• Lemey P, Salemi M & Vandamme A-M. (2009). The Phylogenetic Handbook,
2nd Edition. Cambridge University Press.
Computer Software:
• BEAST (Bayesian Evolutionary Analysis Sampling Trees)
- http://beast.bio.ed.ac.uk/
• MEGA (Molecular Evolutionary Genetics Analysis)
- http://megasoftware.net/
• MrBayes (Bayesian inference of phylogeny)
- http://mrbayes.csit.fsu.edu/
• PhyML (Maximum likelihood phylogenetics)
- http://www.atgc-montpellier.fr/phyml/
• HyPhy/DATAMONKEY (Selection, recombination & hypothesis testing)
- http://datamonkey.org/
• RDP3 (Recombination detection program)
- darwin.uvigo.es/rdp/rdp.html
• PAUP* (Phylogenetic Analysis Using Parsimony *and other methods)
- http://paup.csit.fsu.edu/
Topics in Evolutionary Inference
• Estimating genetic distances between sequences
• Inferring phylogenetic trees
• Detecting recombination events
• The inference of selection pressures (particularly
detecting positive selection)
• Estimating rates of evolutionary change
• Inferring demographic history (population dynamics)
• Phylogeography
The Quasispecies
Useful summary reference:
• Bull JJ, Meyers LA & Lachmann M. (2005). Quasispecies made
simple. PLoS Comp.Biol. 1:e61.
The Quasispecies
• Idea introduced by Manfred Eigen as a mathematical
model of early life forms (RNA replicators) based upon
chemical kinetics and first used in virology by Esteban
Domingo in the 1970s. Now the dominant model in RNA
virus evolution.
• A distribution of variant genomes ordered around the
fittest sequence (often called the ‘master sequence’) and
produced by a combination of mutation and selection
(“mutation-selection” balance). Only functions at high
mutation rates.
• Only considers intra-host evolution.
The Quasispecies
• The frequency of any variant in the quasispecies is a
function of its own replication rate and the probability that
it is produced by the erroneous replication of other
variants in the population.
• Viral genomes are not independent entities due to
mutational coupling (i.e. variants are linked in mutational
space). The entire mutant distribution forms an organised
structure which acts like (quasi) a single unit (species).
• Natural selection acts on the mutant distribution as a
whole, not on individual variants, and the quasispecies
evolves to maximise its average replication fitness. So, it
is a form of group selection.
• Important implication: low fitness variants can outcompete high fitness variants if they are surrounded by
beneficial mutational neighbours (“survival of the flattest”).
The Quasispecies
‘survival of the fittest’
‘survival of the flattest’
“Survival of the Flattest”
Experimental Verification of
Quasispecies Dynamics
Population A = red (high replication rate)
Population B = blue (low replication rate)
• However, this only occurs at artificially elevated mutation rates
• Sanjuán R, Cuevas JM, Furió V, Holmes EC & Moya A. (2007). Selection for robustness in
mutagenized RNA viruses. PLoS Genet. 3: e93.
Do RNA Viruses Form Quasispecies?
• Most people simply use the quasispecies as a synonym for genetic
diversity. However, genetic diversity is not the same as the quasispecies!
• The quasispecies works in theory, in “digital organisms” and perhaps in
some laboratory populations where mutation rates are increased artificially
(i.e. when RNA viruses are about to breech the “error threshold”).
However, quasispecies do not occur in laboratory populations with
‘normal’ error rates.
• No good evidence as yet that RNA viruses in nature form quasispecies:
- no evidence that selection acts on the whole population
- mutation rates are too low
• The mutation rate required for the survival of the flattest (> 2 per genome
replication) is higher than that seen in nature (< 1 per genome
replication)…this only occurs during the treatment of viral infections with
mutagens (“lethal mutagenesis”).
Shameless Self-Publicity
• Amazon.com Sales Rank: # 666,415 in Books
Estimating Genetic Distances Between Sequences
Estimating Genetic Distance
SIVcpz
HIV-1
ATGGGTGCGA GAGCGTCAGT TCTAACAGGG GGAAAATTAG ATCGCTGGGA
ATGGGTGCGA GAGCGTCAGT ATTAAGCGGG GGAGAATTAG ATCGATGGGA
SIVcpz
HIV-1
AAAAGTTCGG CTTAGGCCCG GGGGAAGAAA AAGATATATG ATGAAACATT
AAAAATTCGG TTAAGGCCAG GGGGAAAGAA AAAATATAAA TTAAAACATA
SIVcpz
HIV-1
TAGTATGGGC AAGCAGGGAG CTGGAAAGAT TCGCATGTGA CCCCGGGCTA
TAGTATGGGC AAGCAGGGAG CTAGAACGAT TCGCAGTTAA TCCTGGCCTG
SIVcpz
HIV-1
ATGGAAAGTA AGGAAGGATG TACTAAATTG TTACAACAAT TAGAGCCAGC
TTAGAAACAT CAGAAGGCTG TAGACAAATA CTGGGACAGC TACAACCATC
SIVcpz
HIV-1
TCTCAAAACA GGCTCAGAAG GACTGCGGTC CTTGTTTAAC ACTCTGGCAG
CCTTCAGACA GGATCAGAAG AACTTAGATC ATTATATAAT ACAGTAGCAA
SIVcpz
HIV-1
TACTGTGGTG CATACATAGT GACATCACTG TAGAAGACAC ACAGAAAGCT
CCCTCTATTG TGTGCATCAA AGGATAGAGA TAAAAGACAC CAAGGAAGCT
SIVcpz
HIV-1
CTAGAACAGC TAAAGCGGCA TCATGGAGAA CAACAGAGCA AAACTGAAAG
TTAGACAAGA TAGAG--GAA -----GAGCA AAACAAAAGT AA---GAAAA
SIVcpz
HIV-1
TAACTCAGGA AGCCGTGAAG GGGGAGCCAG TCAAGGCGCT AGTGCCTCTG
AAGCACAGCA AGC-----AG CAGCTGACA- -CAGGACAC- AG--CAGC--
SIVcpz
HIV-1
CTGGCATTAG TGGAAATTAC
CAGG--TCAG CCAAAATTAC
Multiple Substitutions at a Single Site
- Hidden Information
A
Example 1
T
A
Only count 1 mutation
when 2 have occurred
C
A
Example 2
A
T
Count 0 mutations
when 3 have occurred
C
The Problem of Multiple Substitution
% Divergence
Actual
Observed
Hidden
information
75
50
25
Time
• When % divergence is low, observed distance (p) is a good estimator of
genetic distance (d)
• When % divergence is high, p underestimates d and a “correction
statistic” is required i.e. a model of DNA substitution
Models of DNA Substitution
• Models of DNA sequence evolution are required to
recover the missing information through correcting for
multiple substitutions.
i. The probability of substitution between bases
(e.g. A to C, C to T…)
ii. The probability of substitution along a sequence
(different sites/regions evolve at different rates)
Models of DNA Substitution 1
(Jukes-Cantor, 1969)
• Assumptions:
i. All bases evolve independently
ii. All bases are at equal frequency
iii. Each base can change with equal probability ( )
iv. Mutations arise according to a Poisson distribution
(rare and independent events)
• From this the number of substitutions per site (d) can be
estimated by;
d = -3/4 In (1-4/3P)
where P is the proportion of observed nucleotide differences
between 2 sequences.
A
a
C
a
a
a
a
T
a
G
All substitutions occur at the same rate (a)
Is this model too simple for real data?
A
b
C
a
b
b
a
T
b
G
Transitions (a) and transversions (b) occur at a different rate
Models of DNA Substitution 2
(Kimura 2-parameter, 1980)
• Assumptions:
i. All bases evolve independently
ii. All bases are at equal frequency
iii. Transitions and transversions occur with different
probabilities ( and )
iv. The Jukes-Cantor model is applied to transitions and
transversions independently
• From this the expected number of substitutions per site (d)
can be estimated by;
d = -1/2 In (1-2P-Q)√1-2Q
where P is the proportion of observed transitions and Q the
proportion of observed transversions between 2 sequences
Models of DNA Substitution
Simplest
(few parameters)
1. Base frequencies are equal and
all substitutions are equally likely
(Jukes-Cantor)
2. Base frequencies are equal but transitions and
transversions occur at different rates
(Kimura 2-parameter)
3. Unequal base frequencies and transitions and
transversions occur at different rates
(Hasegawa-Kishino-Yano)
4. Unequal base frequencies and all
Most complex
(many parameters) substitution types occur at different rates
(General Reversible Model)
All these models can be tested using the program jMODELTEST
(darwin.uvigo.es/software/jmodeltest.html)
Models of DNA Substitution
i. The probability of substitution between bases
(e.g. A to C, C to T…)
ii. The probability of substitution along a sequence
(different sites/regions evolve at different rates)
A Gamma Distribution Can be Used to
Model Among-Site Rate Heterogeneity
Frequent among-site
rate variation
Little among-site
rate variation
Estimates of a Shape Parameter of
Among Site Rate Variation
Gene
Prolactin
Albumin
C-myc
Ctyochrome b (mtDNA)
Insulin
D-loop (mtDNA)
12S rRNA (mtDNA)
a
1.37
1.05
0.47
0.44
0.40
0.17
0.16
• Viruses are usually characterized by extensive among-site rate variation
(a < 1).
Estimating Genetic Distance:
SIVcpz vs HIVlai
• Uncorrected (p-distance)
• Jukes-Cantor
• Kimura 2-parameter
• Hasegawa-Kishino-Yano
• General reversible
• General reversible + gamma
= 0.406
= 0.586
= 0.602
= 0.611
= 0.620
= 1.017
Other Models
• Allowing a different rate of nucleotide substitution for
each codon position in a coding sequence (SRD06; tends
to work better than gamma distributions in RNA viruses)
• Allowing different sets of nucleotides to change along
different lineages (“covarion” model)
e.g. sites that are variable in bacteria might be
conserved in eukaryotes
• Accounting for the non-independence of nucleotides
(caused by protein and RNA secondary structures)
Inferring Phylogenetic Trees
Important Problems in Molecular
Phylogenetic Analysis
• Is there a tree at all (e.g. recombination)?
• Many possible trees:
- For 10 taxa there are 2 x 106 unrooted trees
- For 50 taxa there are 3 x 1074 unrooted trees
- efficient and powerful search algorithms
• Choosing the right model of nucleotide substitution
• Rate variation among lineages (causes “long branch
attraction”). Need a representative sample of taxa.
Why Having a Representative
Sample of Taxa is Important
small tree
large tree
long branches drawn together
(convergent sites pull branches together)
long branches far apart
(convergent sites distributed across tree)
Long branch attraction
= convergent site
= informative site
Tree-Building Methods
No explicit model
of sequence evolution
Explicit model
of sequence evolution
Application
of the
parsimony
principle
pairwise
comparison
of
sequences
Statistical
approach
parsimony
distance
maximum likelihood
and bayesian
Methods for Inferring Phylogenetic Trees
• Parsimony (PAUP*)
Find tree with the minimum number of mutations between sequences (i.e.
choose tree with the least convergent evolution)
• Neighbor-Joining (PAUP*, MEGA)
Estimate genetic distances between sequences and cluster these distances
into a tree that minimises genetic distance over the whole tree
• Maximum Likelihood (PAUP*, GARLi, PhyML, RaxML,
MEGA)
Determine the probability of a tree (and branch lengths) given a particular
model of molecular evolution and the observed sequence data
• Bayesian (BEAST, Mr.Bayes)
Similar to likelihood but where there is information about the prior
distribution of parameters. Also returns a (posterior) distribution of trees
Distance Methods
๏ Advantages:
- Allows the use of an explicit model of evolution
- Very fast
- Simple
๏ Disadvantages:
- Only produces one tree with no indication of its quality
- Reduces all sequence information into a single distance
value
- Dependent on the evolutionary model used (preferentially
this model should be estimated from the data)
Optimality Methods
๏ Parsimony
- Fast
- Not statistically consistent with most models of evolution
- “The” method for morphological data
๏ Maximum Likelihood
- Requires explicit statement of evolutionary model
- Slow
- Statistically consistent
- Most commonly used with molecular data
Maximum Likelihood in Phylogenetics
•
Best described by Joe Felsenstein
‣
Felsenstein, J. (1981). Evolutionary
trees from DNA sequences: a maximum
likelihood approach. J. Mol. Evol. 17,
368-376
•
Now considered the most statistically valid
approach to molecular phylogenetics along
with the closely related Bayesian methods
•
Allows us to incorporate extremely detailed
models of molecular evolution
Likelihood
•
Likelihood is a quantity proportional to the probability of
observing an outcome/data/event X given a hypothesis
H
P ( X | H ) or P ( X | p )
•
then we would talk about the likelihood
L(p|X)
that is, the likelihood of the parameters given the data.
•
In this case the hypothesis is a tree + branch lengths
and the data are the sequences
R.A. Fisher
(looking suitably grumpy)
Assumes an explicit model of molecular
evolution, such as those described previously
Bayesian Phylogenetics
๏ Using Bayesian statistics, you search for a set of plausible trees instead
of a single best tree
๏ In this method, the “space” that you search in is limited by prior
information
๏ The posterior distribution of trees can be translated to a probability of
any branching event
- Allows estimate of uncertainty!
- BUT incorporates prior beliefs
Andrew Rambaut will
explain in more detail…
Searching Through ‘Tree Space’
Searching Through Tree Space
๏ There are two ways in which we can search through tree
space to find the best tree for our data:
– Branch-and-bound: finds the optimal tree by implicitly
checking all possible trees (cutting of paths in the
search tree that cannot possibly lead to optimal trees)
– Heuristic: searches by randomly perturbing the tree,
does not check all trees and cannot guarantee to find
the optimal one(s). Most commonly used.
(exhaustive searching is only possible for very small
data sets)
Global Maximum Likelihood tree
local optimum
Likelihood
Heuristic
searching
Starting tree of the
heuristic search
Trees
Starting tree of the
heuristic search
Bootstrapping (How Robust is a Tree?)
Non-Parametric Bootstrap
• Statistical technique that uses random resampling of data to
determine sampling error.
• Characters are resampled with replacement to create many
replicate data sets. A tree is then inferred from each replicate.
• Agreement among the resulting trees is summarized with a
consensus tree. The frequencies of occurrence of groups,
bootstrap proportions, are a measure of support for those
groups
Parametric Bootstrap (Monte Carlo simulation)
• Compare the likelihoods of competing trees on the data.
• Simulate replicate sequences using the parameters (including
the tree) obtained for the worse tree (null hypothesis).
• Compare the likelihoods trees for each replicate data set as
before to create a null distribution.
Non-Parametric Bootstrapping
1
2
3
4
5
6
A
A
A
A
A
A
C
C
C
T
T
T
C
C
C
C
C
G
T
T
T
T
T
G
G
G
A
A
A
A
G
G
C
T
T
A
1
1
2
3
4
5
6
G
G
A
A
A
A
G
G
A
A
A
A
G
G
C
T
T
A
...
A
A
A
A
A
A
T
T
T
T
T
G
C
C
C
T
T
T
Resample with
replacement multiple times
12 3456
1000
1
2
3
4
5
6
T
T
T
T
T
G
G
G
C
T
T
A
C
C
C
C
C
G
C
C
C
C
C
G
A
A
A
A
A
A
G
G
A
A
A
A
Detecting Recombination
Recombination & Reassortment
• The Problems:
- Generates new genetic configurations
- Complicates our attempts to infer phylogenetic
history and other evolutionary processes (e.g.
positive selection)
• The Solutions:
- Find recombinants and remove them from the data
set (usual plan)
- Incorporate recombinants into an explicit
evolutionary model (far harder)
• “Topological incongruence”, where different gene regions (or
genes) produce different phylogenetic trees, is the strongest
signal for recombination (although conservative)
Methods for Recombination Detection
• Measure level of linkage disequilibrium:
- LDhat, D’
• Look for changes in patterns of sequence similarity (often pairwise):
- GENECOV, RDP, Max Chi-Square, SimPlot, SiScan, TOPAL
• Look for incongruent phylogenetic trees:
- BOOTSCAN, 3SEQ, LARD, PLATO, LIKEWIND
• Look for “networked” evolution
- SplitsTree, NeighborNet
• Look for excessive convergent evolution:
- Homoplasy test, PIST
• See http://www.bioinf.manchester.ac.uk/recombination/programs.shtml
for a more complete list
• Many of these methods are available in the Recombination Detection
Program (RDP3) – http://darwin.uvigo.es/rdp/rdp.html
Sliding Window Diversity Plots can Graphically
Show Recombination (e.g. “SimPlot”)
Hepatitis B virus
• Magiorkinis et al. Gene 349, 165-171 (2005).
Detecting Recombination:
Looking for Incongruent Trees
• Different genes produce different trees
A
Gene
region 1
B
Gene
region 2
C
Maximum likelihood break-point
• Programme “LARD” (a maximum likelihood approach)
• Compute likelihood of each possible breakpoint in the alignment
• Identify breakpoint with the highest likelihood in the alignment
• Compare recombination likelihood to that with no recombination
• Assess significance with Monte Carlo simulation
Although reassortment is commonplace in influenza virus, the
occurrence of homologous recombination is highly controversial
Analyzing Natural Selection
Ways of Measuring Selection Pressures
(Especially Detecting Positive Selection)
• Phylogenetic methods:
Identify cases of strong parallel or convergent evolution
• Population genetic methods:
(i) Look for regional reductions in genetic diversity, usually
using SNPs (commonly used with genomic data)
(ii) Compare estimates of effective population size obtained
using different measures of genetic diversity (e.g. the H
statistic of Fay & Wu)
(iii) Estimate the speed of allele fixation compared to neutrality
• Combined phylogenetic and population genetic methods:
Compare the relative numbers of nonsynonymous (dN) and
synonymous (dN) substitutions per site
Detecting Positive Selection by Examining
Patterns/Rates of Fixation
• Bhatt S, Holmes EC & Pybus OG. (2011). The genomic rate of molecular adaptation of the
human influenza A virus. Mol.Biol.Evol. 28, 2443-2451.
Measuring Selection Pressures
• Compare the ratio of synonymous (dS) and nonsynonymous
(dN) substitutions per site (dN/dS = ):
Ser
Met
Seq 1: TCA
ATG
†
*
Seq 2: TCG ATA
Ser
Ile
†Synonymous substitution
Leu
Gly
Gly
TTA
GGG GGA
†
†
**
CTA
GGT ATA
Leu
Gly
Ile
*Nonsynonymous substitution
dN/dS < 1.0 = purifying selection
dN/dS ~ 1.0 = neutral evolution
dN/dS > 1.0 = positive selection
• Cases where dN > dS ( > 1) are evidence for positive
selection because the rate of fixation of nonsynonymous
changes (dN) is greater than the neutral mutation rate (dS)
which is impossible under genetic drift
Analysing Selection Pressures
in Genes Using dN/dS
• Pairwise methods:
(i) Compute dS and dN in each pair of sequences and then compute the
mean across all pairs
(ii) Various methods, including:
- Nei & Gojobori 1986 (distance matrix method)
- Li et al. 1985 (distance matrix method)
- Yang et al. 2000 (maximum likelihood method)
(iii) Problems of pseudo-replication, sometimes use poor substitution
models, and lack of power (many false-negatives)
• Site-by-site (and branch) methods:
(i) Incorporate phylogenetic relationships of sequences (i.e. estimate dN/dS
along a tree)
(ii) Allow variable selection pressures among codons and realistic models
of nucleotide substitution
(iii) Can employ parsimony, likelihood or Bayesian methods
(iv) Has now been extended to account for directional selection (DEPS)
(v) Tendency for false-positive results, especially in branch-site methods
A NALYZE YOUR
DATA
H OME H ELP CITATIONS J OB Q UEUE S TATS HYP HY PACKAGE
Datamonkey
http://www.datamonkey.org/
Jul 27th, 2011. Two new methods in the branch-site family (i.e. where dN/dS is varied along sites and branches) have
been made available for codon alignments.
Branch-site REL is suitable for detecting those lineages where a proportion of sites evolved with dN > dS.
MEME is designed to identify those sites where a proportion of lineages evolved with dN > dS.
• Online version of the more
powerful HyPhy package
Welcome to the free public server for detecting signatures of positive and
negative selection from coding sequence alignments using state-of-the-art
statistical models. This service is brought to you by the viral evolution group at
School Of Medicine of the University of California, San Diego. Over its lifetime
Datamonkey.org has processed 111549 analyses at a rate of 122.433 jobs/day
(over the last 30 days).
Datamonkey.org can help you answer the following questions ( publications citing
datamonkey.org ) :
Which codon sites are under diversifying positive or negative selection?
• Contains multiple programs for
the analysis of selection
pressures (and recombination)
Analyze your data.
Three different codon-based maximum likelihood methods, SLAC , FEL and
[Run SCUEAL]
REL , can be used estimate the dN/dS (also known as Ka/Ks or ! ) ratio at
[Run UDS analysis]
every codon in the alignment. An exhaustive discussion of each approach
can be found in the methodology paper . All methods can also take
recombination into account . This is done by screening the sequences for recombination breakpoints,
identifying non-recombinant regions and allowing each to have its own phylogentic tree.
Is there evidence of selection in my alignment?
The PARRIS method, developed by Konrad Scheffler and colleagues , extends traditional codon-based
likelihood ratio tests to detect if a proportion of sites in the alignment evolve with dN/dS>1. The method
takes recombination and synonymous rate variation into account.
What is the evolutionary fingerprint of a gene?
The ESD method, described in a recent paper , fits a versatile general discrete bivariate model of site-bysite selective force variation to partition all sites into selective classes, and obtains an approximate
posterior distribution of this partititoning. The resulting "noisy" distribution of selective regimes is the
evolutionary fingerprint of a gene. The EVF (evolutionary fingerprinting) module implements this
procedure, and can also infer which individual sites appear to be positively selected while accounting
for parameter estimation error (analogous to the BEB methodology of the PAML package).
Which codon sites are under positive or negative selection at the population level?
The codon-based maximum likelihood IFEL method can investigate whether sequences sampled from
a population (e.g. viral sequences from different hosts) have been subject to selective pressure at the
population level (i.e. along internal branches). A discussion of the method and its application can be
found here
Did selective pressure vary along lineages, i.e. over time?
The codon-based genetic algorithm GABranch method can automatically partition all branches of the
phylogeny describing non-recombinant data into groups according to dN/dS. Robust multi-model
inference is used to collate results from all models examined during the run to provide confidence
intervals on dN/dS for each branch and guard against model misspecification and overfitting ( method
details ).
How about episodic diversifying selection (branch-site methods)? Using the modeling framework , which
allows the efficient estimations with models which permit dN/dS variation along both sites and lineages,
Datamonkey implements two tests geared towards finding lineages and sites subject to episodic
diversifying selection (EDS).
Variable Selection Pressures in RNA Viruses
Intra-Host Evolution of HIV-1
SIHIGPGRAFYTTGE
SIPIGPGRAFYTTGQ
SIHIGPGGAFYTTGQ
SIHIGPGRAFYTTGD
SIPIGPGRAFYTTGD
GIHIGPGSAFYATGD
SIHIGPGRAFYTTGG
SIHIGPGRAVYTTGQ
GIHIGPGSAFYATGG
GIHIGPGRAVYTTEQ
RIHIGPGRAVYTTEQ
GIHIGPGSAFYATGR
RIYIGPGRAVYTTEQ
GIHIGPGSAVYATGG
RIYIGPGSAVYTTEQ
GIHIGPGSAFYATGG
RIGIGPGRSVYTAEQ
GIHIGPGSAVYATGD
GIHIGPGRAFYATGD
GIHIGPGRAVYTTGD
RIYIGPGRAVYTTDQ
Tip of the V3 loop (part of the
envelope protein of HIV-1)
- diversity in a single patient
• The HIV-1 envelope protein is under
very strong positive selection to help
the virus escape from the human
immune response (the V3 loop contains
epitopes for neutralising antibodies and
cytotoxic T-lymphocytes (CTLs).
• V3 loop dN/dS = 13.182
(Nielsen & Yang. Genetics 148, 929. 1998).