Transcript Lecture 3 Introduction to characters and parsimony analysis

Assessing Phylogenetic Hypotheses
and Phylogenetic Data
• We use numerical phylogenetic methods because most
data includes potentially misleading evidence of
relationships
• We should not be content with constructing
phylogenetic hypotheses but should also assess what
‘confidence’ we can place in our hypotheses
• This is not always simple! (but do not despair!)
Assessing Data Quality
• We expect (or hope) our data will be well structured
and contain strong phylogenetic signal
• We can test this using randomisation tests of
explicit null hypotheses
• The behaviour or some measure of the quality of our
real data is contrasted with that of comparable but
phylogenetically uninformative data determined by
randomisation of the data
Random Permutation
• Random permutation destroys any correlation among characters to that
expected by chance alone
• It preserves number of taxa, characters and character states in each
character (and the theoretical maximum and minimum tree lengths)
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Original structured data with
strong correlations among
characters
Randomly permuted data with
correlation among characters
due to chance alone
Matrix Randomisation Tests
• Compare some measure of data quality
(hierarchical structure) for the real and many
randomly permuted data sets
• This allows us to define a test statistic for
the null hypothesis that the real data are no
better structured than randomly permuted and
phylogenetically uninformative data
• A permutation tail probability (PTP) is the
proportion of data sets with as good or better
measure of quality than the real data
Structure of Randomisation Tests
• Reject null hypothesis if, for example, more than 5%
of random permutations have as good or better
measure than the real data
Frequency
FAIL
TEST
95% cutoff
PASS
TEST
reject null hypothesis
Measure of data quality (e.g. tree length, ML, pairwise incompatibilities)
GOOD
BAD
Matrix Randomisation Tests
• Measures of data quality include:
1. Tree length for most parsimonious trees - the
shorter the tree length the better the data
(PAUP*)
2. Any other objective function (Likelihood, Least
Squares Fit, etc)
3. Numbers of pairwise incompatibilities between
characters (pairs of incongruent characters) - the
fewer character conflicts the better the data
Matrix Randomization Tests
Ciliate SSUrDNA
Real data
Randomly
permuted
Min = 430
Max = 927
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tracheloraphis
Spirostomum
Gruberia
Euplotes
Tetrahymena
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Tracheloraphis
Spirostomum
Euplotes
Gruberia
Strict consensus
1 MPT
L = 618
CI = 0.696, RI = 0.714
PTP = 0.01
PC-PTP = 0.001
Significantly non random
3 MPTs
L = 792
CI = 0.543, RI = 0.272
PTP = 0.68
PC-PTP = 0.737
Not significantly different
from random
Matrix Randomisation Tests - use
and limitations
• Can detect very poor data - that provides
no good basis for phylogenetic inferences
(throw it away!)
• However, only very little may be needed to
reject the null hypothesis (passing test 
great data)
• Doesn’t indicate location of this structure
(more discerning tests are possible)
Assessing Phylogenetic
Hypotheses - groups on trees
• Several methods have been proposed that attach
numerical values to internal branches in trees that
are intended to provide some measure of the strength
of support for those branches and the corresponding
groups
• These methods include:
character resampling methods - the bootstrap and jackknife
comparisons with suboptimal trees - decay analyses
additional randomisation tests
Bootstrapping (non-parametric)
• Bootstrapping is a modern
statistical technique that
uses computer intensive
random resampling of data to
determine sampling error or
confidence intervals for some
estimated parameter
Bootstrapping
• Characters are resampled with replacement to
create many bootstrap replicate data sets
• Each bootstrap replicate data set is analysed (e.g.
with parsimony, distance, ML)
• Agreement among the resulting trees is summarized
with a majority-rule consensus tree
• Frequency of occurrence of groups, bootstrap
proportions (BPs), is a measure of support for those
groups
• Additional information is given in partition tables
Bootstrapping
Original data matrix Resampled data matrix
Taxa
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Outgp
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Characters
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R Y Y Y Y Y
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Characters
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R R Y Y Y Y
R R Y Y Y Y
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Randomly resample characters from the original data
with replacement to build many bootstrap replicate
data sets of the same size as the original - analyse
each replicate data set
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Summarise the results of
multiple analyses with a
majority-rule consensus tree
Bootstrap proportions (BPs)
are the frequencies with
which groups are encountered
in analyses of replicate data
sets
96%
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66%
Outgroup
Outgroup
Outgroup
Bootstrapping - an example
Ciliate SSUrDNA - parsimony bootstrap
Ochromonas (1)
Symbiodinium (2)
100
Prorocentrum (3)
Euplotes (8)
84
Tetrahymena (9)
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100
Loxodes (4)
Tracheloraphis (5)
100
100
Majority-rule consensus
Spirostomum (6)
Gruberia (7)
Partition Table
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Freq
----------------.**...... 100.00
...**.... 100.00
.....**.. 100.00
...****.. 100.00
...******
95.50
.......**
84.33
...****.*
11.83
...*****.
3.83
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2.50
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1.00
.**.....*
1.00
Bootstrapping - random data
Randomly permuted data
- parsimony bootstrap
Majority-rule consensus
(with minority components)
Partition Table
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Freq
----------------.*****.**
71.17
..**.....
58.87
.***.*.**
26.00
....*..*.
26.00
.....*..*
21.00
.*......*
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.*..**.**
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Bootstrap - interpretation
• Bootstrapping was introduced as a way of establishing
confidence intervals for phylogenies
• This interpretation of bootstrap proportions (BPs) depends on
assuming that the original data is a random (fair) sample from
independent and identically distributed data
• However, several things complicate this interpretation
- Perhaps the assumptions are unreasonable - making any statistical
interpretation of BPs invalid
- Some theoretical work indicates that BPs are very conservative, and
may underestimate confidence intervals - problem increases with
numbers of taxa
- BPs can be high for incongruent relationships in separate analyses and can therefore be misleading (misleading data -> misleading BPs)
- with parsimony it may be highly affected by inclusion or exclusion of
only a few characters
Bootstrap - interpretation
• Bootstrapping is a very valuable and widely used technique it (or some suitable) alternative is demanded by some
journals, but it may require a pragmatic interpretation:
• BPs depend on two aspects of the support for a group - the
numbers of characters supporting a group and the level of
support for incongruent groups
• BPs thus provides an index of the relative support for groups
provided by a set of data under whatever interpretation of
the data (method of analysis) is used
Bootstrap - interpretation
• High BPs (e.g. > 85%) is indicative of strong ‘signal’ in the
data
• Provided we have no evidence of strong misleading signal
(e.g. base composition biases, great differences in branch
lengths) high BPs are likely to reflect strong phylogenetic
signal
• Low BPs need not mean the relationship is false, only that it
is poorly supported
• Bootstrapping can be viewed as a way of exploring the
robustness of phylogenetic inferences to perturbations in the
the balance of supporting and conflicting evidence for groups
Jackknifing
• Jackknifing is very similar to bootstrapping and
differs only in the character resampling strategy
• Some proportion of characters (e.g. 50%) are
randomly selected and deleted
• Replicate data sets are analysed and the results
summarised with a majority-rule consensus tree
• Jackknifing and bootstrapping tend to produce
broadly similar results and have similar
interpretations
Decay analysis
• In parsimony analysis, a way to assess support
for a group is to see if the group occurs in
slightly less parsimonious trees also
• The length difference between the shortest
trees including the group and the shortest
trees that exclude the group (the extra steps
required to overturn a group) is the decay
index or Bremer support
• Can be extended to any optimality criterion and
to other relationships
Decay analysis -example
Ciliate SSUrDNA data
Ochromonas
+27
Symbiodinium
Prorocentrum
+45
Loxodes
Tracheloraphis
Spirostomum
+15
Gruberia
+10
Euplotes
+7
Tetrahymena
Randomly permuted data
+1
+1
+8
+3
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Tracheloraphis
Spirostomum
Euplotes
Gruberia
Decay indices - interpretation
• Generally, the higher the decay index the better the
relative support for a group
• Like BPs, decay indices may be misleading if the data
is misleading
• Unlike BPs decay indices are not scaled (0-100) and
it is less clear what is an acceptable decay index
• Magnitude of decay indices and BPs generally
correlated (i.e. they tend to agree)
• Only groups found in all most parsimonious trees have
decay indices > zero
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Extending Support Measures
• The same measures (BP, JP & DI) that
are used for clades/splits can also be
determined for triplets and quartets
• This provides a lot more information
because there are more
triplets/quartets than there are clades
• Furthermore....
The Decay Theorem
• The DI of an hypothesis of relationships is
equal to the lowest DI of the resolved triplets
that the hypothesis entails
• This applies equally to BPs and JPs as well as
DIs
• Thus a phylogenetic chain is no stronger than
its weakest link!
• and, measures of clade support may give a
very incomplete picture of the distribution of
support
Bootstrapping with Reduced Consensus
X A B C D E F G H I J
X A B C D E J I HG F
A B C D E X J I HG F
A B C D E J I HG F
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A B C D E F G H I J
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Leaf Stability
• Leaf stability is the average of supports of
the triplets/quartets containing the leaf
Pinpointing Uncertainty
Comparing competing phylogenetic
hypotheses - tests of two (or more)
trees
• Particularly useful techniques are those designed to
allow evaluation of alternative phylogenetic
hypotheses
• Several such tests allow us to determine if one tree
is statistically significantly worse than another:
Winning sites, Templeton, Kishino-Hasegawa, parametric
bootstrapping (SOWH)
Shimodaira-Hasegawa, Approximately Unbiased
Tests of two trees
• Tests are of the null hypothesis that the differences
between two trees (A and B) are no greater than
expected from sampling error
• The simplest ‘wining sites’ test sums the number of
sites supporting tree A over tree B and vice versa
(those having fewer steps on, and better fit to, one
of the trees)
• Under the null hypothesis characters are equally
likely to support tree A or tree B and a binomial
distribution gives the probability of the observed
difference in numbers of winning sites
The Templeton test
• Templeton’s test is a non-parametric Wilcoxon
signed ranks test of the differences in fits of
characters to two trees
• It is like the ‘winning sites’ test but also takes
into account the magnitudes of differences in
the support of characters for the two trees
Eosauropterygia
2
Placodus
Lepidosauriformes
Archosauromorpha
Younginiformes
Claudiosaurus
Araeoscelidia
Paleothyris
Captorhinidae
Parareptilia
1
Synapsida
Diadectomorpha
Seymouriadae
Templeton’s test - an example
Recent studies of the relationships of
turtles using morphological data have
produced very different results with
turtles grouping either within the
parareptiles (H1) or within the diapsids
(H2) the result depending on the
morphologist
This suggests there may be:
- problems with the data
- special problems with turtles
- weak support for turtle relationships
Parsimony analysis of the most recent data favoured H2
However, analyses constrained by H2 produced trees
that required only 3 extra steps (<1% tree length)
The Templeton test was used to evaluate the trees and showed
that the slightly longer H1 tree found in the constrained analyses
was not significantly worse than the unconstrained H2 tree
The morphological data do not allow choice between H1 and H2
Kishino-Hasegawa test
• The Kishino-Hasegawa test is similar in using
differences in the support provided by individual
sites for two trees to determine if the overall
differences between the trees are significantly
greater than expected from random sampling error
• It is a parametric test that depends on assumptions
that the characters are independent and identically
distributed (the same assumptions underlying the
statistical interpretation of bootstrapping)
• It can be used with parsimony and maximum
likelihood - implemented in PHYLIP and PAUP*
Kishino-Hasegawa test
Sites favouring tree A
Mean
Expected
Sites favouring tree B
0
Distribution of Step/Likelihood differences at each site
Under the null hypothesis the mean
of the differences in parsimony
steps or likelihoods for each site is
expected to be zero, and the
distribution normal
From observed differences we
calculate a standard deviation
If the difference between trees (tree
lengths or likelihoods) is attributable
to sampling error, then characters
will randomly support tree A or B and
the total difference will be close to
zero
The observed difference is
significantly greater than zero if it is
greater than 1.95 standard deviations
This allows us to reject the null
hypothesis and declare the suboptimal tree significantly worse than
the optimal tree (p < 0.05)
Kishino-Hasegawa test
Ochromonas
Ciliate SSUrDNA
Symbiodinium
Prorocentrum
Sarcocystis
Theileria
Plagiopyla n
Plagiopyla f
Trimyema c
Trimyema s
Cyclidium p
Cyclidium g
Cyclidium l
Glaucoma
Colpodinium
Tetrahymena
Parsimonious character
optimization of the presence and
absence of hydrogenosomes
suggests four separate origins of
within the ciliates
Paramecium
Opisthonecta
Colpoda
Dasytrichia
Entodinium
Spathidium
Loxophylum
Homalozoon
Metopus c
Metopus p
Stylonychia
Onychodromous
Oxytrichia
Maximum likelihood tree
Loxodes
Tracheloraphis
Spirostomum
Gruberia
Blepharisma
Discophrya
Trithigmostoma
Questions
- how reliable is this result?
- in particular how well supported
is the idea of multiple origins?
- how many origins can we
confidently infer?
anaerobic ciliates with hydrogenosomes
Kishino-Hasegawa test
Ochromonas
Symbiodinium
Prorocentrum
Sarcocystis
Theileria
Plagiopyla n
Plagiopyla f
Trimyema c
Trimyema s
Cyclidium p
Cyclidium g
Cyclidium l
Dasytrichia
Entodinium
Loxophylum
Homalozoon
Spathidium
Metopus c
Metopus p
Loxodes
Tracheloraphis
Spirostomum
Gruberia
Blepharisma
Discophrya
Trithigmostoma
Stylonychia
Onychodromous
Oxytrichia
Colpoda
Paramecium
Glaucoma
Colpodinium
Tetrahymena
Opisthonecta
Ochromonas
Symbiodinium
Prorocentrum
Sarcocystis
Theileria
Plagiopyla n
Plagiopyla f
Trimyema c
Trimyema s
Cyclidium p
Metopus c
Metopus p
Dasytrichia
Entodinium
Cyclidium g
Cyclidium l
Loxophylum
Spathidium
Homalozoon
Loxodes
Tracheloraphis
Spirostomum
Gruberia
Blepharisma
Discophrya
Trithigmostoma
Stylonychia
Onychodromous
Oxytrichia
Colpoda
Paramecium
Glaucoma
Colpodinium
Tetrahymena
Opisthonecta
Two topological constraint trees
Parsimony analyse with
topological constraints found
the shortest trees forcing
hydrogenosomal ciliate lineages
together, thereby reducing
the number of separate
origins of hydrogenosomes
Each of the constrained
parsimony trees were
compared to the ML tree and
the Kishino-Hasegawa test
used to determine which of
these trees were significantly
worse than the ML tree
Kishino-Hasegawa test
Test summary and results (simplified)
No.
Origins
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3
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3
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2
2
2
2
2
2
2
1
Constraint
tree
ML
MP
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(cp,rc)
(cp,m)
(pt,rc)
(pt,m)
(rc,m)
(pt,cp,rc)
(pt,rc,m)
(pt,cp,m)
(cp,rc,m)
(pt,cp)(rc,m)
(pt,m)(rc,cp)
(pt,rc)(cp,m)
(pt,cp,m,rc)
Extra
Steps
+10
+13
+113
+47
+96
+22
+63
+123
+100
+40
+124
+77
+131
+140
+131
Difference
and SD
-13  18
-21  22
-337  40
-147  36
-279  38
-68  29
-190  34
-432  40
-353  43
-140  37
-466  49
-222  39
-442  48
-414  50
-515  49
Significantly
worse?
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Constrained analyses used to
find most parsimonious trees
with less than four separate
origins of hydrogenosomes
Tested against ML tree
Trees with 2 or 1 origin are
all significantly worse than
the ML tree
We can confidently conclude
that there have been at
least three separate origins
of hydrogenosomes within the
sampled ciliates
Problems with tests of trees
• To be statistically valid, the Kishino-Hasegawa test
should be of trees that are selected a priori
• However, most applications have used trees selected
a posteriori on the basis of the phylogenetic analysis
• Where we test the ‘best’ tree against some other
tree the KH test will be biased towards rejection of
the null hypothesis
• Only if null hypothesis is not rejected will result be
safe from some unknown level of bias
Problems with tests of trees
• The Shimodaira-Hasegawa test is a more statistically
correct technique for testing trees selected a
posteriori and is implemented in PAUP*
• However it requires selection of a set of plausible
topologies - hard to give practical advice
• Parametric bootstrapping (SOWH test) is an
alternative - but it is harder to implement and may
suffer from an opposite bias due to model misspecification
• The Approximately Unbiased test (implemented in
CONSEL) may be the best option currently
Problems with tests of trees
Taxonomic Congruence
• Trees inferred from different data sets
(different genes, morphology) should agree if
they are accurate
• Congruence between trees is best explained by
their accuracy
• Congruence can be investigated using consensus
(and supertree) methods
• Incongruence requires further work to explain
or resolve disagreements
Reliability of Phylogenetic Methods
• Phylogenetic methods (e.g. parsimony,
distance, ML) can also be evaluated in terms
of their general performance, particularly
their:
consistency - approach the truth with more data
efficiency - how quickly (how much data)
robustness - sensitivity to violations of assumptions
• Studies of these properties can be analytical
or by simulation
Reliability of Phylogenetic Methods
• There have been many arguments that ML
methods are best because they have desirable
statistical properties, such as consistency
• However, ML does not always have these
properties
– if the model is wrong/inadequate (fortunately this
is testable to some extent)
– properties not yet demonstrated for complex
inference problems such as phylogenetic trees
Reliability of Phylogenetic Methods
• “Simulations show that ML methods generally
outperform distance and parsimony methods over a
broad range of realistic conditions”
Whelan et al. 2001 Trends in Genetics 17:262-272
• But…
• Most simulations cover a narrow range of very
(unrealistically) simple conditions
–
–
few taxa (typically just four!)
few parameters (standard models - JC, K2P etc)
Reliability of Phylogenetic Methods
• Simulations with four taxa have shown:
- Model based methods - distance and maximum
likelihood perform well when the model is accurate
(not surprising!)
- Violations of assumptions can lead to inconsistency
for all methods (a Felsenstein zone) when branch
lengths or rates are highly unequal
- Maximum likelihood methods are quite robust to
violations of model assumptions
- Weighting can improve the performance of parsimony
(reduce the size of the Felsenstein zone)
Reliability of Phylogenetic Methods
• However:
- Generalising from four taxon simulations may be dangerous as
conclusions may not hold for more complex cases
- A few large scale simulations (many taxa) have suggested that
parsimony can be very accurate and efficient
- Most methods are accurate in correctly recovering known
phylogenies produced in laboratory studies
• More realistic simulations are needed if they are to
help in choosing/understanding methods
• You can try your own…