Assessing Phylogenetic Hypotheses and Phylogenetic Data

1
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!)

2
Assessing Data Quality

• We expect (or hope) our data will be well
  structured and contain strong phylogenetic signal
• We can test this using randomization tests of
  explicit null hypotheses
• The behaviour of some measure of the quality of
  our real data is contrasted with that of
  comparable but phylogenetically uninformative
  data determined by randomization of the data

3
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)

T
A
X
A


C
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C
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Original structured data with strong correlations
among characters
1
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-
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N
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-
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D

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C
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1
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Randomly permuted data with any correlation
among characters due to chance
R
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P
N
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U
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E
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4
Matrix Randomization 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

5
Structure of Randomization Tests

• Reject null hypothesis if, for example, more than
  5 of random permutations have as good or better
  measure than the real data

6
Matrix Randomization Tests

• Measures of data quality include
• 1. Tree length for most parsimonious trees - the
  shorter the tree length the better the data
  (PAUP)
• 2. Skewness of the distribution of tree lengths
  (PAUP)

7
Matrix Randomization Tests
Ciliate SSUrDNA
Min 430 Max 927
1 MPT L 618 PTP 0.01 Significantly non random
Real data
3 MPTs L 792 PTP 0.68 Not significantly
different from random
Random data
Strict consensus
8
Skewness of Tree Length Distributions

• Studies with random (and phylogenetically
  uninformative) data showed that the distribution
  of tree lengths tends to be normal

shortest
NUMBER OF TREES
tree
Tree length

• In contrast, phylogenetically informative data
  is expected to have a strongly skewed
  distribution with few shortest trees and few
  trees nearly as short

shortest
NUMBER OF TREES
tree
Tree length
9
Skewness - example
10
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

11
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

12
Bootstrapping (non-parametric)

• Characters are resampled with replacement to
  create many bootstrap replicate data sets
• Each bootstrap replicate data set is analysed
• 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

13
Bootstrapping
Resampled data matrix
Original data matrix


Characters
Characters
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
Taxa 1 2 2 5 5 6 6 8
Taxa 1 2 3 4 5 6 7 8
A R R R Y Y Y Y Y
A R R Y Y Y Y Y Y
B R R R Y Y Y Y Y
B R R Y Y Y Y Y Y
C Y Y Y Y Y R R R
C Y Y Y Y Y R R R
D Y Y Y R R R R R
D Y Y R R R R R R
Outgp R R R R R R R R
Outgp R R R R R R R R
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
D
A
B
C
D
A
B
C
B
C
D
A
1
5
1
2
5
96
2
8
8
7
2
6
6
66
2
6
5
1
4
3
Outgroup
Outgroup
Outgroup
14
Bootstrapping - an example
Partition Table
Ciliate SSUrDNA - parsimony bootstrap
123456789 Freq ----------------- .......
100.00 ....... 100.00 .......
100.00 ..... 100.00 ...
95.50 ....... 84.33 ....
11.83 .... 3.83 ..
2.50 ...... 1.00 ...... 1.00
Ochromonas (1)
Symbiodinium (2)
100
Prorocentrum (3)
Euplotes (8)
84
Tetrahymena (9)
96
Loxodes (4)
100
Tracheloraphis (5)
100
Spirostomum (6)
100
Gruberia (7)
Majority-rule consensus
15
Bootstrapping - random data
Partition Table
123456789 Freq ----------------- ..
71.17 ....... 58.87 .......
26.43 ....... 25.67 ...
23.83 ....... 21.00 ....
18.50 ....... 16.00 ......
15.67 ..... 13.17 .....
12.67 ...... 12.00 .......
12.00 ..... 11.00 .......
10.80 ...... 10.50 ...... 10.00
Randomly permuted data - parsimony bootstrap
Majority-rule consensus (with minority components)
16
Bootstrap - interpretation

• Bootstrapping was introduced as a way of
  establishing confidence intervals for phylogenies
  
• This interpretation of bootstrap proportions
  (BPs) depends on the assumption that the original
  data is a random sample from a much larger set of
  independent and identically distributed data
• However, several things complicate this
  interpretation
• Perhhaps 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 -gt misleading BPs)
• with parsimony it may be highly affected by
  inclusion or exclusion of only a few characters

17
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

18
Bootstrap - interpretation

• High BPs (e.g. gt 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

19
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