Support for trees and nodes

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Support for trees and nodes
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Assessing phylogenetic hypothesis

• We should not be content with constructing
  phylogenetic hypothesis but should also assess
  what confidence we can place in our hypothesis

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Assigning confidence intervals to phylogenies

• Resampling methods
• bootstrap (non parametric)
• jackknife
• Other methods
• decay analyses (only MP)
• posterior probability (ML bayesian)

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Assigning confidence intervals to phylogenies

• The sampling error
• we use samples in our studies
• the values stimated from a sample of a population
  will be more or less close to the real value but
  rarely they will coincide
• A way of calculating the sampling error is taking
  multiple samples from the population and
  comparing the estimations obtained for each of
  them.

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Bootstrapping

• The frecuency with which a certain group appears
  is a measure of the goodness of that group
• These values are shown in a consensus tree and
  some additional information is given on a table

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Bootstrapping
Pseudorreplicate-1
Original matrix

Characters Taxa 1 2 2 2 5 5 8 8 A
R R R R Y Y Y Y B R R R R Y Y Y Y C
Y Y Y Y Y Y R R D Y Y Y Y R R R R Outgroup
R R R R R R R R
Characters Taxa 1 2 3 4 5 6 7 8 A
R R Y Y Y Y Y Y B R R Y Y Y Y Y Y C
Y Y Y Y Y R R R D Y Y R R R R R R Outgroup
R R R R R R R R
Pseudorreplicate-2
The pseudoreplicates are obtained from the
original matrix with replacement to built a new
matrix of the same size than the original one.
Characters Taxa 3 3 4 4 5 7 7 8 A
Y Y Y Y Y Y Y Y B Y Y Y Y Y Y Y Y C
Y Y Y Y Y R R R D R R R R R R R R Outgroup
R R R R R R R R
Pseudorreplicate-n
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Bootstrapping
Real phylogeny stimate
Trees obtained from the 100 pseudo-replicates
Case-1
30
60
10
Case-2
31
20
49
Consensus Bootstrap case-2
Consensus Bootstrap case-1
AB 90 ABC 60 CD 40 BCD 10
80 49 51 20
80
51
90
60
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Bootstrapping
Partition table
SSUrDNA Ciliates - parsimony
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
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Interpretation of Bootstraps (BPs)

• Felsenstein (1985) is a measure of repeatibility
• Probability that the internal branch appears when
  a new analysis is done with an independent sample
  
• Felsenstein y Kishino (1993) is a measure of
  exactitud
• probability that the internal branch is in the
  real tree

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Interpretation of Bootstraps (BPs)

• BPs provide an index of the relative support for
  groups provided by a set of data under a certain
  method of analysis.
• High BPs are indicative of strong signal in the
  data
• Provided we have no evidence of strong misleading
  signal (e.g. base composition bias, great
  differences in branch lengths) high BPs are
  likely to reflect strong phylogenetic signal

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Interpretation of Bootstraps (BPs)

• Low BPs need not mean the relationship is false,
  only that is poorly supported (by this data)

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Interpretation of Bootstraps (BPs)

• 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

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Interpretation of Bootstraps (BPs)

• 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

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Interpretation of Bootstraps (BPs)

• 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

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Jackknifing

• Jackknifing is similar to bootstrapping, the only
  difference being in the way the data are
  resampled
• A certain proportion of data are eliminated at
  random (por ej. 50)
• The pseudoreplicates are analysed and the results
  are summarised in a majority-rule consensus
  tree
• Jackknifing and bootstrapping use to give similar
  results and are interpreted in a similar way

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Assigning confidence intervals to phylogenies

• Resampling methods
• bootstrap (non parametric)
• jackknife
• Other methods
• decay analyses (only MP)
• posterior probability (ML bayesian)

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Posterior Probability

• In the Bayesian method of inference for every
  node its posterior probability is calculated
  (BPP).
• This value has a direct interpretation from the
  statistical point of view
• The probability that the given group is true,
  given a model, the premises and the data
  (Huelsenbeck, 2002)
• However, the BPP values, with the same data, use
  to be a lot higher than bootstrap values.

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Posterior Probability vs. bootstrap

• Douady et al., 2003 proposed to treat bootstrap
  and posterior probability as the lower and upper
  limits respectively.
• Alfaro et al., 2003 find that BPP can give high
  values for branches that are very short (being
  true)
• What is clear the two values are not equivalent
  and consequently it is not possible to compare
  them.