Molecular Systematics

1
Introduction to characters and parsimony analysis
2
Character evolution

• Heritable changes in features (morphology, gene
  sequences, etc.) provide the basis for inferring
  phylogeny
• Such changes delimit what are usually referred to
  as the states of characters (e.g. presence or
  absence of a feature or different nucleotide
  bases at specific sites in a sequence)
• The utility of characters depends on how often
  the changes that produce the different character
  states occur independently (homoplasy)

3
Unique and unreversed characters

• Given a heritable evolutionary change that is
  unique and unreversed (e.g. the origin of hair)
  in an ancestral species, the presence of the
  novelty in any taxa must be due to inheritance
  from the ancestor.
• Similarly absence in any taxa must be because the
  taxa are not descendants of that ancestor
• The novelty will be a homology acting as a badge
  or marker for the descendants of the ancestor
• The taxa with the novelty will be a clade (e.g.
  Mammalia)

4
Unique and unreversed characters- Hair

• Because hair evolved only once and is unreversed
  it is homologous and provides unambiguous
  evidence for the clade Mammalia

Human
Lizard
HAIR
absent
present
Dog
Frog
change or step
5
Homoplasy - Independent evolution

• Homoplasy is similarity that is not homologous
  (not due to common ancestry)
• Homoplasy is the result of independent evolution
  (convergence, parallelism, reversal)
• Homoplasy can provide misleading evidence of
  phylogenetic relationships

6
Homoplasy - independent evolution- Tails

• Loss of tails evolved independently in humans and
  frogs - there are two steps on the true tree

Human
Lizard
TAIL
absent
present
Frog
Dog
7
Homoplasy - misleading evidence of phylogeny

• If misinterpreted as homology, the absence of
  tails would be evidence for a wrong tree grouping
  humans with frogs and lizards with dogs

Lizard
Human
TAIL
absent
present
Dog
Frog
8
Homoplasy - reversal

• Reversals are evolutionary changes back to an
  ancestral condition
• As with any homoplasy, reversals can provide
  misleading evidence of relationships

True tree
Wrong tree
9
3
4
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7
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10
1
2
5
1
3
4
6
7
8
9
10
2
5
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Homoplasy - a fundamental problem of phylogenetic
inference

• If there were no homoplastic similarities
  inferring phylogeny would be easy - all the
  pieces of the jig-saw would fit together neatly
• Distinguishing the misleading evidence of
  homoplasy from the reliable evidence of homology
  is a fundamental problem of phylogenetic inference

10
Homoplasy and Incongruence

• If we assume that there is a single correct
  phylogenetic tree then
• When characters support conflicting phylogenetic
  trees we know that there must be some misleading
  evidence of relationships among the incongruent
  or incompatible characters
• Incongruence between two characters implies that
  at least one of the characters is homoplastic and
  that at least one of the trees the character
  supports is wrong

11
Incongruence or Incompatibility
Human
Lizard
HAIR
absent
present
Dog
Frog

• These trees and characters are incongruent. Both
  trees cannot be correct and at least one
  character must be homoplastic

Lizard
Human
TAIL
absent
present
Dog
Frog
12
Distinguishing homology and homoplasy

• Morphologists use a variety of techniques to
  distinguish homoplasy and homology
• Homologous features are expected to display
  detailed similarity (in position, structure,
  development) whereas homoplastic similarities are
  more likely to be superficial
• As recognised by Darwin congruence with other
  characters provides the most compelling evidence
  for homology

13
The importance of congruence

• The importance, for classification, of trifling
  characters, mainly depends on their being
  correlated with several other characters of more
  or less importance. The value indeed of an
  aggregate of characters is very evident ........
  a classification founded on any single character,
  however important that may be, has always failed.
• Charles Darwin, Origin of Species

14
Congruence - 4

• We prefer the true tree because it is supported
  by multiple congruent characters

Human
Lizard
MAMMALIA
Hair Single bone in lower jaw Lactation
Frog
Dog
15
Homoplasy in molecular data

• Incongruence and therefore homoplasy can be
  common in molecular sequence data
• One reason is that characters have a limited
  number of alternative character states ( e.g. A,
  G, C and T)
• In addition, these states are chemically
  identical so that homology and homoplasy are
  equally similar and cannot be distinguished
  through detailed study of structure or
  development

16
Parsimony analysis

• Parsimony methods provide one way of choosing
  among alternative phylogenetic hypotheses
• The parsimony criterion favours hypotheses that
  maximise congruence and minimise homoplasy
• It depends on the idea of the fit of a character
  to a tree

17
Character Fit

• Initially, we can define the fit of a character
  to a tree as the minimum number of steps required
  to explain the observed distribution of character
  states among taxa
• This is determined by parsimonious character
  optimization
• Characters differ in their fit to different trees

18
Character Fit - Amniota
Rayfinned fish
Rayfinned fish
salamaders
salamaders
mammals
mammals
crocodiles
crocodiles
lungfish
snakes
lungfish
snakes
lizards
lizards
turtles
turtles
birds
birds
frogs
frogs
3 steps
1 step
19
Parsimony Analysis

• Given a set of characters, such as aligned
  sequences, parsimony analysis works by
  determining the fit (number of steps) of each
  character on a given tree
• The sum over all characters is called Tree Length
• Most parsimonious trees (MPTs) have the minimum
  tree length needed to explain the observed
  distributions of all the characters

20
Parsimony in practice
Of these two trees, Tree 1 has the shortest
length and is the most parsimonious Both trees
require some homoplasy (extra steps)
21
Results of parsimony analysis

• One or more most parsimonious trees
• Hypotheses of character evolution associated with
  each tree (where and how changes have occurred) -
  this may be very useful
• Branch lengths (amounts of change associated with
  branches)
• Various tree and character statistics describing
  the fit between tree and data
• Suboptimal trees - optional

22
Parsimony - advantages

• is a simple method - easily understood operation
• does not seem to depend on an explicit model of
  evolution
• gives both trees and associated hypotheses of
  character evolution
• should give reliable results if the data is well
  structured and homoplasy is either rare or widely
  (randomly) distributed on the tree

23
Parsimony - disadvantages

• May give misleading results if homoplasy is
  common or concentrated in particular parts of the
  tree, e.g
• thermophilic convergence
• base composition biases
• long branch attraction
• Underestimates branch lengths

24
Parsimony can be inconsistent

• Felsenstein (1978) developed a simple model
  phylogeny including four taxa and a mixture of
  short and long branches
• Under this model parsimony will give the wrong
  tree

Long branches are attracted but the
similarity is homoplastic

• With more data the certainty that parsimony will
  give the wrong tree increases - so that parsimony
  is statistically inconsistent
• Advocates of parsimony initially responded by
  claiming that Felsensteins result showed only
  that his model was unrealistic
• It is now recognised that the long-branch
  attraction (in the Felsenstein Zone) is one of
  the most serious problems in phylogenetic
  inference

25
Methods other than parsimony
26
Phylogenetic analysis - different methods

• Character-based methods
• Maximum parsimony
• Maximum likelihood
• Distance-based methods

27
Maximum Likelihood 1

• Maximum likelihood methods of phylogenetic
  inference evaluate a hypothesis about
  evolutionary history (the branching order and
  branch lengths of a tree) in terms of a
  probability that a proposed model of the
  evolutionary process and the hypothesised history
  (tree) would give rise to the data we observe -
  so given a model and data we can estimate a tree
  (the maximum likelihood tree)

28
Maximum Likelihood 2

• Maximum likelihood estimates a parameter from
  observed data under an explicit model
• There is an explicit link between model tree
  data (poor model poor tree?)
• Likelihood also provides ways of evaluating
  models in terms of their log likelihoods,
  provided they are nested i.e. one model is a
  special case of the other

29
Maximum likelihood tree reconstruction 1
1
3
1 CGAGAC 2 AGCGAC 3 AGATTA 4 GGATAG
Tree A
4
2
What is the probability that unrooted Tree A
(rather than another tree) could have generated
the data shown under our chosen model ?
30
Maximum likelihood tree reconstruction 1
3
4
1
2
1 CGAGAC 2 AGCGAC 3 AGATTA 4 GGATAG
Tree A
note rooting is arbitrary
What is the probability that unrooted Tree A
(rather than another tree) could have generated
the data shown under our chosen model ?
31
Maximum likelihood tree reconstruction 2
1 CGAGA C 2 AGCGA C 3 AGATT A 4 GGATA G
ACGT
Tree A
j
4 x 4 possibilities
The likelihood for a particular site j is the sum
of the probabilities of every possible
reconstruction of ancestral states under a chosen
model
32
Maximum likelihood tree reconstruction 3

• The likelihood of Tree A is the product of the
  likelihoods at each site
• The likelihood is usually evaluated by summing
  the log of the likelihoods (because the summed
  probabilities are so small) at each site and
  reported as the log likelihood of the full tree
• The Maximum likelihood tree is the one with the
  highest likelihood (might not be Tree A i.e. it
  could be another tree topology)

33
Maximum likelihood tree reconstruction 4

• How are the probabilities of change calculated ?
• The probabilities used to calculate likelihoods
  depend on the assumed model

34
Typical assumptions of ML substitution models

• The probability of any change is independent of
  the prior history of the site (a Markov Model)
• Substitution probabilities do not change with
  time or over the tree (a homogeneous Markov
  process)
• Change is time reversible e.g. the rate of change
  of A to T is the same as T to A

35
Maximum likelihood models 1

• The model incorporates information about the
  rates at which each nucleotide is replaced by
  each alternative nucleotide
• For DNA this can be expressed as a 4 x 4 rate
  matrix
• Other model parameters may include
• Site by site rate variation - often modelled as a
  statistical distribution - for example a gamma
  distribution

36
Maximum likelihood models 2

• Model parameters can be
• estimated from the data (using maximum likelihood
  in PAUP)
• can be pre-set based upon assumptions about the
  data (for example that for all sequences all
  sites change at the same rate and all
  substitutions are equally likely - e.g. the
  widely used Jukes and Cantor Model)
• wherever possible avoid assumptions which are
  violated by the data because they can lead to
  incorrect trees

37
The true tree for Deinococcus and Thermus
Thermus
Aquifex
Deinococcus
Bacillus
The true tree
38
The Jukes and Cantor model is the simplest model
The JC model is a one parameter model 1) it
assumes that all changes are equally probable
(p0.25) 2) unless modified it assumes all sites
can change and that they do so at the same rate
39
Output of JC ML analysis for (Thermus,
Deinococcus, Bacillus, Aquifex)
Tree 3 -log likelihood -4132
Tree 2 -log likelihood -4101 True tree
Tree 1 -log likelihood -4090 Best tree
The Jukes and Cantor model in ML is unable to
recover the true tree for this data set
40
The 16S rRNA genes of Aquifex, Bacillus,
Deinococcus and Thermus
Exclude characters command in PAUP - exclude
constant sites
Character-exclusion status changed 859 of
1273 characters excluded Total number of
characters now excluded 859 Number of
included characters 414
Does the JC model fit these data?
Base frequencies command in PAUP
Taxon A C G
T sites ------------------------------------
-------------------------- Aquifex 0.12319
0.38164 0.38164 0.11353 414 Deinococc
0.23188 0.22222 0.27295 0.27295
414 Thermus 0.13317 0.35835 0.37530
0.13317 413 Bacillus 0.23188
0.22705 0.26570 0.27536
414 ----------------------------------------------
---------------- Mean 0.18006 0.29728
0.32387 0.19879 413.75
41
Models can be made more parameter rich to
increase their realism 1

• The most common additional parameters are
• A correction to allow different substitution
  rates for each type of nucleotide change
• A correction for the proportion of sites which
  are unable to change
• A correction for variable site rates at those
  sites which can change
• PAUP will estimate the values of these additional
  parameters for you

42
A gamma distribution can be used to model site
rate heterogeneity
43
The GTR model of sequence evolution
The general time reversable model (GTR) is the
most general substitution model because it
assigns different rates for each type of
substitution. For example for the 16S ribosomal
RNA data for Deinococcus, Thermus, Aquifex and
Bacillus
Tree number 1 -Ln likelihood 3985.30400
Estimated R-matrix -2.7325625
0.4419956 1.42028 0.87028688
0.4419956 -5.2448524 1.2621698
3.540687 1.42028 1.2621698
-3.6824498 1 0.87028688
3.540687 1 -5.4109739
Estimated value of proportion of invariable
sites 0.228318 Estimated value of gamma shape
parameter 0.610459
44
Models can be made more parameter rich to
increase their realism 2

• But the more parameters you estimate from the
  data the more time needed for an analysis and the
  more sampling error accumulates
• One might have a realistic model but large
  sampling errors
• Realism comes at a cost in time and precision!
• Fewer parameters may give an inaccurate estimate,
  but more parameters decrease the precision of the
  estimate
• In general use the simplest model which fits the
  data
• Use PAUP to compare nested models incorporating
  additional parameters for their likelihoods

45
Models can be made more parameter rich to
increase their realism 3
JC -inv gamma correction for variable sites -
4029
JC ML tree -4090
JC -invariable sites - 4030
GTR-inv gamma correction for variable sites -
3985
46
The 16S rRNA genes of Aquifex, Bacillus,
Deinococcus, Thermus and Thermus ruber
Exclude characters command in PAUP - exclude
constant sites
Character-exclusion status changed 837
characters excluded Total number of characters
now excluded 837 Number of included
characters 436
Base frequencies command in PAUP
Taxon A C G
T sites ------------------------------------
-------------------------- ruber 0.19725
0.27294 0.29587 0.23394 436 Aquifex
0.12156 0.38073 0.38532 0.11239
436 Deinococc 0.22477 0.22936 0.28211
0.26376 436 Thermus 0.13103
0.35862 0.37931 0.13103 435 Bacillus
0.22477 0.23394 0.27523 0.26606
436 ----------------------------------------------
---------------- Mean 0.17990 0.29509
0.32354 0.20147 435.80
47
Output of GTR-inv sites ML analysis for
(Deinococcus, Bacillus, Aquifex, thermus and
Thermus ruber)
Tree 3 -log likelihood 4437 Best tree True
tree
Tree 2 -log likelihood 4447
Tree 1 -log likelihood 4439
With the addition of Thermus ruber which has a
base composition which is intermediate between
thermophiles and mesophiles GTR-inv sites ML
recovers the Thermus Deinococcus relationship
48
Estimation of ML substitution model parameters

• Yang (1995) has shown that parameter estimates
  are reasonably stable across tree topologies
  provided trees are not too wrong. Thus one can
  obtain a tree using a quick method (useful when
  many sequences are being analysed) and then
  estimate parameters on that tree. These
  parameters can then be used in a search for the
  Maximum Likelihood Tree.

49
Parameter estimates using the tree scores
command in PAUP
Use PAUP tree scores to use ML to estimate over
this tree 1) Proportion of invariant sites 2)
Gamma shape parameter for variable sites 3)
Substitution parameters for all types of change
Maximum parsimony tree
50
ML Parameter estimates over a parsimony tree
using tree scores in PAUP
Tree number 1 -Ln likelihood 4432.16903
Estimated R-matrix -2.992539
0.53399075 1.6835489 0.77499941
0.53399075 -6.0877637 1.0048052
4.5489678 1.6835489 1.0048052
-3.6883541 1 0.77499941
4.5489678 1 -6.3239672
Corresponding Q-matrix -0.77509276
0.12637319 0.52569668 0.12302289
0.11475088 -1.1506065 0.31375553
0.72210013 0.36178289 0.2377952
-0.75831742 0.15873934 0.16654196
1.0765496 0.31225508 -1.5553467 Estimated
value of proportion of invariable sites
0.302946 Estimated value of gamma shape
parameter 0.629797
These values can then be used as the starting
parameters for a full likelihood search
51
Maximum Likelihood Tree
52
Maximum Likelihood -advantages

• Mathematically rigorous performs well in
  computer simulations
• Allows investigation of the fit between model and
  data
• Provides a simple way of comparing trees
  according to their likelihoods (difference tests
  - Kishino Hasegawa Test)

53
Maximum Likelihood -disadvantages

• Maximum likelihood will only be consistent
  (converge on the true tree) if evolution proceeds
  according to the assumed model How well does
  the model fit the data ?
• Becomes impossible computationally if many taxa
  or many model parameters