Introduction to characters
and parsimony analysis
Genetic Relationships
• Genetic relationships exist between individuals within
populations
• These include ancestor-descendent relationships and more
indirect relationships based on common ancestry
• Within sexually reducing populations there is a network of
relationships
• Genetic relations within populations can be measured with
a coefficient of genetic relatedness
Phylogenetic Relationships
• Phylogenetic relationships exist between lineages (e.g.
species, genes)
• These include ancestor-descendent relationships and more
indirect relationships based on common ancestry
• Phylogenetic relationships between species or lineages are
(expected to be) tree-like
• Phylogenetic relationships are not measured with a simple
coefficient
Phylogenetic Relationships
• Traditionally phylogeny reconstruction was dominated by
the search for ancestors, and ancestor-descendant
relationships
• In modern phylogenetics there is an emphasis on indirect
relationships
• Given that all lineages are related, closeness of
phylogenetic relationships is a relative concept.
Phylogenetic relationships
• Two lineages are more closely related to each other than to
some other lineage if they share a more recent common
ancestor - this is the cladistic concept of relationships
Hypothetical
ancestral
lineage
ak
O
ad
To
Fr
og
• Phylogenetic hypotheses are hypotheses of common
ancestry
(Frog,Toad)Oak
Phylogenetic Trees
LEAVES
terminal branches
A
B
node 1
C
D
E
F
node 2
G
H
I
J
polytomy
interior
branches
A CLADOGRAM
ROOT
CLADOGRAMS AND
PHYLOGRAMS
C
A
B C D E H
I
J
F
G
D
E
A B
G
H
RELATIVE TIME
I
J
F
ABSOLUTE
TIME or
DIVERGENCE
Trees - Rooted and Unrooted
A
B C D
E F
G H
I
J
A
B C D E
ROOT
ROOT
E
D
ROOT
F
A
H
B
C
J
I
G
H
I
J
F
G
Characters and Character
States
• Organisms comprise sets of features
• When organisms/taxa differ with respect to
a feature (e.g. its presence or absence or
different nucleotide bases at specific sites in
a sequence) the different conditions are
called character states
• The collection of character states with
respect to a feature constitute a character
Character evolution
• Heritable changes (in morphology, gene
sequences, etc.) produce different character
states
• Similarities and differences in character states
provide the basis for inferring phylogeny (i.e.
provide evidence of relationships)
• The utility of this evidence depends on how often
the evolutionary changes that produce the
different character states occur independently
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 novel character state 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 is a homology acting as badge or marker
for the descendants of the ancestor
• The taxa with the novelty are a clade (e.g. Mammalia)
Unique and unreversed characters
• Because hair evolved only once and is unreversed
(not subsequently lost) it is homologous and provides
unambiguous evidence for of relationships
Human
Lizard
HAIR
Frog
change
or step
Dog
absent
present
Homoplasy - Independent evolution
• Homoplasy is similarity that is not homologous
(not due to common ancestry)
• It is the result of independent evolution
(convergence, parallelism, reversal)
• Homoplasy can provide misleading evidence of
phylogenetic relationships (if mistakenly
interpreted as homology)
Homoplasy - independent evolution
• Loss of tails evolved independently in
humans and frogs - there are two steps on
the true tree
Lizard
Human
TAIL (adult)
Frog
Dog
absent
present
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
Human
Lizard
TAIL
Frog
Dog
absent
present
Homoplasy - reversal
• Reversals are evolutionary changes back to an
ancestral condition
• As with any homoplasy, reversals can provide
misleading evidence of relationships
True tree
1
2 3 4
5 6 7 8 9 10 1
Wrong tree
2
7 8 3 4
5 6
9 10
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
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
Incongruence or Incompatibility
Lizard
Human
HAIR
Frog
Dog
absent
present
• These trees and characters are incongruent - both trees
cannot be correct, at least one is wrong and at least one
character must be homoplastic
Human
Lizard
TAIL
Frog
Dog
absent
present
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 Charles Darwin congruence with
other characters provides the most compelling
evidence for homology
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, Ch. 13
Congruence
• We prefer the ‘true’ tree because it is supported
by multiple congruent characters
Lizard
Frog
Human
Dog
MAMMALIA
Hair
Single bone in lower jaw
Lactation
etc.
Homoplasy in molecular data
Incongruence and therefore homoplasy can be
common in molecular sequence data
– There are a limited number of alternative character
states ( e.g. Only A, G, C and T in DNA)
– Rates of evolution are sometimes high
Character states are chemically identical
– homology and homoplasy are equally similar
– cannot be distinguished by detailed study of
similarity and differences
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
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
Tree A
1 step
Hair
absent
present
Tree B
2 steps
Bird
Bat
Human
Cocodile
Kangeroo
Frog
Human
Bat
Kangeroo
Bird
Cocodile
Frog
Character Fit
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
-
-
Human
Bat
-
-
Kangeroo
wings
-
-
6
Cocodile
5
placenta
4
lactation
3
hair
Frog
2
amnion
1
antorbital
fenestra
CHARACTERS
Bird
Frog
Parsimony in practice
6
6
4
5
Tree 1
3
2
+
-
-
-
+
+
Crocodile
+
-
-
-
+
-
Kangeroo
+
+
+
-
-
-
+
+
+
+
-
+
Human
+
+
+
+
-
-
Tree 1
1
1
1
1
1
2
7
Tree 2
1
2
2
2
2
1
10
FIT
Bat
4
TREE
LENGTH
2
5
3
6
Tree 2
Of these two trees, Tree 1 has the shortest length
and is the most parsimonious
Both trees require some homoplasy (extra steps)
3
2
1
Human
Bird
Bat
Cocodile
Kangeroo
1
Frog
TAXA
Bird
5
4
Results of parsimony analysis
• One or more most parsimonious trees
• Hypotheses of character evolution associated with
each tree (where and how changes have occurred)
• Branch lengths (amounts of change associated with
branches)
• Various tree and character statistics describing the fit
between tree and data
• Suboptimal trees - optional
Character types
• Characters may differ in the costs
(contribution to tree length) made by different
kinds of changes
• Wagner (ordered, additive)
0 1 2 (morphology, unequal costs)
• Fitch (unordered, non-additive)
one step
A G (morphology, molecules)
two steps
T C
(equal costs for all changes)
Character types
• Sankoff (generalised)
A G (morphology, molecules)
one step
five steps
T C (user specified costs)
• For example, differential weighting of transitions and
transversions
• Costs are specified in a stepmatrix
• Costs are usually symmetric but can be asymmetric
also (e.g. costs more to gain than to loose a restriction
site)
Stepmatrices
transversions
Py
Pu
• Stepmatrices specify the costs of changes within a
character
PURINES (Pu)
A
G
T
C
PYRIMIDINES (Py)
transitions
Py
Py
Pu
Pu
A
From C
G
T
A
0
5
1
5
To
C
5
0
5
1
G
1
5
0
5
T
5
1
5
0
Different characters (e.g 1st, 2nd and 3rd)
codon positions can also have different
weights
Weighted parsimony
• If all kinds of steps of all characters have equal
weight then parsimony:
– Minimises homoplasy (extra steps)
– Maximises the amount of similarity due to
common ancestry
– Minimises tree length
• If steps are weighted unequally parsimony
minimises tree length - a weighted sum of the
cost of each character
Why weight characters?
Number of Characters
• Many systematists consider weighting unacceptable, but weighting is
unavoidable (unweighted = equal weights)
• Transitions may be more common than transversions
• Different kinds of transitions and transversions may be more or less
common
• Rates of change may vary with codon positions
• The fit of different characters on trees may indicate differences in their
reliabilities
250
200
Ciliate SSUrDNA data
150
100
50
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
Number of steps
• However, equal weighting is the commonest procedure and is the
simplest (but probably not the best) approach
Different kinds of changes
differ in their frequencies
To
A
A
C
G
T
Transitions
Transversions
C
From
G
T
Unambiguous changes
on most parsimonious
tree of Ciliate SSUrDNA
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
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
• Model of evolution is implicit - behaviour of method not well
understood
• Parsimony often justified on purely philosophical grounds - we
must prefer simplest hypotheses - particularly by
morphologists
• For most molecular systematists this is uncompelling
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
A
B
Model tree
p
p
q
C
q
q
D
Parsimony tree
Rates or
Branch lengths
p >> q
C
A
Wrong
B
D
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
Felsenstein’s 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
Finding optimal trees - exact
solutions
• Exact solutions can only be used for small
numbers of taxa
• Exhaustive search examines all possible
trees
• Typically used for problems with less
than 10 taxa
Finding optimal trees - exhaustive search
B
C
Starting tree, any 3 taxa
1
A
Add fourth taxon (D) in each of three possible positions -> three trees
E
B
D
D
C
B
C
2b
2a
A
B
C
E
D
2c
A
E
E
A
E
Add fifth taxon (E) in each of the five possible positions on each of the
three trees -> 15 trees, and so on ....
Finding optimal trees - exact
solutions
• Branch and bound saves time by discarding families
of trees during tree construction that cannot be
shorter than the shortest tree found so far
• Can be enhanced by specifying an initial upper
bound for tree length
• Typically used only for problems with less than 18
taxa
Finding optimal trees - branch and bound
C2.1
C
D
C2.2
B
B
C
A1
B
C3.1
C
C3.2
D
C2.3
C3.3
A
C2.4
B2
C2.5
B
E
A
B
C
B1
C1.5
A
A
B
D
D
E
E
C
C1.2
C
C
A
B
C3.5
D E
B
D
D
C1.1
C3.4
B3
A
E
A
C1.3
D
B
C
A
C1.4
C
A
Finding optimal trees - heuristics
• The number of possible trees increases exponentially with
the number of taxa making exhaustive searches
impractical for many data sets (an NP complete problem)
• Heuristic methods are used to search tree space for most
parsimonious trees by building or selecting an initial tree
and swapping branches to search for better ones
• The trees found are not guaranteed to be the most
parsimonious - they are best guesses
Finding optimal trees - heuristics
• Stepwise addition
Asis - the order in the data matrix
Closest -starts with shortest 3-taxon tree adds taxa in order
that produces the least increase in tree length (greedy
heuristic)
Simple - the first taxon in the matrix is a taken as a
reference - taxa are added to it in the order of their
decreasing similarity to the reference
Random - taxa are added in a random sequence, many
different sequences can be used
• Recommend random with as many (e.g. 10-100) addition
sequences as practical
Finding most parsimonious trees heuristics
• Branch Swapping:
Nearest neighbor interchange (NNI)
Subtree pruning and regrafting (SPR)
Tree bisection and reconnection (TBR)
Other methods ....
Finding optimal trees - heuristics
• Nearest neighbor interchange (NNI)
C
A
D
E
F
B
G
A
D
C
C
E
A
D
E
F
B
G
F
B
G
Finding optimal trees - heuristics
• Subtree pruning and regrafting (SPR)
A
C
D
E
F
B
G
C
D
E
C
A
F
B
G
E
F
G
B
D
A
Finding optimal trees - heuristics
• Tree bisection and reconnection (TBR)
A
C
D
E
F
B
G
E
A
C
A
B
G
F
D
F
B
G
D
C
E
Finding optimal trees - heuristics
• Branch Swapping
Nearest neighbor interchange (NNI)
Subtree pruning and regrafting (SPR)
Tree bisection and reconnection (TBR)
• The nature of heuristic searches means we cannot
know which method will find the most
parsimonious trees or all such trees
• However, TBR is the most extensive swapping
routine and its use with multiple random addition
sequences should work well
Tree space may be populated by local minima
and islands of optimal trees
RANDOM ADDITION SEQUENCE REPLICATES
FAILURE
SUCCESS
Branch
Swapping
Branch Swapping
FAILURE
Branch Swapping Tree
Length
Local
Minimum
GLOBAL
MINIMUM
Local
Minima
Searching with topological constraints
• Topological constraints are user-defined
phylogenetic hypotheses
• Can be used to find optimal trees that either:
1. include a specified clade or set of
relationships
2. exclude a specified clade or set of
relationships (reverse constraint)
Searching with topological constraints
A
B
C
D
E
F
G
CONSTRAINT TREE
((A,B,C,D)(E,F,G))
EFG
ABCD
A
A
B
C
D
E
F
B
C
E
D
F
G
G
EFG
ABCD
Compatible with reverse constraint tree
Incompatible with constraint tree
Compatible with constraint tree
Incompatible with reverse constraint tree
Searching with topological constraints
backbone constraints
• Backbone constraints specify relationships
among a subset of the taxa
A
B
D
E
BACKBONE CONSTRAINT
((A,B)(D,E))
relationships of taxon C are not specified
A
B
D
E
possible positions of taxon C
Compatible with backbone constraint
Incompatible with reverse constraint
A
D
B
E
Incompatible with backbone constraint
Compatible with reverse constraint
Parsimonious Character Optimization
0
A
1 => 0
0
B
*
1
C
1
D
=
rigin
nd
eversal
ACCTRAN) 0 => 1
*
=
0
E
OR parallelism
2 separate origins
0 => 1 (DELTRAN)
Homoplastic characters often have
alternative equally parsimonious
optimizations
Commonly used varieties are:
ACCTRAN - accelerated transformation
DELTRAN - delayed transformation
Consequently, branch lengths are not
always fully determined
PAUP reports minimum and maximum branch lengths
Missing data
• Missing data is ignored in tree building but can lead to alternative
equally parsimonious optimizations in the absence of homoplasy
1
A
single
origin
0 => 1
on any
one of 3
branches
?
B
?
C
0
D
0
E
Abundant missing data can lead
to multiple equally parsimonious
trees.
*
*
*
This can be a serious problem
with morphological data but is
unlikely to arise with molecular
data unless analyses are of
incomplete data
Multiple optimal trees
• Many methods can yield multiple equally
optimal trees
• We can further select among these trees with
additional criteria, but
• Typically, relationships common to all the
optimal trees are summarised with consensus
trees
Consensus methods
• A consensus tree is a summary of the agreement
among a set of fundamental trees
• There are many consensus methods that differ in:
1. the kind of agreement
2. the level of agreement
• Consensus methods can be used with multiple trees
from a single analysis or from multiple analyses
Strict consensus methods
• Strict consensus methods require agreement across all the
fundamental trees
• They show only those relationships that are unambiguously
supported by the parsimonious interpretation of the data
• The commonest method (strict component consensus)
focuses on clades/components/full splits
• This method produces a consensus tree that includes all and
only those full splits found in all the fundamental trees
• Other relationships (those in which the fundamental trees
disagree) are shown as unresolved polytomies
• Implemented in PAUP
Strict consensus methods
TWO FUNDAMENTAL TREES
A
B
C
D
E
A
F
B
C
B
A
G
D
E
C
F
E
D
G
STRICT COMPONENT CONSENSUS TREE
F
G
Majority-rule consensus methods
• Majority-rule consensus methods require agreement across
a majority of the fundamental trees
• May include relationships that are not supported by the
most parsimonious interpretation of the data
• The commonest method focuses on clades/components/full
splits
• This method produces a consensus tree that includes all and
only those full splits found in a majority (>50%) of the
fundamental trees
• Other relationships are shown as unresolved polytomies
• Of particular use in bootstrapping
• Implemented in PAUP
Majority rule consensus
THREE FUNDAMENTAL TREES
A
B
C
D
E
F
G
B
A
A
E
C
B
C
D
F
E
D
F
B
C
G
66
100
Numbers indicate frequency of
clades in the fundamental trees
A
G
66
66
66
MAJORITY-RULE COMPONENT CONSENSUS TREE
E
D
F
G
Reduced consensus methods
• Focuses upon any relationships (not just full splits)
• Reduced consensus methods occur in strict and
majority-rule varieties
• Other relationships are shown as unresolved
polytomies
• May be more sensitive than methods focusing only
on clades/components/full splits
• Strict reduced consensus methods are implemented
in RadCon
Types of Cladistic Relationships
COMPONENTS / CLADES
FIVE LEAF TREE
B
C
D
A
E
A
B
C
D
E
ROOTED TRIPLETS
A
B C
D E
A
X
Z
X
A
B
D
D
E
B
A
B
E
D
E
C
A
C
D
B
C
D
A
C
E
B
C
E
Y
(a)
A
B
C
D
E
FOUR LEAF SUBTREE
A
B
D
E
Y
D
A
B
D
E
A
B
C
E
Z
D
E
A
B
5-TAXON STATEMENTS
4-TAXON STATEMENTS
(d)
(b)
3-TAXON STATEMENTS
(c)
Reduced consensus methods
TWO FUNDAMENTAL TREES
A
B
C
D
E
F
G
A
G
B
C
D
E
F
A B C D E F G
A
B
C
D
E
F
Strict component consensus
completely unresolved
STRICT REDUCED CONSENSUS TREE
Taxon G is excluded
Consensus methods
strict reduced cladistic
Three fundamental trees strict (component)
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Tracheloraphis
Spirostomum
Euplotes
Gruberia
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Spirostomumum
Tracheloraphis
Euplotes
Gruberia
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Spirostomumum
Euplotes
Tracheloraphis
Gruberia
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Euplotes
Spirostomumum
Tracheloraphis
Gruberia
Euplotes excluded
majority-rule
100
100
66
66
100
100
Ochromonas
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Spirostomum
Euplotes
Tracheloraphis
Gruberia
Symbiodinium
Prorocentrum
Loxodes
Tetrahymena
Spirostomum
Tracheloraphis
Gruberia
Ochromonas
Consensus methods
Use strict methods to identify those relationships
unambiguously supported by parsimonious
interpretation of the data
Use reduced methods where consensus trees are
poorly resolved
Use majority-rule methods in bootstrapping
Avoid other methods which have ambiguous
interpretations