PARSIMONY ANALYSIS

Genetic RelationshipsGenetic Relationships

• Genetic relationships exist between individuals within Genetic relationships exist between individuals within populationspopulations

• These include ancestor-descendent relationships and more These include ancestor-descendent relationships and more indirect relationships based on common ancestryindirect relationships based on common ancestry

• Within sexually reducing populations there is a network of Within sexually reducing populations there is a network of relationshipsrelationships

• Genetic relations within populations can be measured with Genetic relations within populations can be measured with a coefficient of genetic relatednessa coefficient of genetic relatedness

Phylogenetic RelationshipsPhylogenetic Relationships• Phylogenetic relationships exist between lineages (e.g. Phylogenetic relationships exist between lineages (e.g.

species, genes)species, genes)

• These include ancestor-descendent relationships and more These include ancestor-descendent relationships and more indirect relationships based on common ancestryindirect relationships based on common ancestry

• Phylogenetic relationships between species or lineages are Phylogenetic relationships between species or lineages are (expected to be) tree-like(expected to be) tree-like

• Phylogenetic relationships are not measured with a simple Phylogenetic relationships are not measured with a simple coefficient coefficient

Phylogenetic RelationshipsPhylogenetic Relationships• Traditionally phylogeny reconstruction was dominated by Traditionally phylogeny reconstruction was dominated by

the search for ancestors, and ancestor-descendant the search for ancestors, and ancestor-descendant relationshipsrelationships

• In modern phylogenetics there is an emphasis on indirect In modern phylogenetics there is an emphasis on indirect relationshipsrelationships

• Given that all lineages are related, closeness of Given that all lineages are related, closeness of phylogenetic relationships is a relative concept. phylogenetic relationships is a relative concept.

Phylogenetic relationshipsPhylogenetic relationships• Two lineages are more closely related to each other than to Two lineages are more closely related to each other than to

some other lineage if they share a more recent common some other lineage if they share a more recent common ancestor - this is the cladistic concept of relationships and ancestor - this is the cladistic concept of relationships and pertains to rooted treespertains to rooted trees

• Phylogenetic hypotheses are hypotheses of common Phylogenetic hypotheses are hypotheses of common ancestry ancestry

Rooted TreesRooted Trees

A B C D E F G H I J

ROOT

polytomy

terminal branches

interiorbranches

node 1 node 2

LEAVES

A CLADOGRAM

CLADOGRAMS AND CLADOGRAMS AND PHYLOGRAMSPHYLOGRAMS

ABSOLUTE TIME or DIVERGENCE

RELATIVE TIME

A B

C DE

FG

HI

J

A B C D E F GH I J

Trees - Rooted and UnrootedTrees - Rooted and Unrooted

ROOTA

B

C

D E

F

GH

I

J

A B C D E F GH I J

ROOT

A B C D E F G H I J

ROOT

Characters and Character Characters and Character StatesStates

• Organisms comprise sets of featuresOrganisms comprise sets of features

• When organisms/taxa differ with respect to When organisms/taxa differ with respect to a feature (e.g. its presence or absence or a feature (e.g. its presence or absence or different nucleotide bases at specific sites in different nucleotide bases at specific sites in a sequence)a sequence) the different conditions are the different conditions are called called character states character states

• The collection of character states with The collection of character states with respect to a feature constitute a respect to a feature constitute a charactercharacter

Character evolutionCharacter evolution• Heritable changes (in morphology, gene Heritable changes (in morphology, gene

sequences, etc.) produce different character statessequences, etc.) produce different character states

• Similarities and differences in character states Similarities and differences in character states provide the basis for inferring phylogeny (i.e. provide the basis for inferring phylogeny (i.e. provide evidence of relationships)provide evidence of relationships)

• The utility of this evidence depends on how often The utility of this evidence depends on how often the evolutionary changes that produce the the evolutionary changes that produce the different character states occur independentlydifferent character states occur independently

Unique and unreversed charactersUnique and unreversed characters• Given a heritable evolutionary change that is Given a heritable evolutionary change that is uniqueunique

and and unreversedunreversed (e.g. the origin of hair) in an ancestral (e.g. the origin of hair) in an ancestral species, the presence of the novel character state in species, the presence of the novel character state in any taxa must be due to inheritance from the ancestorany taxa must be due to inheritance from the ancestor

• Similarly, absence in any taxa must be because the Similarly, absence in any taxa must be because the taxa are not descendants of that ancestortaxa are not descendants of that ancestor

• The novelty is a The novelty is a homologyhomology acting as badge or marker acting as badge or marker for the descendants of the ancestorfor the descendants of the ancestor

• The taxa with the novelty are a clade (e.g. Mammalia)The taxa with the novelty are a clade (e.g. Mammalia)

Unique and unreversed charactersUnique and unreversed characters• Because hair evolved only once and is unreversed Because hair evolved only once and is unreversed

(not subsequently lost) it is (not subsequently lost) it is homologoushomologous and provides and provides unambiguous evidence for of relationshipsunambiguous evidence for of relationships

Lizard

Frog

Human

Dog

HAIR

absentpresent

change or step

• Homoplasy is similarity that is not homologous Homoplasy is similarity that is not homologous (not due to common ancestry)(not due to common ancestry)

• It is the result of independent evolution It is the result of independent evolution (convergence, parallelism, reversal)(convergence, parallelism, reversal)

• Homoplasy can provide misleading evidence of Homoplasy can provide misleading evidence of phylogenetic relationships (if mistakenly phylogenetic relationships (if mistakenly interpreted as homology)interpreted as homology)

Homoplasy - Independent evolution

Homoplasy - independent evolutionHomoplasy - independent evolution

HumanLizard

Frog Dog

TAIL (adult)

absentpresent

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

Homoplasy - misleading evidence of Homoplasy - misleading evidence of phylogenyphylogeny

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

Human

Frog

Lizard

Dog

TAIL

absentpresent

Homoplasy - reversalHomoplasy - reversal• Reversals are evolutionary changes back to an Reversals are evolutionary changes back to an

ancestral conditionancestral condition

• As with any homoplasy, reversals can provide As with any homoplasy, reversals can provide misleading evidence of relationshipsmisleading evidence of relationships

True tree Wrong tree101 2 3 4 5 67 8 91 2 3 4 5 6 7 8 9 10

Homoplasy - a fundamental Homoplasy - a fundamental problem of phylogenetic inferenceproblem of phylogenetic inference

• If there were no homoplastic similarities If there were no homoplastic similarities inferring phylogeny would be easy - all the inferring phylogeny would be easy - all the pieces of the jig-saw would fit together neatlypieces of the jig-saw would fit together neatly

• Distinguishing the misleading evidence of Distinguishing the misleading evidence of homoplasy from the reliable evidence of homoplasy from the reliable evidence of homology is a fundamental problem of homology is a fundamental problem of phylogenetic inferencephylogenetic inference

Homoplasy and IncongruenceHomoplasy and Incongruence• If we assume that there is a single correct If we assume that there is a single correct

phylogenetic tree then:phylogenetic tree then:

• When characters support conflicting phylogenetic When characters support conflicting phylogenetic trees we know that there must be some misleading trees we know that there must be some misleading evidence of relationships among the evidence of relationships among the incongruentincongruent or or incompatibleincompatible characters characters

• Incongruence between two characters implies that at Incongruence between two characters implies that at least one of the characters is homoplastic and that at least one of the characters is homoplastic and that at least one of the trees the character supports is wrongleast one of the trees the character supports is wrong

Incongruence or IncompatibilityIncongruence or Incompatibility

• These trees and characters are incongruent - both trees cannot These trees and characters are incongruent - both trees cannot be correct, at least one is wrong and at least one character must be correct, at least one is wrong and at least one character must be homoplasticbe homoplastic

Lizard

Frog

Human

Dog

HAIR

absentpresent

Human

Frog

Lizard

Dog

TAIL

absentpresent

Distinguishing homology and Distinguishing homology and homoplasy homoplasy

• Morphologists use a variety of techniques to Morphologists use a variety of techniques to distinguish homoplasy and homologydistinguish homoplasy and homology

• Homologous features are expected to display detailed Homologous features are expected to display detailed similarity (in position, structure, development) similarity (in position, structure, development) whereas homoplastic similarities are more likely to be whereas homoplastic similarities are more likely to be superficialsuperficial

• Very different features that are homologous are Very different features that are homologous are expected to be ‘connected’ by intermediatesexpected to be ‘connected’ by intermediates

The importance of congruenceThe importance of congruence

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

• Charles Darwin: Origin of Species, Ch. 13Charles Darwin: Origin of Species, Ch. 13

CongruenceCongruence

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

Lizard

Frog

Human

Dog

MAMMALIAHairSingle bone in lower jawLactationetc.

Homoplasy in molecular dataHomoplasy in molecular data• Incongruence and therefore homoplasy can be Incongruence and therefore homoplasy can be

common in molecular sequence datacommon in molecular sequence data– There are a limited number of alternative character There are a limited number of alternative character

states ( e.g. Only A, G, C and T in DNA)states ( e.g. Only A, G, C and T in DNA)

– Rates of evolution are sometimes highRates of evolution are sometimes high

• Character states are chemically identical Character states are chemically identical – homology and homoplasy are equally similarhomology and homoplasy are equally similar

– cannot be distinguished by detailed study of cannot be distinguished by detailed study of similarity and differencessimilarity and differences

Parsimony analysisParsimony analysis

• Parsimony methods provide one way of Parsimony methods provide one way of choosing among alternative phylogenetic choosing among alternative phylogenetic hypotheses hypotheses

• The parsimony criterion favours hypotheses The parsimony criterion favours hypotheses that maximise congruence and minimise that maximise congruence and minimise homoplasyhomoplasy

• It depends on the idea of the fit of a character to It depends on the idea of the fit of a character to a treea tree

Character Fit Character Fit • Initially, we can define the fit of a character to Initially, we can define the fit of a character to

a tree as the minimum number of steps a tree as the minimum number of steps required to explain the observed distribution of required to explain the observed distribution of character states among taxa character states among taxa

• This is determined by This is determined by parsimonious character parsimonious character optimizationoptimization

• Characters differ in their fit to different treesCharacters differ in their fit to different trees

Character FitCharacter Fit

Parsimony AnalysisParsimony Analysis• Given a set of characters, such as aligned Given a set of characters, such as aligned

sequences, parsimony analysis works by sequences, parsimony analysis works by determining the fit (number of steps) of each determining the fit (number of steps) of each character on a given treecharacter on a given tree

• The sum over all characters is called The sum over all characters is called Tree Tree LengthLength

• Most parsimonious trees (MPTs) have the Most parsimonious trees (MPTs) have the minimum tree length needed to explain the minimum tree length needed to explain the observed distributions of all the charactersobserved distributions of all the characters

Parsimony in practiceParsimony in practice

Of these two trees, Tree 1 has the shortest length and is the most parsimoniousBoth trees require some homoplasy (extra steps)

Results of parsimony analysisResults of parsimony analysis• One or more most parsimonious treesOne or more most parsimonious trees

• Hypotheses of character evolution associated with Hypotheses of character evolution associated with each tree (where and how changes have occurred) each tree (where and how changes have occurred)

• Branch lengths (amounts of change associated with Branch lengths (amounts of change associated with branches)branches)

• Various tree and character statistics describing the fit Various tree and character statistics describing the fit between tree and databetween tree and data

• Suboptimal trees - optionalSuboptimal trees - optional

Character typesCharacter types

• Characters may differ in the costs Characters may differ in the costs (contribution to tree length) made by different (contribution to tree length) made by different kinds of changeskinds of changes

• WagnerWagner (ordered, additive) (ordered, additive)

00 11 22 (morphology, unequal costs)(morphology, unequal costs)

• FitchFitch (unordered, non-additive)(unordered, non-additive)

AA G (morphology, molecules) G (morphology, molecules)

TT C C (equal costs for all changes)(equal costs for all changes)

one step

two steps

Character typesCharacter types• SankoffSankoff (generalised) (generalised) AA G (morphology, molecules) G (morphology, molecules)

TT C C (user specified costs)(user specified costs)For example, differential weighting of transitions and For example, differential weighting of transitions and

transversionstransversions

Costs are specified in a Costs are specified in a stepmatrixstepmatrix

Costs are usually symmetric but can be asymmetric also (e.g. Costs are usually symmetric but can be asymmetric also (e.g. costs more to gain than to loose a restriction site)costs more to gain than to loose a restriction site)

one step

five steps

StepmatricesStepmatrices• Stepmatrices specify the costs of changes within a characterStepmatrices specify the costs of changes within a character

A C G TA 0 5 1 5C 5 0 5 1G 1 5 0 5T 5 1 5 0

To

From

A G

CT

PURINES (Pu)

PYRIMIDINES (Py)

transitions Py Py Pu Pu

tra

nsv

ers

ion

s

Py

Pu

Different characters (e.g 1st, 2nd and 3rd) codon positions can also have differentweights

Weighted parsimonyWeighted parsimony• If all kinds of steps of all characters have equal If all kinds of steps of all characters have equal

weight then parsimony:weight then parsimony:– Minimises homoplasy (extra steps)Minimises homoplasy (extra steps)

– Maximises the amount of similarity due to Maximises the amount of similarity due to common ancestry common ancestry

– Minimises tree lengthMinimises tree length

• If steps are weighted unequally parsimony If steps are weighted unequally parsimony minimises tree length - a weighted sum of the minimises tree length - a weighted sum of the cost of each charactercost of each character

Why weight characters?Why weight characters?

Ciliate SSUrDNA data

Num

ber

of

Chara

cters

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210

Number of steps

• Many systematists consider weighting unacceptable, but weighting is Many systematists consider weighting unacceptable, but weighting is unavoidable (unweighted = equal weights)unavoidable (unweighted = equal weights)

• Different kinds of changes may be more of less commonDifferent kinds of changes may be more of less commone.g. transitions/ transversions, codon positions, lopps and stems, e.g. transitions/ transversions, codon positions, lopps and stems,

domains etc. domains etc. • The fit of different characters on trees may indicate differences in their The fit of different characters on trees may indicate differences in their

reliabilitiesreliabilities

• However, equal weighting is the commonest procedure and is the However, equal weighting is the commonest procedure and is the simplest (but probably not the best) approachsimplest (but probably not the best) approach

Different kinds of changes Different kinds of changes differ in their frequenciesdiffer in their frequencies

ToA C G T

From

A

C

G

T

Transitions

Transversions

Unambiguous changeson most parsimonious tree of Ciliate SSUrDNA

Parsimony - advantagesParsimony - advantages

• is a simple method - easily understood operationis a simple method - easily understood operation

• does not seem to depend on an explicit model of does not seem to depend on an explicit model of evolutionevolution

• gives both trees and associated hypotheses of gives both trees and associated hypotheses of character evolutioncharacter evolution

• should give reliable results if the data is well should give reliable results if the data is well structured and homoplasy is either rare or widely structured and homoplasy is either rare or widely (randomly) distributed on the tree(randomly) distributed on the tree

Parsimony - disadvantagesParsimony - disadvantages• May give misleading results if homoplasy is common or May give misleading results if homoplasy is common or

concentrated in particular parts of the tree, e.g:concentrated in particular parts of the tree, e.g:- thermophilic convergencethermophilic convergence- base composition biasesbase composition biases- long branch attractionlong branch attraction

• Underestimates branch lengthsUnderestimates branch lengths• Model of evolution is implicit - behaviour of method not well Model of evolution is implicit - behaviour of method not well

understoodunderstood• Parsimony often justified on purely philosophical grounds - we Parsimony often justified on purely philosophical grounds - we

must prefer simplest hypotheses - particularly by must prefer simplest hypotheses - particularly by morphologistsmorphologists

• For most molecular systematists this is uncompellingFor most molecular systematists this is uncompelling

Parsimony can be inconsistentParsimony can be inconsistent• Felsenstein (1978) developed a simple model phylogeny including four Felsenstein (1978) developed a simple model phylogeny including four

taxa and a mixture of short and long branchestaxa and a mixture of short and long branches

• Under this model parsimony will give the wrong treeUnder this model parsimony will give the wrong treeA B

C D

Model tree

p pq

q q

Rates or Branch lengths

p >> q

A

B

C

D

Parsimony tree

Wrong

• 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

Long branches are attracted but the similarity is homoplastic

Finding optimal trees - exact Finding optimal trees - exact solutionssolutions

• Exact solutions can only be used for small Exact solutions can only be used for small numbers of taxanumbers of taxa

• Exhaustive search Exhaustive search examines all possible examines all possible trees trees

• Typically used for problems with less Typically used for problems with less than 10 taxathan 10 taxa

Finding optimal trees - exhaustive searchFinding optimal trees - exhaustive search

A

B C

1

2a

Starting tree, any 3 taxa

A

B D

C

A

BD C

A

B C

D2b 2c

E

E

EE

E

Add fourth taxon (D) in each of three possible positions -> three trees

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 Finding optimal trees - exact solutionssolutions

• Branch and bound Branch and bound saves time by discarding families saves time by discarding families of trees during tree construction that cannot be of trees during tree construction that cannot be shorter than the shortest tree found so farshorter than the shortest tree found so far

• Can be enhanced by specifying an initial upper Can be enhanced by specifying an initial upper bound for tree lengthbound for tree length

• Typically used only for problems with less than 18 Typically used only for problems with less than 18 taxataxa

Finding optimal trees - branch and boundFinding optimal trees - branch and bound

A

B C

B1

A

B D

C

A

B C

D

B3

A1

A

B E

D

CC1.1

A

B D

E

CC1.3

A

B D

C

EC1.2

A

B

CC1.4

E D

A

B C

C1.5

ED

A

BD C

B2

C2.1

C2.2

C2.3

C2.4

C2.5

C3.1

C3.2

C3.3

C3.4

C3.5

Finding optimal trees - heuristics Finding optimal trees - heuristics

• The number of possible trees increases exponentially with The number of possible trees increases exponentially with the number of taxa making exhaustive searches the number of taxa making exhaustive searches impractical for many data sets (an NP complete problem)impractical for many data sets (an NP complete problem)

• Heuristic methods are used to search tree space for most Heuristic methods are used to search tree space for most parsimonious trees by building or selecting an initial tree parsimonious trees by building or selecting an initial tree and swapping branches to search for better onesand swapping branches to search for better ones

• The trees found are not guaranteed to be the most The trees found are not guaranteed to be the most parsimonious - they are best guessesparsimonious - they are best guesses

Finding optimal trees - heuristicsFinding optimal trees - heuristics• Stepwise additionStepwise addition AsisAsis - the order in the data matrix - the order in the data matrix ClosestClosest -starts with shortest 3-taxon tree adds taxa in order -starts with shortest 3-taxon tree adds taxa in order

that produces the least increase in tree length (greedy that produces the least increase in tree length (greedy heuristic)heuristic)

SimpleSimple - the first taxon in the matrix is a taken as a - the first taxon in the matrix is a taken as a reference - taxa are added to it in the order of their reference - taxa are added to it in the order of their decreasing similarity to the referencedecreasing similarity to the reference

RandomRandom - taxa are added in a random sequence, many - taxa are added in a random sequence, many different sequences can be useddifferent sequences can be used

• Recommend random with as many (e.g. 10-100) addition Recommend random with as many (e.g. 10-100) addition sequences as practicalsequences as practical

Finding most parsimonious trees - Finding most parsimonious trees - heuristicsheuristics

• Branch Swapping:Branch Swapping:

Nearest neighbor interchange (NNI)Nearest neighbor interchange (NNI)

Subtree pruning and regrafting (SPR)Subtree pruning and regrafting (SPR)

Tree bisection and reconnection (TBR)Tree bisection and reconnection (TBR)

Other methods .... Other methods ....

Finding optimal trees - heuristicsFinding optimal trees - heuristics

• Nearest neighbor interchange (NNI)Nearest neighbor interchange (NNI)

A

B

C DE

F

G

A

B

D CE

F

G

A

B

C D

E

F

G

Finding optimal trees - heuristicsFinding optimal trees - heuristics

• Subtree pruning and regrafting (SPR)Subtree pruning and regrafting (SPR)

A

B

C DE

F

G

A

B

C DE

F

G

C

D

G

B

A

E F

Finding optimal trees - heuristicsFinding optimal trees - heuristics

• Tree bisection and reconnection (TBR)Tree bisection and reconnection (TBR)

Finding optimal trees - heuristicsFinding optimal trees - heuristics

• Branch SwappingBranch Swapping Nearest neighbor interchange (NNI)Nearest neighbor interchange (NNI) Subtree pruning and regrafting (SPR)Subtree pruning and regrafting (SPR) Tree bisection and reconnection (TBR)Tree bisection and reconnection (TBR)

• The nature of heuristic searches means we cannot The nature of heuristic searches means we cannot know which method will find the most know which method will find the most parsimonious trees or all such treesparsimonious trees or all such trees

• However, TBR is the most extensive swapping However, TBR is the most extensive swapping routine and its use with multiple random addition routine and its use with multiple random addition sequences should work wellsequences should work well

Tree space may be populated by local minima Tree space may be populated by local minima and islands of optimal treesand islands of optimal trees

GLOBAL MINIMUM

LocalMinimum

LocalMinima

TreeLength

RANDOM ADDITION SEQUENCE REPLICATES

SUCCESSFAILURE FAILURE

Branch SwappingBranch Swapping

Branch Swapping

Searching with topological constraintsSearching with topological constraints• Topological constraints are user-defined Topological constraints are user-defined

phylogenetic hypothesesphylogenetic hypotheses

• Can be used to find optimal trees that either:Can be used to find optimal trees that either:

1. include a specified clade or set of 1. include a specified clade or set of relationshipsrelationships

2. exclude a specified clade or set of 2. exclude a specified clade or set of relationships (reverse constraint) relationships (reverse constraint)

Searching with topological constraintsSearching with topological constraints

A B C D E F G

ABCDEFG

((A,B,C,D)(E,F,G))

A B C D E F G

ABCDEFG

A B C E D F G

Compatible with constraint tree

CONSTRAINT TREE

Incompatible with reverse constraint tree

Compatible with reverse constraint treeIncompatible with constraint tree

Searching with topological constraintsSearching with topological constraintsbackbone constraintsbackbone constraints

• Backbone constraints specify relationships among a subset of the taxaBackbone constraints specify relationships among a subset of the taxa

A B D E

A B D E

A D B E

possible positions of taxon CCompatible with backbone constraintIncompatible with reverse constraint

Incompatible with backbone constraintCompatible with reverse constraint

BACKBONE CONSTRAINT((A,B)(D,E))

relationships of taxon C are not specified