characters

Introduction to characters and parsimony analysis : 

Introduction to characters and parsimony analysis

Genetic Relationships: 

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 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: 

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: 

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 Phylogenetic hypotheses are hypotheses of common ancestry

Phylogenetic Trees: 

Phylogenetic Trees A CLADOGRAM

CLADOGRAMS AND PHYLOGRAMS: 

CLADOGRAMS AND PHYLOGRAMS ABSOLUTE TIME or DIVERGENCE RELATIVE TIME A B C D E F G H I J A B C D E F G H I J

Trees - Rooted and Unrooted: 

Trees - Rooted and Unrooted

Characters and Character States: 

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: 

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: 

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: 

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 Lizard Frog Human Dog HAIR absent present change or step

Slide13: 

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

Homoplasy - independent evolution: 

Homoplasy - independent evolution Human Lizard Frog Dog TAIL (adult) absent present Loss of tails evolved independently in humans and frogs - there are two steps on the true tree

Homoplasy - misleading evidence of phylogeny: 

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 Frog Lizard Dog TAIL absent present

Homoplasy - reversal: 

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 10 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10

Homoplasy - a fundamental problem of phylogenetic inference: 

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: 

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: 

Incongruence or Incompatibility These trees and characters are incongruent - both trees cannot be correct, at least one is wrong and at least one character must be homoplastic Lizard Frog Human Dog HAIR absent present Human Frog Lizard Dog TAIL absent present

Distinguishing homology and homoplasy : 

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 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: 

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: 

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 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 : 

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

Character Fit: 

Character Fit

Parsimony Analysis: 

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

Parsimony in practice: 

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)

Results of parsimony analysis: 

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: 

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) A G (morphology, molecules) T C (equal costs for all changes) one step two steps

Character types: 

Character types Sankoff (generalised) A G (morphology, molecules) 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) one step five steps

Stepmatrices: 

Stepmatrices Stepmatrices specify the costs of changes within a character A G C T PURINES (Pu) PYRIMIDINES (Py) transitions Py Py Pu Pu transversions Py Pu Different characters (e.g 1st, 2nd and 3rd) codon positions can also have different weights

Weighted parsimony: 

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?: 

Why weight 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 However, equal weighting is the commonest procedure and is the simplest (but probably not the best) approach Ciliate SSUrDNA data Number of Characters 0 50 100 150 200 250 Number of steps

Different kinds of changes differ in their frequencies: 

Different kinds of changes differ in their frequencies To A C G T From A C G T Transitions Transversions Unambiguous changes on most parsimonious tree of Ciliate SSUrDNA

Parsimony - advantages: 

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: 

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: 

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 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 solutions: 

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: 

Finding optimal trees - exhaustive search A B C 1 2a Starting tree, any 3 taxa A B D C A B D C A B C D 2b 2c E E E E 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 solutions: 

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: 

Finding optimal trees - branch and bound A B C B1 A B D C A B C D B3 A1 A B E D C C1.1 A B D E C C1.3 A B D C E C1.2 A B C C1.4 E D A B C C1.5 E D A B D 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 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: 

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: 

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: 

Finding optimal trees - heuristics Nearest neighbor interchange (NNI)

Finding optimal trees - heuristics: 

Finding optimal trees - heuristics Subtree pruning and regrafting (SPR)

Finding optimal trees - heuristics: 

Finding optimal trees - heuristics Tree bisection and reconnection (TBR)

Finding optimal trees - heuristics: 

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: 

Tree space may be populated by local minima and islands of optimal trees GLOBAL MINIMUM Local Minimum Local Minima Tree Length RANDOM ADDITION SEQUENCE REPLICATES SUCCESS FAILURE FAILURE Branch Swapping Branch Swapping Branch Swapping

Searching with topological constraints: 

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: 

Searching with topological constraints A B C D E F G ABCD EFG ((A,B,C,D)(E,F,G)) A B C D E F G ABCD EFG A B C E D F G Compatible with constraint tree CONSTRAINT TREE Incompatible with reverse constraint tree Compatible with reverse constraint tree Incompatible with constraint tree

Searching with topological constraintsbackbone constraints: 

Searching with topological constraints backbone constraints Backbone 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 C Compatible with backbone constraint Incompatible with reverse constraint Incompatible with backbone constraint Compatible with reverse constraint BACKBONE CONSTRAINT ((A,B)(D,E)) relationships of taxon C are not specified

Parsimonious Character Optimization: 

Parsimonious Character Optimization A B C D E * * 0 => 1 = = OR parallelism 2 separate origins 0 => 1 (DELTRAN) origin and reversal (ACCTRAN) 0 0 1 1 0 1 => 0 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 Missing data is ignored in tree building but can lead to alternative equally parsimonious optimizations in the absence of homoplasy A B C D E * * single origin 0 => 1 on any one of 3 branches 1 ? ? 0 0 * 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: 

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: 

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 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: 

Strict consensus methods A B C D E F G A B C E D F G TWO FUNDAMENTAL TREES A B C D E F G STRICT COMPONENT CONSENSUS TREE

Majority-rule consensus methods: 

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: 

Majority rule consensus A B C D E F G A B C E D F G A B C E D F G MAJORITY-RULE COMPONENT CONSENSUS TREE A B C E F D G 100 66 66 66 66 THREE FUNDAMENTAL TREES Numbers indicate frequency of clades in the fundamental trees

Reduced consensus methods: 

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: 

Types of Cladistic Relationships

Reduced consensus methods: 

Reduced consensus methods A B C D E F G TWO FUNDAMENTAL TREES STRICT REDUCED CONSENSUS TREE Taxon G is excluded A G B C D E F A B C D E F A B C D E F G Strict component consensus completely unresolved

Consensus methods: 

Consensus methods Spirostomumum Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Spirostomum Tracheloraphis Gruberia Three fundamental trees majority-rule strict (component) strict reduced cladistic Euplotes excluded 100 100 100 100 66 66

Consensus methods: 

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