Introduction to characters and parsimony analysis
Genetic Relationships <ul><li>Genetic relationships exist between individuals within populations </li></ul><ul><li>These i...
 
Phylogenetic Relationships <ul><li>Phylogenetic relationships exist between lineages (e.g. species, genes) </li></ul><ul><...
Phylogenetic Relationships <ul><li>Traditionally phylogeny reconstruction was dominated by the search for ancestors, and a...
Phylogenetic relationships <ul><li>Two lineages are more closely related to each other than to some other lineage if they ...
Phylogenetic Trees A CLADOGRAM
CLADOGRAMS AND PHYLOGRAMS ABSOLUTE TIME or  DIVERGENCE RELATIVE TIME B A C D E H G F I J B C E D H G I J F A
Trees - Rooted and Unrooted
Characters and Character States <ul><li>Organisms comprise sets of features </li></ul><ul><li>When  organisms/taxa differ ...
Character evolution <ul><li>Heritable changes (in morphology, gene sequences, etc.) produce different character states </l...
Unique and unreversed characters <ul><li>Given a heritable evolutionary change that is  unique  and  unreversed  (e.g. the...
Unique and unreversed characters <ul><li>Because hair evolved only once and is unreversed (not subsequently lost) it is  h...
To distinguish between an ancestral and a derived character state: (1) If a sequence has the same base as the common ances...
To distinguish between an ancestral and a derived character state: (2)Unique derived character states are  autapomorphies ...
<ul><li>Homoplasy is similarity that is not homologous (not due to common ancestry) </li></ul><ul><li>It is the result of ...
Homoplasy: Homoplasy  is a poor indicator of evolutionary relationships because the similarity does not reflect shared anc...
Homoplasy - independent evolution Human Lizard Frog Dog TAIL (adult) absent present <ul><li>Loss of tails evolved independ...
Homoplasy - misleading evidence of phylogeny <ul><li>If misinterpreted as homology, the absence of tails would be evidence...
Homoplasy - reversal <ul><li>Reversals are evolutionary changes back to an ancestral condition </li></ul><ul><li>As with a...
Parallel evolution: the independent evolution of same feature from same ancestral condition.
Convergent evolution: the independent evolution of same feature from different ancestral condition.
Homoplasy - a fundamental problem of phylogenetic inference <ul><li>If there were no homoplastic similarities inferring ph...
Homoplasy and Incongruence <ul><li>If we assume that there is a single correct phylogenetic tree then: </li></ul><ul><li>W...
Incongruence or Incompatibility <ul><li>These trees and characters are incongruent - both trees cannot be correct, at leas...
Distinguishing homology and homoplasy  <ul><li>Morphologists use a variety of techniques to distinguish homoplasy and homo...
The importance of congruence <ul><li>“ The importance, for classification, of trifling characters, mainly depends on their...
Congruence <ul><li>We prefer the ‘true’ tree because it is supported by multiple congruent characters </li></ul>Lizard Fro...
Homoplasy in molecular data <ul><li>Incongruence and therefore homoplasy can be common in molecular sequence data </li></u...
Parsimony analysis <ul><li>Parsimony methods provide one way of choosing among alternative phylogenetic hypotheses  </li><...
Character Fit  <ul><li>Initially, we can define the fit of a character to a tree as the minimum number of steps required t...
Character Fit
Parsimony Analysis <ul><li>Given a set of characters, such as aligned sequences, parsimony analysis works by determining t...
Parsimony informative sites <ul><li>Not all sites are considered informative for tree construction </li></ul><ul><li>The o...
 
 
Operation of the Fitch Algorithm
Parsimony in practice Of these two trees, Tree 1 has the shortest length and is the most parsimonious Both trees require s...
Class exercise in the operation of the Fitch Algorithm : What is the total observed length of this tree ? A A G T C
Results of parsimony analysis <ul><li>One or more most parsimonious trees </li></ul><ul><li>Hypotheses of character evolut...
Character types <ul><li>Characters may differ in the costs (contribution to tree length) made by different kinds of change...
Character types <ul><li>Sankoff  (generalised) </li></ul><ul><li>A   G  (morphology, molecules) </li></ul><ul><li>T   C  (...
Stepmatrices <ul><li>Stepmatrices specify the costs of changes within a character </li></ul>A G C T PURINES (Pu) PYRIMIDIN...
Weighted parsimony <ul><li>If all kinds of steps of all characters have equal weight then parsimony: </li></ul><ul><ul><li...
Why weight characters? <ul><li>Many systematists consider weighting unacceptable, but weighting is unavoidable (unweighted...
Different kinds of changes differ in their frequencies To A C G T From A C G T Transitions Transversions Unambiguous chang...
Parsimony - advantages <ul><li>is a simple method - easily understood operation </li></ul><ul><li>does not seem to depend ...
Parsimony - disadvantages <ul><li>May give misleading results if homoplasy is common or concentrated in particular parts o...
Parsimony can be inconsistent <ul><li>Felsenstein (1978) developed a simple model phylogeny including four taxa and a mixt...
Finding optimal trees - exact solutions <ul><li>Exact solutions can only be used for small numbers of taxa </li></ul><ul><...
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...
Finding optimal trees - heuristics  <ul><li>The number of possible trees increases exponentially with the number of taxa m...
Finding optimal trees - heuristics <ul><li>Stepwise addition </li></ul><ul><li>Asis  - the order in the data matrix </li><...
Finding most parsimonious trees - heuristics <ul><li>Branch Swapping: </li></ul><ul><li>Nearest neighbor interchange (NNI)...
Finding optimal trees - heuristics <ul><li>Nearest neighbor interchange (NNI) </li></ul>A B C D E F G A B D C E F G A B C ...
Finding optimal trees - heuristics <ul><li>Subtree pruning and regrafting (SPR) </li></ul>A B C D E F G A B C D E F G C D ...
Finding optimal trees - heuristics <ul><li>Tree bisection and reconnection (TBR) </li></ul>
Finding optimal trees - heuristics <ul><li>Branch Swapping </li></ul><ul><li>Nearest neighbor interchange (NNI) </li></ul>...
Tree space may be populated by local minima and islands of optimal trees GLOBAL  MINIMUM Local Minimum Local Minima Tree L...
Parsimonious Character Optimization A B C D E * * 0 => 1 = = OR   parallelism 2 separate origins 0 => 1   (DELTRAN) origin...
Multiple optimal trees <ul><li>Many methods can yield multiple equally optimal trees </li></ul><ul><li>We can further sele...
Consensus methods <ul><li>A consensus tree is a summary of the agreement among a set of fundamental trees </li></ul><ul><l...
Strict consensus methods <ul><li>Strict consensus methods require agreement across all the fundamental trees </li></ul><ul...
Strict consensus methods A B C D E F G A B C E D F G TWO  FUNDAMENTAL  TREES STRICT COMPONENT CONSENSUS TREE A B C D E F G
Majority-rule consensus methods <ul><li>Majority-rule consensus methods require agreement across a majority of the fundame...
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...
Reduced consensus methods <ul><li>Focuses upon any relationships (not just full splits) </li></ul><ul><li>Reduced consensu...
Reduced consensus methods TWO FUNDAMENTAL TREES STRICT REDUCED CONSENSUS TREE Taxon G is excluded A B C D E F A B C D E F ...
Consensus methods Three fundamental trees Spirostomumum From these 3 fundamental trees , construct  (1) the Strict compone...
Consensus methods Spirostomumum Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Spirostomum Tracheloraphis Gruber...
Consensus methods <ul><li>Use strict methods to identify those relationships unambiguously supported by parsimonious inter...
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Characters.ppt

  1. 1. Introduction to characters and parsimony analysis
  2. 2. Genetic Relationships <ul><li>Genetic relationships exist between individuals within populations </li></ul><ul><li>These include ancestor-descendent relationships and more indirect relationships based on common ancestry </li></ul><ul><li>Within sexually reducing populations there is a network of relationships </li></ul><ul><li>Genetic relations within populations can be measured with a coefficient of genetic relatedness </li></ul>
  3. 4. Phylogenetic Relationships <ul><li>Phylogenetic relationships exist between lineages (e.g. species, genes) </li></ul><ul><li>These include ancestor-descendent relationships and more indirect relationships based on common ancestry </li></ul><ul><li>Phylogenetic relationships between species or lineages are (expected to be) tree-like </li></ul><ul><li>Phylogenetic relationships are not measured with a simple coefficient </li></ul>
  4. 5. Phylogenetic Relationships <ul><li>Traditionally phylogeny reconstruction was dominated by the search for ancestors, and ancestor-descendant relationships </li></ul><ul><li>In modern phylogenetics there is an emphasis on indirect relationships </li></ul><ul><li>Given that all lineages are related, closeness of phylogenetic relationships is a relative concept. </li></ul>
  5. 6. Phylogenetic relationships <ul><li>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 </li></ul><ul><li>Phylogenetic hypotheses are hypotheses of common ancestry </li></ul>
  6. 7. Phylogenetic Trees A CLADOGRAM
  7. 8. CLADOGRAMS AND PHYLOGRAMS ABSOLUTE TIME or DIVERGENCE RELATIVE TIME B A C D E H G F I J B C E D H G I J F A
  8. 9. Trees - Rooted and Unrooted
  9. 10. Characters and Character States <ul><li>Organisms comprise sets of features </li></ul><ul><li>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 </li></ul><ul><li>The collection of character states with respect to a feature constitute a character </li></ul>
  10. 11. Character evolution <ul><li>Heritable changes (in morphology, gene sequences, etc.) produce different character states </li></ul><ul><li>Similarities and differences in character states provide the basis for inferring phylogeny (i.e. provide evidence of relationships) </li></ul><ul><li>The utility of this evidence depends on how often the evolutionary changes that produce the different character states occur independently </li></ul>
  11. 12. Unique and unreversed characters <ul><li>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 </li></ul><ul><li>Similarly, absence in any taxa must be because the taxa are not descendants of that ancestor </li></ul><ul><li>The novelty is a homology acting as badge or marker for the descendants of the ancestor </li></ul><ul><li>The taxa with the novelty are a clade (e.g. Mammalia) </li></ul>
  12. 13. Unique and unreversed characters <ul><li>Because hair evolved only once and is unreversed (not subsequently lost) it is homologous and provides unambiguous evidence for of relationships </li></ul>Lizard Frog Human Dog HAIR absent present change or step
  13. 14. To distinguish between an ancestral and a derived character state: (1) If a sequence has the same base as the common ancestor then it is the primitive or pleisomorphic state; otherwise it is a derived or apomorphic state. Pleisomorphy Apomorphy
  14. 15. To distinguish between an ancestral and a derived character state: (2)Unique derived character states are autapomorphies , shared derived states are synapomorphies.
  15. 16. <ul><li>Homoplasy is similarity that is not homologous (not due to common ancestry) </li></ul><ul><li>It is the result of independent evolution (convergence, parallelism, reversal) </li></ul><ul><li>Homoplasy can provide misleading evidence of phylogenetic relationships (if mistakenly interpreted as homology) </li></ul>Homoplasy - Independent evolution
  16. 17. Homoplasy: Homoplasy is a poor indicator of evolutionary relationships because the similarity does not reflect shared ancestry. It is sometimes useful to distinguish between different types of homoplasy …. Convergence, Parallel substitution and Reversals (Secondary Loss)
  17. 18. Homoplasy - independent evolution Human Lizard Frog Dog TAIL (adult) absent present <ul><li>Loss of tails evolved independently in humans and frogs - there are two steps on the true tree </li></ul>
  18. 19. Homoplasy - misleading evidence of phylogeny <ul><li>If misinterpreted as homology, the absence of tails would be evidence for a wrong tree: grouping humans with frogs and lizards with dogs </li></ul>Human Frog Lizard Dog TAIL absent present
  19. 20. Homoplasy - reversal <ul><li>Reversals are evolutionary changes back to an ancestral condition </li></ul><ul><li>As with any homoplasy, reversals can provide misleading evidence of relationships </li></ul>True tree Wrong tree 10 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10
  20. 21. Parallel evolution: the independent evolution of same feature from same ancestral condition.
  21. 22. Convergent evolution: the independent evolution of same feature from different ancestral condition.
  22. 23. Homoplasy - a fundamental problem of phylogenetic inference <ul><li>If there were no homoplastic similarities inferring phylogeny would be easy - all the pieces of the jig-saw would fit together neatly </li></ul><ul><li>Distinguishing the misleading evidence of homoplasy from the reliable evidence of homology is a fundamental problem of phylogenetic inference </li></ul>
  23. 24. Homoplasy and Incongruence <ul><li>If we assume that there is a single correct phylogenetic tree then: </li></ul><ul><li>When characters support conflicting phylogenetic trees we know that there must be some misleading evidence of relationships among the incongruent or incompatible characters </li></ul><ul><li>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 </li></ul>
  24. 25. Incongruence or Incompatibility <ul><li>These trees and characters are incongruent - both trees cannot be correct, at least one is wrong and at least one character must be homoplastic </li></ul>Lizard Frog Human Dog HAIR absent present Human Frog Lizard Dog TAIL absent present
  25. 26. Distinguishing homology and homoplasy <ul><li>Morphologists use a variety of techniques to distinguish homoplasy and homology </li></ul><ul><li>Homologous features are expected to display detailed similarity (in position, structure, development) whereas homoplastic similarities are more likely to be superficial </li></ul><ul><li>As recognised by Charles Darwin congruence with other characters provides the most compelling evidence for homology </li></ul>
  26. 27. The importance of congruence <ul><li>“ 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.” </li></ul><ul><li>Charles Darwin: Origin of Species, Ch. 13 </li></ul>
  27. 28. Congruence <ul><li>We prefer the ‘true’ tree because it is supported by multiple congruent characters </li></ul>Lizard Frog Human Dog MAMMALIA Hair Single bone in lower jaw Lactation etc.
  28. 29. Homoplasy in molecular data <ul><li>Incongruence and therefore homoplasy can be common in molecular sequence data </li></ul><ul><ul><li>There are a limited number of alternative character states ( e.g. Only A, G, C and T in DNA) </li></ul></ul><ul><ul><li>Rates of evolution are sometimes high </li></ul></ul><ul><li>Character states are chemically identical </li></ul><ul><ul><li>homology and homoplasy are equally similar </li></ul></ul><ul><ul><li>cannot be distinguished by detailed study of similarity and differences </li></ul></ul>
  29. 30. Parsimony analysis <ul><li>Parsimony methods provide one way of choosing among alternative phylogenetic hypotheses </li></ul><ul><li>The parsimony criterion favours hypotheses that maximise congruence and minimise homoplasy </li></ul><ul><li>It depends on the idea of the fit of a character to a tree </li></ul>
  30. 31. Character Fit <ul><li>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 </li></ul><ul><li>This is determined by parsimonious character optimization </li></ul><ul><li>Characters differ in their fit to different trees </li></ul>
  31. 32. Character Fit
  32. 33. Parsimony Analysis <ul><li>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 </li></ul><ul><li>The sum over all characters is called Tree Length </li></ul><ul><li>Most parsimonious trees (MPTs) have the minimum tree length needed to explain the observed distributions of all the characters </li></ul>
  33. 34. Parsimony informative sites <ul><li>Not all sites are considered informative for tree construction </li></ul><ul><li>The only sites considered parsimony-informative are those where at least 2 sequences have one character state at this site and at least 2 others have a DIFFERENT IDENTICAL character state. </li></ul>
  34. 37. Operation of the Fitch Algorithm
  35. 38. 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)
  36. 39. Class exercise in the operation of the Fitch Algorithm : What is the total observed length of this tree ? A A G T C
  37. 40. Results of parsimony analysis <ul><li>One or more most parsimonious trees </li></ul><ul><li>Hypotheses of character evolution associated with each tree (where and how changes have occurred) </li></ul><ul><li>Branch lengths (amounts of change associated with branches) </li></ul><ul><li>Various tree and character statistics describing the fit between tree and data </li></ul><ul><li>Suboptimal trees - optional </li></ul>
  38. 41. Character types <ul><li>Characters may differ in the costs (contribution to tree length) made by different kinds of changes </li></ul><ul><li>Wagner (ordered, additive) </li></ul><ul><li>0 1 2 (morphology, unequal costs) </li></ul><ul><li>Fitch (unordered, non-additive) </li></ul><ul><li>A G (morphology, molecules) </li></ul><ul><li>T C (equal costs for all changes) </li></ul>one step two steps
  39. 42. Character types <ul><li>Sankoff (generalised) </li></ul><ul><li>A G (morphology, molecules) </li></ul><ul><li>T C (user specified costs) </li></ul><ul><li>For example, differential weighting of transitions and transversions </li></ul><ul><li>Costs are specified in a stepmatrix </li></ul><ul><li>Costs are usually symmetric but can be asymmetric also (e.g. costs more to gain than to loose a restriction site) </li></ul>one step five steps
  40. 43. Stepmatrices <ul><li>Stepmatrices specify the costs of changes within a character </li></ul>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 A C G T A 0 5 1 5 C 5 0 5 1 G 1 5 0 5 T 5 1 5 0 To From
  41. 44. Weighted parsimony <ul><li>If all kinds of steps of all characters have equal weight then parsimony: </li></ul><ul><ul><li>Minimises homoplasy (extra steps) </li></ul></ul><ul><ul><li>Maximises the amount of similarity due to common ancestry </li></ul></ul><ul><ul><li>Minimises tree length </li></ul></ul><ul><li>If steps are weighted unequally parsimony minimises tree length - a weighted sum of the cost of each character </li></ul>
  42. 45. Why weight characters? <ul><li>Many systematists consider weighting unacceptable, but weighting is unavoidable (unweighted = equal weights) </li></ul><ul><li>Transitions may be more common than transversions </li></ul><ul><li>Different kinds of transitions and transversions may be more or less common </li></ul><ul><li>Rates of change may vary with codon positions </li></ul><ul><li>The fit of different characters on trees may indicate differences in their reliabilities </li></ul><ul><li>However, equal weighting is the commonest procedure and is the simplest (but probably not the best) approach </li></ul>Ciliate SSUrDNA data Number of Characters 0 50 100 150 200 250 Number of steps 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0
  43. 46. 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
  44. 47. Parsimony - advantages <ul><li>is a simple method - easily understood operation </li></ul><ul><li>does not seem to depend on an explicit model of evolution </li></ul><ul><li>gives both trees and associated hypotheses of character evolution </li></ul><ul><li>should give reliable results if the data is well structured and homoplasy is either rare or widely (randomly) distributed on the tree </li></ul>
  45. 48. Parsimony - disadvantages <ul><li>May give misleading results if homoplasy is common or concentrated in particular parts of the tree, e.g: </li></ul><ul><ul><li>thermophilic convergence </li></ul></ul><ul><ul><li>base composition biases </li></ul></ul><ul><ul><li>long branch attraction </li></ul></ul><ul><li>Underestimates branch lengths </li></ul><ul><li>Model of evolution is implicit - behaviour of method not well understood </li></ul><ul><li>Parsimony often justified on purely philosophical grounds - we must prefer simplest hypotheses - particularly by morphologists </li></ul><ul><li>For most molecular systematists this is uncompelling </li></ul>
  46. 49. Parsimony can be inconsistent <ul><li>Felsenstein (1978) developed a simple model phylogeny including four taxa and a mixture of short and long branches </li></ul><ul><li>Under this model parsimony will give the wrong tree </li></ul><ul><li>With more data the certainty that parsimony will give the wrong tree increases - so that parsimony is statistically inconsistent </li></ul><ul><li>Advocates of parsimony initially responded by claiming that Felsenstein’s result showed only that his model was unrealistic </li></ul><ul><li>It is now recognised that the long-branch attraction (in the Felsenstein Zone ) is one of the most serious problems in phylogenetic inference </li></ul>Long branches are attracted but the similarity is homoplastic
  47. 50. Finding optimal trees - exact solutions <ul><li>Exact solutions can only be used for small numbers of taxa </li></ul><ul><li>Exhaustive search examines all possible trees </li></ul><ul><li>Typically used for problems with less than 10 taxa </li></ul>
  48. 51. 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 ....
  49. 52. Finding optimal trees - heuristics <ul><li>The number of possible trees increases exponentially with the number of taxa making exhaustive searches impractical for many data sets (an NP complete problem) </li></ul><ul><li>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 </li></ul><ul><li>The trees found are not guaranteed to be the most parsimonious - they are best guesses </li></ul>
  50. 53. Finding optimal trees - heuristics <ul><li>Stepwise addition </li></ul><ul><li>Asis - the order in the data matrix </li></ul><ul><li>Closest -starts with shortest 3-taxon tree adds taxa in order that produces the least increase in tree length (greedy heuristic) </li></ul><ul><li>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 </li></ul><ul><li>Random - taxa are added in a random sequence, many different sequences can be used </li></ul><ul><li>Recommend random with as many (e.g. 10-100) addition sequences as practical </li></ul>
  51. 54. Finding most parsimonious trees - heuristics <ul><li>Branch Swapping: </li></ul><ul><li>Nearest neighbor interchange (NNI) </li></ul><ul><li>Subtree pruning and regrafting (SPR) </li></ul><ul><li>Tree bisection and reconnection (TBR) </li></ul><ul><li>Other methods .... </li></ul>
  52. 55. Finding optimal trees - heuristics <ul><li>Nearest neighbor interchange (NNI) </li></ul>A B C D E F G A B D C E F G A B C D E F G
  53. 56. Finding optimal trees - heuristics <ul><li>Subtree pruning and regrafting (SPR) </li></ul>A B C D E F G A B C D E F G C D G B A E F
  54. 57. Finding optimal trees - heuristics <ul><li>Tree bisection and reconnection (TBR) </li></ul>
  55. 58. Finding optimal trees - heuristics <ul><li>Branch Swapping </li></ul><ul><li>Nearest neighbor interchange (NNI) </li></ul><ul><li>Subtree pruning and regrafting (SPR) </li></ul><ul><li>Tree bisection and reconnection (TBR) </li></ul><ul><li>The nature of heuristic searches means we cannot know which method will find the most parsimonious trees or all such trees </li></ul><ul><li>However, TBR is the most extensive swapping routine and its use with multiple random addition sequences should work well </li></ul>
  56. 59. 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
  57. 60. 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
  58. 61. Multiple optimal trees <ul><li>Many methods can yield multiple equally optimal trees </li></ul><ul><li>We can further select among these trees with additional criteria, but </li></ul><ul><li>Typically, relationships common to all the optimal trees are summarised with consensus trees </li></ul>
  59. 62. Consensus methods <ul><li>A consensus tree is a summary of the agreement among a set of fundamental trees </li></ul><ul><li>There are many consensus methods that differ in: </li></ul><ul><li>1. the kind of agreement </li></ul><ul><li>2. the level of agreement </li></ul><ul><li>Consensus methods can be used with multiple trees from a single analysis or from multiple analyses </li></ul>
  60. 63. Strict consensus methods <ul><li>Strict consensus methods require agreement across all the fundamental trees </li></ul><ul><li>They show only those relationships that are unambiguously supported by the parsimonious interpretation of the data </li></ul><ul><li>The commonest method ( strict component consensus ) focuses on clades/components/full splits </li></ul><ul><li>This method produces a consensus tree that includes all and only those full splits found in all the fundamental trees </li></ul><ul><li>Other relationships (those in which the fundamental trees disagree) are shown as unresolved polytomies </li></ul><ul><li>Implemented in PAUP </li></ul>
  61. 64. Strict consensus methods A B C D E F G A B C E D F G TWO FUNDAMENTAL TREES STRICT COMPONENT CONSENSUS TREE A B C D E F G
  62. 65. Majority-rule consensus methods <ul><li>Majority-rule consensus methods require agreement across a majority of the fundamental trees </li></ul><ul><li>May include relationships that are not supported by the most parsimonious interpretation of the data </li></ul><ul><li>The commonest method focuses on clades/components/full splits </li></ul><ul><li>This method produces a consensus tree that includes all and only those full splits found in a majority (>50%) of the fundamental trees </li></ul><ul><li>Other relationships are shown as unresolved polytomies </li></ul><ul><li>Of particular use in bootstrapping </li></ul><ul><li>Implemented in PAUP </li></ul>
  63. 66. 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
  64. 67. Reduced consensus methods <ul><li>Focuses upon any relationships (not just full splits) </li></ul><ul><li>Reduced consensus methods occur in strict and majority-rule varieties </li></ul><ul><li>Other relationships are shown as unresolved polytomies </li></ul><ul><li>May be more sensitive than methods focusing only on clades/components/full splits </li></ul><ul><li>Strict reduced consensus methods are implemented in RadCon </li></ul>
  65. 68. Reduced consensus methods TWO FUNDAMENTAL TREES STRICT REDUCED CONSENSUS TREE Taxon G is excluded A B C D E F A B C D E F G Strict component consensus completely unresolved A B C D E F G A G B C D E F
  66. 69. Consensus methods Three fundamental trees Spirostomumum From these 3 fundamental trees , construct (1) the Strict component tree (2) The Strict reduced cladistic (3) The majority rule tree Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Tracheloraphis Euplotes Gruberia Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Spirostomumum Euplotes Tracheloraphis Gruberia Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Euplotes Spirostomumum Tracheloraphis Gruberia
  67. 70. 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 Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Tracheloraphis Euplotes Gruberia Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Spirostomumum Euplotes Tracheloraphis Gruberia Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Euplotes Spirostomumum Tracheloraphis Gruberia Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Tracheloraphis Spirostomum Euplotes Gruberia Ochromonas Symbiodinium Prorocentrum Loxodes Tetrahymena Spirostomum Euplotes Tracheloraphis Gruberia
  68. 71. Consensus methods <ul><li>Use strict methods to identify those relationships unambiguously supported by parsimonious interpretation of the data </li></ul><ul><li>Use reduced methods where consensus trees are poorly resolved </li></ul><ul><li>Use majority-rule methods in bootstrapping </li></ul><ul><li>Avoid other methods which have ambiguous interpretations </li></ul>
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