Intro to Phylogenetic Tree Reconstruction

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Intro to Phylogenetic Tree Reconstruction

• Basics

• Phylogeny   (evolutionary) relationships between
  any set of species
• Hypothesis   All organisms on Earth are
  evolutionarily related via a common ancestor
• Evidence   similarity of many molecular
  mechanisms and genetic materials

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Intro to Phylogenetic Tree Reconstruction

• Basics

• Phylogeny can be represented as a tree.
• 2 Types of Phylogenetics
• classic phylogenetics based on morphological
  characters
• modern phylogenetics based on information
  extracted from sequence data (DNA, RNA and
  proteins)
• based on characters sites on sequences
• Assumption
• Sequences have descended from common ancestral
  genes/species,but difficult to distinguish
  orthologues from paralogues
• Phylogenetic tree of a group of sequences does
  not necessarily represent the true phylogenetic
  tree of host species

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Intro to Phylogenetic Tree Reconstruction

• Phylogenetic Trees

• leaves species
• internal nodes (hypothetical) ancestors
• nodes species or character values (states)
• edges evolutionary relationships between nodes
• edge lengths evolutionary distance between
  nodes (evolutionary time)
• restrict ourselves to binary trees only
• ok, as we can use distances of 0
• rooted vs. unrooted trees
• root represents the ultimate ancestor of the
  group of sequences(includes hierarchy)

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Intro to Phylogenetic Tree Reconstruction

• Phylogenetic Tree Reconstruction (Inference)
  Problem

• Given
• n species
• m characters
• for each species, values for all characters
• Want fully labelled phylogenetic tree that
  'best' explains the given data (i.e. maximize a
  target function (score) )
• Assumptions
• characters are mutually independent
• after two species diverged, their further
  evolution is independent of each other
• Simple Solution check them all out and pick the
  best one
• problem too many possibilities to check
• n species -gt (2n-3)!! different rooted trees
• n 20 -gt 1021 trees

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Intro to Phylogenetic Tree Reconstruction

• Distance-Based Algorithms

• Idea
• begin with a set of distances di between each
  pair i,j of seq.
• find the tree that predicts the observed sequence
  data as accurately as possible
• How to find the tree
• 1. general idea given pairwise distance dij and
  tree T predicting pairwise distance dij', find
  the T that minimizes SSQ(T) gt Least Squares
  Methodbut NP-complete

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Intro to Phylogenetic Tree Reconstruction

• Distance-Based Algorithms

• 2. Clustering UPGMA (Unweighted Pair Group
  Method Using Arithmetic Averages)
• Idea cluster sequences at each stage, merge two
  groups and create a new node in the tree
• build the tree bottom up from the leaves
• result rooted tree with molecular clock property
  (MCP)
• 11 correspondence between distance and
  evolutionary time
• not always true in reality some sequences evolve
  faster
• If 'true' tree doesn't have MCP, UPGMA will give
  incorrect results

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Intro to Phylogenetic Tree Reconstruction

• Distance-Based Algorithms

• 3. Clustering Neighbor Joining
• guarantees to generate correct tree in polynomial
  time if distance is additive
• (weaker than MCP, so more reasonable still, not
  always true)

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• Phylogenetics and Phylogenetic Trees

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Why do a phylogenetic analysis

• important for deciphering relationships in gene
  function and protein structure and function in
  different organisms
• helps to utilize genetic information of a model
  organism to analyze a second organism
• helps to sort out gene family relationships
• valuable tool for tracing the evolutionary
  history of genes

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Performing a phylogenetic analysis

• Start with reasonable multiple sequence
  alignment
• Examine either sequence variation in each column
  or no. of differences between each pair of
  sequences
• Produce a tree representation of the sequences
  based on similarity/differences

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Methods of evaluating sequence relationships

• sequence A ERKSIQDLFQSFTLFERRLLIEF
• sequence B ERLSISELIGSLRLYERRLIIEY
• sequence C DRKSISDLIGSLRLA---LLIEF
• sequence D DRK---DLISSLRKA---LLIEW
• 1. Account for all column variations
• A,B and C,D form similar groups
  based on col. 1
• A,C,D based on col. 3
• 2. Count differences between sequences
• A,B 17/23 similar, 6/23 different
• C,D 21/23 similar, 2/23 different
• C and D are very closely related by either method

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What is a tree?

• a graphical representation of the sequence
  similarities among a group of nucleic acid or
  protein sequences

13
?????

• ?????????? ????????? ( Molecular Phylogenetics
  )- ??? ??? ????? ?????? ???????????? ???
  ??????????? ?? ???? ??? ????? ????? ?? ????????
  ????????? ?????? ?????????.
• ????? phylogeny ?????? ?????? ??? ????? ???
  ????? ???' ?? ???????? ( Phylogenetic Tree - PT
  ).

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??????

• ????? ??? ?? taxonomic units , ?''? ??????
  ???? ?????? ?????? ???????? ?? ??????????.
• ????? ???????? ?? operational taxonomic units
  (OTUs)???????? ?? ??????????? ?? ?? ????? (???? ,
  ?? ????? ???).
• ????? ??????? ??????? ?? ??????????? ?? ?? ?????
  ?? ???????? ????? ????? ?????? ??????????? (??
  ????) ???????? ???' ??????? ????????.
• ????? ??? ???????? ?? ?????? ???? ???' ????? ???
  ?- scaled ?- unscaled edges . ?''? ???? ???? ????
  ????? ???? ?????? ( scaled ) ?? ??.

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????? 1
Two alternative representations of a phylogenetic
tree for fife OTUs . (a) Unscaled branches
extant OTUs are lined up and nodes are positioned
proportionally to times of divergence. (b) Scaled
branches lengths of branches are proportional to
the numbers of molecular changes.
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Example 1

• Two alternative representations of a phylogenetic
  tree for fife OTUs .
• (a) Unscaled branches extant OTUs are lined up
  and nodes are positioned proportionally to times
  of divergence.
• (b) Scaled branches lengths of branches are
  proportional to the numbers of molecular changes.

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?????? - ????

• additive tree ??? ?? ?? ?????? ????? ??
  ?"????" ??? ????/?????????? ???????? ???, ???? ,
  ?- (b) ?? ???? ?????, ????? ????? ??? A ?- B ???
  213.
• ??? ???? ????? ??? ???? ????? ( rooted tree ) ??
  ??? ???? ( unrooted tree ) .

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????? 2

• Rooted and
• unrooted phylogenetic trees .
• Arrows indicate the unique path leading from the
  root (R) to OTU D .

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?????? - ????

• additive tree species tree ??? ?? ?????? ????.
• orthologous genes ???? ????? ?????
  ??????????? ?????.
• paralogous genes ???? ????? ????? ????? ????????
  
• homologous genes ???? ????? ???? ????.
• clade ( monophyletic group ) ???? ?????
  ???????? ??? ?????? ?? ???? ???? ??.

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????? 3
Phylogenetic tree of birds , reptiles , and
mammals . The reptiles does constitute a natural
clade since they share ancestors with the birds ,
which are included in the Reptilia . Birds
and crocodiles , on the other hand , constitute a
clade ( Archosauria ) since they
share a common ancestor ( black box ) not shared
any other organism.
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Phylogenetic Prediction

• A phylogenetic analysis of a family of related
  nucleic acid or protein sequences is a
  determination of how the family might have been
  derived during evolution.
• The evolutionary relationships among the
  sequences are depicted by placing the sequences
  as outer branches on a tree.
• The branching relationships on the inner part of
  the tree then reflect the degree to which
  different sequences are related.

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Phylogenetic Prediction

• Two sequences that are very much alike will be
  located as neighboring outside branches and will
  be joined by a common branch beneath them.
• The object of phylogenetic analysis is to
  discover all of the branching relationships in
  the tree and the branch lengths.
• The chapter 6 of David Mounts Bioinformatics
  presents procedures for phylogenetic analysis,
  with an emphasis on the complexity of the problem
  and advice for solving difficult analyses.

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Relationship of Phylogenetic Analysis to
Sequence Alignment

• The commonest method of multiple sequence
  alignment (CLUSTALW) is the progressive alignment
  method.
• The progress is supposed to represent a reliable
  history of the evolutionary changes that have
  occurred.
• A sequence alignment reveals which positions in
  the sequences were conserved and which diverged
  from a common ancestor sequence, as illustrated
  in the next slide.

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Sequence similarity

• Origin of similar sequences.
• Sequences 1 and 2 are each assumed to be derived
  from a common ancestor sequence. Some of the
  ancestor sequence can be inferred from conserved
  positions in the two sequences.
• For positions that vary, there are two possible
  choices at these sites in the ancestor.

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• Clusterization

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Methods of tree reconstruction

• ???? ??? ????? ?????? ??
• ? Distance Matrix Method ( DMM )
• ? Maximum Parsimony Methods
• Maximum Likelihood Methods ?
• Method of Invariants ?
• Mount pp248-254

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Maximum Parsimony Method

• This method predicts the evolutionary tree that
  minimizes the number of steps required to
  generate the observed variation in the sequences.
• A multiple sequence alignment is required to
  predict variation.
• For each aligned position, PT that require the
  smallest number of changes are identified.
• This method is used for sequences that are quite
  similar and for small number of sequences.
• One or more unrooted trees are predicted.

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Maximum Parsimony Method

• The main programs are in the Phylip package
• 1. DNAPARS treats gaps as a fifth nucleotide
  state.
• 2. DNAPENNY branch and bound search
• 3. DNACOMP
• and so on and so fore

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Methods of tree reconstruction

• ???? ??? ????? ?????? ??
• ? Distance Matrix Method ( DMM )
• ? Maximum Parsimony Methods
• Maximum Likelihood Methods ?
• Method of Invariants ?
• ??????? ?????? ???? ????? ?"????" ??? ??????
  (???????).
• ?????? ????? ??? ?????? ???? ???????? ??????.
• ?????? ??? ????? ?? ?????? ????? ??? ????
  (??????) ?? ??????? ??? ????? / ?????????? ??????.

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Least Squares Method

• ????? , ???? ????? NP-complete, ????????? ???? ??
  ??? ?????????? UPGMA
• ( Unweighted Pair Group Method with Arithmetic
  mean ) .
• Input ?? Dij ?? distance matrix,
• ?? Wij ?? weights
• Find the tree T that minimizes SSQ(T)
• n
• SSQ(T) ??wij (Dij dij)²
• i1 i?j

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UPGMA Unweighted Pair Group Method with
Arithmetic mean

• Initialization
• 1. Initialize n clusters with the given species,
  one species per cluster.
• 2. Set the size of each cluster to 1 .
• 3. In the output tree T, assign a leaf for each
  species.

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UPGMA Unweighted Pair Group Method with
Arithmetic mean

• Iteration
• 1. Find the i and j that have the smallest
  distance Dij.
• 2. Create a new cluster - (ij), which has n(ij)
  ni nj members.
• 3. Connect i and j on the tree to a new node,
  which corresponds to the new cluster (ij), and
  give the two branches connecting i and j to (ij)
  length each.

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UPGMA Unweighted Pair Group Method with
Arithmetic mean

• Iteration
• 4. Compute the distance from the new cluster to
  all other clusters (except for i and j, which are
  no longer relevant) as a weighted average of the
  distances from its components
• 5. Delete the columns and rows in D that
  correspond to clusters i and j, and add a column
  and row for cluster (ij), with D(ij),k computed
  as above.
• 6. Return to 1 until there is only one cluster
  left.

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UPGMA Unweighted Pair Group Method with
Arithmetic mean

• Complexity
• The time and space complexity of UPGMA is O(n2),
  since there are n-1 iterations, with O(n) work in
  each one.

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????? 4
(a) The true phylogenetic tree. (b) The
erroneous phylogenetic tree reconstructed by
using the UPGMA method , which does not take
into account the possibility of unequal
substitution rates along different branches .
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Neighbor Joining (NJ)

• ????????? NJ ???? ???? ????? ?????? ??? ??????
  ?? Least Square Method.
• ???? ??? ???? ?? ???? ???? ????????. ?????? ???
  ???? ?? ?- clusters ??? ???? ?????? ??? ???? , ??
  ?????? ???? ???????? .
• ??? ??????? ????????? ???? ????? ?? ?- ancestor
  ????? ?? ??? species ???.
• ??? ????? i????? ui ???? ???? ?????? ??? ?????
  ???' ?????
• 
  
• 
  Dik
  
  
  ? ui ----------
• 
  k?i (n-2)
  
• ?? ??? ?????? ?? ???????? ?? ???? ????? ??????
  (minimum-evolution criterion), ???????? i ?- j
  ?????? ?- cluster ???? ??? ?? ????????? ?? ???
  ?????? ???? ??
• Dij ui uj ??? ???? ?????. ??????? dk,(ij) ??
  ????? ????? ??????? ???' ????? ?? ???? ?????
  ???????? .

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Neighbor Joining (NJ)

• Initialization same as in UPGMA
• 1. Initialize n clusters with the given species,
  one species per cluster.
• 2. Set the size of each cluster to 1 .
• 3. In the output tree T, assign a leaf for each
  species.

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Neighbor Joining (NJ)

• Iteration
• 
  Dik 1. For each species ,
  compute ui ? ------
• 
  k?i (n-2)
  
• 2. Choose the i and j for which Dij ui uj
  is smallest .
• 3. Join clusters i and j to a new cluster
  (ij) , with a corresponding node in T .
  
• Calculate the branch lengths from i and j to
  the new node as
• di,(ij) ½ Dij ½(ui uj)
  , dj,(ij) ½ Dij ½(ui uj).
• 4. Compute the distance between the new cluster
  and each other cluster
• Dik Djk
  - Dij
• D(ij),k
  --------------------
• 
  2

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Neighbor Joining (NJ)

• Iteration
• 5. Delete clusters i and j from the tables, and
  replace them by (ij).
• 6. If more than two nodes ( clusters ) remain ,
  go back to 1. Otherwise , connect the two
  remaining nodes by a branch of length Dij .
• ??? ????? ?? NJ ??? O(n²) , ??? UPGMA.

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Feng-Doolittle algorithm

• Sequence-sequence alignments usual pairwise.
• Sequence-group the highest scoring pairwise
  alignments determines the s-g alignment.
• Group-group again the best pairwise sequence
  alignment among all pairs.
• After an alignment is completed, gap symbols are
  replaced with a neutral X character.