Dan Graur

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Methods of Tree Reconstruction

• Dan Graur

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Molecular phylogenetic approaches 1.
distance-matrix (based on distance measures) 2.
character-state (based on character states) 3.
maximum likelihood (based on both character
states and distances)
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DISTANCE-MATRIX METHODS In the distance matrix
methods, evolutionary distances (usually the
number of nucleotide substitutions or amino-acid
replacements between two taxonomic units) are
computed for all pairs of taxa, and a
phylogenetic tree is constructed by using an
algorithm based on some functional relationships
among the distance values.
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Multiple Alignment
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Compute pairwise distances by correcting for
multiple hits at a single sites
Number of differences ? Number of changes
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Distance Matrix
Units Numbers of nucleotide substitutions per
1,000 nucleotide sites
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Distance Methods UPGMA Neighbor-relations N
eighbor joining
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UPGMA Unweighted pair-group method with
arithmetic means
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UPGMA employs a sequential clustering algorithm,
in which local topological relationships are
identified in order of decreased similarity, and
the tree is built in a stepwise manner.
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simple OTUs
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composite OTU
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UPGMA works fine with ultrametric
distances! Q What happens if the distances are
only additive? Q What happens if the distances
are not additive?
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Neighborliness methods The neighbors-relation
method (Sattath Tversky) The neighbor-joining
method (Saitou Nei)
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In an unrooted bifurcating tree, two OTUs are
said to be neighbors if they are connected
through a single internal node.
Neighbors ? Sister Taxa
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A
C
B
D
lt

Four-Point Condition
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The Neighbor Joining Method
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In distance-matrix methods, it is assumed
Similarity ? Kinship
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From Similarity to Relationship

• Similarity Relationship, only if genetic
  distances increase with divergence times.

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From Similarity to Relationship

• Similarities among OTUs can be due to
• Ancestry
• Shared ancestral characters (symplesiomorphies)
• Shared derived characters (synapomorphy)
• Homoplasy
• Convergent events
• Parallel events
• Reversals

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Parsimony Methods
Willi Hennig 1913-1976
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Occams razor
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Pluralitas non est ponenda sine neccesitate.
(Plurality should not be posited without
necessity.) William of Occam or Ockham (ca.
1285-1349) English philosopher Franciscan monk
Excommunicated by Pope John XXII
(Avignon). Responded with a treatise
demonstrating that the pope was heretic.
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MAXIMUM PARSIMONY METHODS Maximum parsimony
involves the identification of a topology that
requires the smallest number of evolutionary
changes to explain the observed differences among
the OTUs under study. In maximum parsimony
methods, we use discrete character states, and
the shortest pathway leading to these character
states is chosen as the best or maximum parsimony
tree. Often two or more trees with the same
minimum number of changes are found, so that no
unique tree can be inferred. Such trees are said
to be equally parsimonious.
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uninformative
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informative
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Inferring the maximum parsimony tree 1.
Identify all the informative sites. 2. For each
possible tree, calculate the minimum number of
substitutions at each informative site. 3. Sum
up the number of changes over all the informative
sites for each possible tree. 4. Choose the tree
associated with the smallest number of changes as
the maximum parsimony tree.
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In the case of four OTUs, an informative site can
only favor one of the three possible alternative
trees. Thus, the tree supported by the largest
number of informative sites is the most
parsimonious tree.
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Variants of Parsimony Wagner-Fitch Unordered.
Character state changes are symmetric and can
occur as often as neccesary. Camin-Sokal
Complete irreversibility. Dollo Partial
irreversibility. Once a derived character is
lost, it cannot be regained. Weighted Some
changes are more likely than others. Transversion
A type of weighted parsimony, in which
transitions are ignored.
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Fitchs (1971) method for inferring nucleotides
at internal nodes
The set at an internal node is the intersection
(?) of the two sets at its immediate descendant
nodes if the intersection is not empty. The set
at an internal node is the union (?) of the two
sets at its immediate descendant nodes if the
intersection is empty. When a union is required
to form a nodal set, a nucleotide substitution at
this position must be assumed to have occurred.
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Fitchs (1971) method for inferring nucleotides
at internal nodes
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total number of substitutions in a tree tree
length
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Searching for the maximum-parsimony tree
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Exhaustive Examine all trees, get the best tree
(guaranteed). Branch-and-Bound Examine some
trees, get the best tree (guaranteed). Heuristic
Examine some trees, get a tree that may or may
not be the best tree.
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Exhaustive
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Branch-and-Bound
Rationale The length of a tree with n1 OTUs can
either be equal to or larger than the length of a
tree with n OTUs.
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Branch -and- Bound
Obtain a tree by a fast method. (e.g., the
neighbor-joining method) Compute numbers of
substitutions (L) for this tree. Turn L into an
upper bound value. Rationale the maximum
parsimony tree must be either equal in length to
L or shorter.
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Branch -and- Bound
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Heuristic
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Likelihood

• Example Coin tossing
• Data 10 tosses 6 heads 4 tails
• Hypothesis Binomial distribution

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LIKELIHOOD IN MOLECULAR PHYLOGENETICS

• The data are the aligned sequences
• The model is the probability of change from one
  character state to another (e.g., Jukes Cantor
  1-P model).
• The parameters to be estimated are Topology
  Branch Lengths

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