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Molecular Phylogenetics. Dan Graur. 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). DISTANCE-MATRIX METHODS

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slide6
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)

slide7
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.

distance matrix
Distance Matrix*

*Units: Numbers of nucleotide substitutions per 1,000 nucleotide sites

slide10
Distance Methods:

UPGMA Neighbor-relations

Neighbor joining

slide11
UPGMA

Unweighted pair-group method with arithmetic means

slide12
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.
slide18
Neighborliness methods

The neighbors-relation method (Sattath & Tversky)

The neighbor-joining method (Saitou & Nei)

slide19
In an unrooted bifurcating tree, two OTUs are said to be neighbors if they are connected through a single internal node.
slide20
If we combine OTUs A and B into one composite OTU, then the composite OTU (AB) and the simple OTU C become neighbors.
slide21
A

+

+

+

C

B

D

<

=

Four-Point Condition

from similarity to relationship
From Similarity to Relationship
  • Similarity = Relationship, only if genetic distances increase with divergence times (monotonic distances).
slide26
From Similarity to Relationship

Similarities among OTUs can be due to:

  • Ancestry:
    • Shared ancestral characters (plesiomorphies)
    • Shared derived characters (synapomorphy)
  • Homoplasy:
    • Convergent events
    • Parallel events
    • Reversals
slide28
Parsimony Methods:

Willi Hennig

1913-1976

slide29
“Pluralitas non est ponenda sine neccesitate.”

(Plurality should not be posited without necessity.)

Occam’s razor

William of Occam or Ockham (ca. 1285-1349)

English philosopher & Franciscan monk

Excommunicated by Pope John XXII in 1328.

Officially rehabilitated by Pope Innocent VI in 1359.

slide30
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.

slide39
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.

slide40
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.

slide41
With more than 4 OTUs, an informative site may favor more than one tree, and the maximum parsimony tree may not necessarily be the one supported by the largest number of informative sites.
slide42
The informative sites that support the internal branches in the inferred tree are deemed to be synapomorphies.

All other informative sites are deemed to be homoplasies.

slide46
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.

slide48
Fitch’s (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.

number of unions = minimum number of substitutions

slide49
4 substitutions

3 substitutions

Fitch’s (1971) method for inferring nucleotides at internal nodes

slide53
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.

slide54
Ascendant tree 2

Descendant trees of tree 2

Exhaustive

slide55
Branch

-and-

Bound

slide56
Branch

-and-

Bound

Obtain a tree by a fast method. (e.g., the neighbor-joining method)

Compute minimum number of substitutions (L).

Turn L into an upper bound value.

Rationale: (1) the maximum parsimony tree must be either equal in length to L or shorter. (2) A descendant tree is either equal in length or longer than the ascendant tree.

slide57
Branch

-and-

Bound

likelihood
Likelihood
  • Example: Coin tossing
  • Data: Outcome of 10 tosses: 6 heads + 4 tails
  • Hypothesis: Binomial distribution
likelihood in molecular phylogenetics
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
background maximum likelihood
Background: Maximum Likelihood

How to calculate ML score for a tree :

1... j ... ...N

... ... ...

Seq x: C...GGACGTTTA...C

Seq y: C...AGATCTCTA...C

... ... ...

background maximum likelihood1
R: root

A

C

B

Background: Maximum Likelihood

Calculate likelihood for a single site j given tree :

where

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