Molecular phylogenetics
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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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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

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


Distance Methods:

UPGMA Neighbor-relations

Neighbor joining


UPGMA

Unweighted pair-group method with arithmetic means


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.





Neighborliness methods

The neighbors-relation method (Sattath & Tversky)

The neighbor-joining method (Saitou & Nei)


In an unrooted bifurcating tree, two OTUs are said to be neighbors if they are connected through a single internal node.


If we combine OTUs A and B into one composite OTU, then the composite OTU (AB) and the simple OTU C become neighbors.


A composite OTU (AB) and the simple OTU C become neighbors.

+

+

+

C

B

D

<

=

Four-Point Condition


In distance-matrix methods, it is assumed: composite OTU (AB) and the simple OTU C become neighbors.

Similarity Kinship


From similarity to relationship
From Similarity to Relationship composite OTU (AB) and the simple OTU C become neighbors.

  • Similarity = Relationship, only if genetic distances increase with divergence times (monotonic distances).


From Similarity to Relationship composite OTU (AB) and the simple OTU C become neighbors.

Similarities among OTUs can be due to:

  • Ancestry:

    • Shared ancestral characters (plesiomorphies)

    • Shared derived characters (synapomorphy)

  • Homoplasy:

    • Convergent events

    • Parallel events

    • Reversals


Parsimony Methods: composite OTU (AB) and the simple OTU C become neighbors.

Willi Hennig

1913-1976


“Pluralitas non est ponenda sine neccesitate.” composite OTU (AB) and the simple OTU C become neighbors.

(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.


MAXIMUM PARSIMONY METHODS composite OTU (AB) and the simple OTU C become neighbors.

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.


invariant composite OTU (AB) and the simple OTU C become neighbors.


variant composite OTU (AB) and the simple OTU C become neighbors.


uninformative composite OTU (AB) and the simple OTU C become neighbors.


informative composite OTU (AB) and the simple OTU C become neighbors.


Inferring the maximum parsimony tree: composite OTU (AB) and the simple OTU C become neighbors.

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.


In the case of four OTUs, an informative site composite OTU (AB) and the simple OTU C become neighbors. 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.


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.


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.


Parsimony is based solely on synapomorphies the inferred tree are deemed to be


Variants of Parsimony the inferred tree are deemed to be

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.



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


4 substitutions internal nodes

3 substitutions

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




Exhaustive internal nodes = 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.


Ascendant tree 2 internal nodes

Descendant trees of tree 2

Exhaustive


Branch internal nodes

-and-

Bound


Branch internal nodes

-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.


Branch internal nodes

-and-

Bound


Heuristic internal nodes


Likelihood
Likelihood internal nodes

  • Example: Coin tossing

  • Data: Outcome of 10 tosses: 6 heads + 4 tails

  • Hypothesis: Binomial distribution


Likelihood in molecular phylogenetics
LIKELIHOOD IN MOLECULAR PHYLOGENETICS internal nodes

  • 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 internal nodes

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 internal nodes

A

C

B

Background: Maximum Likelihood

Calculate likelihood for a single site j given tree :

where


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