Molecular Phylogenetics

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) 6

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

GCGGCTCA TCAGGTAGTT GGTG-G GCGGCCCA TCAGGTAGTT GGTG-G GCGTTCCA TC--CTGGTT GGTGTG GCGTCCCA TCAGCTAGTT GTTG-G GCGGCGCA TTAGCTAGTT GGTG-A *** ** * * *** * ** Spinach Rice Mosquito Monkey Human

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Spinach Rice Mosquito Monkey Human Spinach 0.0

Distance Matrix

* Rice 9 0.0

Mosquito Monkey Human 106 91 86 118 122 122 0.0

55 0.0

51 3 0.0

*

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

Distance Methods:

UPGMA Neighbor-relations Neighbor joining

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UPGMA

Unweighted pair-group method with arithmetic means

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UPGMA employs a

sequential clustering algorithm

manner. , in which local topological relationships are identified in order of decreased similarity, and the tree is built in a stepwise 12

simple OTUs

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composite OTU

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UPGMA only works if the distances are strictly ultrametric.

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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.

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If we combine OTUs A and B into one composite OTU, then the composite OTU (AB) and the simple OTU C become neighbors. 20

+ A B < C D + = +

Four-Point Condition

d

(

A

,

B

) 

d

(

C

,

D

) 

d

(

A

,

C

) 

d

(

B

,

D

) 

d

(

A

,

D

) 

d

(

B

,

C

)

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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 (monotonic distances). 25

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 26

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Parsimony Methods:

Willi Hennig

1913-1976

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“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.

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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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Sequences 1 1 2 3 4 A A A A 2 A G G G 3 G C A A 4 A C T G G G A A * Site 5 6 T T T T 7 T T C C * 8 C C C C 9 A T A T * invariant

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Sequences 1 1 2 3 4 A A A A 2 A G G G 3 G C A A 4 A C T G G G A A * Site 5 6 T T T T 7 T T C C * 8 C C C C 9 A T A T * variant

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Sequences 1 1 2 3 4 A A A A 2 A G G G 3 G C A A 4 A C T G G G A A * Site 5 6 T T T T 7 T T C C * 8 C C C C 9 A T A T * uninformative

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Sequences 1 1 2 3 4 A A A A 2 A G G G 3 G C A A 4 A C T G G G A A * Site 5 6 T T T T 7 T T C C * 8 C C C C 9 A T A T * 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. 40

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. 41

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

.

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Parsimony is based solely on synapomorphies

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

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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

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Fitch’s (1971) method for inferring nucleotides at internal nodes 4 substitutions 3 substitutions

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total number of substitutions in a tree =

tree length

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Searching for the maximum-parsimony tree



Number of OTUs Number of possible rooted tree

 2 3 4 5 8 9 6 7 1 3 15 105 954 10,395 135,135 2,027,025 10 15 34,459,425 213,458,046,676,875

20 8,200,794,532,637,891,559,375

 52

Exhaustive = Examine all the best tree (guaranteed).

trees, get 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

Ascendant tree 2 Descendant trees of tree 2 54

Branch -and Bound

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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 tree.

L

or shorter. (2) A descendant tree is either equal in length or longer than the ascendant 56

Branch -and Bound

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Heuristic

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Likelihood

L

=

P

(

data

|

tree

) • Example: • Data: Coin tossing Outcome of 10 tosses: 6 heads + 4 tails • Hypothesis: Binomial distribution 61

• • •

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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Background: Maximum Likelihood max  [

P

(

data

|  )]

L



P

(

data

|  ) 1... j ... ...N

... ... ...

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

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

... ... ...

ln

L

 ln

L

( 1 )  ...

 ln

L

(

j

)  ...

 ln

L

(

N

) 64

B Background: Maximum Likelihood Calculate likelihood for a single site

j

 R: root

L

(

j

) 

m

 

S



m CL

(

R



m

) A where

S

 {

A

,

C

,

G

,

T

}

v AB v AC

C

CL

(

A



i

)     

k



S

  

l



S P ik P il

(

v

(

v AB AC

)

CL

(

B

)

CL

(

C

 

k l

)   )   65