Dan Graur

1
Molecular Phylogenetics

• Dan Graur

2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
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)
7
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.
8
Multiple Alignment
9
Distance Matrix
Units Numbers of nucleotide substitutions per
1,000 nucleotide sites
10
Distance Methods UPGMA Neighbor-relations N
eighbor joining
11
UPGMA Unweighted pair-group method with
arithmetic means
12
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.
13
simple OTUs
14
composite OTU
15
(No Transcript)
16
(No Transcript)
17
A1
A Use a method that does not assume
ultrametricity.
18
Neighborliness methods The neighbors-relation
method (Sattath Tversky) The neighbor-joining
method (Saitou Nei)
19
In an unrooted bifurcating tree, two OTUs are
said to be neighbors if they are connected
through a single internal node.
20
(No Transcript)
21
A
C
B
D
lt

Four-Point Condition
22
(No Transcript)
23
(No Transcript)
24
In distance-matrix methods, it is assumed
Similarity ? Kinship
25
From Similarity to Relationship

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

26
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

27
(No Transcript)
28
Parsimony Methods
Willi Hennig 1913-1976
29
Occams razor
30
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.
31
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.
32
(No Transcript)
33
(No Transcript)
34
uninformative
35
informative
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
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.
41
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.
42
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.
43
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.
44
(No Transcript)
45
Parsimony is based solely on synapomorphies
46
(No Transcript)
47
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.
48
Fitchs (1971) method for inferring nucleotides
at internal nodes
49
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.
number of unions minimum number of
substitutions
50
Fitchs (1971) method for inferring nucleotides
at internal nodes
51
(No Transcript)
52
total number of substitutions in a tree tree
length
53
Searching for the maximum-parsimony tree
54
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.
55
Exhaustive
56
Branch -and- Bound
57
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.
58
Branch -and- Bound
59
Heuristic
60
(No Transcript)
61
(No Transcript)
62
Likelihood

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

63
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

64
(No Transcript)
65
Background Maximum Likelihood
How to calculate ML score for a tree
1... j ... ...N ... ...
... Seq x C...GGACGTTTA...C Seq y
C...AGATCTCTA...C ... ... ...
66
Background Maximum Likelihood
Calculate likelihood for a single site j given
tree
where