BCB 444/544
Lecture 30
Phylogenetics – Distance-Based
Methods
#30_Nov02
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
11/02/07
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Required Reading
(before lecture)
Wed Oct 30 - Lecture 29
Phylogenetics Basics
• Chp 10 - pp 127 - 141
Thurs Oct 31 - Lab 9
Gene & Regulatory Element Prediction
Fri Oct 30 - Lecture 30
Phylogenetic – Distance-Based Methods
• Chp 11 - pp 142 – 169
Mon Nov 5 - Lecture 31
Phylogenetics – Parsimony and ML
• Chp 11 - pp 142 - 169
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Assignments & Announcements
Mon Oct 29 - HW#5
HW#5 = Hands-on exercises with phylogenetics
and tree-building software
Due: Mon Nov 5
(not Fri Nov 1 as previously posted)
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BCB 544 "Team" Projects
Last week of classes will be devoted to Projects
• Written reports due:
• Mon Dec 3 (no class that day)
• Oral presentations (20-30') will be:
• Wed-Fri Dec 5,6,7
• 1 or 2 teams will present during each class period
 See Guidelines for Projects posted online
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BCB 544 Only:
New Homework Assignment
544 Extra#2
Due:
√PART 1 - ASAP
PART 2 - meeting prior to 5 PM Fri Nov 2
Part 1 - Brief outline of Project, email to Drena & Michael
after response/approval, then:
Part 2 - More detailed outline of project
Read a few papers and summarize status of problem
Schedule meeting with Drena & Michael to discuss ideas
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Seminars this Week
BCB List of URLs for Seminars related to Bioinformatics:
http://www.bcb.iastate.edu/seminars/index.html
• Nov 2 Fri - BCB Faculty Seminar 2:10 in 102 ScI
• Bob Jernigan BBMB, ISU
• Control of Protein Motions by Structure
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Chp 10 - Phylogenetics
SECTION IV MOLECULAR PHYLOGENETICS
Xiong: Chp 10 Phylogenetics Basics
•
•
•
•
•
•
Evolution and Phylogenetics
Terminology
Gene Phylogeny vs. Species Phylogeny
Forms of Tree Representation
Why Finding a True Tree is Dificult
Procedure of Building a Phylogenetic Tree
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Tree Building Procedure
• Choose molecular markers
• Perform MSA
• Choose a model of evolution
• Determine tree building method
• Assess tree reliability
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Choice of Molecular Markers
• Very closely related organisms - nucleic acid
sequence will show more differences
• For individuals within a species - faster mutation
rate is in noncoding regions of mtDNA
• More distantly related species - slowly evolving
nucleic acid sequences like ribosomal RNA or
protein sequences
• Very distantly related species - use highly
conserved protein sequences
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Multiple Sequence Alignment
• Most critical step in tree building - cannot
build correct tree without correct
alignment
• Should build alignments with multiple
programs, then inspect and compare to
identify the most reasonable one
• Most alignments need manual editing
• Make sure important functional residues align
• Align secondary structure elements
• Use full alignment or just parts
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Automatic Editing of Alignments
• Rascal and NorMD – correct alignment
errors, remove potentially unrelated or
highly divergent sequences
• Gblocks – detect and eliminate poorly
aligned positions and divergent regions
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How do we measure divergence
between sequences?
• Simple measure – just count the
number of substitutions observed
between the sequences in the MSA
• Problem – number of substitutions may
not represent the number of
evolutionary events that actually
occurred
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Multiple Substitutions
C
A
T
G
A
Just because we only see one difference, does not
mean that there was only one evolutionary event
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Multiple Substitutions
A
A
T
G
A
Just because we only see no difference, does not
mean that there were no evolutionary events
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Choosing Substitution Models
• Statistical models of evolution are
used to correct for the multiple
substitution problem
• Focus on DNA models
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Jukes-Cantor Model
• Jukes-Cantor model
assumes all
nucleotides are
substituted with
equal probability
• Can be used to
correct for multiple
substitutions
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Many Other Models
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Evolutionary Models for Protein
Sequences
• PAM and JTT substitution matrices
already take into account multiple
substitutions
• There are also models similar to
Jukes-Cantor for protein sequences
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What about differences in mutation rates
between positions within a sequence?
• One of our assumptions was that all positions in a
sequence are evolving at the same rate
• Bad assumption
• Third position in a codon changes with higher frequency
• In proteins, some amino acids can change and others
cannot
• This variation is called among-site rate
heterogeneity
• Many tree building programs have parameters
meant to deal with this problem – adds to
complexity of getting the correct tree
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Chp 11 – Phylogenetic Tree Construction Methods
and Programs
SECTION IV MOLECULAR PHYLOGENETICS
Xiong: Chp 11 Phylogenetic Tree Construction Methods
and Programs
•
•
•
•
Distance-Based Methods
Character-Based Methods
Phylogenetic Tree Evaluation
Phylogenetic Programs
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Tree Construction
• Two main categories of tree building
methods
• Distance-based
• Overall similarity between sequences
• Character-based
• Consider the entire MSA
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Distance-Based Methods
• Given a MSA and an evolutionary
model, calculate the distance between
all pairs of sequences
• Construct distance matrix
• Construct phylogenetic tree based on
the distance matrix
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Distance Matrices
a
a
b
c
0
6
7
0
3
d
14
a
10
b
b
0
9
c
0
d
c
d
0 1 2 34 5 6 7 8
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Distance-Based Methods
• Two ways to construct a tree based on
a distance matrix
• Clustering
• Optimality
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Clustering-Based Methods
• E.g., UPGMA and Neighbor-Joining
• A cluster is a set of taxa
• Interspecies distances translate into
intercluster distances
• Clusters are repeatedly merged
• “Closest” clusters merged first
• Distances are recomputed after merging
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UPGMA
• UPGMA – Unweighted Pair Group Method
Using Arithmetic Average
• Uses molecular clock assumption – all taxa
evolve at a constant rate and are equally
distant from the root (ultrametric tree)
• This assumption is usually wrong
• So why use UPGMA?
• Very fast
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UPGMA Example
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UPGMA Example
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UPGMA Example
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UPGMA Example
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Neighbor Joining
• Idea: Find a pair of taxa that are
close to each other but far from
other taxa
• Implicitly finds a pair of neighboring
taxa
• No molecular clock assumption
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Neighbor Joining
• NJ corrects for unequal evolutionary
rates between sequences by using a
conversion step
• The conversion step requires
calculation of “r-values” and
“transformed r-values”
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Neighbor Joining
The r-value for a sequence is:
ri   dij
The sum of the distances between
sequence i and all other sequences
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Neighbor Joining
The transformed r-value for a sequence is:
ri
r 'i 
n2
Where n is the number of taxa
Transformed r-values are used to
determine the distance of a taxon to
the nearest node
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Neighbor Joining
The converted distance between two
sequences is:
1
d 'ij  d ij  ri  rj 
2
These converted distances are used
in building the tree
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Neighbor Joining
The final equation we need is for computing the
distance from a new cluster to each taxa.
Assume taxa i and j were merged into a cluster
u. The distance from taxa i to cluster u is:
d iu

d  r ' r ' 

ij
i
j
2
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Neighbor Joining Example
A
B
B
0.40
C
0.35
0.45
D
0.60
0.70
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C
0.55
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Neighbor Joining Example
• Initialize tree into a star shape with
all taxa connected to the center
• Step 1: Compute r-values and
transformed r-values for all taxa
rA  d AB  d AC  d AD  0.4  0.35  0.6  1.35
rA
1.35
r'A 

 0.675
42
2
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Neighbor Joining Example
• Step 2: Compute converted distances
1
d ' AB  d AB  rA  rB 
2
1
 0.4  1.35  1.55
2
 1.05
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Neighbor Joining Example
• Step 3: Fill out converted distance
matrix
A
B
B
-1.05
C
-1
-1
D
-1
-1
C
-1.05
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Neighbor Joining Example
• Step 4: Create a node by merging closest taxa
• In this example, the distance between A and B is
the same as the distance between C and D
• We can pick either pair to start with
• Let’s pick A and B and create a node called U
A
B
?
U
C
D
?
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A
B
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Neighbor Joining Example
• Step 5: Compute branch lengths
• Use the equation for computing the distance from
a taxa to a node
d AU

d AB  r ' A r ' B 

2

0.4  0.675  0.775

2
 0.15
0.15
U
0.25
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A
B
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Neighbor Joining Example
• Step 6: Construct reduced distance matrix by
computing converted distances from each taxa to
the new node U
• In UPGMA, we simply calculated the average
d CU


d AC  dUA   d BC  dUB 

2


0.35  0.15  0.45  0.25

 0 .2
2
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Neighbor Joining Example
Our reduced distance matrix:
U
C
0.20
D
0.45
C
0.55
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Neighbor Joining Example
• From here, we go back to step 1
• Continue until all taxa have been decomposed from
the star tree
•
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Optimality-Based Methods
• Clustering methods produce a single tree with no
ability to judge how good it is compared to
alternative tree topologies
• Optimality-based methods compare all possible
tree topologies and select a tree that best fits the
distance matrix
• Two algorithms:
• Fitch-Margoliash
• Minimum evolution
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Fitch-Margoliash
• Selects best tree among all possible trees based on
minimum deviation between distances calculated in
the tree and distances in the distance matrix
• Basically, a least squares method
• Dij = distance between i and j in matrix
• dij = distance between i and j in tree
• Objective: Find tree that minimizes

1i jn
2
(Dij  dij )
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Minimum Evolution
• Similar to Fitch-Margoliash, but uses a
different optimality criterion
• Searches for a tree with the minimum total
branch length
• This is an indirect way of achieving the best
fit of the branch lengths with the original
data
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Summary of Distance-Based Methods
• Clustering-based methods:
• Computationally very fast and can handle large datasets
that other methods cannot
• Not guaranteed to find the best tree
• Optimality-based methods:
• Better overall accuracies
• Computationally slow
• All distance-based methods lose all sequence
information and cannot infer the most likely state
at an internal node
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