1. #30 - Phylogenetics Distance-Based Methods
BCB 444/544
11/02/07
Lecture 30
Phylogenetics – Distance-Based Methods
#30_Nov02
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

2. Required Reading (before lecture)
#30 - Phylogenetics Distance-Based Methods
Required Reading (before lecture)
11/02/07
Wed Oct 30 - Lecture 29
Phylogenetics Basics
Chp 10 - pp
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

3. Assignments & Announcements
#30 - Phylogenetics Distance-Based Methods
Assignments & Announcements
11/02/07
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)
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

4. #30 - Phylogenetics Distance-Based Methods
11/02/07
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

5. BCB 544 Only: New Homework Assignment
#30 - Phylogenetics Distance-Based Methods
11/02/07
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, 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

6. #30 - Phylogenetics Distance-Based Methods
11/02/07
Seminars this Week
BCB List of URLs for Seminars related to Bioinformatics:
Nov 2 Fri - BCB Faculty Seminar 2:10 in 102 ScI
Bob Jernigan BBMB, ISU
Control of Protein Motions by Structure
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

7. #30 - Phylogenetics Distance-Based Methods
11/02/07
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

8. Tree Building Procedure
Choose molecular markers
Perform MSA
Choose a model of evolution
Determine tree building method
Assess tree reliability
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

9. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

10. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

11. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

12. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

13. Multiple SubstitutionsC A T G
Just because we only see one difference, does not mean that there was only one evolutionary event
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

14. Multiple SubstitutionsA T G
Just because we only see no difference, does not mean that there were no evolutionary events
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

15. Choosing Substitution Models
Statistical models of evolution are used to correct for the multiple substitution problem
Focus on DNA models
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

16. Can be used to correct for multiple substitutions
Jukes-Cantor Model
Jukes-Cantor model assumes all nucleotides are substituted with equal probability
Can be used to correct for multiple substitutions
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

17. Many Other Models
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

18. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

19. This variation is called among-site rate heterogeneity
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

20. Chp 11 – Phylogenetic Tree Construction Methods and Programs
#30 - Phylogenetics Distance-Based Methods
11/02/07
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods
BCB 444/544 Fall 07 Dobbs

21. Two main categories of tree building methods Distance-based
Tree Construction
Two main categories of tree building methods
Distance-based
Overall similarity between sequences
Character-based
Consider the entire MSA
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

22. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

23. Distance Matrices a a 0 b 6 0 c 7 3 0 d 14 10 9 0 a b c d b c d 1 2 35 6 7 8
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

24. Distance-Based Methods
Two ways to construct a tree based on a distance matrix
Clustering
Optimality
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

25. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

26. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

27. UPGMA Example
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

28. UPGMA Example
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

29. UPGMA Example
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

30. UPGMA Example
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

31. Implicitly finds a pair of neighboring taxa
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

32. 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”
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

33. The r-value for a sequence is:
Neighbor Joining
The r-value for a sequence is:
The sum of the distances between sequence i and all other sequences
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

34. The transformed r-value for a sequence is:
Neighbor Joining
The transformed r-value for a sequence is:
Where n is the number of taxa
Transformed r-values are used to determine the distance of a taxon to the nearest node
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

35. The converted distance between two sequences is:
Neighbor Joining
The converted distance between two sequences is:
These converted distances are used in building the tree
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

36. 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:
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

37. Neighbor Joining ExampleC
0.40
0.35
0.45 D
0.60
0.70
0.55
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

38. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

39. Neighbor Joining Example
Step 2: Compute converted distances
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

40. Neighbor Joining Example
Step 3: Fill out converted distance matrix A B C
-1.05 -1 D
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

41. 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 B ? A A U B ? D C
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

42. Neighbor Joining Example
Step 5: Compute branch lengths
Use the equation for computing the distance from a taxa to a node
0.15 A U B
0.25
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

43. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

44. Neighbor Joining Example
Our reduced distance matrix: U C
0.20 D
0.45
0.55
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

45. Neighbor Joining Example
From here, we go back to step 1
Continue until all taxa have been decomposed from the star tree
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

46. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

47. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

48. Similar to Fitch-Margoliash, but uses a different optimality criterion
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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods

49. 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
BCB 444/544 F07 ISU Terribilini #30- Phylogenetics - Distance-Based Methods