1. Phylogenetic trees Sushmita Roy BMI/CS 576
Oct 1st, 2013

2. Key concepts in this section
What are phylogenies or phylogenetic trees?
Terminology such as extant, ancestral, branch point, branch length, orthologs, paralogs, taxon
Why build phylogenetic trees?
How to build phylogenetic trees?
Distance-based methods
Parsimony methods
Minimize the number of changes
Probabilistic methods
Find the tree that best explains the data using probabilistic models

3. What are phylogenetic trees?
A tree that describes evolutionary relationships among entities
Species, genes, strains
Leaves represent extant entities
Internal nodes represent ancestral species
Such a tree is inferred from observations in existing organisms.

4. Tree of life aims to represents the phylogeny of all species on earth
From

5. Phylogenetic tree of 29 mammals
Lindbald-Toh et al, 2011, Nature

6. Why phylogenetic trees?
Understand how organisms are related
Do humans and chimpanzees share a common ancestor or do humans and gorillas?
Ask how closely organisms are related
Humans and chimpanzees shard a common ancestor 5mya
Provide insight into the evolutionary history of species
How specific functions have evolved
Language evolution
Identify signatures of conservation of sequence
Conjecture the fate of specific regions of the genome
Will the human Y disappear?
Inform multiple sequence alignments

7. Orthologs and paralogs
Two sequences in two species that have a a common ancestor
Diverged due to a speciation event
Used to create a “species tree”
Paralogs:
Two sequences in the same species that arose from a gene duplication event
Captured in a “gene tree”.

8. Phylogenetic tree basics
Leaves represent things (genes, species, individuals/strains) being compared
the term taxon (taxa plural) is used to refer to these when they represent species and broader classifications of organisms
For example if taxa are species, the tree is a species tree
Internal nodes are hypothetical ancestral units
Phylogenetic trees can be rooted or unrooted
the root represents the common ancestor
In a rooted tree, path from root to a node represents an evolutionary path
Gives directionality to evolutionary time
An unrooted tree specifies relationships among taxa, but not from an ancestor

9. Tree basics Internal node: Ancestral 2 5 9 8 8 6 Branch length 6 7 71 4 1 2 3 4 5 3
Leaf node: Extant
Unrooted tree
Rooted tree
Each tree topology represents a different evolutionary history
For a species tree, internal nodes represent speciation events

10. Internal nodes represent ancestral species
Tree of Life project (

11. Rooting a tree
An unrooted tree can be converted to a rooted tree using an outgroup species
Outgroup: a species known to be more distantly related all the species than each of the species themselves
Find the branch where the outgroup is selected to be added
That gives the root

12. Tree counting A rooted tree with n leaf nodes has
n-1 internal nodes
2n-2 edges/branches
An unrooted tree with n leaf nodes has
n-2 internal nodes
2n-3 edges/branches
A root can be added to any of these branches to give 2n-3 rooted trees for any unrooted tree
For three taxa there is one unrooted tree and three rooted trees

13. Tree counting 1 1 3 3 1 2 3 2 2 1 An unrooted tree 3 3 2 1 2 1 3 2 1 3
Possible positions for root
Rooted trees

14. Tree counting
Instead of adding a root we could add a branch for the n+1th taxon 4 1 1 1 3 3 3 2 2 2 1 1 4 3 2 3 2 1 1 3 3 2 2 4

15. Tree counting With four nodes, we have five branches
Each of the branches can give rise to five trees of six nodes
Thus we have 3*5 trees
In general for n nodes we can have
(1)(3)(5)..(2n-5) unrooted trees

16. Constructing phylogenetic trees
Three types of methods
Distance based methods
Parsimony methods
Probabilistic approaches
Most methods start with pairwise distance methods
We have already seen one method!

17. Methods for phylogenetic tree reconstruction
Distance-based methods
UPGMA
Neighbor joining
Assume additivity and sometimes a “molecular clock”
Additivity means we can add up the branch lengths of the tree connecting two nodes and get their distances.
Alignment-based methods
Parsimony
Probabilistic

18. Defining distance between sequences
Fractional alignment difference for two sequences i and j
pij = mij/Lij
Gives an estimate of changes per site
mij: Number of mismatches
Assumes that changes have happened only once
Underestimates the distance between sequences
Assumes all sequences change at the same rate
Jukes Cantor distance
The simplest, evolutionary distance

19. UPGMA relies on the molecular clock assumption
Sequences diverge at the same rate at different points in the phylogeny
Distance from any leaf to root is the same.
If this is true the data is said to be ultrametric

20. The molecular clock assumption & ultrametric data
Ultrametric data: for any triplet of sequences, i, j, k, the distances are either all equal, or two are equal and the remaining one is smaller A B C D E 8 5 3 4 3
d_ij <= max(d_ik, d_jk) 2 1 A E D B C

21. Problems with the molecular clock assumption3 2 4 2 3 4 1 1
Constructed by UPGMA
Actual tree

22. Neighbor joining The ultra-metric property is too strong
Most sequences diverge at different rates
A more relaxed requirement is that of additivity
Distance between a pair of species/nodes is equal to the sum of the branch lengths
Uses a similar idea to construct trees as UPGMA
That is consider pairs of nodes and joins them
Produces unrooted trees

23. How to select nodes for merging?
Given all pairwise distances for n sequences
dij denote the distance between node i and j
Should we select node pairs with the smallest dij? A B C D
0.4
0.1
Should we merge A and B?

24. Need to correct for long branches
L: current set of leaves
ri : Average distance from other nodes

25. Defining the distance to a new node
dkm? i m k j
New node
Given dij, dim, djm, how to calculate distance to new node k?

26. Algorithm for NJ Initialization Iteration Terminate
T be set the of leaf nodes
L = T
Estimate ri for all i in L
Estimate Dij
Iteration
Pick a pair i, j from L such that Dij is smallest
Define new node k
Estimate dik, djk, add edge between k and i, and between k to j
Add k to T, remove i and j from L
Estimate Dmn for all nodes m, n in L
Terminate
If L has two nodes, add the edge between these two.

27. An example with neighbor joining
Consider 5 sequences: A, B, C, D, E
Distance matrix
What is the tree inferred by the Neighbor joining algorithm? B C D E A 5 4 9 8 10 7 6 B C D E

28. Can we check for additivity?
Check for additivity: For four leaves, i, j, k, l and the distances dij, dik, dil, djk, djl, dkl j i l k
The three sums of two distances j j i j i i l l l k k k
Should be such that two of these are equal, and larger than the third.