1. Phylogenetic Trees - Parsimony Tutorial #13
© Ydo Wexler & Dan Geiger .

2. Phylogenetic Trees - Reminder
phylogenetic tree: diagram showing evolutionary lineages of species/genes
why construct trees?
to understand lineage of various species
to understand how various functions evolved
to understand multiple alignments

3. Phylogenetic Trees - Methods
There are several methods with which we estimate how good a tree describes the data
(and thus the evolution process)
Distance based methods
Parsimony
Likelihood

4. Phylogenetic Trees - Reminder
leaves represent objects (genes, species) being compared
internal nodes are hypothetical ancestral units
in a rooted tree, path from root to a node represents an evolutionary path
an unrooted tree specifies relationships among objects, but not evolutionary paths

5. Parsimony Based Approches
given: character-based data
do: find a tree that explains the data with a minimal number of changes

6. Parsimony Example
there are various trees that could explain the phylogeny of the following sequences: AAG, AAA, GGA, AGA
AAA
AGA
AAG
GGA
AAA
AGA
AAG
GGA
parsimony prefers the second tree because it requires less substitution events

7. Parsimony Based Approches
usually these approaches involve two separate components:
A search through the space of trees
A procedure to find the minimum number of changes needed to explain the data (for a given tree topology)

8. Fitch’s Algorithm
traverse tree from leaves to root determining set of possible states (e.g. nucleotides) for each internal node
traverse tree from root to leaves picking ancestral states for internal nodes

9. Fitch’s Algorithm – Step 1
do a post-order (from leaves to root) traversal of tree
Determine possible states Ri of internal node i with children j and k

10. Fitch’s Algorithm – Step 1
# of changes = # union operations T T
AGT CT GT C T G T A T

11. Fitch’s Algorithm – Step 2
do a pre-order (from root to leaves) traversal of tree
select state rj of internal node j with parent i

12. Fitch’s Algorithm – Step 2CT C A G
AGT GT T CT C A G
AGT GT T CT C A G
AGT GT T CT C A G
AGT GT T CT C A G
AGT GT T CT C A G
AGT GT

13. Weighted Version of Fitch’s Algorithm
instead of assuming all state changes are equally likely, use different costs S(a,b) for different changes
1st step of algorithm is to propagate costs up through tree

14. Weighted Version of Fitch’s Algorithm
want to determine min. cost Ri(a)
of assigning character a to node i
for leaves:

15. Weighted Version of Fitch’s Algorithm
want to determine min. cost Ri(a)
of assigning character a to node i
for internal nodes: a i j k b

16. Weighted Version of Fitch’s Algorithm – Step 2
do a pre-order (from root to leaves) traversal of tree
select minimal cost character for root
For each internal node j, select character that produced minimal cost at parent i

17. Exploring the Space of Trees
we’ve considered how to find the minimum number of changes for a given tree topology
need some search procedure for exploring the space of tree topologies
Given n sequences there are Possible rooted trees

18. Exploring the Space of Trees
taxa (n) # trees
4 15
,135
,405,375

19. Limitations of Sequence Based Phylogenetic trees
Sequences must be Orthologues, NOT Paralogues to draw evolutionary inferences.
Will not work with Recombinational DNA transfer between genomes (common in viruses and Prokaryotes).
Does not apply to larger DNA sequences involving DNA crossovers (“Family Trees”).