Tree Reconstruction

1
Tree Reconstruction
2
Phylogenetic tree

• Nodes DNA (RNA, mtDNA) sequences, proteins,
  species taxonomic units (TUs)
• Branches ancestral relations between Tus
• Terminal (extant) nodes, leaves OTUs (O for
  operational)

3
Tree reconstruction

• Neighbor joining (Distance) methods
• Maximum parsimony methods (W. Fitch)
• Maximum likelihood methods (J. Felsenstein)
• W. H. Li, Molecular Evolution, 1997

4
Rooted, unrooted trees
C
D
B
E
A
unrooted
D
E
A
B
C
rooted
5
How many geneological trees can we propose for a
given number of terminal nodes
n number of OTUs
6
n NR NU
2 1 1
3 3 1
4 15 3
5 105 15
6 954 105
7 10 395 954
8 135 135 10 395
9 2 027 025 135 135
10 34 459 425 2 027 025
7
Neighbor joining

• UPGMA unweighted pair group method with
  arithmetic mean
• Start from distance matrix
• () Find the minimum distance OTUs
• And merge them
• Update distance matrix, go to ()

8
Maximum parsimony

• Principle of max parsimony searches for a tree
  that requires the smallest number of evolutionary
  changes to explain differences among OTUs
• Informative sites

9

• Assume topology of the tree for each site
  compute minimal number of mutations to explain
  the configuration
• Rule The set at an interior node is the
  intersection of its two immediate descendants if
  the intersection is not empty, otherwise it is
  the union of the descendant sets

10

• The index of the tree is the sum of indices for
  all informative sites
• Go through all possible trees to search for
  optimal one

11
Maximum likelihood

• Need a probabilistic model for nucleotide
  substitution

A,C,T,G 1,2,3,4
time0
We analyze evoution of one site S. Given Si,
time0 what is the probability of Sj, timet
timet
12

• Compute the likelihood function for a given tree
• Go through all possible trees to search for
  optimal one

13
Software
PHYLIP (Phylogeny Inference Package)
Version 3.57c     by Joseph
Felsenstein     July, 1995