1. Phylogenies and the Tree of Life
Basic Principles of Phylogenetics
Parsimony - Distance - Likelihood
Topologies - Super Trees - Testing
Networks
Challenges
Empirical Investigations:
Molecular Clock
Biochemical rates
Selection Strength
Tree shapes
Branching Patterns
Rootings
Open Questions

2. Central Principles of Phylogeny Reconstruction
TTCAGT
TCCAGT
GCCAAT
Parsimony s2 s1 s4 s3 1 2
Total Weight: 3 s2 s1 s4 s3 1
3 2
0.4
0.6
0.3
0.7
1.5
Distance s2 s1 s4 s3
L=3.1*10-7
Parameter estimates
Likelihood

3. From Distance to Phylogenies
What is the relationship of a, b, c, d & e?
a b c d e a b c d e
Molecular clock
No Molecular clock a c b d e 7 4 3 2 6 1 11 7 8 5 a c b d e a c b 7 8 b e 14

4. Enumerating Trees: Unrooted & valency 32 1 3 1 2 3 4 1 4 2 3 1 2 3 4 1 2 3 4 5
Recursion: Tn= (2n-5) Tn-1
Initialisation: T1= T2= T3=1 4 5 6 7 8 9 10 15 20 3
105
945
10345

5. Heuristic Searches in Tree Space
Nearest Neighbour Interchange T2 T1 T4 T3 T2 T1 T4 T3 T2 T1 T4 T3
Subtree regrafting T4 T3 s4 s5 s6 s1 s2 s3 T4 T3 s4 s5 s6 s1 s2 s3
Subtree rerooting and regrafting T4 T3 s4 s5 s6 s1 s2 s3 T4 T3 s4 s5 s6 s1 s2 s3

6. Assignment to internal nodes: The simple way.C A T G ?
What is the cheapest assignment of nucleotides to internal nodes, given some (symmetric) distance function d(N1,N2)??
If there are k leaves, there are k-2 internal nodes and 4k-2 possible assignments of nucleotides. For k=22, this is more than 1012.

7. 5S RNA Alignment & Phylogeny
Hein, 1990 9 11 10 6 8 7 5 4 3 1 2 17 16 15 14 13 12
Transitions 2, transversions 5
Total weight
10 tatt-ctggtgtcccaggcgtagaggaaccacaccgatccatctcgaacttggtggtgaaactctgccgcggt--aaccaatact-cg-gg-gggggccct-gcggaaaaatagctcgatgccagga--ta
17 t--t-ctggtgtcccaggcgtagaggaaccacaccaatccatcccgaacttggtggtgaaactctgctgcggt--ga-cgatact-tg-gg-gggagcccg-atggaaaaatagctcgatgccagga--t-
9 t--t-ctggtgtctcaggcgtggaggaaccacaccaatccatcccgaacttggtggtgaaactctattgcggt--ga-cgatactgta-gg-ggaagcccg-atggaaaaatagctcgacgccagga--t-
14 t----ctggtggccatggcgtagaggaaacaccccatcccataccgaactcggcagttaagctctgctgcgcc--ga-tggtact-tg-gg-gggagcccg-ctgggaaaataggacgctgccag-a--t-
3 t----ctggtgatgatggcggaggggacacacccgttcccataccgaacacggccgttaagccctccagcgcc--aa-tggtact-tgctc-cgcagggag-ccgggagagtaggacgtcgccag-g--c-
11 t----ctggtggcgatggcgaagaggacacacccgttcccataccgaacacggcagttaagctctccagcgcc--ga-tggtact-tg-gg-ggcagtccg-ctgggagagtaggacgctgccag-g--c-
4 t----ctggtggcgatagcgagaaggtcacacccgttcccataccgaacacggaagttaagcttctcagcgcc--ga-tggtagt-ta-gg-ggctgtccc-ctgtgagagtaggacgctgccag-g--c-
15 g----cctgcggccatagcaccgtgaaagcaccccatcccat-ccgaactcggcagttaagcacggttgcgcccaga-tagtact-tg-ggtgggagaccgcctgggaaacctggatgctgcaag-c--t-
8 g----cctacggccatcccaccctggtaacgcccgatctcgt-ctgatctcggaagctaagcagggtcgggcctggt-tagtact-tg-gatgggagacctcctgggaataccgggtgctgtagg-ct-t-
12 g----cctacggccataccaccctgaaagcaccccatcccgt-ccgatctgggaagttaagcagggttgagcccagt-tagtact-tg-gatgggagaccgcctgggaatcctgggtgctgtagg-c--t-
7 g----cttacgaccatatcacgttgaatgcacgccatcccgt-ccgatctggcaagttaagcaacgttgagtccagt-tagtact-tg-gatcggagacggcctgggaatcctggatgttgtaag-c--t-
16 g----cctacggccatagcaccctgaaagcaccccatcccgt-ccgatctgggaagttaagcagggttgcgcccagt-tagtact-tg-ggtgggagaccgcctgggaatcctgggtgctgtagg-c--t-
1 a----tccacggccataggactctgaaagcactgcatcccgt-ccgatctgcaaagttaaccagagtaccgcccagt-tagtacc-ac-ggtgggggaccacgcgggaatcctgggtgctgt-gg-t--t-
18 a----tccacggccataggactctgaaagcaccgcatcccgt-ccgatctgcgaagttaaacagagtaccgcccagt-tagtacc-ac-ggtgggggaccacatgggaatcctgggtgctgt-gg-t--t-
2 a----tccacggccataggactgtgaaagcaccgcatcccgt-ctgatctgcgcagttaaacacagtgccgcctagt-tagtacc-at-ggtgggggaccacatgggaatcctgggtgctgt-gg-t--t-
5 g---tggtgcggtcataccagcgctaatgcaccggatcccat-cagaactccgcagttaagcgcgcttgggccagaa-cagtact-gg-gatgggtgacctcccgggaagtcctggtgccgcacc-c--c-
13 g----ggtgcggtcataccagcgttaatgcaccggatcccat-cagaactccgcagttaagcgcgcttgggccagcc-tagtact-ag-gatgggtgacctcctgggaagtcctgatgctgcacc-c--t-
6 g----ggtgcgatcataccagcgttaatgcaccggatcccat-cagaactccgcagttaagcgcgcttgggttggag-tagtact-ag-gatgggtgacctcctgggaagtcctaatattgcacc-c-tt-

8. Cost of a history - minimizing over internal states
A C G T
d(C,G) +wC(left subtree)
A C G T
A C G T

9. Cost of a history – leaves (initialisation).
A C G T
Initialisation: leaves
Cost(N)= 0 if
N is at leaf,
otherwise infinity G A
Empty
Cost 0
Empty
Cost 0

10. Fitch-Hartigan-Sankoff Algorithm
(A,C,G,T)
(9,7,7,7)
(A, C, G,T)
(10,2,10,2)
The cost of cheapest tree hanging from this node given there is a “C” at this node
(A,C,G,T)
* 0 * *
(A,C,G,T)
* * * 0
(A,C,G,T)
* * 0 * 5 A C 2 G T

11. Felsenstein-Cavendar (1979)
The Felsenstein Zone
Felsenstein-Cavendar (1979) s3 s1 s2 s4
Reconstructed Tree s4 s3 s2 s1
True Tree
Patterns:(16 only 8 shown)
Should be after stoch.proc.

12. Bootstrapping 500 1 2 ATCTGTAGTCT 10230101201 ATCTGTAGTCT ??????????
Felsenstein (1985)
ATCTGTAGTCT
500 1 2 3 4
??????????
ATCTGTAGTCT 1 2
?????????? 1 3 4
Find example 1 2 3 4

13. Assignment to internal nodes: The simple way.C A T G ?
If branch lengths and evolutionary process is known, what is the probability of nucleotides at the leaves?
Cctacggccatacca a ccctgaaagcaccccatcccgt
Cttacgaccatatca c cgttgaatgcacgccatcccgt
Cctacggccatagca c ccctgaaagcaccccatcccgt
Cccacggccatagga c ctctgaaagcactgcatcccgt
Tccacggccatagga a ctctgaaagcaccgcatcccgt
Ttccacggccatagg c actgtgaaagcaccgcatcccg
Tggtgcggtcatacc g agcgctaatgcaccggatccca
Ggtgcggtcatacca t gcgttaatgcaccggatcccat

14. Probability of leaf observations - summing over internal states
A C G T
P(CG) *PC(left subtree)
A C G T
A C G T

15. Output from Likelihood Method.s1 s2 s3 s4 s5
No Molecular Clock
6.9 -/+1.3
11.4 -/+1.9
3.9 -/+0.8
10.9 -/+2.1
9.9 -/+1.2
11.6 -/+2.1
2n-3 lengths estimated
4.1 -/+0.7 s1 s2 s3 s4 s5
Now
Duplication Times
Amount of Evolution
Molecular Clock
23 -/+5.2
12 -/+2.2
11.1 -/+1.8
5.9 -/+1.2
n-1 heights estimated
Likelihood: 7.9*   =
Likelihood: 6.2*   =
ln(7.9*10-14) –ln(6.2*10-12) is 2 – distributed with (n-2) degrees of freedom

16. The Molecular Clock
First noted by Zuckerkandl & Pauling (1964) as an empirical fact.
How can one detect it?
Known Ancestor, a, at Time t s1 s2 a
Unknown Ancestors s1 s2 s3 ??

17. Rootings
Purpose
1) To give time direction in the phylogeny & most ancient point
2) To be able to define concepts such a monophyletic group.
1) Outgrup: Enhance data set with sequence from a species definitely distant to all of them. It will be be joined at the root of the original data
2) Midpoint: Find midpoint of longest path in tree.
3) Assume Molecular Clock.

18. Rooting the 3 kingdoms
3 billion years ago: no reliable clock - no outgroup
Given 2 set of homologous proteins, i.e. MDH & LDH can the archea, prokaria and eukaria be rooted? E P A
LDH
MDH E P A
Root?? E P A
LDH/MDH
Given 2 set of homologous proteins, i.e. MDH & LDH can the archea, prokaria and eukaria be rooted? E P A
LDH/MDH

19. The generation/year-time clock Langley-Fitch,1973s1 s3 s2 l2 l1 l3
Absolute Time Clock: s1 s3 s2
{l1 = l2 < l3} l3
Some rooting techniquee
l1 = l2
Generation Time Clock:
Elephant
Mouse
100 Myr
Absolute Time Clock
Generation Time
variable
constant

20. The generation/year-time clock Langley-Fitch,1973s1 s3 s2
Any Tree
Generation Time Clock
Can the generation time clock be tested?
Assume, a data set: 3 species, 2 sequences each s1 s3 s2 s1 s3 s2

21. The generation/year-time clock Langley-Fitch,1973s1 s3 s2
l1 = l2 l3 s1 s3 s2 l2 l1 l3
dg: 2
dg: k-1
k=3: degrees of freedom: 3
k: dg: 2k-3 s1 s3 s2 l2 l1 l3 s1 s3 s2
c*l2
c*l1
c*l3
k=3, t=2: dg=4
k, t: dg =(2k-3)-(t-1)

22. Fibrinopeptide A phylogeny:
& b – globin, cytochrome c, fibrinopeptide A & generation time clock
Langley-Fitch,1973
Fibrinopeptide A phylogeny:
Human
Gorilla
Donkey
Gibbon
Monkey
Rabbit
Cow
Rat
Pig
Horse
Goat
Llama
Sheep
Dog
Relative rates
a-globin
– globin
cytochrome c
fibrinopeptide A

23. Almost Clocks
(MJ Sanderson (1997) “A Nonparametric Approach to Estimating Divergence Times in the Absence of Rate Constancy” Mol.Biol.Evol ), J.L.Thorne et al. (1998): “Estimating the Rate of Evolution of the Rate of Evolution.” Mol.Biol.Evol. 15(12) , JP Huelsenbeck et al. (2000) “A compound Poisson Process for Relaxing the Molecular Clock” Genetics )
I Smoothing a non-clock tree onto a clock tree (Sanderson)
II Rate of Evolution of the rate of Evolution (Thorne et al.).
The rate of evolution can change at each bifurcation
III Relaxed Molecular Clock (Huelsenbeck et al.).
At random points in time, the rate changes by multiplying with random variable (gamma distributed)
Comment: Makes perfect sense. Testing no clock versus perfect is choosing between two unrealistic extremes.

24. Spannoids Advantage: Decomposes large trees into small trees1 2 3 4
Spanning tree
Steiner tree 2 5 4 1 3 6
1-Spannoid
2-Spannoid
Advantage: Decomposes large trees into small trees
Questions: How to find optimal spannoid?
How well do they approximate?

25. Profiloids and Staroids
Profile HMM s1 s2 sk
Ideal large phylogeny
A phylogeny of profiles - a staroid
HMM1
HMM2
HMM3
Questions:
Parameter changes on edges relating HMMs
Choosing Optimal Staroids