1. Lecture 8 – Searching Tree Space

2. The Search Tree

3. A. Nearest-neighbor interchange (NNI)
There are 2(n – 3) NNI rearrangements for any tree. 2

4. B. Subtree Pruning-Regrafting (SPR)
4(n – 3)(n – 2) SPR rearrangements

5. C. Tree bisection-reconnection (TBR)
All branches are bisected, and reconnected in all possible ways. It’s not possible to
generalize how many TBR rearrangements could be made for a tree of a given
size (as we could with NNI & SPR), but TBR swapping searches tree space more
thoroughly, than SPR or NNI.

6. How greedy should we be?
26 taxon data set and first, let’s be very greedy .
Ignore ties in building starting tree and in swapping.
NNI, examine 42 trees
SPR, examine 2072 trees
TBR, examine 5816 trees
Less greedy - save all equally optimal trees at each step.
NN, examine 140 trees
SPR, examine 6212 trees
TBR, examine 16,604 trees

7. Random Addition Sequence and Tree Islands
So in the above example, using the least greedy strategies and using starting trees
generated by 100 random addition sequences, we’ll look at 341,355 different trees.
First Last First Times
Island Size tree tree Score replicate hit

8. Transforming Tree Space
May be better off spending less effort searching on one island and more
effort searching for multiple islands
Parsimony Ratchet (Nixon Cladistics. 15: 407 )
Alternate searches using real data and searches on perturbed data set.
Get a starting tree by stepwise addition from the real data
Reweight a random set (20-25%) characters: this transforms tree space.
Hill climb from the starting tree via greedy TBR with perturbed data.
If a better tree is found, use that tree to start TBR using original data.
This is iterated a couple hundred times.

9. MCMC approach to search tree space and permits down-hill moves.
Simulated Annealing
Designed to search a large, complex, discrete search space.
Laura Salter Kubatko was one of the first to apply it to phylogenies as a means of estimating ML trees (Salter and Perl, Syst. Biol. 50:7).
MCMC approach to search tree space and permits down-hill moves.
 Steps:
Generate an initial state (a starting tree). Initially, a random tree was used.
Propose a stochastic change to the initial state (usually a minor change).
This was initially derived via a random NNI.
If the proposal improves the tree (has a better ML score), the move is accepted.
Proposals (NNIs) that degrade the tree are accepted with a small probability
proportional to how much worse the proposed tree is.
Early on, the acceptance probability is high and decreases as the search runs.

10. RAxML & Alternating Criteria
Stamatakis permits use of a modified simulated annealing in RAxML.
First, he starts with a tree generated by stepwise addition using parsimony
(randomized addition sequence).
The SA approach be can used to alter topology via (lazy) SPR under ML, but only the branches involved in the swapping are reoptimized.
Third, RAxML builds proposals to alter branch lengths and model
parameters that are only accepted if they improve the likelihood (i.e.,
this aspect of the searches are entirely hill climbing). These optimizations
are cursory and halted with a liberal stopping rule.
This approach allows pretty thorough searches of tree space really quickly, which permits us to estimate ML trees for very large data sets (e.g., thousands of taxa).

11. Genetic Algorithms Paul Lewis (1998. Mol. Biol. Evol. 15:277)
There are n individuals: tree with parameters and branch lengths.
Ranked by their likelihood. Tree with highest fitness leaves k offspring in the next generation.
Other trees leave offspring proportional to rank.
All offspring are subject to branch length and model mutations.
Some offspring ((n-1)/m) are subject to random SPR mutations.

12. Recombination searches tree space broadly.
Genetic Algorithms
Recombination searches tree space broadly.
GARLi was written by Derek Zwickl and modifies Lewis’ GA.
Topological mutations include NNI & SPR rearrangements and some local SPR.
Starting trees are generated via stepwise addition with random addition sequences.
This approach allows thorough searches of tree space for up to a couple thousand taxa.