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The tree topology is perturbed every ten cycles with either the nearest
neighbor interchange (NNI) proposal shown in figure 2.7
or the subtree pruning and re-grafting (SPR) proposal (Swofford et al., 1996)
shown in figure 2.8.
Each cycle a randomly chosen branch length is modified with a figure
drawn from a normal distribution centred at zero.
When the branch length becomes negative special rules which can lead
to a topology change are applied (Jow et al., 2002). If the branch
is an internal branch then one of the two nearest neighbor topologies is
proposed with each having equal probability; this is the Nearest Neighbour
Interchange described above. The new internal branch
length is set to
(see figure
2.9). If the branch is a terminal branch, we cannot
apply the NNI algorithm and we simply use a reflecting boundary.
The new proposed length is
.
The acceptance rate for the SPR and the NNI proposals are usually
quite low. The ``local'' NNI proposal, induced by a branch length
modification, has a better acceptance rate.

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Gowri-Shankar Vivek
2003-04-24