Dear Luobin,

HyPhy does not presently implement TBR. It is not terrible difficult but rather tedious to add it (a lot of book-keeping). It has been on my list of things to do for a while.

Most of HyPhy topology search analyses have been parallelized to run on MPI.

However, it is worth noting, that HyPhy is not primarily a phylogeny package (it is geared towards quantifying and testing the evolutionary process, e.g. rates, selection, recombination etc), and many of the methods are slow compared to state-of-the-art packages like PAUP* and PhyML. NJ and NNI branch swapping can be quite fast, on the other hand.

Cheers,
Sergei