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Also, we develop an effective MIP-based tree partitioning heuristic for finding good quality solutions for large size problems.
We found that most ancestral states for deep as well as shallow nodes of the angiosperm tree were largely unaffected by changes in models (number of transition rates in model, value of transition rates, tree partitioning).
The rationale for including two grades in our tree partitioning scheme is that members of these grades may have inherited ancestral transition rates, while the large clades nested in them may have shifted to distinct evolutionary regimes characterized by different transition rates.
Therefore, it will be necessary to conduct additional work on other clades, traits and rate heterogeneity models (including new approaches for automatic identification of rate shifts without a priori tree partitioning) before it can be asserted whether the results of this study are general.
For instance, Xu et al. (2001) suggested gene expression data clustering based on MST, which rigorously converts a multidimensional clustering problem to a tree partitioning problem.
Considering an improvement of other methods by including the graph information (as in [ 15]) we expect that it might give a better result for the tree partitioning algorithm as well.
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There are four character and tree partition combinations for which Mk1 and Mk2 are equally well fitted to the data.
However, a serious problem of ALM is that the multicast tree may be fragile, and peer failure causes tree partitions.
Branches of the tree partition the cabinet while leaves fill the remaining partitioning space (see Fig. 2).
At each node, two daughter tree partitions are defined.
The robustness of the tree partitions was evaluated by using the bootstrap analysis with a neighbor-joining search.
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