Important Quartet Puzzling and NNI Operation. An efficient tree reconstruction method (IQPNNI) is introduced to reconstruct a phylogenetic tree based on DNA or amino acid sequence data. Our approach combines various fast algorithms to generate a list of potential candidate trees. The key ingredient is the definition of so-called important quartets (IQs), which allow the computation of an intermediate tree in O(n^2) time for n sequences. The resulting tree is then further optimized by applying the nearest neighbor interchange (NNI) operation. Subsequently a random fraction of the sequences is deleted from the best tree found so far. The deleted sequences are then re-inserted in the smaller tree using the important quartet puzzling (IQP) algorithm. These steps are repeated several times and the best tree, with respect to the likelihood criterion, is considered as the inferred phylogenetic tree. Moreover, we suggest a rule, which indicates when to stop the search.

IQPNNI Features:
1. Model parameter estimations fail in rare cases for parameter-rich model
2. Invar+Gamma rate heterogeneity
3. Compatibility issue with GCC 4.3.2
4. BIONJ tree is now reconstructed twice from the initial distances and the corrected maximum-likelihood distances

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