In this paper we introduce a new quartet-based method. This method makes use of the Bayes (or quartet) weights of quartets as those used in the quartet puzzling. However, all the weights from the related quartets are accumulated to form a global quartet weight matrix. This matrix provides integrated information and can lead us to recursively merge small sub-trees to larger ones until the final single tree is obtained. The experimental results show that the probability for the correct tree to be among a very small number of trees constructed using our method is very high. These significant results open a new research direction to further investigate more efficient algorithms for phylogenetic inference.
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