In the context of phylogenetic tree reconstruction, divisive clustering methods can be used to infer phylogenetic trees in a top-down way. These methods have the important advantage of providing an explanation for the resulting topology, since the splits are described by polymorphic locations in the sequences. However, the quality of the resulting trees is rather variable. In this work, we argue that trees induced by top-down methods can be viewed not just as phylogenetic trees, but also as identifying constraints that the real phylogenetic tree must satisfy. We analyzed trees inferred by Clus-φ, a distance based method for phylogenetic tree reconstruction based on a conceptual clustering method that extends the well-known decision tree learning approach. Each split defines two subclusters, such that the total branch length of the tree is minimized. However, the split does not define how the subclusters have to be connected. We propose a post-processing method that processes the clustering tree bottom-up, at each split finding the internal branch that connects the two subclusters with a minimal number of mutations. To evaluate this method we used a number of synthetic datasets generated by an evolutionary process simulator. In general, the post-processed Clus-φ trees are more similar to the underlying target trees of the synthetic datasets than the original Clus-φ trees, which shows that the post-processing step yields a better approximation of the target tree. When we consider Neighbor Joining and Parsimony results in this comparative analysis, we observe that the post-processed Clus-φ trees tend to be better than the NJ trees and are comparable to the parsimony trees. The results show that trees resulting from top-down phylogenetic tree construction can be improved by post-processing them. This post-processing is based on the viewpoint that the methods do not necessarily return the correct tree, but return constraints that the correct tree must satisfy. These constraints allow to guide the search for the tree with a minimal number of mutations in a more exhaustive way than the greedy search performed by parsimony methods. In general, the quality of post-processed Clus-φ trees are comparable to that of parsimony trees.
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