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The supertree problem asking for a tree displaying a set of consistent inputtrees has been largely considered for the reconstruction of species trees.Here, we rather explore this framework for the sake of reconstructing a genetree from a set of input gene trees on partial data. In this perspective, thephylogenetic tree for the species containing the genes of interest can be usedto choose among the many possible compatible "supergenetrees", the most naturalcriteria being to minimize a reconciliation cost. We develop a variety ofalgorithmic solutions for the construction and correction of gene trees usingthe supertree framework. A dynamic programming supertree algorithm forconstructing or correcting gene trees, exponential in the number of inputtrees, is first developed for the less constrained version of the problem. Itis then adapted to gene trees with nodes labeled as duplication or speciation,the additional constraint being to preserve the orthology and paralogyrelations between genes. Then, a quadratic time algorithm is developed forefficiently correcting an initial gene tree while preserving a set of "trusted"subtrees, as well as the relative phylogenetic distance between them, in bothcases of labeled or unlabeled input trees. By applying these algorithms to theset of Ensembl gene trees, we show that this new correction framework isparticularly useful to correct weaklysupported duplication nodes. The C++source code for the algorithms and simulations described in the paper areavailable at https://github.com/UdeM-LBIT/SuGeT.

Gene Tree Construction and Correction using SuperTree and Reconciliation