SuperTriplets: a triplet-based supertree approach to phylogenomics. Motivation: Phylogenetic tree-building methods use molecular data to represent the evolutionary history of genes and taxa. A recurrent problem is to reconcile the various phylogenies built from different genomic sequences into a single one. This task is generally conducted by a two-step approach whereby a binary representation of the initial trees is first inferred and then a maximum parsimony (MP) analysis is performed on it. This binary representation uses a decomposition of all source trees that is usually based on clades, but that can also be based on triplets or quartets. The relative performances of these representations have been discussed but are difficult to assess since both are limited to relatively small datasets. Results: This article focuses on the triplet-based representation of source trees. We first recall how, using this representation, the parsimony analysis is related to the median tree notion. We then introduce SuperTriplets, a new algorithm that is specially designed to optimize this alternative formulation of the MP criterion. The method avoids several practical limitations of the triplet-based binary matrix representation, making it useful to deal with large datasets. When the correct resolution of every triplet appears more often than the incorrect ones in source trees, SuperTriplets warrants to reconstruct the correct phylogeny. Both simulations and a case study on mammalian phylogenomics confirm the advantages of this approach. In both cases, SuperTriplets tends to propose less resolved but more reliable supertrees than those inferred using Matrix Representation with Parsimony. Availability: Online and JAVA standalone versions of SuperTriplets are available at