Résumé
In the field of phylogenetics, the evolutionary history of a set of organisms is commonly depicted by a species tree – whose internal nodes represent speciation events – while the evolutionary history of a gene family is depicted by a gene tree – whose internal nodes can also represent macro-evolutionary events such as gene duplications and transfers. As speciation events are only part of the events shaping a gene history, the topology of a gene tree can show incongruences with that of the corresponding species tree. These incongruences can be used to infer the macro-evolutionary events undergone by the gene family. This is done by embedding the gene tree inside the species tree and hence providing a reconciliation of those trees. In the past decade, several parsimony-based methods have been developed to infer such reconciliations, accounting for gene duplications (D), transfers (T) and losses (L). The main contribution of this paper is to formally prove an important assumption implicitly made by previous works on these reconciliations, namely that solving the (maximum) parsimony DTL reconciliation problem in the discrete framework is equivalent to finding a most parsimonious DTL scenario in the continuous framework. In the process, we also prove several intermediate results that are useful on their own and constitute a theoretical toolbox that will likely facilitate future theoretical contributions in the field.