Reconstructible phylogenetic networks: no need to distinguish the indistinguishable

International audienceMost proposed methods for phylogenetic network reconstruction evaluate candidate networks on the basis of the trees they display. This is certainly true for all methods based on data consisting of clusters of taxa, triplets, quartets, or trees with any number of leaves, but also for sequence-based approaches such as the first formalisations of maximum parsimony and maximum likelihood for networks.This poses a problem: from the perspective of these methods, all networks that display the same set of trees are ”indistinguishable”, as the objective function assigns the same score to all networks displaying the same set of trees. This problem is partially solved by accounting for branch lengths, although this merely reduces the size of the classes of indistinguishable networks. In this talk we propose a novel definition of what constitutes a ”uniquely reconstructible” network: for each class of indistinguishable networks, we define a canonical form. Under mild assumptions, the canonical form is unique. Given data coming from any phylogenetic network, only its canonical equivalent can be uniquely reconstructed. This is a fundamental limitation that implies a drastic reduction of the solution space in phylogenetic network inference