In phylogenetics, a set of gene trees is often summarized by a consensus tree, such as the majority consensus, which is based on the set of all splits that are present in more than 50% of the input trees. A "consensus network" is obtained by lowering the threshold and considering all splits that are contained in 10% of the trees, say, and then computing the corresponding splits network. By construction and in practice, a consensus network usually shows the majority tree, extended by a number of

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... rectangles that represent local rearrangements around internal nodes of the consensus tree. This may lead to the false conclusion that the input trees do not differ in a significant way because "even a phylogenetic network" does not display any large discrepancies. To harness the full potential of a phylogenetic network, we introduce the new concept of an anti-consensus network that aims at representing the largest interesting discrepancies found in a set of gene trees. We provide an efficient algorithm for computing an anti-consensus and illustrate its application using a set of gene trees from species and strains in the genus Kosakonia.