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Phylogenetic networks are increasingly being considered as better suited torepresent the complexity of the evolutionary relationships between species. Oneclass of phylogenetic networks that has received a lot of attention recently isthe class of orchard networks, which is composed of networks that can bereduced to a single leaf using cherry reductions. Cherry reductions, alsocalled cherry-picking operations, remove either a leaf of a simple cherry(sibling leaves sharing a parent) or a reticulate edge of a reticulate cherry(two leaves whose parents are connected by a reticulate edge). In this paper,we present a fixed-parameter tractable algorithm to solve the problem offinding a maximum agreement cherry-reduced subnetwork (MACRS) between tworooted binary level-1 networks. This is first exact algorithm proposed to solvethe MACRS problem. As proven in earlier work, there is a direct relationshipbetween finding an MACRS and calculating a distance based on cherry operations.As a result, the proposed algorithm also provides a distance that can be usedfor the comparison of level-1 networks.

Finding agreement cherry-reduced subnetworks in level-1 networks