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Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms, including-but not limited to-speciation ([Formula see text]), gene duplication ([Formula see text]), gene loss ([Formula see text]), and horizontal gene transfer ([Formula see text]). The reconstruction of a gene tree representing the evolution of a gene family constrained by a species tree is an importan