Abstract
A fundamental task in evolutionary biology is the amalgamation of a collection P of leaf-labelled trees into a single parent tree. A desirable feature of any such amalgamation is that the resulting tree preserves all of the relationships described by the trees in P . For unrooted trees, deciding if there is such a tree is NP-complete. However, two polynomial-time approaches that sometimes provide a solution to this problem involve the computation of the semi-dyadic and the split closure of a set of quartets that underlies P . In this paper, we show that if a leaf-labelled tree T can be recovered from the semi-dyadic closure of some set Q of quartet subtrees of T , then T can also be recovered from the split-closure of Q . Furthermore, we show that the converse of this result does not hold, and resolve a closely related question posed in [S. Böcker, D. Bryant, A. Dress, M. Steel, Algorithmic aspects of tree amalgamation, Journal of Algorithms 37 (2000) 522–537].
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