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Quartet trees displayed by larger phylogenetic trees have long been used asinputs for species tree and supertree reconstruction. Computational constraintsprevent the use of all displayed quartets in many practical problems due to thenumber of taxa. We introduce the notion of an Efficient Quartet System (EQS) torepresent a phylogenetic tree with a subset of the quartets displayed by thetree. We show mathematically that the set of quartets obtained from a tree viaan EQS contains all of the combinatorial information of the tree itself. Usingperformance tests on simulated datasets, we also demonstrate that using an EQSto reduce the number of quartets in pipelines for summary methods of speciestree inference and supertree inference results in only small reductions inaccuracy.

Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods