Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods
Ruth Davidson, MaLyn Lawhorn, Joseph Rusinko, Noah Weber

Quartet trees which are displayed by larger phylogenetic trees have long been used as inputs for species tree and supertree reconstruction. Computational constraints prevent the use of all displayed quartets when the number of genes or number of taxa is large. We introduce the Efficient Quartet System (EQS) to represent a phylogenetic tree with a subset of the quartets displayed by the tree. We show mathematically that the set of quartets obtained from a tree via EQS contains all of the combinatorial information of the tree itself. We also demonstrate via performance tests on some simulated datasets that the use of EQS to reduce the number of quartets input to quartet-based species tree methods (including summary methods) and supertree methods only corresponds to small reductions in accuracy.