Invariant Based Quartet Puzzling

Abstract

Traditional Quartet Puzzling algorithms use maximum likelihood methods to reconstruct quartet trees, and a puzzling algorithm to combine these quartets into a tree for the full collection of $n$ taxa. We propose a variation of Quartet Puzzling in which the quartet trees are reconstructed using biologically symmetric invariants. We find that under certain conditions, invariant based quartet puzzling outperforms Quartet Puzzling using maximum likelihood.