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Open Access Research

Invariant based quartet puzzling

Joseph P Rusinko1* and Brian Hipp2

Author Affiliations

1 Department of Mathematics, Winthrop University, 142 Bancroft Hall, Rock Hill, SC 29733, USA

2 Department of Mathematics, Winthrop University, 142 Bancroft Hall, Rock Hill, SC 29733, USA

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Algorithms for Molecular Biology 2012, 7:35  doi:10.1186/1748-7188-7-35

Published: 6 December 2012



First proposed by Cavender and Felsenstein, and Lake, invariant based algorithms for phylogenetic reconstruction were widely dismissed by practicing biologists because invariants were perceived to have limited accuracy in constructing trees based on DNA sequences of reasonable length. Recent developments by algebraic geometers have led to the construction of lists of invariants which have been demonstrated to be more accurate on small sequences, but were limited in that they could only be used for trees with small numbers of taxa. We have developed and tested an invariant based quartet puzzling algorithm which is accurate and efficient for biologically reasonable data sets.


We found that our algorithm outperforms Maximum Likelihood based quartet puzzling on data sets simulated with low to medium evolutionary rates. For faster rates of evolution, invariant based quartet puzzling is reasonable but less effective than maximum likelihood based puzzling.


This is a proof of concept algorithm which is not intended to replace existing reconstruction algorithms. Rather, the conclusion is that when seeking solutions to a new wave of phylogenetic problems (super tree algorithms, gene vs. species tree, mixture models), invariant based methods should be considered. This article demonstrates that invariants are a practical, reasonable and flexible source for reconstruction techniques.

Phylogenetic reconstruction; Invariants; Quartet puzzling