Quartet Methods

A Distance Quartet Puzzling Algorithm.
Phylogenetic analysis increasingly employs sophisticated mathematical tools ranging from stochastic modelling of Markov processes, principal component analysis, or integer programming to various branches of combinatorics, including extremal combinatorics and combinatorial analysis of multivariate relationships, in particular those derived from (dis)similarity data. The work presented here deals with the latter topics, that is, the construction of phylogenetic trees from quartets (resolved trees on four leaves). Most formulations of the problem are NP-hard. Here we consider a new version that has a polynomial time solution. We present applications of this algorithm for idenitfying putative clades and for elucidating spurious phylogenetic relationships. Also, we note that our algorithm can be applied to weighted sets of quartets.

Finally, we will present some output trees and differences using the four variants of the algorithm.