BCD Beam Search: considering suboptimal partial solutions in Bad Clade Deletion supertrees.

Markus Fleischauer,Sebastian Böcker

doi:10.7717/peerj.4987

Abstract

Supertree methods enable the reconstruction of large phylogenies. The supertree problem can be formalized in different ways in order to cope with contradictory information in the input. Some supertree methods are based on encoding the input trees in a matrix; other methods try to find minimum cuts in some graph. Recently, we introduced Bad Clade Deletion (BCD) supertrees which combines the graph-based computation of minimum cuts with optimizing a global objective function on the matrix representation of the input trees. The BCD supertree method has guaranteed polynomial running time and is very swift in practice. The quality of reconstructed supertrees was superior to matrix representation with parsimony (MRP) and usually on par with SuperFine for simulated data; but particularly for biological data, quality of BCD supertrees could not keep up with SuperFine supertrees. Here, we present a beam search extension for the BCD algorithm that keeps alive a constant number of partial solutions in each top-down iteration phase. The guaranteed worst-case running time of the new algorithm is still polynomial in the size of the input. We present an exact and a randomized subroutine to generate suboptimal partial solutions. Both beam search approaches consistently improve supertree quality on all evaluated datasets when keeping 25 suboptimal solutions alive. Supertree quality of the BCD Beam Search algorithm is on par with MRP and SuperFine even for biological data. This is the best performance of a polynomial-time supertree algorithm reported so far.

Highlights

Supertree methods assemble phylogenetic trees with non-identical but overlapping taxon sets into a larger supertree that contains all taxa of each input tree
We evaluate the performance of the Bad Clade Deletion (BCD) Beam Search algorithm against the original BCD algorithm, matrix representation with parsimony (MRP) (Baum, 1992; Ragan, 1992), and SuperFine (Swenson et al, 2012)
We describe results for different BCD Beam Search variants in comparison to BCD, MRP and SuperFine on simulated and biological data

Summary

Introduction

Supertree methods assemble phylogenetic trees with non-identical but overlapping taxon sets into a larger supertree that contains all taxa of each input tree. Conflicts can be caused by estimation errors during source tree computation, or by evolutionary processes (e.g., incomplete lineage sorting or horizontal gene transfer) resulting in conflicting gene trees. The latter problem is known as Gene Tree Species Tree Reconciliation problem; for this problem, methods were developed that incorporate evolutionary processes such as the coalescent process (Liu et al, 2009; Larget et al, 2010; Liu, Yu & Edwards, 2010; Liu & Yu, 2011; Whidden, Zeh & Beiko, 2014; Mirarab et al, 2014; Allman, Degnan & Rhodes, 2016). Supertree methods are complemented by supermatrix methods, which do not combine the trees but rather the “raw” sequence data (von Haeseler, 2012)

Methods

Results

Conclusion