Exact Algorithms for Duplication-Transfer-Loss Reconciliation with Non-Binary Gene Trees

Abstract

Duplication-Transfer-Loss (DTL) reconciliation is a powerful method for studying gene family evolution in the presence of horizontal gene transfer. DTL reconciliation seeks to reconcile gene trees with species trees by postulating speciation, duplication, transfer, and loss events. Efficient algorithms exist for finding optimal DTL reconciliations when the gene tree is binary. In practice, however, gene trees are often non-binary due to uncertainty in the gene tree topologies, and DTL reconciliation with non-binary gene trees is known to be NP-hard. In this paper, we present the first exact algorithms for DTL reconciliation with non-binary gene trees. Specifically, we (i) show that the DTL reconciliation problem for non-binary gene trees is fixed-parameter tractable in the maximum degree of the gene tree, (ii) present an exponential-time, but in-practice efficient, algorithm to track and enumerate all optimal binary resolutions of a non-binary input gene tree, and (iii) apply our algorithms to a large empirical data set of over 4700 gene trees from 100 species to study the impact of gene tree uncertainty on DTL-reconciliation and to demonstrate the applicability and utility of our algorithms. The new techniques and algorithms introduced in this paper will help biologists avoid incorrect evolutionary inferences caused by gene tree uncertainty.

On Inferring Additive and Replacing Horizontal Gene Transfers Through Phylogenetic Reconciliation

“…Phylogenetic methods for inferring transfer events can be divided into two classes: (i) Those that implicitly assume that all transfers are replacing transfers and that all discordance between gene trees and species trees is due to these replacing transfer events, e.g., [1,5,6,13,15,17,23,28], and (ii) those based on the Duplication-Transfer-Loss (DTL) reconciliation framework, which model gene duplication and gene loss as additional sources of gene tree/species tree discordance, but implicitly assume that all transfers are additive transfers, e.g., [2,8,10,11,16,20,22,[24][25][26][27]29]. Thus, no existing phylogenetic method models both additive and replacing transfers.…”

Horizontal gene transfer of Chlamydia: Novel insights from tree reconciliation

“…1.6) [ 25 ] after the species trees were generated. To evaluate candidate HGTs RANGER-DTL 2.0 [ 19 ] was applied. In contrast to RANGER-DTL 1.0, RANGER-DTL 2.0 is capable of sampling the space of all optimal reconciliations uniformly at random and computing multiple optimal reconciliations and accounting for the variability in optimal reconciliation scenarios [ 19 ].…”

“…It is quite advantageous in inferring tree reconciliation-based HGT information with hundreds of organisms with a reasonable running time. Following initial identification of HGTs in Chlamydia e, in order to improve the accuracy of the identification, we additionally evaluated the reliability of each potential candidate HGT events and mapping assignments using RAxML [ 18 ] and RANGER-DTL 2.0 software package [ 19 ].…”

Reconstruction of time-consistent species trees

“…We note in passing that many types of reconciliation problems become NP-hard as soon as HGT and timeconsistency are involved, see e.g. [37,[40][41][42][43][44][45]. Moreover, there are exponentially many species trees, for each of them there may be a time-consistent reconciliation map or not for a given event-labeled gene tree.…”