Abstract
Phylogenetic tree reconciliation is a widely-used method to understand gene family evolution. For eukaryotes, the duplication-loss-coalescence (DLC) model seeks to explain incongruence between gene trees and species trees by postulating gene duplication, gene loss, and deep coalescence events. While efficient algorithms exist for inferring optimal DLC reconciliations, they assume that only one individual is sampled per species. In recent work, we demonstrated that with additional samples, there exist gene tree topologies that are impossible to reconcile with any species tree. However, our algorithm required the gene tree to be binary whereas, in practice, gene trees are often non-binary due to uncertainty in the reconstruction process. In this work, we consider for the first time reconciliation under the DLC model with non-binary gene trees. Specifically, we describe an efficient algorithm that takes as input an arbitrary gene tree with an arbitrary number of samples per species and either (1) determines that there is a valid reconcilable binary resolution of that tree and constructs one such resolution or (2) determines that there exists no valid reconcilable binary resolution of that tree. Our work makes it possible to systematically analyze non-binary gene trees and will help biologists identify incorrect gene tree topologies and thus avoid incorrect evolutionary inferences.
M. Dohlen and C. Pekker—These authors contributed equally to this work.
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Notes
- 1.
Branch lengths are not used in this work, so a tree always refers to a tree topology.
- 2.
The proof considers only the single unique path between two genes in a binary tree.
- 3.
Note that this locus tree is distinct from the locus tree of Rasmussen and Kellis [25].
- 4.
For example, in Fig. 3, swapping leaves labeled \(a_2\) with leaves labeled \(c_1\) would result in an irreconcilable LEG and thus a multifurcating gene tree for which there exists no reconcilable binarization.
- 5.
While most reconciliation algorithms do not support multiple samples per species nor non-binary gene trees, the former extension is fairly straightforward while the latter requires new algorithms.
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Acknowledgments
This work was supported by funds from the Department of Computer Science and the Dean of Faculty of Harvey Mudd College and by the U.S. National Science Foundation under grant IIS-1419739.
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Cheng, R. et al. (2018). Reconciliation Feasibility of Non-binary Gene Trees Under a Duplication-Loss-Coalescence Model. In: Jansson, J., MartÃn-Vide, C., Vega-RodrÃguez, M. (eds) Algorithms for Computational Biology. AlCoB 2018. Lecture Notes in Computer Science(), vol 10849. Springer, Cham. https://doi.org/10.1007/978-3-319-91938-6_2
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