2022 Fiscal Year Annual Research Report
Phylogenetic Network Simplification
| Project/Area Number |
22H03550
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| Allocation Type | Single-year Grants |
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| Research Institution | Kyoto University |
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Principal Investigator |
ジャンソン ジェスパー 京都大学, 情報学研究科, 特定准教授 (60536100)
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Keywords | algorithm / computational complexity / MUL-tree / pruning / phylogenetics |
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| Outline of Annual Research Achievements |
A multi-labeled tree (or MUL-tree, for short) is a phylogenetic tree in which every leaf label may appear more than once. Such trees have applications to the construction of phylogenetic networks by folding operations [Huber & Moulton, Mathematical Biology, 2006]. We considered the MUL-tree Set Pruning for Consistency problem (MULSETPC), which takes as input a set of MUL-trees and asks if there exists a perfect pruning of each MUL-tree that results in a consistent set of single-labeled trees. MULSETPC was known to be NP-complete [Gascon, Dondi, and El-Mabrouk, Proceedings of IWOCA 2021] when the MUL-trees are binary, each leaf label is used at most three times, and the number of MUL-trees is unbounded. We resolved an open question posed by Gascon et al. by proving a much stronger result, namely that MULULSETPC is NP-complete even when there are only two MUL-trees, every leaf label is used at most twice, and either every MUL-tree is binary or every MUL-tree has constant height. Furthermore, we introduced an extension of MULSETPC that we call MULSETPComp, which replaces the notion of consistency with compatibility, and proved that MULSETPComp is NP-complete even when there are only two MUL-trees, every leaf label is used at most thrice, and every MUL-tree has constant height. Finally, we designed a polynomial-time algorithm for instances of MULSETPC with a constant number of binary MUL-trees, in the special case where every leaf label occurs exactly once in at least one MUL-tree.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
We have not yet achieved the results that we had hoped to achieve in the first year of this project.
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| Strategy for Future Research Activity |
We plan to define new distance functions for formally measuring how much branching structure is lost/retained when replacing a phylogenetic network by another one. We will aim for functions that are efficiently computable, biologically meaningful, and able to distinguish between many kinds of non-isomorphic networks. One idea that we will try is to extend the rooted triplet distance to take multiple occurrences of the same triplet within a network into account. In addition, some alternatives to investigate and draw inspiration from are the various methods developed for comparing phylogenetic trees such as the nearest neighbor interchange distance, which counts how many branch-swap transformations are needed to turn one tree into the other, and variants of the Kendall-Colijn metric, the path-length-difference distance, the subtree prune-and-regraft distance, the size of a maximum agreement subtree, and the tree edit distance.
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