An extension of the classic Buneman theorem from phylogenetic trees to networks
Abstract
Phylogenetic networks provide a natural framework for representing reticulate evolutionary events such as horizontal gene transfer and hybridization. In the present manuscript, we investigate the identifiability of phylogenetic networks under (hardwired) parsimony, a natural extension of Maximum Parsimony from trees to networks. More precisely, we ask which structural features of a network can be uniquely inferred from so-called Ak-alignments under this criterion. While identifiability has been studied extensively for phylogenetic trees under parsimony, little is known about the identifiability of networks under hardwired parsimony. We take a first step towards addressing this gap by developing a general framework for studying identifiability under hardwired parsimony. We then use this framework to show that the tree of blobs of a phylogenetic network can be reconstructed from its A1-alignment. This result can be viewed as a natural extension of Buneman's well-known splits equivalence theorem. Finally, we show that, under hardwired parsimony, cycles of length at least $5$ cannot in general be uniquely identified from character data, establishing a fundamental limitation of hardwired parsimony.
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BibTeX
@misc{wilde2026extension,
title = {{An extension of the classic Buneman theorem from phylogenetic trees to networks}},
author = {Mirko Wilde and Mareike Fischer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41725},
eprint = {2610.41725},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41725},
}
RIS
TY - UNPB
TI - An extension of the classic Buneman theorem from phylogenetic trees to networks
AU - Mirko Wilde
AU - Mareike Fischer
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41725
UR - https://arxiv.org/abs/2610.41725
AB - Phylogenetic networks provide a natural framework for representing reticulate evolutionary events such as horizontal gene transfer and hybridization. In the present manuscript, we investigate the identifiability of phylogenetic networks under (hardwired) parsimony, a natural extension of Maximum Parsimony from trees to networks. More precisely, we ask which structural features of a network can be uniquely inferred from so-called A_k-alignments under this criterion. While identifiability has been studied extensively for phylogenetic trees under parsimony, little is known about the identifiability of networks under hardwired parsimony. We take a first step towards addressing this gap by developing a general framework for studying identifiability under hardwired parsimony. We then use this framework to show that the tree of blobs of a phylogenetic network can be reconstructed from its A_1-alignment. This result can be viewed as a natural extension of Buneman's well-known splits equivalence theorem. Finally, we show that, under hardwired parsimony, cycles of length at least $5$ cannot in general be uniquely identified from character data, establishing a fundamental limitation of hardwired parsimony.
ER -