article · Bulletin of Mathematical Biology · 2026
Counting Rankings of Tree-Child Networks
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Abstract
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are 'tree-child networks' and a 'ranking' of such a network is a temporal ordering of the ancestral speciation and hybridization events. In this short note, we investigate the question of counting such rankings on any given binary (or semi-binary) tree-child network. We also investigate the relationship between rankable tree-child networks and the class of 'normal' networks. Finally, we provide an explicit asymptotic expression for the expected number of rankings of a tree-child network chosen uniformly at random.
Cite this paper
Zhang, Q., & Steel, M. (2026). Counting Rankings of Tree-Child Networks. Bulletin of Mathematical Biology, 88(3). https://doi.org/10.1007/s11538-026-01606-6
Zhang, Qiang, and Mike Steel. “Counting Rankings of Tree-Child Networks.” Bulletin of Mathematical Biology, vol. 88, no. 3, 2026, https://doi.org/10.1007/s11538-026-01606-6.
Zhang, Qiang, and Mike Steel. 2026. “Counting Rankings of Tree-Child Networks.” Bulletin of Mathematical Biology 88 (3). https://doi.org/10.1007/s11538-026-01606-6.
Zhang, Q. and Steel, M. (2026) ‘Counting Rankings of Tree-Child Networks’, Bulletin of Mathematical Biology, 88(3). Available at: https://doi.org/10.1007/s11538-026-01606-6.
@article{zhang2026counting,
title = {{Counting Rankings of Tree-Child Networks}},
author = {Zhang, Qiang and Steel, Mike},
journal = {Bulletin of Mathematical Biology},
volume = {88},
number = {3},
year = {2026},
doi = {10.1007/s11538-026-01606-6}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.