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.
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Qiang Zhang
Mike Steel
Bulletin of Mathematical Biology
University of Canterbury
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Zhang et al. (Sat,) studied this question.
www.synapsesocial.com/papers/69a760fdc6e9836116a2e7c1 — DOI: https://doi.org/10.1007/s11538-026-01606-6