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How many evolutionary family trees have reticulations?

Hao Yu, Louxin Zhang

May 22, 2026

Phylogenetic networks map how species diverge with hybridization and horizontal gene transfer mixed in—messier than simple trees. Yu and Zhang counted how many such networks exist with a given number of reticulation events across a given number of species, deriving an asymptotic formula. This matters because understanding the combinatorial landscape of possible networks helps evaluate which evolutionary histories are plausible.
Published as Asymptotic Counting of Binary Phylogenetic Networks arXiv:2605.23126
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