Year: 2026
Type: preprint
Abstract: Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $σ$-space, a moduli space of fully nested ultrametric phylogenetic trees with a fixed leaf map. Generalizing the $τ$-space of Gavryushkin and Drummond, $σ$-space is constructed as a cubical complex parametrised by nested ranked tree topologies and inter-event time coordinates of the combined host and parasite speciation events. We characterise admissible orderings via binary \textit{nesting sequences} and organise them into a natural poset. We show that $σ$-space is contractible and satisfies Gromov's cube condition, and is therefore CAT(0). In particular, it admits unique geodesics and well-defined Fréchet means. We further describe its geometric structure, including boundary strata corresponding to cospeciation events, and relate it to products of ultrametric tree spaces via natural forgetful maps.
Source: arXiv (Cornell University)
Authors: Grindstaff, G., Hoekzema, R. S.
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7151979655
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