Caterpillar trees are asymmetric, balanced trees are symmetric
q-bio.PE
Submitted: 2026-10-19
Updated: 2026-10-19
Comments: 11 pages, 2 figures (and 6 little icons)
License: http://creativecommons.org/licenses/by/4.0/
The gist: Two conjectures of Allman, Long and Rhodes are proven.
Abstract
Two conjectures of Allman, Long and Rhodes are proven. The ultrametric exchangeable model captures the symmetries in allele distributions of ultrametric mechanistic models of coalescence and substitution in mathematical phylogeny. The dimension of this model with respect to the species tree leaf count is shown to be greatest for caterpillar trees and least for balanced trees.
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