Open Research Index

Linked-site block laws of all lengths identify the collapsed mutation-scaled genealogy

X. Lee, N. Volkov

Palomar Registrypalomar/PALOMAR-2026-10-29-000003Oct 29, 2026q-bio.PEscore 0

This entry formalizes an identifiability theorem for three sampled sequences whose sites all share one random three-tip genealogy (complete linkage). A genealogy is a pair of branch lengths (u, v), where u is the height of the cherry and v is the length of the upper internal branch, together with a label in Fin 3 recording which pair of tips forms the cherry. Its law is an arbitrary finite measure that is almost everywhere supported on nonnegative branch lengths. Given the genealogy, sites evolve independently under the K-state equal-rates mutation model with a uniform root distribution and…

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