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2021 Sufficient condition for root reconstruction by parsimony on binary trees with general weights
Sebastien Roch, Kun-Chieh Wang
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Electron. Commun. Probab. 26: 1-13 (2021). DOI: 10.1214/21-ECP423


We consider the problem of inferring an ancestral state from observations at the leaves of a tree, assuming the state evolves along the tree according to a two-state symmetric Markov process. We establish a general branching rate condition under which maximum parsimony, a common reconstruction method requiring only the knowledge of the tree topology (but not of the substitution rates or other parameters), succeeds better than random guessing uniformly in the depth of the tree. We thereby generalize previous results of [13, 37]. Our results apply to both deterministic and i.i.d. edge weights.

Funding Statement

Supported by NSF grants DMS-1248176, DMS-1149312 (CAREER), DMS-1614242, CCF-1740707 (TRIPODS), DMS-1902892, DMS-1916378, DMS-2023239, as well as a Simons Fellowship and a Vilas Associates Award.


We thank Mike Steel for helpful discussions and an anonymous reviewer for suggested improvements to a previous version of the manuscript. Please send all queries to


Download Citation

Sebastien Roch. Kun-Chieh Wang. "Sufficient condition for root reconstruction by parsimony on binary trees with general weights." Electron. Commun. Probab. 26 1 - 13, 2021.


Received: 31 December 2020; Accepted: 26 August 2021; Published: 2021
First available in Project Euclid: 27 September 2021

Digital Object Identifier: 10.1214/21-ECP423

Primary: 92D15

Keywords: branching number , Markov model on a tree , parsimony , reconstruction problem


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