Sufficient condition for root reconstruction by parsimony on binary trees with general weights

TL;DR

This paper identifies a branching rate condition ensuring maximum parsimony reliably reconstructs ancestral states in binary trees with general weights, extending previous theoretical results.

Contribution

It establishes a general branching rate condition for successful root reconstruction by parsimony on weighted binary trees, broadening prior findings.

Findings

Maximum parsimony outperforms random guessing under the new condition

Results apply to both deterministic and i.i.d. edge weights

Generalizes previous theoretical conditions for ancestral state reconstruction

Abstract

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, succeeds better than random guessing uniformly in the depth of the tree. We thereby generalize previous results of (Zhang et al., 2010) and (Gascuel and Steel, 2010). Our results apply to both deterministic and i.i.d. edge weights.