Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees

TL;DR

This paper provides exact conditions under which the root state in Markov models on trees can be reliably reconstructed as the number of leaves grows, with implications for evolutionary biology.

Contribution

It establishes necessary and sufficient conditions for consistent root reconstruction in Markov models on trees, filling a key theoretical gap.

Findings

Derived quantitative bounds on reconstruction error.

Answered a longstanding question by Gascuel and Steel.

Implications for ancestral sequence reconstruction in evolutionary models.

Abstract

We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root state estimator is said to be consistent if the probability that it returns to the true root state converges to 1 as the number of leaves tends to infinity. We also derive quantitative bounds on the error of reconstruction. Our results answer a question of Gascuel and Steel and have implications for ancestral sequence reconstruction in a classical evolutionary model of nucleotide insertion and deletion.