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 [GS10] and have implications for ancestral sequence reconstruction in a classical evolutionary model of nucleotide insertion and deletion [TKF91].
"Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees." Electron. J. Probab. 23 1 - 24, 2018. https://doi.org/10.1214/18-EJP165