Joint identifiability of ancestral sequence, phylogeny and mutation rates under the TKF91 model

TL;DR

This paper derives explicit formulas for jointly identifying ancestral sequences, phylogenies, and mutation rates under the TKF91 model, improving estimation methods and demonstrating their statistical consistency through simulations.

Contribution

It provides new explicit formulas and estimators for joint inference of ancestral sequences, phylogeny, and mutation rates under the TKF91 model, with less restrictive assumptions.

Findings

Explicit formulas for root sequence and pairwise distances

Estimators are statistically consistent with increasing data

Works for non-ultrametric phylogenies

Abstract

We consider the problem of identifying jointly the ancestral sequence, the phylogeny and the parameters in models of DNA sequence evolution with insertion and deletion (indel). Under the classical TKF91 model of sequence evolution, we obtained explicit formulas for the root sequence, the pairwise distances of leaf sequences, as well as the scaled rates of indel and substitution in terms of the distribution of the leaf sequences of an arbitrary phylogeny. These explicit formulas not only strengthen existing invertibility results and work for phylogeny that are not necessarily ultrametric, but also lead to new estimators with less assumption compared with the existing literature. Our simulation study demonstrates that these estimators are statistically consistent as the number of independent samples tends to infinity.