Analysis on the reconstruction accuracy of the Fitch method for inferring ancestral states

Accounting for ambiguity in ancestral sequence reconstruction

MOTIVATION

The reconstruction of ancestral genetic sequences from the analysis of contemporaneous data is a powerful tool to improve our understanding of molecular evolution. Various statistical criteria defined in a phylogenetic framework can be used to infer nucleotide, amino-acid or codon states at internal nodes of the tree, for every position along the sequence. These criteria generally select the state that maximizes (or minimizes) a given criterion. Although it is perfectly sensible from a statistical perspective, that strategy fails to convey useful information about the level of uncertainty associated to the inference.

RESULTS

The present study introduces a new criterion for ancestral sequence reconstruction, the minimum posterior expected error (MPEE), that selects a single state whenever the signal conveyed by the data is strong, and a combination of multiple states otherwise. We also assess the performance of a criterion based on the Brier scoring scheme which, like MPEE, does not rely on any tuning parameters. The precision and accuracy of several other criteria that involve arbitrarily set tuning parameters are also evaluated. Large scale simulations demonstrate the benefits of using the MPEE and Brier-based criteria with a substantial increase in the accuracy of the inference of past sequences compared to the standard approach and realistic compromises on the precision of the solutions returned.

AVAILABILITY AND IMPLEMENTATION

The software package PhyML (https://github.com/stephaneguindon/phyml) provides an implementation of the Maximum A Posteriori (MAP) and MPEE criteria for reconstructing ancestral nucleotide and amino-acid sequences.

On the Accuracy of Ancestral Sequence Reconstruction for Ultrametric Trees with Parsimony

We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under consideration. In particular, for the symmetric four-state substitution model which is also known as Jukes-Cantor model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that for any ultrametric phylogenetic tree and a symmetric model, the Fitch parsimony method using all terminal taxa is more accurate, or at least as accurate, for ancestral state reconstruction than using any particular terminal taxon or any particular pair of taxa. This conjecture had so far only been answered for two-state data by Fischer and Thatte. Here, we focus on answering the biologically more relevant case with four states, which corresponds to ancestral sequence reconstruction from DNA or RNA data.

Predicting the ancestral character changes in a tree is typically easier than predicting the root state

Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed for this purpose. Theoretical results are available that show that when the substitution rates become too large, reconstructing the ancestral state at the tree root is no longer feasible. Here, we also study the reconstruction of the ancestral changes that occurred along the tree edges. We show that, that, depending on the tree and branch length distribution, reconstructing these changes (i.e., reconstructing the ancestral state of all internal nodes in the tree) may be easier or harder than reconstructing the ancestral root state. However, results from information theory indicate that for the standard Yule tree, the task of reconstructing internal node states remains feasible, even for very high substitution rates. Moreover, computer simulations demonstrate that for more complex trees and scenarios, this result still holds. For a large variety of counting, parsimony- and likelihood-based methods, the predictive accuracy of a randomly selected internal node in the tree is indeed much higher than the accuracy of the same method when applied to the tree root. Moreover, parsimony- and likelihood-based methods appear to be remarkably robust to sampling bias and model mis-specification.