Learning to count: robust estimates for labeled distances between molecular sequences.

Researchers routinely estimate distances between molecular sequences using continuous-time Markov chain models. We present a new method, robust counting, that protects against the possibly severe bias arising from model misspecification. We achieve this robustness by generalizing the conventional distance estimation to incorporate the empirical distribution of site patterns found in the observed pairwise sequence alignment. Our flexible framework allows for computing distances based only on a subset of possible substitutions. From this, we show how to estimate labeled codon distances, such as expected numbers of synonymous or nonsynonymous substitutions. We present two simulation studies. The first compares the relative bias and variance of conventional and robust labeled nucleotide estimators. In the second simulation, we demonstrate that robust counting furnishes accurate synonymous and nonsynonymous distance estimates based only on easy-to-fit models of nucleotide substitution, bypassing the need for computationally expensive codon models. We conclude with three empirical examples. In the first two examples, we investigate the evolutionary dynamics of the influenza A hemagglutinin gene using labeled codon distances. In the final example, we demonstrate the advantages of using robust synonymous distances to alleviate the effect of convergent evolution on phylogenetic analysis of an HIV transmission network.