Ancestral sequence reconstructions evaluated by extant sequence cross-validation

Ancestral sequence reconstruction (ASR) has become widely used to analyze the properties of ancient biomolecules and to elucidate the mechanisms of molecular evolution. By recapitulating the structural, mechanistic, and functional changes of proteins during their evolution, ASR has been able to address many fundamental and challenging evolutionary questions where more traditional methods have failed. Despite the tangible successes of ASR, the accuracy of its reconstructions is currently unknown, because it is generally impossible to compare resurrected proteins to the true ancient ancestors that are now extinct. Which evolutionary models are the best for ASR? How accurate are the resulting inferences? Here we answer these questions by applying cross-validation (CV) to sets of aligned extant sequences. To assess the adequacy of a chosen evolutionary model for predicting extant sequence data, our column-wise CV method iteratively cross-validates each column in an alignment. Unlike other phylogenetic model selection criteria, this method does not require bias correction and does not make restrictive assumptions commonly violated by phylogenetic data. We find that column-wise CV generally provides a more conservative criterion than the AIC by preferring less complex models. To validate ASR methods, we also apply cross-validation to each sequence in an alignment by reconstructing the extant sequences using ASR methodology, a method we term extant sequence reconstruction (ESR). We can thus quantify the accuracy of ASR methodology by comparing ESR reconstructions to the corresponding true sequences. We find that a common measure of the quality of a reconstructed sequence, the average probability of the sequence, is indeed a good estimate of the fraction of the sequence that is correct when the evolutionary model is accurate or overparameterized. However, the average probability is a poor measure for comparing reconstructions, because more accurate phylogenetic models typically result in reconstructions with lower average probabilities. In contrast, the entropy of the reconstructed distribution is a reliable indicator of the quality of a reconstruction, as the entropy provides an accurate estimate of the log-probability of the true sequence. Both column-wise CV and ESR are useful methods to validate evolutionary models used for ASR and can be applied in practice to any phylogenetic analysis of real biological sequences.