Toward a semi-supervised learning approach to phylogenetic estimation.

Models have always been central to inferring molecular evolution and to reconstructing phylogenetic trees. Their use typically involves the development of a mechanistic framework reflecting our understanding of the underlying biological processes, such as nucleotide substitu- tions, and the estimation of model parameters by maximum likelihood or Bayesian inference. However, deriving and optimizing the likelihood of the data is not always possible under complex evolutionary scenarios or even tractable for large datasets, often leading to unrealistic simplifying assumptions in the fitted models. To overcome this issue, we coupled stochastic simulations of genome evolution with a new supervised deep learning model to infer key parameters of molecular evolution. Our model is designed to directly analyze multiple sequence alignments and estimate per-site evolutionary rates and divergence, without requiring a known phylogenetic tree. The accuracy of our predictions matched that of likelihood-based phylogenetic inference, when rate heterogeneity followed a simple gamma distribution, but it strongly exceeded it under more complex patterns of rate variation, such as codon models. Our approach is highly scalable and can be efficiently applied to genomic data, as we showed on a dataset of 26 million nucleotides from the clownfish clade. Our simulations also showed that the integration of per-site rates obtained by deep learning within a Bayesian framework led to significantly more accu- rate phylogenetic inference, particularly with respect to the estimated branch lengths. We thus propose that future advancements in phylogenetic analysis will benefit from a semi-supervised learning approach that combines deep-learning estimation of substitution rates, which allows for more flexible models of rate variation, and probabilistic inference of the phylogenetic tree, which guarantees interpretability and a rigorous assessment of statistical support.