Improved estimation of molecular evolution coupling stochastic simulations and deep learning

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 substitutions, 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 tractable for large datasets, often leading to unrealistic simplifying assumptions in the fitted models. To overcome this issue, we couple 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 matches that of likelihood-based phylogenetic inference, when rate heterogeneity follows a simple gamma distribution, but it strongly exceeds 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 show on a dataset of 26 million nucleotides from the clownfish clade. Our simulations also show that the per-site rates obtained by deep learning increase the likelihood of the true tree and could therefore lead to more accurate phylogenetic inference. We 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 assessments of statistical support. ### Competing Interest Statement The authors have declared no competing interest.