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Phylograd: fast column-specific calculation of substitution model gradients
Benjamin Lieser1,2, Georgy Belousov3, Johannes Söding3,4
1Quantitative and Computational Biology, Max Planck Institute for Multidisciplinary Sciences, Am Faßberg 11, Göttingen, 37077, Germany. benjamin.lieser@mpinat.mpg.de.
BMC Bioinformatics
|December 23, 2025
Summary
PhyloGrad significantly speeds up phylogenetic tree reconstruction by enabling efficient computation of column-specific evolutionary models. This new method is much faster and uses less memory than existing automatic differentiation tools, facilitating novel model exploration.
Area of Science:
- Computational Biology
- Phylogenetics
- Bioinformatics
Background:
- Phylogenetic tree reconstruction tools commonly use single or limited substitution matrices across all sequence alignment columns.
- Exploring column-specific rate matrices is computationally intensive due to the complexity of calculating gradients for matrix exponentials.
Purpose of the Study:
- To develop an efficient method for computing gradients of the log-likelihood in phylogenetic analysis.
- To enable the practical implementation of models with column-specific rate matrices.
Main Methods:
- Introduced PhyloGrad, a Rust-implemented tool with Python bindings for reverse-mode automatic differentiation.
- Applied Felsenstein's algorithm and supports any time-reversible substitution model.
Main Results:
- PhyloGrad demonstrates 30-100x speedup and 10-100x memory reduction compared to PyTorch's automatic differentiation.
- It is at least 10x faster than IQ-TREE3 for global model fitting.
- Accelerates optimization and facilitates exploration of novel site-specific models.
Conclusions:
- PhyloGrad overcomes computational barriers in phylogenetic model optimization.
- Enables broader adoption and development of sophisticated, site-specific evolutionary models.
- Advances the field of phylogenetics by making complex models computationally tractable.
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