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Likelihood-free inference of phylogenetic tree posterior distributions
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Introduces Phyloformer 2, a likelihood-free neural posterior estimator for phylogenetic trees that combines an EvoFormer-inspired encoder (evoPF) with a BayesNJ factorized merge-based tree distribution.
Problem
Phylogenetic inference requires likelihood evaluations that are costly and intractable under realistic sequence evolution models, and existing likelihood-free methods only handle quartets or give point estimates of distances rather than full tree posteriors.
Approach
A parameterized posterior over full phylogenies factorized over a canonical succession of pairwise subtree merges (softmin merge scores plus Gamma/Beta branch-length distributions), with sequence embeddings from a pair-and-MSA transformer (evoPF) trained end-to-end by maximizing simulated log-probability.
Key results
- On LG+G8 data with 10-175 leaves, Phyloformer 2 greedy MAP gives better normalized RF accuracy than IQ-TREE and FastTree, and is about one order of magnitude faster than FastTree and two orders faster than IQ-TREE.
- Under intractable-likelihood models (Cherry, SelReg, Potts), PF2 topological error is reported as two to three times lower than likelihood-based methods.
- PF2 posterior branch probabilities are generally well calibrated on 196 simulated 50-taxon alignments, with a tendency to underestimate support.
Surprising findings
- Most of the topological accuracy gain over Phyloformer comes from the BayesNJ loss rather than the evoPF encoder, since PF2_MAE with distances plus FastME is only slightly better than PF.
- On two empirical datasets (NagyA1, ShenA9) PF2 performs slightly worse than other methods, attributed to erroneous gaps in poorly aligned empirical data.
Limitations
- Scalability limited to about 200 sequences on 16GB VRAM due to memory footprint.
- Requires aligned sequences; sensitive to alignment quality and erroneous gaps in empirical data.
- Distribution shift between simulated training data and empirical data may cause overconfident inference; the Cherry dataset contains an unrealistic co-evolution level due to a simulation error.
Experimental setup
Datasets: LG+G8 simulated tree-MSA dataset (IQ-TREE AliSim, rescaled birth-death priors) Multi-size LG+G8 dataset MCMC fine-tuning dataset (RevBayes uniform+exponential prior) Cherry dataset (from Phyloformer paper) SelReg dataset (from Phyloformer paper) Potts model PF00072 simulated dataset Empirical gene families (cyanobacteria, NagyA1, ShenA9 and others)
Benchmarks: Normalized Robinson-Foulds distance on simulated 10-200 taxa alignments Kuhner-Felsenstein distance Cherry model and SelReg benchmarks Potts PF00072 benchmark RevBayes posterior samples (50 taxa) Empirical cyanobacteria and other gene-family datasets
Metrics: normalized Robinson-Foulds distance Kuhner-Felsenstein distance branch posterior calibration runtime memory usage
Baselines: Phyloformer IQ-TREE FastTree FastME RevBayes PF2_MAE
Builds on: Phyloformer EvoFormer (AlphaFold 2) neural posterior estimation MSA Transformer sequential Monte Carlo phylogenetic sampler
Closest papers by meaning
- PhyloGen: Language Model-Enhanced Phylogenetic Inference via Graph Structure Generation (NeurIPS 2024 · similarity 0.92)
- Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes (NeurIPS 2026 · similarity 0.92)
- PhyloGFN: Phylogenetic inference with generative flow networks (ICLR 2024 · similarity 0.90)
- Variational Phylogenetic Inference with Products over Bipartitions (ICML 2025 · similarity 0.89)
- PhyloVAE: Unsupervised Learning of Phylogenetic Trees via Variational Autoencoders (ICLR 2025 · similarity 0.86)
- Sample Complexity of Branch-length Estimation by Maximum Likelihood (ICML 2025 · similarity 0.86)
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