Copy number alterations (CNAs) provide key information on tumor evolution and are now accessible at single-cell resolution through low-coverage DNA sequencing. Reconstructing accurate phylogenies from scDNA data is challenged by the complexity of copy number evolution and the inherent noise in single-cell measurements. Several methods have been developed for this purpose, but unlike classical sequence-based phylogenetics, they do not apply probabilistic distance corrections that account for finite-length observations. Such corrections, as in the Jukes-Cantor model, are essential for theoretically consistent tree inference. We present Cellmates, a statistical framework for reconstructing copy number phylogenies from single-cell read counts using probabilistically corrected, additive distances. Such distances are estimated through an efficient expectation-maximization procedure, implemented with the use of a tailored Hidden Markov Model, and then combined with a neighbor joining variant that explicitly accounts for a diploid root node. Results on simulated and real tumor datasets show that Cellmates reconstructs accurate phylogenies and outperforms other methods while remaining computationally efficient. As a consequence, Cellmates provides a statistically grounded framework for copy number evolution from single-cell data.

Background: Phylogenetic tree reconstruction from single cell data based on copy-number alterations (CNAs) is an important problem in cancer genomics. Methods have been developed to address this problem by computing pairwise distances between copy-number profiles and employing a tree reconstruction algorithm. Despite the tight interplay between distance estimation and tree reconstruction, these two steps are often treated as separate problems, with the choice of the reconstruction algorithm receiving little attention. Most methods rely on classical Neighbor Joining (NJ), an algorithm designed for unrooted phylogenies that does not account for the fixed diploid root inherent to copy-number evolution.

Results: We identify the Deepest Least Common Ancestor NJ (DLCA–NJ), not previously applied in this context, as the appropriate algorithm for phylogenies from copy-number data. By leveraging the known diploid root, it consistently outperforms standard NJ on simulated benchmarks across all evaluated metrics, with the most pronounced improvement in root placement accuracy. Building on these findings, we introduce Sparse Rooted Neighbor Joining (SRNJ), a scalable adaptation of DLCA–NJ. SRNJ significantly reduces running time while trading off only a minor loss in accuracy. We provide theoretical and empirical evidence of robustness to mutation rate using both synthetic and real biological datasets.

Conclusions: Rooted NJ variants offer a principled way to exploit the known diploid root when reconstructing phylogenies from copy-number data, and SRNJ extends this advantage to datasets whose size places the full distance matrix out of reach. The gains are clearest where distances are reliable, as on simulated data, while on real data accuracy appears to be constrained by distance estimation rather than by the reconstruction algorithm, leaving room for improvement as callers advance.

Sampling random spanning arborescences in directed graphs is critical for applications in network analysis, optimization, and machine learning. While many state-of-the-art methods perform well on graphs with high conductance, they often fail or generalize poorly on low-conductance graphs. Inspired by Wilson's algorithm, we propose a novel sampling approach that overcomes this limitation by using dynamic programming to compute random walk probabilities. This avoids both inefficient walk simulations and numerically unstable Laplacian determinant calculations. Our method demonstrates superior efficiency and sampling quality in simulations, and is the only one to handle low-conductance graphs effectively.

Clonal tree inference brings crucial insights to the analysis of tumor heterogeneity and cancer evolution. Recent progress in single cell sequencing has prompted a demand for more advanced probabilistic models of copy number evolution, coupled with inference methods which can account for the noisy nature of the data along with dependencies between adjacent sites in copy number profiles. We present VICTree, a variational inference based algorithm for joint Bayesian inference of clonal trees, together with a novel Tree-structured Mixture Hidden Markov Model (TSMHMM) which combines HMMs related through a tree with a mixture model. For the tree inference, we introduce a new algorithm, LARS, for sampling directed labeled multifurcating trees. To evaluate our proposed method, we conduct experiments on simulated data and on samples of multiple myeloma and breast cancer. We demonstrate VICTree’s capacity for reliable clustering, clonal tree reconstruction, copy number evolution and the utility of the ELBO for model selection. Lastly, VICTree’s results are compared in terms of quality and speed of inference to other state-of-the-art methods. The code for VICTree is available on GitHub: github.com/Lagergren-Lab/victree and the full paper on bioRxiv.