SDSR: A Spectral Divide-and-Conquer Approach for Species Tree Reconstruction

2026-03-10

AI Summary

This study addresses the computational challenges posed by gene tree–species tree discordance and the scalability limitations inherent in analyzing large-scale phylogenomic datasets. The authors propose a scalable divide-and-conquer algorithm grounded in spectral graph theory, which— for the first time—integrates spectral clustering with a recursive partitioning strategy to decompose the species set. Subtrees are reconstructed on each subset using existing methods such as CA-ML or ASTRAL and then efficiently merged. Under the multispecies coalescent model, the algorithm enjoys theoretical guarantees for accurate species tree recovery while substantially reducing computational complexity. Empirical evaluations on simulated data demonstrate up to a tenfold speedup compared to full-data analyses, without compromising topological accuracy.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Machine Learning: Scalability of ML Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Recovering a tree that represents the evolutionary history of a group of species is a key task in phylogenetics. Performing this task using sequence data from multiple genetic markers poses two key challenges. The first is the discordance between the evolutionary history of individual genes and that of the species. The second challenge is computational, as contemporary studies involve thousands of species. Here we present SDSR, a scalable divide-and-conquer approach for species tree reconstruction based on spectral graph theory. The algorithm recursively partitions the species into subsets until their sizes are below a given threshold. The trees of these subsets are reconstructed by a user-chosen species tree algorithm. Finally, these subtrees are merged to form the full tree. On the theoretical front, we derive recovery guarantees for SDSR, under the multispecies coalescent (MSC) model. We also perform a runtime complexity analysis. We show that SDSR, when combined with a species tree reconstruction algorithm as a subroutine, yields substantial runtime savings as compared to applying the same algorithm on the full data. Empirically, we evaluate SDSR on synthetic benchmark datasets with incomplete lineage sorting and horizontal gene transfer. In accordance with our theoretical analysis, the simulations show that combining SDSR with common species tree methods, such as CA-ML or ASTRAL, yields up to 10-fold faster runtimes. In addition, SDSR achieves a comparable tree reconstruction accuracy to that obtained by applying these methods on the full data.

Problem

• species tree reconstruction
• gene tree discordance
• computational scalability
• multispecies coalescent
• phylogenetics

Innovation

• spectral graph theory
• divide-and-conquer
• species tree reconstruction
• multispecies coalescent
• scalable phylogenetics