THE UNIVERSITY OF CHICAGO
Introducing the Spectral Tree: A new geometry of evolutionary diversity
Published in Cell Systems in 2025
What shape does biological diversity take? For centuries, evolutionary biology has answered this with the tree—a metaphor for descent with modification. But if what if three isn’t just a conceptual framework? What if it’s embedded in the statistics of variation across life?
In our paper, we introduced a new mathematical paradigm called the Spectral Tree—a tree inferred directly from the eigenspectrum of extant diversity that is recoverable without any phylogenetic reconstruction, further tuning or optimization, or mechanistic assumptions. We applied this to all bacteria in the UniProt database, creating a Spectral Tree for bacteria, then studied a bank of commensal strains procured from the gut microbiome of many healthy human donors. Our Spectral Tree revealed (i) differences between individual strains of the same species (so-called ‘strain-level variation’ for the aficionados) and that (ii) these strain-level differences were driven by which donor the bacterium came from. What does this mean? It means that there is evolution of individual bacteria happening in each one of us that could be the nucleus for further speciation events and new donor-specific selection pressures for further bacterial evolution.
This study represented a profound shift in our laboratory’s understanding of conceptualizing extant diversity. Using nothing but distances between entities—be they proteins, morphologies, or other high-dimensional representations—we could imagine creating a hierarchy that directly emerges from spectral decomposition of variation. That is, the low-rank structure of the similarity matrix itself encodes a tree—a representation that is smooth, ordered, and deeply constrained.
Our findings challenged traditional ideas about what constitutes ‘noise’ in biological data. What looks like high-dimensional scatter is, under spectral projection, a coherent, low-dimensional hierarchy. In doing so, the Spectral Tree provided the first statistical-mechanical description of hierarchical organization across biological systems—one that sidesteps phylogenetic inference entirely. The implication? The structure of evolution is not inferred—it is immanent. The tree is already there, latent in the geometry of the data.
The challenge now shifts from constructing it to learning how to use it. This has become a focal point of research projects in our laboratory.
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