Linear scaling reveals low-dimensional structure in observable microbial dynamics.

A critical latent dimension, E_c, is drastically lower than the apparent degrees of freedom, yet linearly scales with the number of observables for microbial dynamics captured from limited measurements.

• Why it matters: Microbial community behavior looks complex, but modeling and control often rely on few observables. This work tests whether those observable dynamics are low-dimensional and how that would support prediction with limited information.
• What they did: Variational autoencoders were used to define E_c as the smallest latent dimension achieving high-fidelity reconstruction under a specified criterion. E_c was then evaluated across multiple simulation models and experimental/human microbiome datasets.
• The result: E_c scales linearly with the number of observables across pairwise interactions, consumer-resource dynamics, spatial patches, plasmid transfer, engineered and environment-derived communities, and human microbiomes. This scaling law implies low-dimensional representations can retain information for selected prediction tasks without measuring the full community.

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