No persistent circadian oscillator at genome resolution: pseudo-coherence in gut microbiome dynamics
Diurnal rhythms in the gut microbiome are commonly read as evidence of host-driven entrainment or of microbial oscillators that synchronise to a common clock. We reanalyse hourly genome-resolved (MAG-level) mouse-gut time series with diagnostics tailored to test that interpretation. At this resolution and for both animals in the dataset, the time-frequency representation carries no persistent ridge; the time-averaged spectrum is enhanced at low frequencies and depleted at intermediate frequencies; the lagged covariance is markedly time-asymmetric, with a global imbalance peak near tens of hours; and an amplitude-adjusted Fourier surrogate test identifies a weak time-averaged construction in the candidate circadian band, never as a fixed time-frequency ridge. The two functional guilds that carry the inferred non-normal amplification are identified independently by the rankings of two inferred dynamical modes (the reaction mode, into which fluctuations are transiently amplified, and the non-normal mode, which injects them), and recover the primary polysaccharide degraders of Bacteroidota and the secondary butyrate and propionate fermenters of Bacillota A without invoking any phase information. The conjunction of these signatures matches a stable but strongly non-normal stochastic regime, that is, pseudo-coherence: geometric amplification reshapes stochastic fluctuations onto a low-dimensional reaction subspace, producing intermittent synchronisation-like episodes, broken time-reversal symmetry, and emergent time-averaged characteristic scales without an underlying oscillator. We propose a falsifiable test via high-resolution clock-gene-knockout cohorts.