Stochastic spatiotemporal growth model reproducing the universal statistical laws of the gut microbiome

Although gut microbiomes exhibit host-specific complexity, it is becoming clear that their dynamics are governed by common rules. In this paper, we empirically show that three key statistical laws—the fat-tailed species abundance distribution, the scaling law of fluctuations, and the tent-shaped log growth rate distribution—are quantitatively universal across humans and mice. We further propose a simple stochastic model that comprehensively reproduces these statistical laws. The model is based on a microscopic model representing the dynamics of each species at local sites on the gut wall, modeled as a random multiplicative process. By introducing coarse-grained time and spatial scales that reflect real-world sampling processes, the model provides a physical interpretation of the dynamic properties of the empirical data, including timescales and temporal stochasticity. Furthermore, incorporation of diffusion effects predicts a heterogeneous spatial distribution on the gut wall. This model serves as a fundamental framework for the unified analysis of the spatiotemporal patterns of the gut microbiome.