Origins of scaling laws in microbial dynamics

Abstract

Analysis of high-resolution time series data from the human and mouse gut microbiomes revealed that the gut microbial dynamics can be characterized by several simple scaling laws. It is still unknown if those scaling laws are universal across different habitats, e.g., different body sites, host species, or even free-living microbial communities. Moreover, the underlying mechanisms responsible for those scaling laws remain poorly understood. Here, we demonstrate that those scaling laws are not unique to gut microbiome, but are universal across different habitats, from human skin and oral microbiome to marine plankton bacteria and eukarya communities. Moreover, we find that completely shuffled time series yield very similar scaling laws (up to the change of some exponent values), which prompts us to conjecture that the universal scaling laws in various microbiomes are largely driven by temporal stochasticity of the host or environmental factors. To quantify the temporal stochasticity of those microbiome time series, we perform noise type analysis, finding that the noise types for those time series are all dominated by white and pink noises, indicating their very weak temporal structure and strong temporal stochasticity. Finally, we leverage a simple population dynamics model with both deterministic interspecies interactions and stochastic noise to confirm our conjecture. In particular, we find that the emergence of those scaling laws is jointly determined by interspecies interactions and linear multiplicative noises. The presented results deepen our understanding of the nature of scaling laws in microbial dynamics.