Drivers of diversity within and between microbial communities during stochastic assembly.

No two microbial communities share the same species richness and abundance profiles. Experiments have shown that the assembly of new microbial communities from the same environmental pool is sufficient to generate diversity within and between communities: when microbial dispersal is slower than division, communities exhibit low richness but high between-community dissimilarity; when dispersal is faster, richness increases while dissimilarity decreases. Here, we study a minimal stochastic model that recovers these empirically observed assembly regimes. Our mathematical framework yields explicit expressions for the abundance fluctuation distributions across low-, intermediate- and high-dispersal regimes, providing a quantitative lens on microbiome assembly. We derive analytical predictions for the bimodality coefficient that quantifies the transition between assembly regimes, which appears as a robust metric to predict community richness and dissimilarity. Additionally, we highlight the mean relative abundance as a complementary metric sensitive to differences in microbial traits (e.g. dispersal or division rates). Applying these metrics to experimental data indicates their practical value for the rapid identification of assembly regimes and trait asymmetries. Overall, our study provides general predictions about how stochasticity, timescales and microbial traits influence both within-community diversity (richness) and between-community diversity (dissimilarity) during the assembly of new microbial communities. Our work thus contributes to a better understanding of the factors driving variation in microbiome formation.