Microbiome Damköhler number predicts lotic microbial community succession in river networks

River microbiomes are dynamic contributors to ecosystem function and sensitive indicators of hydrologic processes, yet predictive frameworks for their assembly across drainage networks remain limited. We introduce the microbiome Damköhler number (Da _m), a simple, mechanistic metric that captures the balance between microbial transport and growth. Adapted from chemical engineering, Da _m is defined as the ratio of microbial travel time to microbial community doubling time. Travel time was estimated from mean water residence time and doubling time from temperature-dependent growth rates. We tested this framework using microbiome datasets from four similarly sized US rivers with contrasting hydrology and temperature regimes. Microbial diversity correlated more strongly with Da _m than with basin identity, season, or water chemistry. Nearest Taxon Index (NTI) was consistently positive, indicating that environmental filtering controlled community assembly. Moreover, NTI increased with Da _m, suggesting stronger selection with longer travel times and shorter doubling times. Faith's phylogenetic diversity declined with Da _m, likely reflecting the progressive loss of phylogenetically diverse, non-growing taxa dispersed from surrounding landscapes. To evaluate predictive power, we fit generalized dissimilarity models and found that Da _m explained the largest share of phylogenetic turnover and substantially improved out-of-watershed predictions compared to models without Da _m. These results suggest that river microbiome succession is governed by the interplay between hydrologic transport and growth timescales. Because Da _m can be calculated from residence time and temperature, it provides a scalable, mechanistic predictor of microbiome structure in river networks and offers a unifying framework for forecasting microbial community assembly in flowing waters.