Microbiome Damköhler number predicts lotic microbial community succession in river networks

Abstract

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.

Graphical Abstract

Graphical Abstract.

Introduction

Understanding the distribution, abundance, and function of Earth’s microbiomes has become a central goal in microbial ecology, with discoveries fueled in part by advances in next-generation sequencing, bioinformatics tools, and predictive modeling approaches. Broad scale comparisons of microbiomes show tremendous variability in community composition between habitat types (e.g., soils, lakes, ocean, sediments), and reveal a degree of habitat fidelity [1–3]. Freshwater systems stand out among these environments as hosting particularly high microbial diversity, in part due to extreme habitat heterogeneity across groundwater, streams, rivers, lakes, bogs, fens, and estuaries, but also because of dispersal and habitat transitions as freshwater moves across landscapes through complex drainage networks. Early studies show how freshwater microbiomes are seeded by dispersal from landscapes and document downstream shifts in composition toward typical planktonic communities [4–6]. We sought to develop a model that quantifies this shift in communities across drainage networks in order to better predict the composition of freshwater microbial communities.

As rivers flow from headwaters to the ocean, the ecosystems shift their reliance from allochthonous to autochthonous sources of carbon, nutrients, and energy, as encapsulated in the highly cited River Continuum Concept [7]. River microbial communities appear to track this ecosystem shift [8], transitioning from communities with terrestrial origins in smaller streams [4, 5] to distinct planktonic communities in larger rivers and lakes [2, 9, 10]. Moreover, recent evidence shows how planktonic communities can be diluted with terrestrial microbes during storm events [11]. In a large study of diverse freshwater environments in Quebec, Niño-Garcia et al. [12] showed how this community shift is linked to water residence time (WRT) which sets the time frame for bacterial growth. Recently, Bambakidis et al. [13] expanded on this idea in a detailed seasonal study of the Connecticut River drainage network in which they show that although WRT sets the time frame for bacterial growth, water temperature likely influences microbial growth rate and sets the pace of community succession.

To model these controls on lotic microbiomes, we employed the Damköhler concept, which has become a useful framework for evaluating spatial and temporal variability in river biogeochemistry [14, 15]. This concept was originally developed for chemical engineering applications to describe the influence of mixing on competitive chemical reactions [16, 17]. Damköhler number Da₁ is a unitless ratio defined as the transport time scale divided by the reaction time scale. Liu et al. [14] argue that Da₁ is a useful tool for modeling chemical reactions in river systems where transport time is calculated as instream WRT, and reaction time is calculated as a temperature-dependent value of the time required for a chemical reaction to occur—in their case the transformation of dissolved organic matter (DOM). According to this model, Da < 1 indicates a transport dominant system in which DOM composition is unchanged, and Da > 1 indicates a reaction-dominant system in which DOM undergoes chemical transformations. Ryan et al. [15] found that this Damköhler number representing DOM reactivity was a strong predictor of DOM diversity including the fraction of nitrogenous compounds and the putative number of biogeochemical transformations.

To assess the state of lotic microbial community succession we introduce a microbiome Damköhler number (Da_m) that integrates the influences of WRT and temperature on microbial community diversity. Da_m is defined as the ratio of timescales for microbial immigration and advection to microbial growth, under the assumption that growth is the primary mechanism by which microbial communities change [18, 19]. In this first approximation, microbial growth is estimated from temperature, which is a widely recognized control on microbial metabolic rates and has been shown to correlate with microbial growth in many river ecosystems [20–25]. We acknowledge that growth also depends on organic matter availability and other resources [26–29], but temperature-based estimates provide a practical starting point for modeling growth at large spatial scales. This ratio serves as a mechanistic hypothesis for controls on microbiome composition in streams and rivers where immigration and adaptation are continuous.

River networks play an outsized role in global biogeochemical cycles by transferring and transforming C and N pools between terrestrial ecosystems and the ocean. Microbes are the key players in these biochemical transformations, yet we lack a complete understanding of the drivers of river microbiome community structure and function, and thus the mechanisms underlying ecosystem processes. A predictive understanding of lotic microbiome succession is essential for modeling riverine microbial ecosystem function and for emerging applications such as using river microbiomes as hydrologic tracers (i.e., “genohydrology”) [30–34] and as indicators of environmental stressors [35, 36], land use [37], and microbial metabolism [38]. These studies recognize that while microbiomes retain a memory of the environment where they formed, they are not conservative tracers in lotic ecosystems because their composition changes in response to environmental conditions. Da_m provides a tool to quantify that response and to predict the compositional turnover of river microbiomes.

Materials and methods

We tested Da_m using a dataset of 16S ribosomal ribonucleic acid (rRNA) gene sequences collected from streams and rivers in four similar sized temperate watersheds in the US (Willamette, Deschutes, Gunnison, Connecticut) that feature contrasting land use and hydrology. Water samples were collected during four seasons (winter, spring, summer, fall) across a range of stream orders in each system including both free-flowing and reservoir-influenced reaches (Fig. 1, Table S1) [15]. Geospatial data for each site were acquired using a custom R script [39] that retrieved data from the National Hydrography Dataset version 2 (NHDPlus V2).

Figure 1.

(a) Map of sampling sites in four US watersheds (b) Willamette and Deschutes Rivers in Oregon, (c) Connecticut River in New England, and (d) Gunnison River in Colorado. Each watershed is outlined with a black boarder, and sampling sites are indicated with red circles. Principle coordinates analysis of weighted UniFrac distances among microbial communities in four watersheds with symbols colored to show that river microbial communities do not vary by river basin (e) and vary only weakly by season (f). PERMANOVA model results are shown in Table S2.

Microbial community composition was assessed with 16S rRNA gene amplicon sequencing. DNA samples were collected from river surface waters in acid-washed 2-L bottles, being careful to not resuspend sediments, filtered onto 0.22 μm pore size Sterivex-GP filters, and preserved with sterile RNAlater solution [70% (NH₄)₂SO₄, 10 mM EDTA, 25 mM sodium citrate, pH 5.2]. The preservative was allowed to diffuse into cells for approximately 5 minutes, after which filters were flash-frozen in a portable dry-shipper filled with liquid N₂ until final storage at −80°C. In the lab, filters were removed from Sterivex capsules, and DNA extracted with Zymo DNA/RNA Miniprep kits (R2002) following manufacturer’s instructions.

Microbial community composition analysis followed the procedure described in Bambakidis et al. [13]. Briefly, the V4 region of bacterial and archaeal 16S rRNA genes was polymerase chain reaction (PCR)-amplified with dual barcoded [40] primers 515F (GTGYCAGCMGCCGCGGTAA) [41] and 806R (GGACTACNVGGGTWTCTAAT) [42] using 250 nM primers (final concentration) and HotStarTaq master mix (Qiagen) under the following conditions (94°C for 3 min; 30 cycles of 94°C for 45 s, 50°C for 60 s, 72°C for 90 s; 72°C for 10 min). PCR products were purified and normalized with SequalPrep purification plates (ThermoFisher Scientific), combined, and sequenced on the Illumina MiSeq platform using v2 chemistry (2 × 251 base, paired-end reads). After sequencing, reads were processed with the QIIME2 bioinformatics pipeline [43], clustered into amplicon sequence variants (ASVs; 100% sequence similarity), classified using the Silva v.138 database [44, 45], and rooted in a phylogenetic tree. The taxonomy, phylogenetic tree, metadata, and ASV table files were imported into R (R Core Team 2021) v.4.3.3 and combined into a phyloseq object using the R package phyloseq [46]. Mitochondria, chloroplasts, and singletons were removed, and samples were rarified to 8287 sequences based on the distribution of reads per sample and to eliminate samples with low reads. This rarified phyloseq object contained a total of 181 samples across the four watersheds.

Microbial community travel time was calculated as mean surface WRT following Liu et al. [14] and as described in detail by Ryan et al. [15]. However, because calculated WRT can be extremely long when reservoirs are included (i.e., 100 to 1000 d), often exceeding ecological timescales for microbial succession, we performed sensitivity analyses using maximum reservoir residence times of 7, 15, 30, and 90 days, and 1 year. These thresholds were chosen to reflect biologically relevant timeframes for planktonic community assembly, which typically occurs within days to weeks rather than months or years [12]. For comparison, we also calculated travel time using the full effect of reservoir residence times (i.e., determined by reservoir hydrology), and ignoring the effect of reservoirs on travel time (i.e., river travel time only).

To develop the microbiome Damköhler number we first estimated specific growth rate for microbial communities (μ). Biological growth rates are inherently temperature dependent but can also vary with resource availability and other ecological factors. For this first approximation, we assumed that growth varies with temperature according to the Arrhenius law (Q₁₀), where a 10°C increase in temperature corresponds to a doubling of microbial growth rate. In assuming a μ of 1 d⁻¹ at 15°C, we estimated microbial growth rate as:

where μ is the calculated microbial specific growth rate (in days), μ₁₅ is the assumed specific growth rate at 15°C, Q₁₀ is the Arrhenius law (set to 2), and T_w is the water temperature of the sample (°C).

We then estimated microbial doubling time as:

where, t_d is the calculated doubling time of the microbial community, and μ is the calculated microbial specific growth rate.

The microbiome Damköhler number was estimated as:

where Da_m is the microbiome Damköhler number (unitless), TT is microbial community travel time (d), and t_d is the microbial doubling time (d). We interpreted Da_m < 1 to indicate a transport-dominant system largely comprised of organisms dispersed from land, while Da_m > 1 indicated a reaction-dominant system comprised of organisms adapted to the planktonic niche of the river water column. Across our dataset we found that t_d and TT were not correlated, and that Da_m was negatively related to t_d and positively related to TT (Fig. S1).

To examine microbial community structure using 16S rRNA amplicons, we performed principal coordinates analysis (PCoA) on weighted UniFrac distances with Cailliez correction using the functions beta.div and PCoA in the R packages rbiom [47] and ape [48].

To examine relationships between microbial community structure and environmental variables, we first performed PERMANOVA analysis using models that incorporated categorical (watershed, season) and continuous (temperature, travel time, Da_m) variables of interest. Models were blocked at the site level to account for variation between sites, and weighted UniFrac distances were used as the input microbial dataset. All models were executed using the function adonis2 in the R package vegan [49]. Second, we developed co-inertia models using the R package ade4 [50] as previously described [13]. Briefly, models were fit using correspondence analyses (CA) of the ASV abundance table, and principal components analyses of the environmental variables. After combining both hyperspaces into co-inertia models, the RV were evaluated to interpret the degree of correlation between both datasets, and individual inertia values for each environmental variable were used to interpret the relative role of each variable in describing microbial community structure.

Generalized dissimilarity models (GDM) were used to evaluate the relative importance and predictive power of Da_m in explaining microbial compositional turnover (i.e. beta-diversity) along the river continuum [51]. GDM accounts for nonlinear relationships in ecological data by modeling variation in the rate of compositional turnover along environmental gradients, and the curvilinear relationship between biological distance and environmental or geographical distances [51]. GDM were fit using the R package gdm [52], based on a site-pair table that incorporated the same weighted UniFrac distance matrix used in the PCoA, and the same environmental metadata table used in the co-inertia model. All default parameters were used except for setting bioFormat = 3 to incorporate the pre-existing weighted UniFrac distance matrix. We first fit a full model to evaluate goodness-of-fit and quantify the relative contribution of each predictor to compositional turnover. To assess predictive skill, we performed leave-one-watershed-out (LOWO) analysis to assess the held-out ability of Da_m to predict beta-diversity. Finally, we compared the full model with two alternatives: one excluding Da_m (“noDa_m”) and another excluding both Da_m and geographic location measured with latitude and longitude (“noDa_m-noGeo”), to determine the role of Da_m beyond spatial location and other environmental variables. Models and predictors were evaluated using deviance explained, predicted vs. observed compositional dissimilarity, I-spline height and shape for each environmental variable, and performance metrics including Pearson correlation (r) and root mean square error (RMSE).

As part of the sensitivity analysis, we fit linear mixed-effects models (LMMs) to investigate the relationships between Da_m (fixed effect) and microbial community structure (response variable) across a range of reservoir residence time limits. CA axis 1 scores from the same CA model used for co-inertia analysis served as the response variable. First, we tested whether slopes differed among watersheds by including watershed as a covariate and fitting a mixed model with a Da_m x watershed interaction. All models were fit with fixed slope but random y-intercept, with site as the random effect. Nearly all models showed a non-significant interaction, indicating that the relationship between Da_m and CA axis 1 was consistent among watersheds. Next, we removed watershed and selected the best-fit model using the lowest conditional Akaike information criterion (cAIC). All LMMs were implemented using lmerTest [53] and cAIC4 [54]. Model formulas and details are in Table S2.

Nearest Taxon Index (NTI) was used to measure the degree of phylogenetic clustering of taxa in our samples. We used the R package picante to calculate mean nearest phylogenetic taxon distance for each sample (MNTD_sample) and for global null model communities (MNTD_random) with 100 randomizations using ses.mntd with the taxa.labels setting. NTI was calculated as NTI = −1 * (MNTD_sample − MNTD_random)/sd_MNTD_random, where sd_MNTD_random is the standard deviation of the MNTD_random values. Positive NTI indicates a clustered phylogeny in which taxa are more related than expected by chance, and negative NTI indicates an overdispersed phylogeny in which clustering is lower than expected by chance [55]. We also calculated Faith’s phylogenetic diversity (PD).

Results and discussion

Microbial community diversity in freshwater systems, such as rivers and lakes, has long been recognized as strongly influenced by local seasonal climate cycles across diverse biomes, including arctic [2, 56], boreal [8], temperate [57, 58], and tropical [59, 60] regions. Community composition in these systems has also been linked to a range of biogeochemical features that favor growth of certain microbial taxa and distinguish systems from one another. To capture a broad spectrum of temperature and hydrologic regimes, we selected four watersheds of similar drainage area but contrasting terrestrial landscapes and climates: the Willamette, Deschutes, Gunnison, and Connecticut rivers (Figs 1 and 2). Our dataset comprises 181 samples consisting of seasonal samples collected using a nested sampling design that spanned stream orders 1–7, including sites downstream of reservoirs, and monthly samples from river mouths. In our dataset, microbial community composition did not vary significantly among watersheds and showed only weak seasonal patterns (Fig. 1, Table S3). Instead, composition was strongly associated with water temperature and microbial community travel time (Fig. S2, Table S3).

Figure 2.

Measurements of (a) water temperature and (b) river discharge, and calculations of (c) microbial community doubling time in days, and (d) microbial community travel time in days for end-member stations at the mouths of the four rivers sampled in this study during the year 2020, calculated with 15-day maximum residence time for water contributions from reservoirs. These figures show large differences among the rivers in seasonal patterns of temperature and river discharge. Microbial community doubling time scaled with temperature, being lowest (most rapid growth) during warmer summer months and highest (slowest growth) in winter. Differences in temperature among rivers caused, for example, doubling time to be nearly two times higher during winter in the Connecticut and Gunnison rivers compared to the Deschutes and Willamette rivers. Microbial community travel time is related to river discharge, but considers cumulative WRTs for all connected upstream reaches including those that feature reservoirs that increase travel time [14]. Thus, the Deschutes River has relatively high travel times because of the many dams on its tributaries and the Pelton and Round Butte dams on its mainstem. The Gunnison River also features many dams, including the Blue Mesa and Crystal dams on its mainstem, but contributions from free-flowing tributaries downstream of the dams, including the North Fork Gunnison River, reduces travel time at the river mouth.

These findings align with previous studies conducted across a range of stream orders including in Québec [12], the Connecticut River watershed [13], and the Congo River watershed [61]. In each case, the primary axis of variability reflected a transition from dispersed terrestrial communities in small streams to adapted planktonic communities in large rivers [4, 5]. Collectively, these results support the concept that lotic microbial communities exist in a dynamic state of succession, where the development of planktonic communities counters the influence of terrestrial microbial communities dispersed from land.

Microbiome Damköhler number

The microbiome Damköhler number (Da_m) is the ratio of the time available for microbial community succession to the microbial doubling time. Here, we scaled time for succession as microbial community travel time based on estimates of WRT, and we inferred microbial doubling time from water temperature. According to this model, river microbiomes at low Da_m are dominated by microbes dispersed from land, whereas those at high Da_m are dominated by communities adapted to the planktonic river environment. Because our estimate of doubling time varies only with temperature, Da_m integrates two distinct ecological dimensions: hydrologic transport (travel time) and microbial growth (temperature-dependent doubling time). Consistent with this, travel time and doubling time were only weakly negatively correlated across the dataset (R² = 0.07; Fig. S1). Importantly, microbial betadiversity correlated more strongly with Da_m than with travel time or temperature alone, or with any other variable we examined (Figs 3 and S2C and Tables S3 and S4). Thus, the combined metric captured by Da_m explains variation in microbiome composition more effectively than either of its component variables individually. These findings suggest that WRT and temperature are fundamental physical controls on lotic microbial communities, and that Da_m, by integrating both controls, is strongly associated with river microbiome composition across stream orders, seasons, and biomes.

Figure 3.

(a) PCoA diagram of weighted UniFrac distances among microbial communities in four watersheds with symbols colored by microbiome Damköhler number. (b) Coinertia model of weighted UniFrac distances with physical, chemical, and geospatial parameters microbiome Damköhler number (Da_m), total nitrogen concentration (TN), dissolved organic carbon (DOC) concentration, specific UV absorbance at 254 nm (SUVA, log₁₀ transformed), percent relative abundance of assigned molecular formula containing carbon, hydrogen, oxygen, and nitrogen normalized to the total number of formula (CHON, % relative abundance) [15], total number of putative biochemical transformations normalized by number of peaks (Norm. Trans.) [15], and percent land cover of deciduous forest, mixed forest, and conifer forest upstream of the sampling site.

By including samples from geographically distant watersheds, our results show that the shift from land-derived to river-adapted communities is greater than any geographic differences among rivers. For example, microbiomes in low Da_m streams in the Connecticut and Willamette River watersheds were more similar to each other than to microbiomes at the mouths of their respective rivers (Fig. 3). This pattern is consistent with environment-dependent trends in diversity observed in earlier surveys [1, 62], and suggests that low Da_m streams are populated by communities that formed in non-aquatic habitats such as terrestrial and subsurface environments. Taken together, these observations suggest that ecological succession, rather than spatial variation among basins, is the primary driver of microbial community composition in rivers.

Nearest taxon index

We next investigated controls on microbial community assembly using estimates of NTI, which is a standardized measure of the mean phylogenetic distance to the nearest taxon within a community and is used to assess the degree of phylogenetic clustering. Microbial communities that are shaped by environmental filtering tend to display phylogenetic clustering once an adapted set of phylotypes grow to dominate [55, 63, 64]. These communities also tend to become less phylogenetically diverse as slow- or non-growing taxa are diluted by growth of better-adapted taxa [65]. We found that NTI was always positive, indicating that microbes in rivers were more closely related than would be expected by chance. This suggests that environmental filtering always influences river microbiomes to some extent, favoring closely related taxa with similar ecological traits (Fig. 4a). We also found that NTI correlated positively with Da_m (Fig. 4a) suggesting that communities with higher Da_m had experienced greater environmental filtering. This was supported by calculations of Faith’s PD, which is the sum of the branch lengths of a phylogenetic tree connecting all species within a community. Faith’s PD was negatively correlated with Da_m, suggesting that high Da_m microbiomes have lower diversity, likely as a consequence of environmental filtering and loss of diverse taxa dispersed from land (Fig. 4b).

Figure 4.

Regressions of alpha diversity metrics with logarithmic regression models for (a) NTI and (b) Faith’s PD against microbiome Damköhler number presented on a logarithmic scale.

Prediction of phylogenetic turnover

We fitted GDMs to quantify the ability of Da_m to predict phylogenetic turnover (beta-diversity) across river networks. Weighted UniFrac distances were used instead of conventional indices such as Bray-Curtis to account for evolutionary relationships and relative species abundances [66]. The full GDM explained 32.5% of model deviance, and the I-spline plots indicated that Da_m ranked first as the most important predictor of phylogenetic turnover when other variables were held constant (Fig. S3). Da_m’s maximum I-spline height corresponded to a sum of coefficients of 0.214 (Fig. 5a, Table S5), which was an order of magnitude greater than the next variable (percent mixed forest cover = 0.072; Fig. S3), illustrating the importance of Da_m in driving phylogenetic turnover across the observed Da_m range. We then bootstrapped GDM I-spline importance using resampled site-pairs (B = 200), which showed that Da_m accounted for 50.2% of all partial ecological distance across predictors.

Figure 5.

Results of GDM using weighted UniFrac distances. (a) I-spline for Da_m showing a steep increase in predicted ecological distance with log₁₀ of Da_m. (b) Held-out predictive skill under LOWO cross-validation. Bars show Pearson correlation (r) between GDM-predicted ecological distance and observed dissimilarity for site pairs within the held-out watershed (Connecticut, Deschutes, Gunnison, Willamette). The full model includes all predictors including Da_m variables, whereas noDa_m excludes Da_m-related predictors. Higher r indicates better out-of-watershed generalization of phylogenetic turnover. (c) Held-out predictive skill by model type, showing show Pearson correlation (r) between predicted ecological distance and observed dissimilarity for site pairs. Models include LatLong (geographic distance), noDa_m (environmental predictors excluding Da_m variables), and full (all predictors including Da_m variables). The ranking full > LatLong > noDa_m indicates that environmental gradients predict phylogenetic turnover more effectively than geographic distance, and that Da_m provides unique information not captured by other environmental variables.

To evaluate predictive skill of Da_m, we performed LOWO analysis and compared three models: the full model including Da_m, a model excluding Da_m (“noDa_m”), and a model excluding both Da_m and geographic location (latitude-longitude; “noDa_m-noGeo”). The Full model consistently outperformed alternatives, with median held-out Pearson correlations of 0.558, 0.268, and 0.227, respectively (Fig. 5b). These findings demonstrate that Da_m substantially improves out-of-watershed generalization of phylogenetic turnover and suggests that Da_m provides out-of-sample explanatory power in predicting freshwater beta-diversity.

Across all iterations of LOWO, the addition of geographic location to the noDa_m model (noDa_m vs. noDa_m-noGeo) provided only modest improvement to predictive skill (median Δr = 0.075, range = 0.017–0.132) (Fig. 5c, Table S5). In contrast, adding Da_m to the no Da_m model (full vs. noDa_m) dramatically increased predictive skill by a median Δr of 0.27 (Δr range = 0.124–0.409) across LOWO iterations (Fig. 5c, Table S5). This consistent improvement indicates that hydrologic and temperature gradients, as integrated into Da_m, strongly predicts phylogenetic turnover in river networks. Da_m provides information not captured by other environmental variables (e.g., land cover, DOM chemistry) or geographic distance, predicting clade-weighted dissimilarity and suggesting repeatable clade-level shifts in microbiome composition across watersheds. Collectively, these results support a watershed-independent link between Da_m and phylogenetic structure in river microbiomes.

Model assumptions

Our calculations of Da_m are based on assumptions about doubling time and travel time that introduce a degree of uncertainty. For doubling time, we assumed that growth varies primarily with temperature, using a specific growth rate (μ) of 1 d⁻¹ at 15°C and a Q₁₀ of 2. While temperature is a strong predictor of bacterial productivity in many freshwater systems [20–25], several studies show that growth is also correlated with organic carbon availability and nutrient supply [24, 26–29]. For example, bacterial productivity in the Danube River peaked downstream of the cities of Budapest and Vienna and correlated most strongly with chlorophyll a [26], and in tropical rivers with little temperature variation, growth appeared to be controlled by substrate quantity and quality [24, 27, 28]. Experimental evidence further showed that carbon and nutrient limitation can outweigh temperature effects [28, 29], except at low temperatures (e.g., 4°C) [67]. Thus, although our temperature-based doubling time estimates (range 0.4 d to 2.0 d) are similar to those measured in many freshwater systems [19, 22], they likely oversimplify growth dynamics. Further refinements should incorporate substrate limitation and nutrient availability to improve estimates of μ and Q₁₀.

Microbial community travel time estimates introduce additional complexity. Our calculations are based on mean WRT, which can exceed one year when lakes and reservoirs are included [14]. In our dataset, some sites averaged 1180 days (3.2 years; Table S1). However, planktonic microbial communities assemble on much shorter timescales, as suggested by weekly to monthly shifts in lake microbiomes [56, 68], and by evidence of rapid stabilization of stream microbial diversity within 10 days of residence time [12]. Thus, calculated WRTs can be orders of magnitude longer than the time required for planktonic communities to develop. To address this mismatch, we conducted a sensitivity analysis of Da_m using a range of reservoir travel time thresholds. Da_m was consistently the strongest environmental variable in all co-inertia models (vector sum range 0.670–0.715), with the 7-d and 15-d reservoir limit models exhibiting the greatest model inertia (23.5%) and RV (0.3326), respectfully (Table S6). LMMs further showed that excluding reservoir residence time produced the best fit (cAIC = 97.1, mR² = 0.610, cR² = 0.888) (Table S2), and performance declined as reservoir limits increased. These findings suggest reservoirs exert minimal influence on microbial succession beyond about 15 days. Moreover, the finding of a significant interaction in models 6a and 7a suggests a breakdown in the relationship between Da_m and watershed at high or unlimited reservoir limits, providing further evidence that setting microbially relevant reservoir residence time limits yields a Da_m model that more accurately predicts microbial betadiversity across diverse watershed types. Based on this evidence, we adopted a 15-day reservoir time limit in our Da_m model, which reduced the average calculated microbial community travel time for all sites from 117 days to 9 days, a time scale that is more relevant to aquatic microbiome succession.

Microbial growth and removal processes

As a tool for microbiome prediction, Da_m emphasizes growth and adaptation of river microbiomes and assumes that growth is balanced by processes that remove less-adapted microbes from rivers including grazing by protists [69], hyporheic exchange [70], and sunlight inactivation via ultraviolet radiation (UVR) [71]. Hyporheic exchange can be extensive in smaller streams and rivers [72] and has the potential to limit the development of planktonic communities by capturing cells as they pass through hyporheic sediments. Observational and modeling studies indicate that hyporheic capture of river microbes decreases with increasing discharge [72, 73], suggesting that the potential for planktonic community development may be enhanced in larger rivers where hyporheic exchange is reduced. Sunlight and UVR generally have negative effects on pathogens and enteric bacteria, causing inactivation and death [71, 74]. Yet the effects of UVR on planktonic microbial communities is mixed [75, 76], and in many cases UVR can enhance growth [76, 77]. In this way, sunlight exposure may contribute to community shifts by selectively damaging non-adapted microbial taxa and favoring better-adapted planktonic microbial communities. Hyporheic exchange, sunlight exposure, and other factors that vary along watershed gradients (e.g., water temperature) likely introduce variability to estimates of microbial community doubling time and the pace of community succession. Nonetheless, Da_m provides an effective framework for explaining river microbiome succession across a broad range of stream orders, seasons, and biomes.

Relationship with seasonality

Early studies show strong seasonal variability in river microbiomes [2, 57], but these studies failed to identify drivers of this variability in part because most potential drivers of diversity also varied seasonally. Subsequent investigations determined that variability in hydrology and temperature appear to be the strongest drivers of seasonal shifts in community structure [8, 12, 13, 33]. travel time can vary greatly with seasonal changes in river flow across drainage networks. In temperate watersheds, travel times at any given stream order are longest during typical base flow conditions when discharge is at a minimum and stream velocity is likewise small. Following an influx of water from precipitation or snowmelt, travel time decreases proportionally to the size of the hydrologic event as velocity increases (Fig. 2). Our study incorporated samples from all four seasons, and we found the coefficient of variation (CV) for travel time was as high as 50% at some sites and averaged 8% across all sites. Thus, microbial community travel time can vary on daily to seasonal timescales based on patterns in river flow, precipitation, evapotranspiration, and snowmelt that are unique for each river system with long travel times during baseflow conditions (particularly during summer), and short travel times following storms, spring snow melt, and releases of water from impoundments.

Temperature is the most emergent property of seasonality in mid- and high-latitude systems. Almost every biological process, from metabolic rates to protein folding, is affected by temperature. Microbes possess both indirect and specialized sensing systems to detect and respond to changes in temperature, such as heat and cold shock responses [78, 79]. As such, temperature variability on seasonal timescales likely plays a significant role in microbial metabolic processes, biochemical reaction kinetics, and cell division. In our samples, temperature varied greatly among seasons with CV > 100% at many sites and an average of 68%. It is likely that seasonal variation in temperature-regulated growth rate of microbes plays a significant role in the pace and trajectory of riverine microbial community succession [13].

Da _m integrates these two emergent properties of seasonality – hydrology and temperature – that have historically explained patterns of microbial community structure and succession in river networks. For sites sampled during at least three seasons, the CV for Da_m ranged from 16% to 107%, and averaged 45%, suggesting that Da_m is a sensitive measure of seasonal variability across all stream orders. Our study focused on North American temperate rivers that feature large yet asynchronous seasonal changes in temperature and hydrology. Da_m typically peaks in summer when temperature is at its highest and discharge is low. However, snowmelt and flood events can disrupt this pattern, resulting in transient reductions in Da_m during these periods. In monsoonal rivers where temperature and hydrology vary synchronously, Da_m may vary seasonally within comparatively narrower ranges. Where temperature is less variable, such as in tropical systems, Da_m should vary primarily with travel time as systems experience seasonal variation in precipitation. In polar and boreal rivers, which have great seasonal variability in both temperature and hydrology, ice formation may impact Da_m during winter when small streams stop flowing and larger rivers are restricted by ice [80]. Across all latitudes, we think that Da_m has the potential to be a useful tool for predicting the succession of river microbiomes because it incorporates these two emergent properties of seasonality in river ecosystems.

Conclusion

River microbiomes are the key mediators in riverine biogeochemical processes, serving as sinks for terrestrial organic C and sources of organic C import to the ocean. Streams and rivers play a central role in the global C cycle, emitting 2.0 ± 0.2 Pg-C of CO₂ annually [81]. Given their importance to global biogeochemistry, we sought to predict river microbiome community succession based on the emergent physical properties of rivers, including the impacts of impoundment construction and climate change-driven shifts in hydrology and temperature. Our results show that the pace and trajectory of succession in riverine microbial communities are governed by the time available for community succession, and the temperature-regulated community growth rate. We developed a microbiome Damköhler number, Da_m, that integrates these two controls into a unitless ratio that correlates with the composition, diversity, and phylogenetic clustering of microbial communities across temperate watersheds with contrasting climate, geology, and land use. We suggest that Da_m is a fundamental rule of life for river bacterioplankton, offering a way to predict river microbial succession from temperature and WRT.

Author contributions

Byron C. Crump (Conceptualization, Formal analysis, Funding acquisition, Methodology, Visualization, Writing—original draft), Shaoda Liu (Data curation, Methodology, Software, Writing—review & editing), Peter A. Raymond (Conceptualization, Funding acquisition, Writing—review & editing), and Ted Bambakidis (Data curation, Formal analysis, Methodology, Visualization, Writing—original draft)

Conflicts of interest

The authors declare no competing interests.

Funding

This work was supported by the National Science Foundation (#1840243, #1836768), and a National Science Foundation—US Geological Survey INTERN grant to T.B.

Data availability

DNA sequences generated in this study are available in the Sequence Read Archive at the National Center for Biotechnology Information under BioProject ID PRJNA1242758 (http://www.ncbi. nlm.nih.gov). Physicochemical and geospatial data is archived at ESS-DIVE doi:10.15485/2406989.