In MCoM, any momentary state of the microbial model system is represented by variables describing chemical concentrations and population densities of the model's components. These state variables are time-dependent, where the time t is measured in days. MCoM's state space is comprised of the following variables:

Phytoplankton population densities Pi(t), i∈P (cellsL-1)

We are using index sets P (phototrophs), H (heterotrophs), N (DON compounds), C (DOC compounds), and M (metabolites) throughout the text to enumerate the different components of a specific type. These indices are used extensively to refer to parameters, which occur in different contexts. For instance, Vj→i with i∈H and j∈C denotes the maximal uptake rate of the DOC compound Dj associated with the heterotroph population Hi. For an overview of parameters and associated physical units, we refer to Table S1 in the Supplement. In MCoM, all parameters, as well as the community size and interaction network are fully customizable by configuration files following a scheme described in the README provided with the model's source code (Lücken et al., 2026). The configuration format allows for an explicit definition of all parameters, in particular the interaction matrices shown in Fig. b. Additionally, it provides means for randomized community generation.

In the following subsections, we define the different processes that determine the dynamics in detail. For the formal presentation, we use the notation fX→Y to denote elemental fluxes, where X is the source and Y the sink of the corresponding flow. The unit of a flow is the unit of its source and sink per day. We list all flows in Table S2 of the Supplement. Parameters are indexed by the state variable(s) they adhere to. For instance, δi with i∈P denotes the loss rate for the phytoplankton population Pi, and VN→i denotes the maximal DIN uptake rate for the population Pi. A full list of parameters is given in Table S1. For some parameter, additional information is included in a superscript. E.g., χiChl and χiN denote the cellular chlorophyll and nutrient content, respectively.

Further, please note that we assume fixed stoichiometric molar ratios riC:N (for i∈P and i∈H) and an average cell carbon content χiC. Hence, although the populations are measured in cells density, elemental C- and N-content can be associated unambiguously given riC:N and χiC.

The growth of a phytoplankton population Pi is governed by 1ddtPi=(fC→i︸biomass assimilation-fi→DOC)︸biomass decay/χiC-ΔPi,︸physical transport where χiC is the cellular carbon content, fC→i is the photosynthetic carbon assimilation flux, fi→DOC summarizes losses of biomass to DOC, and Δ is a physical transport rate, which can, e.g., be used to model dilution or washout in chemostat setups. Assuming a fixed stoichiometric composition of the biomass of population Pi, the elemental in- and outfluxes of carbon and nutrient must adhere to the corresponding C:N-ratio riC:N. Algebraically, this is expressed as 2fC→i=riC:N⋅fN→i,︸influx and fi→DOC=riC:N⋅fi→DON.︸outflux

We apply Liebig's minimum principle to distinguish two different growth regimes, depending on the limiting factor. Specifically, light intensity determines the maximal carbon assimilation rate fC→imax⁡, while nutrient availability governs the maximal nutrient assimilation rate fN→imax⁡. As the realized fluxes must adhere to the stoichiometric constraints (), nutrient limitation occurs when 3riC:N⋅fN→imax⁡<fC→imax⁡, and light limitation when riC:N⋅fN→imax⁡>fC→imax⁡.

The bacterial population densities Hi change according to: 10ddtHi=(fDOC→i︸biomass assimilation-fi→DOC)︸biomass decay/χiC-ΔHi,︸physical transport where fDOC→i describes the carbon assimilation into biomass from DOC compounds and fi→DOC the loss of biomass to organic compounds. As for phytoplankton, heterotrophs are modelled with a fixed stoichiometric composition riC:N, which is preserved by imposing 11fDOC→i=riC:N(fDON→i+fN→i),︸influx and fi→DOC=riC:N⋅fi→DON.︸outflux

Since heterotrophic populations are assumed to obtain nutrients from inorganic and organic sources, the constraint for the influx involves both sources. Importantly, the DOM assimilation fluxes are aggregates of fluxes from individual compounds, i.e., 12fDOC→i=∑j∈Cfj→i, and fDON→i=∑j∈Nfj→i.

Growth may be limited either by DOC or by total (organic and inorganic) nutrient availability, and the realized assimilation flux is determined by a minimum principle comparing maximal total assimilation rates of carbon (fDOC→imax⁡) and nutrient (fN→imax⁡+fDON→imax⁡). A population Hi is nutrient limited if 13riC:NfN→imax⁡+fDON→imax⁡<fDOC→imax⁡, and energy limited if the opposite holds.

The dynamics of individual DOM compounds are considered to follow the form 26addtDj=fH→j+fP→j+fC→j-fj→H-fj→C-ΔDj, for j∈C,26bddtDj=fH→j+fP→j︸population decay+fN→j︸exudation-fj→H-fj→N︸uptake-ΔDj,︸physical transport for j∈N.

Here, influxes originate from phytoplankton and heterotroph population decay and from DOM exudation by phytoplankton, and outfluxes correspond to consumption by heterotrophs.

In Sects.  and , we introduced the aggregate fluxes fi→DOC and fi→DON, i∈P or i∈H. To determine their impact on the concentrations on individual DOM compounds Dj, we assume specific partitioning coefficients 27∑j∈CRi→j=∑j∈NRi→j=1.

That is, the individual fluxes are calculated as 28afi→j=Ri→jfi→DOC, for j∈C,28bfi→j=Ri→jfi→DON, for j∈N.

For simplicity, the excess DOC- or DON-exudation fC→DOCi and fN→DONi by phytoplankton is assumed to follow the same partitioning to individual compounds: 29afC→ji=Ri→jfC→DOCi, for j∈C,29bfN→ji=Ri→jfN→DONi, for j∈N.

Further, we denote the total uptake and remineralization fluxes per compound by 30fj→N=∑i∈Hfj→Ni,fj→C=∑i∈Hfj→Ci,fj→H=∑i∈Hfj→i.

Metabolite pools Mj are modelled without any specific stoichiometry, since their contribution to the total DOM is assumed to be negligible. The energy expenditure for their synthesis is modelled by the corresponding loss term in Eq. (). The concentrations Mj represent a basis to calculate the impact of metabolite Mj on susceptible phytoplankton species as described in Sect. . They are governed by production and decay: 31ddtMj=θj∑i∈Hπi→jfDOC→i︸production-δjMj︸decay-ΔMj︸physical transport.

Here, the coefficient θj determines the amount of biomass required to synthesize a unit of Mj and δj determines the decay rate of Mj.

The change of nutrient concentration is driven by uptake from phytoplankton and heterotrophs and remineralization of DON by heterotrophs. Further, MCoM permits to define an external nutrient concentration Next to model exchange of medium with an external domain: 32ddtN=fDON→N︸remineralization-fN→P+fN→H︸consumption-ΔN-Next︸physical transport.

Here, the aggregate flows are defined as 33fDON→N=∑i∈H∑j∈Nfj→Ni,fN→P=∑i∈PfN→i, and fN→H=∑i∈HfN→i.

A key feature of MCoM is the straightforward scalability to larger interaction networks. The size and connectivity of the interaction network, i.e., the number of phototroph populations, heterotroph populations, metabolites, and organic compounds can be specified in the configuration file, together with respective parameter values and interaction matrices. MCoM offers different built-in ways to define microbial communities and their interaction networks: For controlled set-ups, it is possible to define all rate constants and interactions explicitly. This explicit definition allows the user to write their own algorithms for the generation of the community's interaction network. To generate randomized networks, the entire community or a subset of parameters can be determined stochastically. When employing stochastic network generation, reproducibility can be ensured by setting a seed for the random generation.

Parameter run.system_seed

In the following sections, we evaluate model performance for individual motifs of the interaction network as the smallest unit in diverse microbial communities. In a first example, we apply the simplest version of the model, i.e., a co-culture of one phototrophic and one heterotrophic strain, without any metabolite-induced feedbacks, to an incubation experiment to assess its capability to reproduce the observed temporal variation in cell abundances. cultured Synechococcus populations over a 200 d period in co-cultures with two different heterotrophic bacteria (R. Pomeroyi and Tropicibacter sp.) in nutrient enriched ASW medium. When grown axenically, the phototroph population went extinct around day 75–100. If it was co-cultured with a heterotroph, it remained active until the end of the experiment at day 200. The key interaction was hypothesized to be a mutual exchange of essential resources . Synechococcus provided organic material to the heterotrophs, from which these extracted energy and nutrients. In return, the heterotrophs remineralized nutrients, making them available to Synechococcus again. Although the phototroph population densities reached a peak around days 30–40 for each setup, they showed significantly distinct growth trajectories for the different types of heterotrophs. When grown together with R. Pomeroyi, the subsequent population decay proceeded steadily at a relatively slow rate until reaching 2.7–4.4 × 10⁷ cellsmL-1 at day 200. For Tropicibacter sp., the temporal development after the initial peak is less stable (cf. Fig. c). Within the subsequent 60–70 d, Synechococcus collapsed to minima of 1.0–13.0 × 10⁵ cellsmL-1 attained around days 96–117 for this case. These minima were then followed by a gradual recovery of the population density until reaching another peak at 3.6–14.7 × 10⁷ cellsmL-1 at the penultimate measurement time around day 190, declining again at the last measurement on day 200 to densities 1.1–2.1 × 10⁷ cellsmL-1.

We modelled both co-cultures and the axenic growth using MCoM with fixed growth parameters for the phototroph and specific characteristics for the heterotrophs. We first selected all parameters manually within plausible ranges (cf. Sect. S7 in the Supplement), aiming at a qualitative reproduction of the timing and amplitude of the observed changes in cell densities. Using this parametrization as a starting point, a subset of parameters was used for an automatic maximization of the sum of the R2-values for the different experiments using the Nelder–Mead routine of the scipy.optimization package,. Optimized parameters are: VN→i, fC→imax⁡, and δi for Synechococcus, and VDON→i, VDOC→i, VDON→i, VDON→i, and δi for the heterotrophic bacteria. The exact values are listed in Table S3 in the Supplement. Importantly, we did not assume metabolite interactions, but the observations could be reproduced qualitatively by the exchange of nutrients in inorganic and organic form.

As an important characteristic of R. Pomeroyi, we incorporated the observation that it did not take up ammonium (as demonstrated in another experiment of ). Further the optimized value for YDON (∼ 0.25) implies that R. Pomeroyi immediately remineralizes ∼ 75 % of DON during uptake, thus providing a steady nutrient source for Synechococcus. This recycling of nutrients slowed down the Synechococcus population decline significantly. However, to reproduce the steady decline observed in the experiment, a certain fraction of nutrients must continuously escape the recycling. Otherwise, the total nutrient in both populations and thus their densities would asymptote towards positive constants. We incorporated this by assuming that a fraction (e.g., 10 % for R. Pomeroyi) of the DON release is channelled into a “refractory” pool, which accumulates during the experiment. This pool represents a sink for non-recyclable matter, encompassing not only refractory DON, but all other inaccessible nutrient sinks, e.g., particulate forms.

For the other co-culture, the more severe collapse of the Synechococcus population could be explained by an ongoing competition for inorganic nutrient with Tropicibacter sp., which is assumed to have a higher nutrient affinity (VN/KN) than Synechococcus, i.e., a competitive advantage under low-nutrient conditions. For Tropicibacter sp., the optimized value YDON=0.75 for the assimilated fraction of organic nutrient is significantly higher than for R. pomeroyi, suggesting a more parsimonious remineralization of DON. This leads to a domination of the heterotroph until DOC is depleted and it becomes energy-limited around day 90. During the energy-limited regime, inorganic nutrient is available for Synechococcus once again, which induces a second growth phase.

To explore the impact of DOC exudation and DON remineralization, we included comparative simulations with reduced impact of either process in the Sect. S3 in the Supplement.

In a next step, we evaluate MCoM's ability to model metabolite-induced feedbacks between heterotrophs and phototrophs. For this, we consider Prochlorococcus co-culture experiments conducted by . Cultures were grown on Pro99 medium containing an initial stock of 0.8 mMNH4 and 0.01 % w/v organic carbon sources. Based on the cultures' observed bulk chlorophyll fluorescence over time, clustered the heterotrophs into clearly separated groups exhibiting either inhibitory, neutral or growth-promoting effects on Prochlorococcus. Growth-promoting bacteria induced an earlier (-4 d on average, Fig. b) and more pronounced peak of the phototroph population than observed for the axenic (Fig. a) (or neutrally affected) cases, while inhibitory bacteria significantly delayed the peak (+13 d on average, Fig. c).

We chose two representative examples from the experimental arrays for illustration. In co-culture with a Rhodobacterales strain (HOT5B8), Prochlorococcus growth was clearly promoted (Fig. b), whereas in co-culture with a Marinobacter strain (HOT4B5), growth was inhibited (Fig. c). For the simulations, we used identical parameters for both heterotrophs and only varied the metabolite impact coefficient aM (cf. Eq. , simplified subscript) using aM=-0.137 for the growth promoting case and aM=0.114 for the inhibitory case. All parameters were initially selected manually within plausible ranges. Subsequently, key parameters (VN→H, VN→P, δP, VDOC→H, YDOC→H, aM) were subjected to an automatic minimization using the Nelder–Mead routine of the scipy.optimization package, of the root mean square error of simulated and observed growth curves.

For both modelled co-cultures the simulated metabolite concentrations initially accumulate leading to a saturation at full effect strength around days 8–10 (purple curves in Fig. ). For the growth-promoting case, metabolite effects decrease the loss rate of the Prochlorococcus population. Thereby the net growth rate of phototrophs is increased, leading to larger populations and accelerated depletion of the inorganic nutrient when compared to the axenic. For the inhibitory case, metabolite effects increase the phytoplankton loss rate, resulting in a reduced net growth rate. This implies a slower depletion of the inorganic nutrient stock, in particular after day 15 when DOC (black curve) is depleted and heterotrophic nutrient uptake is reduced during the subsequent DOC-limited growth. For the axenic and promoting co-culture, simulated DOC concentrations increase in the first days due to phototrophic release of organic compounds. In the growth-promoting co-culture, the rate of accumulation slows down with growing heterotrophic densities until nutrient stocks (organic, as well as inorganic) are exhausted around day 15 (day 21 for the axenic culture). When this nutrient limitation sets in Prochlorococcus densities collapse, and DOC release from exudation and mortality accelerates DOC accumulation. However, in the following phase the DOC accumulation rate slows again due to the diminishing release from the shrinking phototroph population. In the co-culture the DOC concentration traverses its maximum around day 28, when release and heterotrophic consumption balance. In the inhibitory co-culture, the slow phototroph growth continuous until the inorganic nutrient stock is depleted around day 30, which triggers a rapid decline. The differences in population peak timing and amplitude are caused by the differing phytoplankton net growth rates in the different scenarios, which largely determine the consumption rate of the inorganic nutrient. In conclusion, with a variation of single parameter (aM) MCoM can capture both, the temporal shifts of the population peaks and the changes of the maximal observed Prochlorococcus density. As far as we have tested it, this cannot be achieved by any other variation of a single heterotroph trait – see the complementary parameter sensitivity analysis in Sect. S4 in the Supplement.

Having evaluated MCoMs ability to reproduce dynamics of individual motifs, which may represent components in a larger microbial interaction network, we now show two examples of MCoM's application when scaled up to more diverse microbial communities. First, we consider a cyclic interaction network to illustrate how feedbacks mediated by metabolite interactions can lead to self-sustained fluctuations in a community of three phytoplankton and three heterotroph populations (Fig a). We model associations of specific heterotroph and phytoplankton species, Hi and Pi, by stipulating that the heterotroph Hi specializes on the consumption of organic matter produced by the phototroph Pi, forming a “consortium”. Due to this syntrophic relationship population peaks of Pi tend to be succeeded by peaks of Hi. Further, different consortia are assumed to be coupled via metabolites, such that metabolites produced by Hi positively affect Pi+1. Effectively, this causes population peaks of Hi to be succeeded by peaks of Pi+1, and so on, leading to a “merry-go-round” succession of consortia. Figure b shows the trajectories of the population densities and metabolite effects in a chemostat with continuous supply of nutrients (Δ = 0.1 d-1 and Next = 5.0 µM). The figure shows a time interval from simulation day 9000 to 10 000 after it has settled on a periodic orbit. The full set of parameters for this system is given in Table S5 in the Supplement. While such a setup may appear highly artificial, it is robust to parameter variations (see Sect. S5 in the Supplement) and illustrates the potential of metabolite feedbacks to incite non-stationarity of population densities even if no environmental forcing is present.

In natural situations, successions are regularly reported as a response to an initial environmental impulse, such as seasonal upwelling of nutrients. These scenarios can also be modelled with MCoM specifying a fluctuation for the parameter environment.nutrient.

Generalizing the notion of a “consortium” as a coherent sub-community, we proceed to communities consisting of separate highly connected groups of species. A consortium in this sense can loosely be defined as a set of phototrophs, DOM compounds, heterotrophs and metabolites, which interact mostly within themselves. That is, within a consortium, heterotrophs feed on DOM released by members of the consortium, and phototroph growth is positively affected by metabolites produced by these heterotrophs. Although competition between consortium members (for nutrients and DOM) is possible, positive feedback loops within a consortium can be expected to facilitate the growth of its members on average.

For each simulated community, two consortia, A and B, were generated, each consisting of ten phototrophs (distinct in their specific photosynthesis characteristics), ten heterotrophs, ten DOC and ten DON compounds, and ten metabolite types. For the generation, we used MCoM's random community generation facilities to generate two consortia (see the README in the source code repository for details). As input for the generation, we prescribed the in- and out-degrees of the microbial nodes, i.e., the number of released and consumed compounds, the number of produced and effective metabolites, and the ranges, from which photosynthesis parameters for the single phototrophs were drawn (cf. Table S6 in the Supplement). MCoM's algorithm then randomly connects the different components adhering to these degrees. Subsequently, we coupled the two consortia by defining a number of shared metabolites, which effect both consortia. This number is called “overlap” in the following. Figure a shows the community structure schematically.

In the following, we assumed an annual cycle of varying average light intensity as shown in Fig. e and continuous nutrient supply (Δ = 0.1 d-1 and Next = 5.0 µM). Figure b–d show the time series of simulated phytoplankton population densities for different degrees of inter-consortial coupling and different initial conditions. In Fig. b and c, we show two simulations for the same community consisting of two consortia with a single overlapping metabolite. This configuration often leads to priority effects, as exemplified by the depicted dynamics: When the phototrophs of consortium A (green curves) are initialized with higher density than the phototrophs of consortium B (see Fig. b), consortium A remains dominant over the whole time span of the simulation (approx. 45 years). Vice versa, consortium B remains dominant if its phototrophs have higher initial density (Fig. c).

Figure d shows a trajectory in a modified network with higher inter-consortial coupling (overlap 5), where priority effects are not observed, i.e., despite differing initial phototroph densities the trajectories converge to identical periodic orbits after a transient time. In such cases, the “crosstalk” between consortia prevents their dynamical separation and an equilibrium, where members of both consortia coexist, is attained independently of the initial state.

We explored this effect systematically. For each of six values of the overlap, we generated 20 communities, each containing two consortia, A and B (20 phototrophs and 20 heterotrophs in total). Each community was initialized twice, with either consortium A or consortium B being dominant, and integrated for 60 years (see Table S6 in the Supplement for a detailed description of parameters). The relative averaged abundance over the last ten years of the simulation is reported for each simulation run in Fig. f. In this panel, for each overlap value, two horizontal bar groups are displayed: the top group corresponds to initializations with consortium A dominant, and the bottom group to consortium B dominant. Each group contains 20 stacked bars (one per community), where each bar represents 100 % relative abundance. The bars are divided into colored segments: shades of green for species from consortium A and shades of red for consortium B, with segment lengths proportional to species' average abundances. Starting from different initial states, priority effects appear as systematic differences in the dominant consortium (i.e., predominantly green vs. red segments) between the top and bottom groups for the same overlap. Convergence is indicated when both groups exhibit similar color distributions.

We categorized all observed regimes either as coexistence, where both consortia contribute more than 10 % to the total abundance, or as dominance of either consortium A or B. For low overlap, communities show pronounced priority effects in most cases, where in general the initially dominant consortium remains dominant. For instance, for zero overlap, none of the simulations ended in coexistence (Fig. g). However, in 1/8 of the simulations the finally dominating consortium was the initially rare one. For one overlapping metabolite, two of 40 runs led to a coexistence of both consortia. Already for an overlap of three metabolites about 50 % of the simulations end in coexistence, and for overlap higher than five (where > 30 % of metabolites are shared between consortia), species coexistence is the most frequent (> 75 %) simulation outcome.

The Synechococcus simulation (Fig. ) illustrates MCoM's capacity to qualitatively reproduce mutualistic and competitive dynamics in batch systems. Our simulations captured the experimental divergence in phototroph trajectories between axenic growth (peak followed by steep decline), and co-cultures with R. pomeroyi (persistently elevated densities) and Tropicibacter (collapse-recovery). The optimized parameters suggest that the observations emerge through differential nutrient utilization patterns by the heterotrophs: 75 % DON remineralization rate and no DIN uptake for R. pomeroyi in contrast to 25 % DON remineralization rate paired with strong competition for DIN in case of Tropicibacter. Additional control simulations (Sect. S3 in the Supplement) confirmed these processes as essential for qualitative reproduction of experimental observations. Reduced DOC exudation altered Synechococcus persistence for the Tropicibacter co-culture by weakening heterotroph competition, that is, elevated sustained Synechococcus densities in Tropicibacter co-cultures, contrasting experimental patterns. On the other hand, suppressed DON remineralization caused the Synechococcus population to collapse in the co-culture with R. pomeroyi.

While qualitative agreement could be achieved, the quantitative reproduction of the extended high-density phase of Synechococcus (approx. days 5–50; Fig. , upper panels) followed by the steep decline in axenic and Tropicibacter co-cultures proved challenging. Capturing the decline requires high loss rates (δ), while rapid initial growth demands a high maximal growth rate. Further, sustained high density implies balanced phototrophic growth and loss. Yet the subsequent collapse requires loss to abruptly dominate growth. This transition is difficult to achieve with constant loss rates, especially in axenic cultures lacking heterotrophic competition. Potential model extensions to improve quantitative fit include: (i) Phototrophic metabolite production (to account for toxic compound accumulation as suggested by ), or (ii) Variable C:N quotas with reserve dynamics, where collapse represents starvation from depleted internal reserves below a critical threshold.

For Prochlorococcus co-cultures (Fig. ), MCoM reproduced divergent phototroph dynamics through metabolite-mediated growth effects. Parameter sensitivity analysis (Sect. S4 in the Supplement) demonstrated that while heterotroph traits (e.g., loss rate δ or nutrient uptake VN) modulate quantitative outcomes (e.g., peak height), a variation of interaction rates aM alone explains the qualitative transition between growth-promoting and inhibitory scenarios. This supports the hypothesis that metabolite exchange is the primary driver of experimental growth trajectory differences . However, we emphasize that both experiment modeling cases serve as mechanistic illustrations of MCoM's capabilities, not as validation of specific biological mechanisms underlying the experimental dynamics.

Microbial ecosystems bear the potential to exhibit complex, non-equilibrium dynamics. It is possible to model such cases using MCoM as illustrated by the implementation of a cyclic dominance motif (Fig. ). While intentionally constructed, this consortium-based, self-sustained “merry-go-round” succession highlights how cross-consortia metabolite signalling (Hi→Pi+1) can drive persistent fluctuations without external forcing. Parameter scans (Sect. S5 in the Supplement) reveal two critical constraints for maintaining cyclic stability: (1) Balanced nutrient uptake rates across consortia (Fig. S3 in the Supplement), because significant deviations in uptake rates induce competitive exclusion (elevated uptake promotes dominance; diminished uptake enables rival takeover); and (2) Sufficient metabolite interaction strength (Fig. S4 in the Supplement), is essential to maintain oscillatory regimes. Weakened interaction rates imply a collapse into hierarchical competition. These breakdown conditions align with ecological theory, emphasizing that non-hierarchical relationships are essential for such dynamics . Though stylized, this example illustrates MCoM's utility in probing how interaction networks may structure complex community successions.

An important assumption in MCoM concerns the parameterization of DOM exudation mechanics. The fundamental nutrient-dependent stoichiometric pattern, where phototrophs exude carbon-rich compounds under nutrient limitation and nitrogen-rich compounds under nutrient sufficiency, is empirically well-established . However, the precise functional form governing the extent and composition of exudates in MCoM represents a tractable implementation rather than a formulation derived from species-specific empirical data. Our approach provides flexibility through user-defined parameters (ri→exC:N and qimax⁡) to accommodate some variability, while explicitly enforcing biochemical constraints (e.g., nitrogen-rich exudates require carbon backbones). Since the mechanistic links between nutrient availability, photosynthetic rate, and exudation dynamics remain an active research area , caution is warranted when making quantitative interpretations.

MCoM employs fixed elemental stoichiometry for phytoplankton and heterotrophs, neglecting documented plasticity in elemental ratios under varying environmental conditions . Future implementations could incorporate adaptive elemental ratios to refine physiological representations. Similarly, interaction strategies are assumed static; extensions might introduce adaptive behaviors like context-dependent algicidal interactions or expand exo-metabolite roles beyond mortality modulation to influence assimilation kinetics or other physiological parameters.

Further, MCoM assumes independent saturation kinetics for organic compound uptake (Eq. ), implying distinct transporter systems and metabolic pathways process each compound without interference. While this simplification aligns with established microbial substrate utilization models e.g.,, biological systems exhibit interdependencies through mechanisms of metabolic regulation or resource allocation. More complex modeling approaches incorporate such mechanisms allowing them to reproduce phenomena like sequential utilization or adaptation to substrate availability .

As a zero-dimensional box model, MCoM lacks explicit spatial resolution. A positive transport term (coefficient Δ>0) in the governing equations represents a bulk exchange with an external reservoir, approximating chemostat conditions and allowing continuos supply of nutrient (see case studies in Sects.  and ). If Δ=0 (Sects.  and ), the equations describe a batch reactor, i.e., a closed system. We note that Δ could serve for future spatially explicit implementations, potentially representing diffusive connectivity in extended frameworks. Such developments would enable modeling of advective-diffusive transport and gradient-driven dynamics.

Environmental variability has an important impact on growth kinetics. In the current version, its configuration is limited to nutrient supply and light intensity, allowing a basic configuration of temporal modes of variation (pulsatile and sinusoidal, plus a rudimentary functionality for noise). We plan to extend these modes and further add temperature-dependent rate modulation in the future.

MCoM is suited to simulate large communities comprising diverse species, DOM compounds, and metabolites. However, the numerical complexity and memory requirements of the simulation rise with system size. We assessed the performance of MCoM in a simple test recording run times for different system sizes. The results are shown in Fig. . For each number n∈{5,10,…,150}, we initialized 16 random networks with n components of each type (heterotrophs, phototrophs, DOC, DON, and metabolites) and 30 % connectivity. That is, for n=30, each phototroph population produces 10 different DOC and 10 different DON compounds and is affected by 10 metabolites. Each heterotroph population produces the same variety of DOM compounds, is able to consume 10 DOC and 10 DON types, and produces 10 different metabolites. We simulated each community for 100 years with an integration step width of dt = 0.025 d, saving the last 10 years of the simulation to disc saving the system's state every dtout = 0.5 d. Asymptotically, the computation time scales as nγ with exponent γ=2.4, as determined by the asymptotic slope of the graph of log⁡n versus logarithmic computation time (dashed red line in the inset of Fig. ).