Microbial communities play an integral role in ecosystems across scales, ranging from their influence on the metabolism of individual organisms [1], to whole-ecosystem biogeochemical cycling [2]. The functioning of any microbial community emerges from the interactions among its constituent species or “strains”. Developing methods to quantify and predict the underlying mechanisms and dynamics of these interactions is a major challenge in both theoretical and applied ecology [1,3–8]. The rapid development of molecular and ’omics technologies means that relatively high-frequency and taxonomically well-resolved data on microbial communities are burgeoning [9–11]. These data provide information on the metabolic capacities (“traits”) of individual microbial cells and the interactions between them, offering a means of linking changes in the composition of genetic and functional traits in the community to its emergent phenotype dynamics [12–14].

Real-world microbial communities are typically composed of complex interaction networks between trillions of cells, thousands of strains, and hundreds of species. This complexity poses a significant challenge to developing a general theory for microbial communities. To tackle this challenge, both inferential and mechanistic mathematical models of microbial communities are needed [15–18]. Inferential models are designed to deduce interactions and their effect on the dynamics of species abundances from empirical time-series data, remaining agnostic to the mechanisms that shape those interactions [19]. That is, these studies infer direct pairwise interactions between species from time series data obtained from various empirical approaches, ranging from co-culture experiments [20] to co-occurrence network snapshots reconstructed from gene sequencing, including metagenome assemblies [21]. This simplicity is advantageous in predicting the dynamical outcome of large microbial communities, where tracking every interaction and resource is impractical, and understanding the underlying mechanisms is not the primary focus.

In contrast to inferential models, mechanistic models aim to predict community dynamics from first principles by incorporating information on metabolic and physiological traits, alongside cellular processes that drive the growth of populations through species-species and species-environment interactions [4,17,22,23].

Inferential and mechanistic approaches complement each other and should ideally agree when compared at relevant spatial and temporal scales for any given microbial community. However, whether inferential pairwise models can accurately capture the inherent complexity of microbial interactions—particularly when these are indirectly generated (e.g., through cross-feeding and higher-order interactions)—and the resulting dynamics remains uncertain [16,18,24–28].

Currently, the most widely used inferential model is the generalized Lotka-Volterra system of ODEs (henceforth, the “GLVM”) [7,17,23,29]. In the GLVM, each population has an intrinsic growth rate, and any pair interacts through two coefficients that quantify their reciprocal effects on each other’s growth and abundance. Advances in high-throughput sequencing have enabled the collection of time-series data on microbial abundances. The GLV model can be fitted to these data to estimate interaction coefficients, providing insights into the structure and dynamics of the community.

Beyond empirical applications, the GLVM has also been used in a large body of theoretical research to derive dynamical properties of microbial communities, including feasibility (existence of a non-trivial equilibrium) and stability to perturbations as well as addition or removal of species [30–33]. However, the validity of these theoretical results also depends on how well the pairwise model approximates the underlying, mechanistic consumer-resource dynamics as an “effective" representation [27,34]. In particular, it remains unclear whether the pivotal assumption of time-scale separation between consumer and resource populations holds under a sufficiently wide range of scenarios [27,34].

Here we compare the dynamic behavior of a relatively general and widely used mechanistic model of microbial consumer-resource dynamics (MiCRM) [4,34,35] and its effective Generalized Lotka-Volterra approximation (GLVA, mathematically the same as the GLVM) and quantify the concordance between them across a range of biologically meaningful scenarios. Specifically, we focus on the GLVA’s error rate, which is the frequency and magnitude of deviations in population dynamics from the approximated model compared to the “true” consumer-resource dynamics, as well as the local stability and reactivity of the equilibria.

Previous research has investigated the behavior of statistically fitted GLV models relative to the corresponding dynamics of substrate mediated interactions finding, for example, that additivity of interactions (a necessary presupposition to the GLV) is not always satisfied [16,18,25]. However, using inferred GLV interactions to validate the effectiveness of pairwise modeling suffers from two main drawbacks, namely: identifiability and the difficulty of accounting for nonlinearities. The identifiability issue stems from the fact that, for any given community, there are an infinite number of GLV parameter combinations which can reproduce the same equilibrium and similar dynamics. Hence, inferred parameters will vary depending on the fitting algorithm and the data. On the other hand, the presence of nonlineairties in the underlying dynamics present a particular challenge because they can be an additional source of error, but the extent to which they influence model inference is hard to quantify precisely [36].

Assessing the performance of an exact first-order representation of resource-mediated interactions (that is, the GLVA) can provide more insight into the specific features which make the system more or less amenable to approximation by pairwise interaction. In particular, we explore how the relative values of different parameters, such as leakage, limit how well the GLVA can capture the dynamics in principle.

We identify parameter spaces of the MiCRM that result in greater disagreement between the models. With the goal of providing both empiricists and theoreticians with criteria for identifying when substrate mediated interactions can be well approximated by pairwise interactions, we also provide a method for quantifying the degree of time-scale separation, which is at the root of the GLVA’s failure.

Our overall approach is to first derive the GLVA from the MiCRM for each particular parameterization of the MiCRM, and then numerically integrate each MiCRM-GLVA ODE system paired to compare their dynamical behaviors.

Although the generalized Lotka-Volterra model has been extensively studied theoretically and used empirically, its suitability for microbial communities in diverse settings remains unclear. By contrasting the dynamics of the MiCRM to its corresponding GLVA, we identified regions of parameter space where pairwise interaction terms did not accurately represent the underlying dynamics. In particular, we found that the accuracy of the GLVA declines rapidly with increasing metabolite leakage and niche overlap.

Furthermore, the GLVA’s dynamics qualitatively diverge from those of the underlying MiCRM: stability is particularly sensitive to leakage, while the deviation of reactivity from the actual dynamics remains unchanged irrespective of the MiCRM’s parameterization. To the best of our knowledge, the accuracy of the GLVA’s dynamics in terms of reactivity has never been investigated. Our results reveal a potentially critical limitation of the GLVA, as intermittently perturbed reactive systems are more likely to settle into alternative stable states [44,48]. Hence, if the approximation undermines the MiCRM’s response to perturbations, it no longer has any bearing on how the underlying system might shift under environmental or demographic stochasticity.

As mentioned in the Methods, our metric for GLVA’s accuracy focuses on discrepancies in relative abundances, meaning that it is highly sensitive to differences in the predicted survival of consumer populations at steady state. This implies that the increasing incidence of errors displayed in Fig 2 B is likely due to mismatches in the equilibrium community composition. Essentially, the GLVA and its corresponding MiCRM systems settle on different stable states.

Interestingly, the GLVA asymmetrically errs on the side of coexistence, as seen from the predominance of simulations where the GLVA overshoots (Fig 2, error is overwhelmingly positively skewed). Since pairwise interaction terms in the GLVA depend on resource concentrations at their steady state, this tendency to overshoot likely arises from the fact that the effective interactions differ both quantitatively (i.e., in terms of strength) and qualitatively (i.e., in terms of presence-absence or directionality) during the initial assembly stages; leading to the survival of infeasible strains before the community arrives at the interaction structure produced by the GLVA. This highlights an important point: although by construction the GLVA has an identical attractor to the MiCRM, it can settle on an alternative attractor given a different set of initial conditions, inconsistent with the actual resource-mediated consumer-consumer interactions. This makes any inferences of pairwise interactions based purely on (sufficiently frequent) temporal snapshots of abundances in co-culture highly context dependent, and limits their utility for predicting community dynamics outside of that context; a limitation that is accentuated under specific regimes (Fig 4). If, on the other hand, intra- and inter-cellular metabolite concentrations can also be tracked along with abundances, the identifiability problem that we raised in the introduction (also see [36]) is somewhat mitigated, enabling more accurate and generalisable inferences.

The GLVA’s behavior at steady state differed from the MiCRM in two important respects: it systematically underestimates stability and fails to qualitatively capture the transient response to perturbations. The GLVA’s tendency towards less stable interaction structures (depicted in Fig 3) reveals a key limitation of pairwise frameworks in that they disregard how resource concentrations constrain consumer populations. In effect, stability in the MiCRM directly incorporates the contributions of all resources. While the GLVA is informed by resource concentrations at equilibrium, it cannot mimic the stabilizing effect of resource limitation. This likely explains why leakage, but not niche overlap, increases the stability gap between the two models. Higher leakage leads to greater positive feedback between consumers, and in the absence of a compensatory response in resource concentrations, this has a net destabilizing effect on the GLVA.

Another detail worth noting about the stability gap is that, since stability is estimated from the dominant eigenvalues of the system at equilibrium, it is equivalent to the dynamics of the slow manifold. When leakage is small, it is virtually guaranteed that the slow manifold will depend solely on the dynamics of consumers. However, as the coupling between consumers and resources strengthens (i.e. more leakage), it increases the likelihood that resources will contribute to the dominant eigenvalues.

While the MiCRM was reactive for every community simulated, the GLVA erroneously predicted the direction of the initial response to perturbations in over half of our data points. In cases where the GLVA displayed positive reactivity, it typically underestimated the strength of the effect by an order of magnitude. Although reactivity is not usually given as much attention as stability, it has been argued that it is at least as important for understanding the effects of chronically disturbed communities [44,49].

As shown in Fig 4, the accuracy of the GLVA can be predicted from an approximate measure of the time-scale separation between consumers and resources. This apparent relationship between the temporal coupling of the consumer-resource system and the GLVA’s performance suggests that the degree of separation, as measured here, serves as a good indicator of when a particular consumer-resource system can be described with consumer abundances alone. More importantly, the degree of separation defines a neighborhood around equilibrium, within which the GLVA will remain below a bounded margin of error compared to the true dynamics. This neighborhood can be understood as the set of initial conditions (likewise, perturbations) for which teq≤ε−1.

It should be noted that this issue was originally raised, albeit indirectly, by MacArthur [38] in terms of the symmetry of the matrix of interactions. If we take a Consumer-Resource model and assume that resources equilibrate quickly compared to the dynamics of the consumer, then the effective interaction matrix is necessarily symmetric. This result was later shown to be incorrect under a wider range of conditions. As Marsland et al. [34] have shown, the requirement of symmetric interactions can be relaxed through specific rescaling procedures. More generally, it appears that some variants of the Consumer-Resource equations are inherently asymmetric and cannot be straightforwardly rescaled, rendering the symmetry of the interaction matrix an inadequate indicator of the validity of the GLV approximation.

Although our analysis focuses on the ability of GLVA to represent the dynamics emerging from metabolite competition and cross-feeding dynamics in the MiCRM, the results can be straightforwardly generalized to any interaction mechanism that is indirectly mediated, such as through chemical stressors [50]. Our method of estimating ε (Section C in S1 Appendix) is directly applicable to any system, provided the ODEs can be defined, and the Jacobian is diagonally dominant.

As such, although the MiCRM’s structure is fairly general in its ability to capture the key elements of microbial consumer-resource dynamics, the question arises whether our results apply to variants of the MiCRM (e.g., different functional responses or the inclusion of essential nutrients). In particular, the issue of timescale separation and strength of consumer-resource coupling is a universal feature of coupled dynamical systems; hence, we do not expect any meaningful differences for a reasonably modified set of ODEs. Whether these insights can be extended to accommodate more complex interaction mechanisms, such as allelopathy or chemically mediated signalling, remains to be seen.

Some systems inherently have a greater timescale separation between consumer and resource pools. For instance, metabolic scaling laws dictate that because phytoplankton are generally much larger than bacteria, they operate on slower timescales. As a result, they interact with their metabolites more slowly than bacteria do, suggesting that the GLVA might, in general, be a more accurate model for quantifying phytoplankton community dynamics.

Overall, these results provide guidelines for the appropriate use of pairwise models in the study of microbial communities. Firstly, theoreticians seeking to apply the generalized Lotka-Volterra model to relate community structure to the system’s dynamic behaviors should verify that the system in question does not exhibit environmental (resource) feedbacks strong enough to invalidate the model’s assumptions. This point becomes especially important when considering the impacts of environmental perturbations (e.g., temperature fluctuations [23,32,50–52]), a topic of increasing importance as we seek to quantify the effects of anthropogenic change. We show that GLV models can systematically mis-predict equilibrium resilience, often underestimating recovery rates and sometimes even predicting no transient amplification when the mechanistic system exhibits strong reactivity. This distinction is crucial for assessing robustness and the risk of regime shifts [44,48]. For empiricists, relying on GLV fits alone could mask early warning signs of collapse or invasion, since resource-mediated overshoot dynamics are not captured by static interaction terms. Validating GLV predictions against actual perturbation experiments, rather than only steady-state outcomes, is therefore crucial to ensure resilience is represented correctly.

Because (ε) can be estimated from basic measurements of nutrient depletion, byproduct accumulation, and microbial growth rates, it offers an empirically accessible “litmus test”. This complements the broader caution that GLV model fits are non-identifiable and may overfit sparse time series: multiple parameter sets can reproduce similar trajectories but differ mechanistically. Collecting additional data on metabolite or resource concentrations and perturbation responses to constrain GLV model fitting may therefore be necessary when consumer-resource coupling is strong [53–55].

Empirically determining ε in microbial communities requires precise monitoring of cell densities as well as substrate and metabolite concentrations. Given well-resolved data, ε can be estimated by perturbing the community and monitoring how long it takes the microbial consumer populations and substrate concentrations to return to a steady state. Another method would be to carry out single-strain culture experiments to determine each of the parameters (in this case: uptake, yield, and metabolite leakage), and use those data to calculate, using resource-explicit models like the MiCRM, the approximate timescale separation a priori. The robustness of the separation of timescales can be more feasibly (but less accurately) assessed from the equilibrium properties of the system, such as the proportion of resources contained in consumer biomass relative to the environment in addition to estimates of average metabolite leakage, given their role in determining characteristic timescales (see equations in Section C in S1 Appendix).

Finally, we note that our results should be interpreted with the understanding that the MiCRM assumes well-mixed conditions, linear uptake kinetics, and constant leakage fractions per species. Real microbes might exhibit more complex dynamics (e.g., threshold-driven secretion, spatial metabolite gradients, or adaptive responses) that could introduce qualitatively new higher-order effects beyond those captured by the basic MiCRM. Our findings will likely still apply; any such complexity would further undermine the accuracy of a GLVA, but the precise thresholds of timescale separation would differ.

In conclusion, the magnitude of metabolite leakage and the resultant cross-feeding, mediated by niche overlap structure, has a strong bearing on the extent to which the GLVA can accurately reproduce the underlying MiCRM dynamics. In particular, we found near-zero correspondence between models regarding reactivity, highlighting the importance of higher-order interactions and the GLVA’s inability to account for them in predicting perturbative behavior. We show that these inaccuracies stem primarily from (the lack of) timescale separation between consumer and resource dynamics, and provide a measure to quantify the strength of this coupling.