Identification of dynamic models of microbial communities

Microbial communities, complex ecological networks crucial for human and planetary health, remain poorly understood in terms of the quantitative principles governing their composition, assembly, and function. Dynamic modeling using ordinary differential equations (ODEs) is a powerful framework for understanding and predicting microbiome behaviors. However, developing reliable ODE models is severely hampered by their nonlinear nature and the presence of significant challenges, particularly critical issues related to identifiability.

Here, we address the identification problem in dynamic microbial community models by proposing an integrated methodology to tackle key challenges. Focusing on nonlinear ODE-based models, we examine four critical pitfalls: identifiability issues (structural and practical), unstable dynamics (potentially leading to numerical blow-up), underfitting (convergence to suboptimal solutions), and overfitting (fitting noise rather than signal). These pitfalls yield unreliable parameter estimates, unrealistic model behavior, and poor generalization. Our study presents a comprehensive workflow incorporating structural and practical identifiability analysis, robust global optimization for calibration, stability checks, and rigorous predictive power assessment. The methodology’s effectiveness and versatility in mitigating these pitfalls are demonstrated through case studies of increasing complexity, paving the way for more reliable and mechanistically insightful models of microbial communities.

Availability

The code that implements the methodology and reproduces the results is available at https://doi.org/10.5281/zenodo.15309438

Supplementary information

Additional information supporting this manuscript is provided at https://doi.org/10.5281/zenodo.15309438 .

Author summary

Microbial communities, vital for human and environmental health, are complex systems whose quantitative behaviors are not yet fully understood. Scientists employ mathematical models to study these communities, but developing accurate models of their dynamics is very challenging. Key difficulties include determining correct model parameters, ensuring model stability, and preventing the models from either under-learning from data or over-learning from noise. This paper presents a new, integrated methodology to overcome these obstacles. The approach provides a systematic workflow incorporating analyses of parameter identifiability, model stability, and predictive capabilities. By addressing these critical pitfalls, this research aims to facilitate the creation of more reliable and mechanistically insightful models, ultimately enhancing our understanding of microbial community dynamics.