Pessimistic optimisation for modelling microbial communities with uncertainty

Optimisation-based mathematical models provide ways to analyse and obtain predictions on microbial communities who play critical roles in the ecological system, human health and diseases. However, there are inherent model and data uncertainties from the existing knowledge and experiments so that the imposed models may not exactly reflect the reality in nature. Here, we aim to have a flexible framework to model microbial communities with uncertainty, and introduce P-OptCom, an extension of an existing method OptCom, based on pessimistic bilevel optimisation. This framework relies on the coordinated decision making between the single upper-level and multiple lower-level decision makers to better approximate community steady states even when the individual microorganisms' behavior deviate from the optimum in terms of their cellular fitness criteria. Our study demonstrates that without experimental knowledge in advance, we are able to analyse the trade-offs among the members of microbial communities and closely approximate the actual experimental measurements.