The human gut microbiota is a dense and dynamic ecological system that contributes significantly to human health and disease. While the identities of the organisms in the gut microbiota are largely known, the ecological and molecular forces that shape community assembly and stability remain unresolved. We developed a generalizable Bayesian parameter estimation framework to build computational models of microbial communities from time-resolved measurements of lower-order assemblages to predict higher-order community dynamics. This method was employed to decipher interactions in a diverse human gut microbiome synthetic ecology. Our results demonstrate that monospecies growth parameters and pairwise interactions dominate the temporal behaviors of multi-species consortia, as opposed to context-dependent interactions. The inferred ecological network as well as a top-down approach pinpointed highly influential organisms and specific ecologically sensitive species that were significantly modulated by microbial inter-relationships. Specific mutually repressing species displayed a prolonged history-dependent response to variations in initial abundance ratios stemming from slow response times to reach a steady-state. Bayesian statistical methods were used to evaluate the constraint of model parameters by the experimental data. Time-dependent measurements of extracellular metabolites provided insights into the molecular basis of inter-species interactions. In sum, these methods can be used to extract microbial ecosystem design principles of stability, community assembly and dynamic response to external perturbations.