Microbial Primer: Bayesian learning of traits from microbial time series data.

Mathematical models are increasingly used to infer traits, interactions and functional dynamics of microbial systems. One common example is a rate-based ordinary differential equation model parameterized with microbial traits. However, fitting such models with associated parameters to data requires a principled approach to extract information from time series while accounting for prior knowledge and measurement noise. These principles often remain implicit and not necessarily well defined. Here, we make the implicit, explicit: introducing Bayesian inference of ecological models for microbial time series, including three detailed case studies of algal population dynamics that follow a birth-death process. Complementing this primer, we provide an online tutorial on Bayesian inverse modelling with cross-programming language support via Python (PyMC) and Julia (Turing). By connecting theory, code, data and a series of hands-on educational modules, this primer aims to bring the utility of Bayesian learning to the broader microbial ecology research community.