Stochastic logistic models reproduce experimental time series of microbial communities
We analyze properties of experimental microbial time series, from plankton and the human microbiome, and investigate whether stochastic generalized Lotka-Volterra models could reproduce those properties. We show that the noise term should be large and that it is a linear function of the species abundance, while the strength of the self-interactions should vary over multiple orders of magnitude. We stress the fact that all the observed stochastic properties can be obtained from a logistic model, i.e. without interactions, even the niche character of the experimental time series. Linear noise is associated with growth rate stochasticity, which is related to changes in the environment. This suggests that fluctuations in the sparsely sampled experimental time series are caused by extrinsic sources.