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Logarithmic growth-rates are fundamental observables for describingecological systems and the characterization of their distributions withanalytical techniques can greatly improve their comprehension. Here a neutralmodel based on a stochastic differential equation with demographic noise, whichpresents a closed form for these distributions, is used to describe thepopulation dynamics of microbiota. Results show that this model cansuccessfully reproduce the log-growth rate distribution of the consideredabundance time-series. More significantly, it predicts its temporal dependence,by reproducing its kurtosis evolution when the time lag $\tau$ is increased.Furthermore, its typical shape for large $\tau$ is assessed, verifying that thedistribution variance does not diverge with $\tau$. The simulated processesgenerated by the calibrated stochastic equation and the analysis of eachtime-series, taken one by one, provided additional support for our approach.Alternatively, we tried to describe our dataset by using a logistic model withan environmental stochastic term. Analytical and numerical results show thatthis model is not suited for describing the leptokurtic log-growth ratesdistribution found in our data. These results effectively support a neutralmodel with demographic stochasticity for describing the growth-rate dynamicsand the stationary abundance distribution of the considered microbiota. Thissuggests that there are no significant parametric demographic differences amongthe species, which can be statistically characterized by the same vital rates.

Growth-rate distributions of gut microbiota time series: neutral models and temporal dependence