Stochastic logistic models reproduce experimental time series of microbial communities

Abstract

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 this is the case when the noise term is large and a linear function of the species abundance, while the strength of the self-interactions varies 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 may be caused by extrinsic sources.

A macroecological description of alternative stable states reproduces intra- and inter-host variability of gut microbiome

“…The Stochastic Logistic Model with environmental noise (SLM, see Methods) is known to describe several statistical properties of abundance fluctuations for microbial species [15, 16]. In particular, it predicts that the distribution of fluctuations at stationarity is a Gamma distribution, which depends on two parameters: K i , the carrying capacity appearing in the SLM, and σ i , which can be interpreted as the amplitude of environmental noise.…”

“…Previous studies [15, 16] showed that the dynamics of the relative abundance λ of a microbial species is best described by the stochastic logistic model with environmental noise where ξ ( t ) is Gaussian white noise. This model has three parameters: τ has the dimension of a time, and determines the time-scale of relaxation to stationarity, K would be the carrying capacity in the absence of noise, and σ measures the intensity of the environmental noise.…”

“…This model has three parameters: τ has the dimension of a time, and determines the time-scale of relaxation to stationarity, K would be the carrying capacity in the absence of noise, and σ measures the intensity of the environmental noise. The model does not include interaction among species, and therefore cannot reproduce patterns of inter-species correlation, but correctly reproduces several patterns of the dynamics of a single species [15, 16]. Most importantly, if σ < 2 the stationary distribution is Gamma with mean and variance .…”

“…Previous studies [15,16] showed that the dynamics of the relative abundance λ of a microbial species is best described by the stochastic logistic model with environmental noisė…”

“…Recent works have characterized the macroecological patterns of community composition [12,13]. Under the macroecological lens, community dynamics is characterized by large and rapid fluctuations with robust and reproducible statistical properties [14][15][16]. These regular patterns are well described by the stochastic logistic model with environmental noise, which assumes that fast environmental fluctuations perturb abundances around a taxa-specific carrying capacity [15,16].…”