Gut microbiota ecology: Biodiversity estimated from hybrid neutral-niche model increases with health status and aging

i. the ELDERMET data set [3, 34], that includes 836 samples from 371 Irish elderly (64 to 102 years old) and 13 young (26 to 46 years old) subjects collected at three time points (T0, T1 and T2); ii. the Biagi & Schnorr data set, composed by the 17 Italian Down Syndrome (DS) adult sub- jects from Biagi et al. [33] and 16 age-matching healthy Italian adults plus 27 Tanzanian Hadza hunter-gatherers [35]; iii. the Odamaki data set [10], that includes 367 community-dwelling Japanese volunteers between 0 and 104 years old; iv. the Kong data set [36], that includes 168 Chinese individuals from 24 to 102 years old; v. the Biagi data set [20], that includes 69 Italians whose age ranges from 22 to 109 years old; vi. the Bian data set [37], that includes 1049 Chinese healthy subjects from 3 to 109 years old self-reported as having a personal and family history of extreme health. A niche-neutral model for the GM We modelled the empirical RSA derived from 16S rRNA data considering three possible scenarios. First, we tested pure neutrality by fitting the data with the 1NB model previously introduced. Then, we relaxed the hypothesis of species equivalence considering a hybrid niche-neutral model (2NB model) that assumes the existence of two non-interacting neutral niches (the evolutionary dynam- ics of each niche is neutral). Finally, we further relaxed the neutral hypothesis contemplating a hybrid niche-neutral model with three niches (3NB model). The 2NB and 3NB models represent a small increase in complexity compared to the pure neutral model [32], by including the possibility

of two or more non-interacting niches with different equilibrium properties [29], each summarized by the parameters characterizing the theoretical distribution obtained from the model. Details on the three models are reported in the Materials and Methods section. According to the selected model, a different population dynamic process is assumed and a different sta- tionary state is reached. Since our aim is not to study the temporal behavior of the GM ecosys- tem, but rather to exploit the modeling approach to characterize the GM biodiversity at the stationary state, here we focus on the theoretical RSA distribution that is obtained from the three models. Then, we test the accuracy of the model in describing the GM by fitting the empirical RSA obtained from the data with such theoretical distribution. The stationary distribution of the RSA hypothesized by the 1NB model is given by the Neg- ative Binomial reported in Eq (1). On the other hand, the expected RSA distribution of the 2NB model is a mixture of two zero-truncated Negative Binomials [38], and following the notation of Eq (1), can be written as PRSAðnÞ ¼ a � y1 � NBðb1; d1; S1Þ þ ð1 aÞ � y2 � NBðb2; d2; S2Þ ð2Þ where α is the mixture coefficient, bi, di and Si are the birth, death, and influx rates of the i-th niche (i = 1,2), and θi is the biodiversity number relative to niche i. Analogously, we assume the stationary RSA distribution for the 3NB model to be a mixture of three zero-truncated Negative Binomials to which 3 biodiversity numbers are associated: θ1,

θ2 and θ3. Indicating with α and β the mixture coefficients, the RSA distribution can be written as PRSAðnÞ ¼ a � y1 � NBðb1; d1; S1Þ þ b � y2 � NBðb2; d2; S2Þ þ ð1 a bÞ � y3 � NBðb3; d3; S3Þ ð3Þ PLOS ONE Gut microbiota biodiversity and healthy aging PLOS ONE | https://doi.org/10.1371/journal.pone.0237207 October 30, 2020 4 / 23