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

All the methods were implemented in python 3.6.8 [49] using the following libraries: patsy [50], pandas [51], numpy [52], scipy [53], matplotlib [54], seaborn [55], pymc [56]. The code to perform the parameter estimation through ABC starting from the OTU abundances table is available on a github repository at https://github.com/UniboDIFABiophysics/ AlphaDiversityPublic. Classical biodiversity indices Results obtained with θrare and θabundant were compared to those obtained when biodiversity was computed using classical biodiversity indices that are based on the empirical relative abun- dance of OTUs. Specifically, we considered Shannon [25], Pielou [27], Hill1 [28], Simpson [26] and Hill2 [28] indices, whose definitions are reported in the following. Let us call pi the proportion of individuals belonging to the i-th OTUs and S the total num- ber of OTUs. Then, 1. Shannon index (entropy) is defined as H = −∑pi�ln(pi) 2. Pielou index (eveness) is defined as J = H/Hmax, were Hmax is the maximum possible value of Shannon index H, that is achieved when pi = 1/S for each i, i.e. Hmax ¼ P 1 S � ln 1 S � 3. Hill1 number (Hill number of order 1) is defined as Hill1 = exp(H) 4. Simspon index is defined as l ¼ P p2 i . Notice that differently from the other indices Simp- son index decreases with biodiversity. 5. Hill2 number (Hill number of order 2) is defined as Hill2 ¼ 1 l Spline regression: Modeling the trend of GM biodiversity with aging The general relationship between the GM biodiversity indices, θrare and θabundant, and aging

was investigated by fitting a natural cubic splines model [57] adjusted for sex (0 = male, 1 = female) and standardized total number of reads, using the library patsy [50] in python 3.6.8 [49]. See the following paragraph “Notes on splines regression” for details. Here, we considered the healthy control subjects from all the data sets except the Italian controls of Schnorr et al., for which age was not available, and the ELDERMET data sets at times greater than 0, for which young controls were not available. Samples with outlier total number of reads (z-score > 4) were removed prior the analysis. These included 6 elderly sub- jects from the ELDERMET study at T0 data set, 8 subjects from the Bian data set, 4 subjects from the Odamaki data set, and 1 subject from the Kong data set. The GM biodiversity estimates, θrare and θabundant, were analysed separately. After standard- izing the diversity indices within each data set, we fitted the natural cubic spline model consid- ering the data set to which the samples belong as confounding variable. The number of degrees of freedom was set to 3 based on the Akaike Information Criteria (AIC) and the Bayesian Information Criteria (BIC), as shown in S3 Fig. The spline regression model was also computed considering classical biodiversity indices, i.e. the Pielou, Shannon, Simpson, Hill1, and Hill2 indices. Notes on splines regression Splines regression models (also referred to as Generalized Additive Models [57]) allow to describe non-linear behaviors in the data using the framework of linear regression, where the

outcome variable is described as the linear combination of generic, non linear functions of the independent variables. While traditionally this was performed combining functions such as PLOS ONE Gut microbiota biodiversity and healthy aging PLOS ONE | https://doi.org/10.1371/journal.pone.0237207 October 30, 2020 17 / 23