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

squares and cubes of the data, the spline regression uses a different set of basis function, one of which is always the average value of the outcome variable, usually referred to as the intercept, albeit improperly. The other functions are chosen from a family of functions depending on the desidered properties. In the case of biological functions, a common approach is to fit with a polynomial (in this case of 3rd order) a subset of the data, while imposing 4 conditions: continu- ity of value, continuity of derivative of first order, continuity of the derivative of second order, and the overall function at the boundaries is linear. These are usually referred to as natural cubic splines. The number of knots (the junction points between different parts of the data set) were chosen using a cross-validation approach, using the AIC criterion as the chosen metric. Due to the constrains required for this functions to create a smooth fit, they can exhibit small fluctua- tions outside the original domain, such as those that can be seen in spline 1 and 3 in Fig 1. Classification and prediction of health status in old age Elderly samples from the ELDERMET data set were classified as healthy or unhealthy accord- ing to the FIM score [58], Barthel index [59] and MMSE score [60] and to the residence set- ting. In particular, for each subject, a score of 1 was assigned for each of the following conditions when they were true: Barthel score � 15 [58], MMSE score � 24 [60], FIM score � 100 [58] and residence setting in Community or Day-Hospital. Then, the subject was

classified as healthy if the sum of the scores was � 3 or unhealthy otherwise. Considering the elderly subjects from the ELDERMET study at T0 that were not outliers according to the total number of reads, we computed a predictive model for health status in old age based on GM biodiversity. After imputing missing data with the Multiple Imputation by Chained Equations (MICE) method [61] and standardizing the covariates, we computed a Principal Component Analysis (PCA) based on the elderly physical and cognitive state scores, (FIM score, Barthel index and MMSE score) and the residence setting (S5 Fig). Most of the variance (91.9%) was explained by the first Principal Component (PC[0]) that was hence con- sidered as the measure of healthy aging in the following predictive model. The predictive model of health status in old age based on GM biodiversity was computed as a Leave-One-Out cross validated linear regression and various possible GM biodiversity mea- surements were adopted as explanatory variables: besides θrare and θabundant, we also consid- ered the Pielou, Shannon, Simpson, Hill1, and Hill2 indices. After dichotomizing the subjects true and predicted health status in healthy/unhealthy, we computed the Area Under the Receiver Operating Characteristic Curve (AUC of ROC). The models were all adjusted for sex and standardized number of reads and computed both with and without the addition of calf circumference, BMI and the inflammatory markers IL-6, IL-8, IL-10, TNFa and CRP as furhter explanatory variables. Supporting information

S1 Fig. Model selection. Logarithm of the ratio of the posterior probabilities of model 2NB and 1NB (left), of model 2NB and 3NB (center) and of model 1NB and 3NB (right). Each pos- terior probability has been increased by a small factor (10−7) to avoid infinite value in the log- ratio. When comparing models 2NB and 1NB (left), data below the red line are those for which the 2NB model is selected rather than the 1NB. When comparing models 2NB and 3NB (center), data above the red line are those for which the 2NB model is selected rather than the 3NB. When comparing models 1NB and 3NB (right), data above the red line are those for which the 1NB model is selected rather than the 3NB. (EPS) PLOS ONE Gut microbiota biodiversity and healthy aging PLOS ONE | https://doi.org/10.1371/journal.pone.0237207 October 30, 2020 18 / 23