In this work we propose an index to estimate the gut microbiota biodiversity using a modeling approach with the aim of describing its relationship with health and aging. The gut microbiota, a complex ecosystem that links nutrition and metabolism, has a pervasive effect on all body organs and systems, undergoes profound changes with age and life-style, and substantially contributes to the pathogenesis of age-related diseases. For these reasons, the gut microbiota is a suitable candidate for assessing and quantifying healthy aging, i.e. the capability of individuals to reach an advanced age, avoiding or postponing major age-related diseases. The importance of the gut microbiota in health and aging has been proven to be related not only to its taxonomic composition, but also to its ecological properties, namely its biodiversity. Following an ecological approach, here we intended to characterize the relationship between the gut microbiota biodiversity and healthy aging through the development a parsimonious model of gut microbiota from which biodiversity can be estimated. We analysed publicly available metagenomic data relative to subjects of different ages, countries, nutritional habits and health status and we showed that a hybrid niche-neutral model well describes the observed patterns of bacterial relative abundance. Moreover, starting from such ecological modeling, we derived an estimate of the gut microbiota biodiversity that is consistent with classical indices, while having a higher statistical power. This allowed us to unveil an increase of the gut microbiota biodiversity during aging and to provide a good predictor of health status in old age, dependent on life-style and aging disorders.