Résumé
Species distribution models, which consist of a species-by-species modeling approach, are widely used in ecology to understand species behavior and predict their distribution based on environmental data. However, in species-rich ecosystems with many rare species, such an approach is doomed to failure. Moreover, univariate approaches ignore species dependencies. However, biodiversity is not merely the sum of species, but the result of multiple interactions. Modeling multivariate count data that allow for flexible dependencies, as well as zero inflation and overdispersion, is a challenge. In this paper, we develop a new family of models called the zero-inflated binary tree Pólya-splitting models. This family allows the decomposition of multivariate count data into a successive sub-model along a known binary partition tree. In the first part, we will present the general form of this model, studying its properties in terms of marginal and conditional properties (distribution and moment). The second part presents the extension to the regression context. Finally, we finish presenting results on a real case study based on an impressive data set consisting of the abundance of more than 180 tree taxa sampled on 1,571 plots covering more than 6 million hectares of tropical rainforests in the Congo basin.