Séance Séminaire

Séminaire de Probabilités et Statistique

The Poisson-lognormal model as a versatile framework for the joint analysis of species abundances [SupAgro]

Joint work with Julien Chiquet, Stéphane Robin and many others Joint Species Abundance Models (JSDM) provide a general multivariate framework to study the joint abundances of all species from a community. JSDM account for both struc- turing factors (environmental characteristics or gradients, such as habitat type or nutrient availability) and potential interactions between the species (competition, mutualism, para- sitism, etc.), which is instrumental in disentangling meaningful ecological interactions from mere statistical associations. Modeling the dependency between the species is challenging because of the count-valued nature of abundance data and most JSDM rely on Gaussian latent layer to encode the dependencies between species in a covariance matrix. The multivariate Poisson-lognormal (PLN) model is one such model, which can be viewed as a multivariate mixed Poisson regres- sion model. The inference of such models raises both statistical and computational issues, many of which were solved in recent contributions using variational techniques and convex optimization. The PLN model turns out to be a versatile framework, within which a variety of analyses can be performed, including multivariate sample comparison, clustering of sites or samples, dimension reduction (ordination) for visualization purposes, or inference of interaction net- works. We will presents the PLN framework and some variants and illustrate them on typical datasets. All the models and methods are implemented in the R package PLNmodels, available from cran.r-project.org.