Abstract
Joint Species Distribution Models (JSDM) provide a general multivariate framework to study the joint abundances of all species from a community. JSDM account for both structuring factors (environmental characteristics or gradients, such as habitat type or nutrient availability) and potential interactions between the species (competition, mutualism, parasitism, 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 regression model. Inferring such models raises both statistical and computational issues, many of which were solved in recent contributions using variational techniques and convex optimization tools. 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 inferring interaction networks. This paper presents the general PLN framework and illustrates its use on a series a typical experimental datasets. All the models and methods are implemented in the R package PLNmodels, available from cran.r-project.org.
Highlights
We focus here on abundance data, and on data which consists of a count associated with each species in each site, date or condition
This paper introduces the Poisson-lognormal (PLN) model— first proposed by Aitchison and Ho (1989)—as a Joint Species Distribution Models (JSDM)
The main difference with generalized linear latent variable models (GLLVMs) as presented in Hui et al (2017) is that the latent variables in Hierarchical Modeling of Species Communities (HMSC) are themselves carefully modeled according to a hierarchical framework with clearly identified terms and effects to ease interpretation of the parameters and decompose variance across terms
Summary
Joint Species Distribution Models (JSDM) have received a lot of attention in the last decade as they provide a general multivariate framework to study the joint abundances of all species from a community, as opposed to species distribution models (SDM: Elith and Leathwick, 2009) where species are considered as disconnected entities At their best, JSDM account for both structuring factors (e.g., environmental gradients, nutrients availability, etc.) and potential interactions between the species (competition, mutualism, parasitism, etc.). Because of its simple form, the PLN model turns out to be versatile in the sense that it provides a convenient framework to carry out a series of typical multivariate statistical analyses This includes multivariate regression in its simplest form, and multivariate sample comparison via linear discriminant analysis (LDA), modelbased clustering using mixture models, dimension reduction via principal component analysis (PCA: Chiquet et al, 2018), and network inference (Chiquet et al, 2019). The last section provides additional information about the PLNmodels package and describes several research leads motivated by current needs in ecological modeling
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