PLN-team · jchiquet · Jun 19, 2026 · Jun 19, 2026 · Jun 19, 2026 · Jun 19, 2026
diff --git a/README.md b/README.md
@@ -6,7 +6,7 @@
 [![R-CMD-check](https://github.com/PLN-team/PLNmodels/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/PLN-team/PLNmodels/actions/workflows/R-CMD-check.yaml)
 [![Coverage
 status](https://codecov.io/gh/pln-team/PLNmodels/branch/master/graph/badge.svg)](https://codecov.io/github/pln-team/PLNmodels?branch=master)
-[![CRAN_Status_Badge](http://www.r-pkg.org/badges/version/PLNmodels.png)](https://cran.r-project.org/package=PLNmodels)
+[![CRAN_Status_Badge](https://www.r-pkg.org/badges/version/PLNmodels)](https://cran.r-project.org/package=PLNmodels)
 [![Lifecycle:
 stable](https://img.shields.io/badge/lifecycle-stable-blue.svg)](https://lifecycle.r-lib.org/articles/stages.html)
 [![](https://img.shields.io/github/last-commit/pln-team/PLNmodels.svg)](https://github.com/pln-team/PLNmodels/commits/master)
@@ -18,8 +18,9 @@ stable](https://img.shields.io/badge/lifecycle-stable-blue.svg)](https://lifecyc
 > of multivariate problems when count data are at play. This package
 > implements efficient variational algorithms to fit such models,
 > accompanied with a set of functions for visualization and diagnostic.
-> See [this deck of slides](https://pln-team.github.io/slideshow/slides)
-> for a comprehensive introduction.
+> See [all the dedicated
+> vignettes](https://pln-team.github.io/PLNmodels/articles/) for a
+> comprehensive introduction.
 
 **PLNmodels** covers the following models, all built around the
 multivariate Poisson-lognormal distribution and sharing a common
@@ -40,7 +41,7 @@ experimental torch backend):
   of PLN models.
 - **ZIPLN**[^8]: a zero-inflated extension of PLN for data with excess
   zeros, with the same family of covariance structures and an optional
-  sparse (`ZIPLNnetwork`) variant.
+  sparse (`ZIPLNnetwork`[^9]) variant.
 
 ## Installation
 
@@ -56,7 +57,7 @@ remotes::install_github("pln-team/PLNmodels@tag_number")  # a specific tagged re
 
 ## Illustration
 
-We illustrate the main models on the `barents` data set[^9]: the
+We illustrate the main models on the `barents` data set[^10]: the
 abundance of 30 fish species observed in 89 sites in the Barents sea,
 along with depth, temperature and geographic coordinates for each site.
 
@@ -272,6 +273,12 @@ table(cluster = myMixture$memberships, zone = barents$zone)
     Statistics and Computing, 35, 2025.
     [doi:10.1007/s11222-025-10729-0](https://doi.org/10.1007/s11222-025-10729-0)
 
-[^9]: Fossheim, M., Nilssen, E. M. and Aschan, M. Fish assemblages in
+[^9]: Tous, J., Chiquet, J., Deacon, A. E., Fontrodona-Eslava, A.,
+    Fraser, D. F. and Magurran, A. E. A JSDM with zero-inflation to
+    improve inference of association networks from count community data
+    with structural zeros. bioRxiv preprint, 2025.
+    [doi:10.1101/2025.07.24.666553](https://doi.org/10.1101/2025.07.24.666553)
+
+[^10]: Fossheim, M., Nilssen, E. M. and Aschan, M. Fish assemblages in
     the Barents Sea. Marine Biology Research, 2(4), 2006.
     [doi:10.1080/17451000600815698](https://doi.org/10.1080/17451000600815698)
diff --git a/README.qmd b/README.qmd
@@ -1,12 +1,14 @@
 ---
 title: "PLNmodels: Poisson lognormal models for multivariate count data"
-format: gfm
+format:
+  gfm:
+    default-image-extension: ""
 ---
 
 <!-- badges: start -->
 [![R-CMD-check](https://github.com/PLN-team/PLNmodels/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/PLN-team/PLNmodels/actions/workflows/R-CMD-check.yaml)
 [![Coverage status](https://codecov.io/gh/pln-team/PLNmodels/branch/master/graph/badge.svg)](https://codecov.io/github/pln-team/PLNmodels?branch=master)
-[![CRAN_Status_Badge](http://www.r-pkg.org/badges/version/PLNmodels)](https://cran.r-project.org/package=PLNmodels)
+[![CRAN_Status_Badge](https://www.r-pkg.org/badges/version/PLNmodels)](https://cran.r-project.org/package=PLNmodels)
 [![Lifecycle: stable](https://img.shields.io/badge/lifecycle-stable-blue.svg)](https://lifecycle.r-lib.org/articles/stages.html)
 [![](https://img.shields.io/github/last-commit/pln-team/PLNmodels.svg)](https://github.com/pln-team/PLNmodels/commits/master)
 <!-- badges: end -->
@@ -23,7 +25,7 @@ knitr::opts_chunk$set(
 
 ## Description
 
-> The Poisson lognormal model and variants[^1] can be used for a variety of multivariate problems when count data are at play. This package implements efficient variational algorithms to fit such models, accompanied with a set of functions for visualization and diagnostic. See [this deck of slides](https://pln-team.github.io/slideshow/slides) for a comprehensive introduction.
+> The Poisson lognormal model and variants[^1] can be used for a variety of multivariate problems when count data are at play. This package implements efficient variational algorithms to fit such models, accompanied with a set of functions for visualization and diagnostic. See [all the dedicated vignettes](https://pln-team.github.io/PLNmodels/articles/) for a comprehensive introduction.
 
 **PLNmodels** covers the following models, all built around the multivariate Poisson-lognormal distribution and sharing a common formula-based interface (covariates, offsets, weights) and a choice of optimization backends (a fast built-in Newton solver, NLOPT, and an experimental torch backend):
 
@@ -32,7 +34,7 @@ knitr::opts_chunk$set(
 - **PLNLDA**: Poisson lognormal discriminant analysis[^4] for the supervised classification of count data.
 - **PLNnetwork**[^5]: sparse inverse-covariance (network) inference via a graphical-lasso-like penalty[^6].
 - **PLNmixture**: model-based clustering[^7] of count data via a mixture of PLN models.
-- **ZIPLN**[^8]: a zero-inflated extension of PLN for data with excess zeros, with the same family of covariance structures and an optional sparse (`ZIPLNnetwork`) variant.
+- **ZIPLN**[^8]: a zero-inflated extension of PLN for data with excess zeros, with the same family of covariance structures and an optional sparse (`ZIPLNnetwork`[^9]) variant.
 
 [^1]: J. Chiquet, M. Mariadassou and S. Robin: The Poisson-lognormal model as a versatile framework for the joint analysis of species abundances, Frontiers in Ecology and Evolution, 2021. [doi:10.3389/fevo.2021.588292](https://www.frontiersin.org/articles/10.3389/fevo.2021.588292/full)
 [^2]: Aitchison, J. and Ho, C. H. The multivariate Poisson-log normal distribution. Biometrika, 76(4), 1989, 643–653.
@@ -42,6 +44,7 @@ knitr::opts_chunk$set(
 [^6]: Friedman, J., Hastie, T. and Tibshirani, R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 2008.
 [^7]: Fraley, C. and Raftery, A. E. MCLUST: Software for model-based cluster analysis. Journal of Classification, 16(2), 1999.
 [^8]: Batardière, B., Chiquet, J., Gindraud, F. and Mariadassou, M. Zero-inflation in the multivariate Poisson lognormal family. Statistics and Computing, 35, 2025. [doi:10.1007/s11222-025-10729-0](https://doi.org/10.1007/s11222-025-10729-0)
+[^9]: Tous, J., Chiquet, J., Deacon, A. E., Fontrodona-Eslava, A., Fraser, D. F. and Magurran, A. E. A JSDM with zero-inflation to improve inference of association networks from count community data with structural zeros. bioRxiv preprint, 2025. [doi:10.1101/2025.07.24.666553](https://doi.org/10.1101/2025.07.24.666553)
 
 ## Installation
 
@@ -55,9 +58,9 @@ remotes::install_github("pln-team/PLNmodels@tag_number")  # a specific tagged re
 
 ## Illustration
 
-We illustrate the main models on the `barents` data set[^9]: the abundance of 30 fish species observed in 89 sites in the Barents sea, along with depth, temperature and geographic coordinates for each site.
+We illustrate the main models on the `barents` data set[^10]: the abundance of 30 fish species observed in 89 sites in the Barents sea, along with depth, temperature and geographic coordinates for each site.
 
-[^9]: Fossheim, M., Nilssen, E. M. and Aschan, M. Fish assemblages in the Barents Sea. Marine Biology Research, 2(4), 2006. [doi:10.1080/17451000600815698](https://doi.org/10.1080/17451000600815698)
+[^10]: Fossheim, M., Nilssen, E. M. and Aschan, M. Fish assemblages in the Barents Sea. Marine Biology Research, 2(4), 2006. [doi:10.1080/17451000600815698](https://doi.org/10.1080/17451000600815698)
 
 ```{r load}
 library(PLNmodels)

diff --git a/vignettes/ZIPLN.Rmd b/vignettes/ZIPLN.Rmd
@@ -50,7 +50,7 @@ mean(microcosm$Abundance == 0)
 
 ### Mathematical background
 
-The zero-inflated PLN model (ZIPLN) combines the Poisson lognormal model [@AiH89] -- see [the PLN vignette](PLN.html) -- with a zero-inflation mechanism: each count $Y_{ij}$ is either a structural zero (with probability $\pi_{ij}$) or drawn from the usual PLN generative process:
+The zero-inflated PLN model (ZIPLN) [@ZIPLN] combines the Poisson lognormal model [@AiH89] -- see [the PLN vignette](PLN.html) -- with a zero-inflation mechanism: each count $Y_{ij}$ is either a structural zero (with probability $\pi_{ij}$) or drawn from the usual PLN generative process:
 \begin{equation}
   \begin{array}{rcl}
   \text{latent space } &   \mathbf{Z}_i \sim \mathcal{N}\left({\boldsymbol\mu},\boldsymbol\Sigma\right) & \\
@@ -66,7 +66,7 @@ Just like PLN, ${\boldsymbol\mu}$ generalizes to $\mathbf{o}_i + \mathbf{x}_i^\t
 - `"col"`: one $\pi_j$ per species.
 - covariates: $\text{logit}(\pi_{ij}) = \mathbf{x}_{0,i}^\top\mathbf{B}_{0,j}$, specified with the formula syntax `Y ~ PLN effect | ZI effect` (see below).
 
-`ZIPLNnetwork` further adds a sparsity penalty on $\boldsymbol\Omega = \boldsymbol\Sigma^{-1}$, exactly as `PLNnetwork` does for PLN (see [the PLNnetwork vignette](PLNnetwork.html) and @PLNnetwork), so that both the excess of zeros and the residual dependency structure between taxa are accounted for.
+`ZIPLNnetwork` further adds a sparsity penalty on $\boldsymbol\Omega = \boldsymbol\Sigma^{-1}$, exactly as `PLNnetwork` does for PLN (see [the PLNnetwork vignette](PLNnetwork.html) and @PLNnetwork), so that both the excess of zeros and the residual dependency structure between taxa are accounted for. See @ZIPLNnetwork for an application to species association networks from count data with structural zeros.
 
 ## Analysis of microcosm with ZIPLN
 

diff --git a/vignettes/article/PLNreferences.bib b/vignettes/article/PLNreferences.bib
@@ -44,6 +44,23 @@ @InProceedings{PLNnetwork
   url = 	 {http://proceedings.mlr.press/v97/chiquet19a.html},
 }
 
+@Article{ZIPLN,
+  author  = {Batardière, Bastien and Chiquet, Julien and Gindraud, François and Mariadassou, Mahendra},
+  title   = {Zero-inflation in the multivariate Poisson lognormal family},
+  journal = {Statistics and Computing},
+  year    = {2025},
+  volume  = {35},
+  doi     = {10.1007/s11222-025-10729-0},
+}
+
+@Unpublished{ZIPLNnetwork,
+  author = {Tous, Jeanne and Chiquet, Julien and Deacon, Amy E. and Fontrodona-Eslava, Ada and Fraser, Douglas F. and Magurran, Anne E.},
+  title  = {A JSDM with zero-inflation to improve inference of association networks from count community data with structural zeros},
+  year   = {2025},
+  note   = {bioRxiv preprint},
+  doi    = {10.1101/2025.07.24.666553},
+}
+
 @inproceedings{trichoptera,
   title={Influence des facteurs météorologiques sur les résultats de piégeage lumineux},
   author={Usseglio-Polatera, P. and Auda, Y.},