Probabilistic models for networks

You will find here all the material I use for my 3 hours class on probabilistic models for network analysis.

Introduction

Ecological networks are made up of nodes, representing biological entities of interest and edges representing the interaction being studied. Stochastic block models (SBMs) and their extension to bipartite networks are convenient tools to modelize heterogeneity in (ecological) networks by introducing blocks of nodes sharing the same pattern of connection. This short-course presents SBMs for unipartite, bipartite or more complex networks and illustrates their flexibility.

Material for the theoretical part

Here are the slides of the course

• The first part is an Introduction to block models Part 1
• The second part will adress the Modelling of a collection of networks Part 2. This part is based on Chabert-Liddell, Barbillon, and Donnet (2022), available on arxiv. This second part will be dealt with only if we have time.

Additional material on Stochastic Block Models can be found the book Chapter 6 Using Latent Block Models to Detect Structure in Ecological Networks in Aubert et al. (2022).

R-tutorial

This class will include an R-tutorial session available here. You can download the TutorialBM.qmd file here

It is mainly based on the R-package sbm. Please find informations here.

Some additional R packages are needed.

install.packages("sbm")
install.packages("GGally") # To plot networks
install.packages('network') 
install.packages('RColorBrewer') # to have nice colors
install.packages('knitr') # to plot nice tables

Note that a shiny application is also proposed. You should install the last version on your machine

remotes::install_github("Jo-Theo/shinySbm")
shinySbm::run_app()

It can also be used online here (not always the latest version).

In case we have anough time, the second part of the tutorial will deal with collection of networks and we will use the R package colSBM available on Github.

remotes::install_github("Chabert-Liddell/colSBM")

The tutorial on colSBM is available at this link

Data sets

• The first part of the tutorial will rely on the fungus-tree interaction network studied by Vacher, Piou, and Desprez-Loustau (2008), available with the package sbm.
  
• We may also analyze the multipartite ecological network collected by Dáttilo et al. (2016) (also available in sbm)
• Finally, we will maybe use the dataset of Thompson and Townsend (2003) provided in the colSBM package

library(sbm)
data("fungusTreeNetwork")
data("multipartiteEcologicalNetwork")
library(colSBM)
data("foodwebs")

References

Aubert, Julie, Pierre Barbillon, Sophie Donnet, and Vincent Miele. 2022. “Using Latent Block Models to Detect Structure in Ecological Networks.” In Statistical Approaches for Hidden Variables in Ecology, 117–34. John Wiley & Sons, Ltd. https://doi.org/https://doi.org/10.1002/9781119902799.ch6.

Chabert-Liddell, Saint-Clair, Pierre Barbillon, and Sophie Donnet. 2022. “Learning Common Structures in a Collection of Networks. An Application to Food Webs.” arXiv. https://doi.org/10.48550/ARXIV.2206.00560.

Dáttilo, Wesley, Nubia Lara-Rodrı́guez, Pedro Jordano, Paulo R. Guimarães, John N. Thompson, Robert J. Marquis, Lucas P. Medeiros, Raul Ortiz-Pulido, Maria A. Marcos-Garcı́a, and Victor Rico-Gray. 2016. “Unravelling Darwin’s Entangled Bank: Architecture and Robustness of Mutualistic Networks with Multiple Interaction Types.” Proceedings of the Royal Society of London B: Biological Sciences 283 (1843).

Thompson, R. M., and C. R. Townsend. 2003. “IMPACTS ON STREAM FOOD WEBS OF NATIVE AND EXOTIC FOREST: AN INTERCONTINENTAL COMPARISON.” Ecology 84 (1): 145–61. https://doi.org/https://doi.org/10.1890/0012-9658(2003)084[0145:IOSFWO]2.0.CO;2.

Vacher, Corinne, Dominique Piou, and Marie-Laure Desprez-Loustau. 2008. “Architecture of an Antagonistic Tree/Fungus Network: The Asymmetric Influence of Past Evolutionary History.” PloS One 3 (3): e1740.