This chapter introduces the statistical methods commonly applied by ecologists working with community data, by giving a general overview of the available tools. In this way, the chapter places joint species distribution models in general – and Hierarchical Modelling of Species Communities (HMSC) in particular – in the broader context of statistical community ecology. The chapter first introduces the wide variety of ordination methods and the substantial contributions they have made to empirical research in community ecology. The chapter next discusses the approaches of co-occurrence analysis and generalised linear models applied to diversity metrics. The chapter concludes by introducing species distribution modelling, highlighting the differences between single-species and joint species distribution models. Although the statistical methods are explained only verbally in this chapter, they are further discussed elsewhere in the book – namely, Chapters 4–8 give the statistical details on single-species and joint species distribution models, and Chapter 11 illustrates ordinations, co-occurrence analysis and joint species distribution models by applying them to a real data example.

This chapter discusses how Hierarchical Modelling of Species Communities (HMSC) can be used to model residual associations among species, with the aim of capturing biotic interactions. The chapter starts with an overview of the different modelling strategies that can be used for estimating biotic interactions in species distribution models. It then builds the statistical approach, first discussing the relationship between occurrence probabilities and co-occurrence probabilities and then describing how latent variables can be used to compactly model co-occurrences in species-rich communities. After introducing the baseline model, the chapter extends it to hierarchical, spatial and temporal study designs, as well as to cases where the biotic interactions depend on the environmental conditions. The chapter then focuses on interpretation, recalling that residual associations can be caused by many processes other than biotic interactions, therefore great caution must be taken when interpreting associations as biotic interactions. The chapter also discusses when and how the estimated species associations can be used to make improved predictions. The chapter finishes with two case studies, the first of which is based on simulated data and the second on sequencing data on dead-wood inhabiting fungi.

This chapter moves to the area for which Hierarchical Modelling of Species Communities (HMSC) is really meant, namely multi-species modelling. Thus, the chapter moves from univariate generalised linear mixed models to multivariate generalised linear mixed models, where the response variable is the vector of species occurrences or abundances. The chapter starts by discussing the difference between stacked species distribution modelling and joint species distribution modelling. It then builds HMSC as a joint species distribution model, first discussing how to model variation among species niches in general, and then adding hierarchical levels to specifically model species niches as a function of species’ traits, phylogenetic relationships or a combination of the two. The chapter illustrates joint species distribution modelling by applying the R-package HMSC-R first to simulated data and then to real data on a plant community.