This chapter provides an overview of the Hierarchical Modelling of Species Communities (HMSC) framework. For this, HMSC is first placed in the context of the widely applied generalised linear mixed modelling. Next, we outline the statistical structure of HMSC and the notation that is used throughout the book. This chapter also introduces the conceptual theoretical framework under which HMSC has been developed, showing how environmental filtering, contingencies on species traits and phylogenetic relationships and biotic filtering are modelled at multiple spatial or temporal scales. Then the five steps of the HMSC analysis workflow are illustrated. As the chapter aims to give a quick overview, it does not fully cover every statistical feature or the details about how different components of the HMSC model can be used for addressing specific study questions in community ecology. These will be covered in the remaining chapters of the book, where HMSC is built step by step, related to ecological theory and illustrated through examples.

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.

This chapter covers the basics of generalised linear mixed models in the univariate context of single-species distribution modelling. The chapter starts by discussing how species distribution models relate to the theory on environmental species niches. The modelling part of the chapter first introduces the linear model, then moves to generalised models, then to mixed models with both fixed and random effects, and finally describes how the explained variance can be partitioned among the explanatory variables. The applied part of the chapter uses both simulated and real data to illustrate how the R-package HMSC-R can be used to analyse generalised linear mixed models. While these analyses are rather standard and could also be conducted with many other packages, the reader is encouraged to go through them, as they provide the simplest way of becoming familiar with the syntax of HMSC-R.