Chapter 1 summarizes the main concepts representing the pillars of trait-based ecology. Key definitions from the literature, and widely used in the book, are synthetized and clarified. This includes an in-depth discussion of which traits are to be considered more functional, dissecting the relationship between species traits and species fitness and how this can change across different habitats. The classic distinction between response and effect traits is introduced, together with some broad open challenges for future research in trait-based ecology.

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.