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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 concluding chapter discusses the strengths and limitations of Hierarchical Modelling of Species Communities (HMSC) in light of the results presented in this book. Concerning the strengths, the chapter notes that HMSC is a unifying framework that encompasses classic approaches such as single-species distribution models and model-based ordinations as special cases, which hence provides simultaneous inferences at the species and community levels. As another key strength, the chapter notes that HMSC can be applied to many kinds of study designs (including hierarchical, temporal or spatial) and many types of data (such as presence–absence, counts and continuous measurements). The chapter further emphasises that HMSC offers the general advantages of model-based approaches, such as tools for model validation and prediction, and that it is especially well suited for predictive modelling of communities with sparse data. Concerning the limitations, the chapter discusses three areas where future development is needed: a broader set of data models, a broader array of model structures related to various ecological and evolutionary processes, and improved computational efficiency.
This chapter focuses on model evaluation and selection in Hierarchical Modelling of Species Communities (HMSC). It starts by noting that even if there are automated procedures for model selection, the most important step is actually done by the ecologist when deciding what kind of models will be fitted. The chapter then discusses different ways of measuring model fit based on contrasting the model predictions with the observed data, as well as the use of information criteria as a method for evaluating model fit. The chapter first discusses general methods that can be used to compare models that differ either in their predictors or in their structure, e.g. models with different sets of environmental covariates, models with and without spatial random effects, models with and without traits or phylogenetic information or models that differ in their prior distributions. The chapter then presents specific methods for variable selection, aimed at comparing models that are structurally identical but differ in the included environmental covariates: variable selection by the spike and slab prior approach, and reduced rank regression that aims at combining predictors to reduce their dimensionality.
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 gives a brief overview of the history of community ecology, starting from the early 20th century debates on how communities should be defined and continuing until the modern conceptual frameworks. The chapter covers the criticism of community ecology, the views and theories that mainstreamed its avenue and the current unifying theoretical frameworks. The chapter discusses how the scale dependency of community processes is one of the main sources of criticism and disagreement among community ecologists. We introduce the early contrasting views and theories, such as the organismic versus individualistic continuum concepts of communities and the niche versus neutral theories. We further discuss the current unifying theoretical frameworks, such as the metacommunity framework, the assembly rules framework and Vellend’s Theory of Ecological Communities. Most importantly, the chapter introduces the concepts and ideas that underlie the ecological assumptions behind species distribution models in general, and Hierarchical Modelling of Species Communities (HMSC) in particular.
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 describes the types of data that empirical community ecologists typically collect, and how these can be incorporated in the Hierarchical Modelling of Species Communities (HMSC) framework as input. While community ecologists apply theoretical, experimental and observational approaches to studying the processes that structure ecological communities, this chapter (and the entire book) focuses mainly on empirical research based on non-manipulative observational data. Understanding the basic features of the data and how they have been collected will be essential for appropriately setting up the HMSC model and interpreting the results. The chapter describes each type of input HMSC data, namely the community data (i.e. the occurrences or abundances of the species), environmental data, data describing the spatio-temporal context, species trait data and phylogenetic data. Finally, the chapter discusses how to best organise the data, as well as how to solve problems arising from missing data.
This chapter applies Hierarchical Modelling of Species Communities (HMSC) to a real dataset on Finnish birds, with the aim of using the case study to simultaneously demonstrate the many uses of HMSC. Specifically, it illustrates the full workflow of a typical HMSC analysis, shows how the researcher can access the full posterior distribution to go beyond the default outputs of HMSC analyses, shows how predictions of HMSC can be used as a starting point for further analyses as well as compares HMSC outputs to results obtained by other statistical methods in community ecology. The chapter starts by outlining the five steps of the HMSC workflow, and then shows how the researcher can access the entire posterior distribution of model parameters or predictions, e.g. for examining the level of statistical support related to either of these. Next the chapter illustrates how one may use HMSC predictions as a starting point for applied research, such as spatial conservation prioritisation or bioregionalisation. Finally, the chapter applies other widely used methods in statistical community ecology such as ordination methods and co-occurrence analysis to the same data, with the aim of comparing how their results relate to those obtained by HMSC.
This chapter describes how Bayesian inference is applied in Hierarchical Modelling of Species Communities (HMSC). The chapter starts by summarising the structure of the core HMSC model. It then briefly recalls some of the fundamentals of Bayesian inference, aimed primarily for those readers who are not very familiar with it. The core part of the chapter describes the structure of the prior distribution of HMSC and explains in particular how the default prior has been chosen. The chapter also briefly discusses how posterior sampling is conducted in HMSC through Markov chain Monte Carlo. The chapter uses the R-package HMSC-R to demonstrate how the prior distribution can be sampled, and to illustrate that samples from the prior distribution are identical to posterior samples if the model does not have any data. Finally, the chapter discusses how the computational time needed to fit an HMSC model depends on the size and type of the data.
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 examines the links between Hierarchical Modelling of Species Communities (HMSC) outputs and the underlying community ecological processes. To do so, the chapter applies HMSC to simulated data generated from an agent-based model with known underlying assembly processes, and then assesses how those processes are captured from the patterns in the data. After simulating data with the spatial agent-based model, the chapter simulates two 'virtual ecologists' who sample data from the simulations, one applying a spatial study design and the other a temporal study design. While the main motivation of the chapter is to assess how community assembly processes translate into HMSC outputs, another motivation is to examine the robustness of HSMC to violations against structural model assumptions – namely, the data generated by the agent-based models violate some of the underlying assumptions of generalised linear mixed models and thus of HMSC. The chapter finishes by summarising what the virtual ecologists learned by applying HMSC to their data, particularly in light of the assembly processes that were used to simulate the data.