Bert van der Veen

Ecologists commonly apply binomial regression to study binary data. Often, the link function in binomial regression is not purposefully chosen, but instead selected on the grounds of interpretation or computation efficiency. However, if the binary response is the result of a latent abundance process, then the link function implies assumptions for this underlying process. The most well-known example of this is the complementary log-log (cloglog) link, which has direct connections with the probability of a positive count under a latent Poisson distribution. On the other hand, counts in ecology are often overdispersed, meaning the assumption of an underlying Poisson abundance process is unrealistic. In this article, we provide a framework for consideration of the link choice in binomial regression, in terms of the latent abundance process that binary responses can represent. Aside from the Poisson case mentioned above, we show that the cloglog link is the right choice if the latent abundance process represents the biomass of individuals, or if the latent abundance process comes from an overdispersed count distribution with a linear mean-variance relationship. For the case where the latent count follows a negative binomial distribution with a quadratic mean-variance relationship, we derive a new generalized complementary log-log (gcloglog) link function, which includes the case of the cloglog link as well as that of the logit link, where the latter implies assuming moderate overdispersion in the form of a geometric distribution. Two simulation studies demonstrate that cloglog and logit link binomial regression can exhibit bias and undercoverage when the latent count is more overdispersed than assumed, while gcloglog link models overcome this issue but in practice require replication in the binomial response for reliable estimation. Two real ecological datasets further illustrate how to use the gcloglog link binomial regression in practice including as a means of sensitivity analysis. We encourage ecologists to give more thought to the choice of link function in binomial regression, based on considering the latent abundance process and its properties.

Biodiversity indices are valuable for ecological science, and also as EBVs for communicating biodiversity trends with stakeholders and policy makers. Although there many are indices to measure biodiversity, the problem is that there are many indices to measure biodiversity. This is because biodiversity has many facets, and each one can be viewed in several ways. The indices that are commonly used (e.g. Hill numbers for alpha diversity) have been developed for specific facets, rather than as part of a whole. Here we present an approach to biodiversity indices that integrates the different levels of species-level biodiversity into one framework. It is based on theory from both statistical and ecological modelling, where we connect the indices to means and variances of species occurrence and abundance. From this we derive new biodiversity indices which either cover the same aspect of biodiversity as old indices, or give us new angles to look at biodiversity. These indices all sum up to the total biodiversity. Because the indices have an underlying model, we can easily incorporate additional drivers, e.g. environmental predictors (to see how they drive community dis-similarity), traits, space and phylogeny. This also opens up the possibility to more directly link the indices to ecological theory and models. We will present the framework, and show how our indices align with traditional measures of alpha and beta diversity, for both species richness and community composition. One of the major benefits of the framework is that it is straightforward to incorporate the sampling design of data (or sampling lack-of-design) into the analysis, extracting estimates of uncertainty, or explicitly incorporate space or time. Overall, our framework better facilitates the development of theoretically sound EBVs, to not only allow us to summarise biodiversity in a consistent way at different levels, but to look at how different impacts, e.g. climate or land use change, will affect spatial patterns of biodiversity.

In this article, we present the case for Generalized Linear Latent Variable Models (GLLVMs) as a go-to choice of statistical method for any community ecologist wanting to tackle a range of present-day ecological research questions. GLLVMs bring tools and capabilities from classic (mixed-effects) regression models to multivariate community analysis, providing a number of novel ways to tailor models specifically to one’s study questions and data properties not available when using non-model-based multivariate methods. In order to facilitate further adoption of these methods by community ecologists, we provide 1) a practitioner-focused and practical overview of the advantages the GLLVM framework brings to the table when addressing different core ecological questions, 2) a number of concrete suggestions for how GLLVMs best can be incorporated into the analytical workflow of community ecologists, and 3) two illustrative worked examples of this workflow in action on real-world data.

Joint species distribution models (JSDMs) have gained considerable traction among ecologists over the past decade, due to their capacity to answer a wide range of questions at both the species‐ and the community‐level. The family of generalised linear latent variable models in particular has proven popular for building JSDMs, being able to handle many response types including presence‐absence data, biomass, overdispersed and/or zero‐inflated counts. We extend latent variable models to handle percent cover response variables, with vegetation, sessile invertebrate and macroalgal cover data representing the prime examples of such data arising in community ecology. Sparsity is a commonly encountered challenge with percent cover data. Responses are typically recorded as percentages covered per plot, though some species may be completely absent or present, that is, have 0% or 100% cover, respectively, rendering the use of beta distribution inadequate. We propose two JSDMs suitable for percent cover data, namely a hurdle beta model and an ordered beta model. We compare the two proposed approaches to a beta distribution for shifted responses, transformed presence‐absence data and an ordinal model for percent cover classes. Results demonstrate the hurdle beta JSDM was generally the most accurate at retrieving the latent variables and predicting ecological percent cover data.

The ecological niche is a fundamental concept in ecology that can be used in order better understand species relationships. The overlap in species niches provides a measure of the likelihood for species to co‐occur. Most approaches that quantify niche overlap have been based on distance and similarity indices, for pairwise combinations of species. In this paper, we suggest that niche overlap can be calculated from the predictions of a model. Using a statistical model to predict niche overlap provides various benefits, includes the possibility to adjust the model to properties of the data. We demonstrate this using an example dataset of an ecological community of Foraminifera species, to which we fit a generalized linear latent variable model (GLLVM). GLLVMs are a flexible class of models that allow to estimate the distribution of species using both measured environmental predictors and residual covariation between species. We demonstrate how to calculate niche overlap from GLLVMs for any combination of species, and separately for different environments. Predicting niche overlap from a model further expands the toolset available to ecologists for the exploration of species co‐occurrence patterns.

Ordination methods have been used by community ecologists to describe and explore the communities they sample by reducing this variation down to a small number of dimensions. More recently, Joint Species Distribution Models have been developed to model and predict the distributions of several species simultaneously. Contemporary models for the data for both of these problems are essentially the same, called Generalised Linear Latent Variable Models (GLLVMs). Based on this we suggest some avenues of cross-fertilisation between the two areas of research. We also describe some of the extensions to GLLVMs, and from this suggest the development of Hierarchical Ordination, as a way of efficiently modelling communities of species in space.

Principal component regression results in lack of fit when important dimensions are omitted, which cannot be assessed from the eigenvalues. I show that the PC-regression estimator can also suffer from increased variance relative to ordinary least squares in such cases.

In community ecology, unconstrained ordination can be used to indirectly explore drivers of community composition, while constrained ordination can be used to directly relate predictors to an ecological community. However, existing constrained ordination methods do not explicitly account for community composition that cannot be explained by the predictors, so that they have the potential to misrepresent community composition if not all predictors are available in the data. We propose and develop a set of new methods for ordination and joint species distribution modelling (JSDM) as part of the generalized linear latent variable model (GLLVM) framework, that incorporate predictors directly into an ordination. This includes a new ordination method that we refer to as concurrent ordination, as it simultaneously constructs unconstrained and constrained latent variables. Both unmeasured residual covariation and predictors are incorporated into the ordination by simultaneously imposing reduced rank structures on the residual covariance matrix and on fixed‐effects. We evaluate the method with a simulation study, and show that the proposed developments outperform canonical correspondence analysis (CCA) for Poisson and Bernoulli responses, and perform similar to redundancy analysis (RDA) for normally distributed responses, the two most popular methods for constrained ordination in community ecology. Two examples with real data further demonstrate the benefits of concurrent ordination, and the need to account for residual covariation in the analysis of multivariate data. This article contextualizes the role of constrained ordination in the GLLVM and JSDM frameworks, while developing a new ordination method that incorporates the best of unconstrained and constrained ordination, and which overcomes some of the deficiencies of existing classical ordination methods.

Understanding the mechanisms of ecological community dynamics and how they could be affected by environmental changes is important. Population dynamic models have well known ecological parameters that describe key characteristics of species such as the effect of environmental noise and demographic variance on the dynamics, the long‐term growth rate, and strength of density regulation. These parameters are also central for detecting and understanding changes in communities of species; however, incorporating such vital parameters into models of community dynamics is challenging. In this paper, we demonstrate how generalized linear mixed models specified as intercept‐only models with different random effects can be used to fit dynamic species abundance distributions. Each random effect has an ecologically meaningful interpretation either describing general and species‐specific responses to environmental stochasticity in time or space, or variation in growth rate and carrying capacity among species. We use simulations to show that the accuracy of the estimation depends on the strength of density regulation in discrete population dynamics. The estimation of different covariance and population dynamic parameters, with corresponding statistical uncertainties, is demonstrated for case studies of fish and bat communities. We find that species heterogeneity is the main factor of spatial and temporal community similarity for both case studies.