Model-based ordination for species with unequal niche widths

Abstract

SummaryIt is common practice for ecologists to examine species niches in the study of community composition. The response curve of a species in the fundamental niche is usually assumed to be quadratic. The center of a quadratic curve represents a species’ optimal environmental conditions, and the width its ability to tolerate deviations from the optimum.Most multivariate methods assume species respond linearly to the environment of the niche, or with a quadratic curve that is of equal width and height for all species. However, it is widely understood that some species are generalists who tolerate deviations from their optimal environment better than others. Rare species often tolerate a smaller range of environments than more common species, corresponding to a narrow niche.We propose a new method, for ordination and fitting Joint Species Distribution Models, based on Generalized Linear Mixed-Effects Models, which relaxes the assumptions of equal tolerances and equal maxima.By explicitly estimating species optima, tolerances, and maxima, per ecological gradient, we can better predict change in species communities, and understand how species relate to each other.

Multispecies models for population dynamics: Progress, challenges and future directions

“…For instance, in JSDMs with latent variable structures, all pairs of species associations or co-occurrences are modelled jointly by searching for the leading axes of variation unaccounted for by the environmental effects. This creates linear combinations of several variables, limiting the dimensionality of the multispecies data (Thorson et al 2015;Ovaskainen & Abrego 2020;van der Veen et al 2021). Instructural equation modelling (SEM), latent variables typically represent a theorized environmental effect measured by one or more indicator variables (Grace et al 2010).…”

Modelling temperature‐driven changes in species associations across freshwater communities

“…Although temperature was included in the random-effect, it was also included as a fixed-effect with quadratic function, to account for potential non-linear responses of species to temperature (Boddy & McIntosh, 2017;Veen et al, 2021).…”

Concurrent ordination: simultaneous unconstrained and constrained latent variable modeling

“…where D j is a positive-definite diagonal matrix that contains the quadratic coefficients for the latent variables per species. Setting again z i = ϵ i for an unconstrained ordination as in van der Veen et al (2021),…”

“…The LV-level error is assumed to follow a multivariate normal distribution, h(ϵ i ) = N {0, diag(σ 2 )}. The integration can be performed with the approaches available in the gllvm R-package previously developed for approximate estimation and inference in GLLVMs for unconstrained ordination (Niku et al 2019a), namely the Laplace approximation (Niku et al 2017) or Variational Approximations (VA, Hui et al 2017;van der Veen et al 2021), and implemented via Template Model Builder (Kristensen et al 2016). The LV-level residual can be obtained as e.g., the means of variational distributions (Hui et al 2017) or the maximum a-posteriori prediction from the Laplace approximation (Niku et al 2017).…”

“…This requires combining recent advances in model-based unconstrained ordination (e.g., Warton et al 2015) with developments in constrained ordination. Recent developments in model-based unconstrained ordination or JSDMs, as part of the Generalized Linear Latent Variable Model (GLLVM, Skrondal & Rabe-Hesketh 2004) framework are due to Hui et al (2015) for the linear response model, and van der Veen et al (2021) for the quadratic response model, while other authors have made important advances in the form of computational and conceptual developments (e.g., Hui 2016; Ovaskainen et al 2017; Tikhonov et al 2017; Niku et al 2019b; Damgaard et al 2020; Zeng et al 2021). Key developments in statistical models for constrained ordination in recent years include Yee & Hastie (2003) for the linear response model, Yee (2004) for the quadratic (or “Gaussian”) response model (but see also Zhang & Thas 2016), and Yee (2006) for semi-parametric response curves (see also Zhu et al 2005; Hawinkel et al 2019).…”