Concurrent ordination: Simultaneous unconstrained and constrained latent variable modelling

Abstract

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.

Predicting niche overlap with model‐based ordination

“…Instead, in this paper, we predicted niche overlap for all potential combinations of overlapping species, starting at pairwise and finally calculating niche overlap for all species in the data. With a dataset of Foraminifera species, we demonstrated some potential applications of the proposed niche overlap measure by fitting a recently developed method for constrained ordination (van der Veen et al 2023). For example, when an individual of P. pertusis has been observed, it is likely to also observe individuals of all other Foraminifera species in the dataset, whereas we could not have drawn that conclusion had we only studied pairwise niche overlap.…”

“…Consequently, niche overlap measures usually do not account for the properties of ecological data, such as pseudoreplication or spatial autocorrelation (Arnqvist 2020), observation bias (Simmonds et al 2020), or mean-variance relationships (Warton and Hui 2017). Not accounting for data properties can lead to spurious results (Harrison 2014) and, for this reason, contemporary ecology has increasingly relied on statistical models to explore and quantify the ecological niche (Austin et al 1990, Guisan and Zimmermann 2000, Jansen and Oksanen 2013, van der Veen et al 2021. The prediction of species niches using regression methods corresponds well with the Hutchinsonian niche concept (Hutchinson 1959), as the niche is represented in multiple dimensions by gradients in resources or in the environment.…”

“…We briefly demonstrate the proposed niche overlap measure by fitting a constrained ordination (van der Veen et al 2023) with a quadratic response function (van der Veen et al 2021) to a dataset of systematically collected abundances of Foraminifera species in the Spermonde archipelago, Indonesia (Cleary and Renema 2007).…”

B-Bind: Biophysical Bayesian Inference for Neurodegenerative Dynamics

“…Opposed to these non-parametric methods, a line of methods states the problem from a model-based, parametric perspective. For example, in the context of ecological niches and species modeling (Hui et al, 2015; O’Hara and van der Veen, 2024; Hui et al, 2023; Popovic, Hui and Warton, 2022; van der Veen et al, 2023; Roberts, 2020; Hoegh and Roberts, 2020), measurements of relative abundances of species are sorted along sites of greater abundance. There, generalized latent variable models are used to represent ordination as latent variables, and no true ordination occurs, but instead, multivariate latent variable ordination is used to represent underlying gradients that influenced species composition.…”