Reduced-Rank Generalised Dissimilarity Modelling (RRGDM): Model-Based Ordination of Dissimilarity Data

(1) Dissimilarity indices offer an effective way to represent multivariate variability in community composition and to quantify beta diversity and its drivers. However, models that regress dissimilarities against environmental predictors face the challenge of linking site-level predictors to a pairwise response. (2) This mismatch is typically circumvented by regressing dissimilarities against distances in predictor values. But this approach does not reflect how environmental variables act on individual samples, complicates the inclusion of standard modelling features such as random effects, and conflates environmental effects on average composition with effects on compositional dispersion. (3) We propose Reduced-Rank Generalised Dissimilarity Modelling (RRGDM), a framework for model-based ordination that resolves the pair-to-site mismatch by reframing dissimilarity modelling as an ordination problem. RRGDM represents dissimilarities as the outcome of sample positions in a shared, low-dimensional latent space that captures community composition. These positions are in turn modelled as a linear function of predictors and error terms, with an associated dispersion sub-model. (4) Through a simulation study and two empirical examples, we show that RRGDM recovers known environmental effects and represents them as ecologically interpretable outputs. RRGDM enables inference on the relative importance of environmental gradients driving beta diversity and disentangles effects on composition versus dispersion. Although motivated by beta diversity, the approach is applicable to other pairwise dissimilarity data.