Evaluating and presenting uncertainty in model‐based unconstrained ordination

Variability in ecological community composition is often analyzed by recording the presence or abundance of taxa in sample units, calculating a symmetric matrix of pairwise distances or dissimilarities among sample units and then mapping the resulting matrix to a low‐dimensional representation through methods collectively called ordination. Unconstrained ordination only uses taxon composition data, without any environmental or experimental covariates, to infer latent compositional gradients associated with the sampling units. Commonly, such distance‐based methods have been used for ordination, but recently there has been a shift toward model‐based approaches. Model‐based unconstrained ordinations are commonly formulated using a Bayesian latent factor model that permits uncertainty assessment for parameters, including the latent factors that correspond to gradients in community composition. While model‐based methods have the additional benefit of addressing uncertainty in the estimated gradients, typically the current practice is to report point estimates without summarizing uncertainty. To demonstrate the uncertainty present in model‐based unconstrained ordination, the well‐known spider and dune data sets were analyzed and shown to have large uncertainty in the ordination projections. Hence to understand the factors that contribute to the uncertainty, simulation studies were conducted to assess the impact of additional sampling units or species to help inform future ordination studies that seek to minimize variability in the latent factors. Accurate reporting of uncertainty is an important part of transparency in the scientific process; thus, a model‐based approach that accounts for uncertainty is valuable. An R package, UncertainOrd, contains visualization tools that accurately represent estimates of the gradients in community composition in the presence of uncertainty.