Comparison of distance-based and model-based ordinations.

Distance-based ordinations have played a critical role in community ecology for more than half a century, but are still under active development. These methods employ a matrix of pairwise distances or dissimilarities between sample units, and map sample units from the high-dimensional distance or dissimilarity space to a low dimensional representation for analysis. Distance- or dissimilarity-based methods employ continuum or gradient ecological theory and a variety of statistical models to achieve the mapping. Recently, ecologists have developed model-based ordinations based on latent vectors and individual species response models. These methods employ the individualistic perspective of Gleason as the ecological model, and Bayesian or maximum likelihood methods to estimate the parameters for the low dimensional space represented by the latent vectors. In this research I compared two distance-based methods (NMDS and t-SNE) with two model-based methods (BORAL and REO) on five data sets to determine which methods are superior for (1) extracting meaningful ecological drivers of variability in community composition; and (2) estimating sample unit locations in ordination space that maximize the goodness-of-fit of individual species response models to the estimated sample unit locations. Environmental variables and species were fitted to the ordinations by Generalized AdditiveModels (GAMs) with Gaussian, negative binomial, or Poisson distribution models as appropriate. Across the five data sets, 22 models of environmental variability and 449 models of species distributions were calculated for each of the ordination methods. To minimize the effects of stochasticity the entire analysis was replicated three times and results averaged across the replicates. Results were evaluated by deviance explained and AIC for environmental variables and species distributions, averaged by ordination method for each data set, and ranked from best to worst. For the four assessments distance-based methods ranked 1 and 2 in three cases, and 1 and 3 in one case, significantly out-performing the model-based methods. t-SNE was the top performing method, out-performing NMDS especially on the more complex data sets. In general the gradient-based theoretical basis and data sufficiency of distance-based methods allowed distance-based methods to outperform model-based methods in every assessment.