Characterising uncertainty in generalised dissimilarity models

Abstract

Generalised dissimilarity modelling (GDM) is a statistical method for analysing and predicting patterns of turnover in species composition, usually in response to environmental gradients that vary in space and time. GDM is becoming widely applied in ecology and conservation science to interpret macro-ecological and biogeographical patterns, to support conservation assessment, predict changes in species distributions under climate change and prioritise biological surveys. Inferential and predictive uncertainty is difficult to characterise using current implementations of GDM, reducing the utility of GDM in ecological risk assessment and conservation decision-making. Current practice is to undertake permutation tests to assess the importance of variables in GDM. Permutation testing overcomes the issue of data-dependence (because dissimilarities are calculated on a smaller number of observations) but it does not give a quantification of uncertainty in predictions. Here, we address this issue by utilising the Bayesian bootstrap, so that the uncertainty in the observations is carried through the entire analysis (including into the predictions). We tested our Bayesian bootstrap GDM (BBGDM) approach on simulated data sets and two benthic species data sets. We fitted BBGDMs and GDMs to compare the differences in inference and prediction of compositional turnover that resulted from a coherent treatment of model uncertainty. We showed that our BBGDM approach correctly identified the signal within the data, resulting in an improved characterisation of uncertainty and enhanced model-based inference. We show that our approach gives appropriate parameter estimates while better representing the underlying uncertainty that arises when conducting inference and making predictions with GDMs. Our approach to fitting GDMs will provide more realistic insights into parameter and prediction uncertainty.