Constraints on interpretation of ecological niche models by limited environmental ranges on calibration areas

Correlational models of species' ecological niches are commonly used to transfer model rules onto other sets of conditions to evaluate species' distributional potential. As with any model fitting exercise, however, interpretation of model predictions outside the range of the independent variables on which models were calibrated is perilous, herein denoted as strict extrapolation to distinguish from extrapolation onto novel combinations of variables. We use novel visualization techniques to characterize model response surfaces for several niche modeling algorithms for a virtual species (wherein the truth is known) and for two transfer-based studies published by one of our group. All modeling algorithms for each species showed strict extrapolation, such that biologically unrealistic response surfaces were reconstructed. We discuss the implications of these results for calibration and interpretation of niche models and analysis of ecological niche evolution. We present Mobility-Oriented Parity (MOP), a modification and extension of the Multivariate Environmental Similarity Surface (MESS) metric currently in use, as a means of both quantifying environmental similarity between calibration and transfer regions and highlighting regions in geographic space where strict extrapolation occurs.