Predicting species distributions in new areas or time periods with alpha-shapes

Abstract

Statistical models relating species distributions to environmental data are now commonly applied to predict where invasive species may become established or how range limits may shift under climate change. As species absences can originate from factors other than an unsuitable environment (e.g. dispersal constraints), the models that discriminate between occupied and unoccupied environments are likely to underestimate potential ranges. However, the techniques that "envelope" the occupied environments (i.e. profile techniques) usually rely on simple convex estimators (e.g. elliptical or rectangular shapes), which tend to overestimate these ranges. Here we describe alpha-shapes, a profile-type technique that relaxes the assumption of convexity. By using native range data for the invasive African clawed frog, we demonstrate how this technique can be used to model climatic envelopes of variable complexity. In particular, we compared predictions from an envelope maximizing discrimination between presences and absences, an envelope tightly enclosing all occupied climatic combinations (i.e. the minimum bounding envelope) and an "expert-based" generalization of the previous. In addition, we also use this technique to identify climatic combinations that are outside the climatic space of the study area (i.e. non-analog climates). The envelope accounting for the absences of the African clawed frog achieved a high discrimination ability (true skill statistics. =. 0.71), but failed to predict many of the areas in which the species occurs. Predictions based on the minimum bounding envelope encompassed all species occurrences while still providing a sharp delineation of its distribution range. The generalized version of the previous envelope also captured all occurrences, but predicted a wider extent of suitable areas. We also found that most parts of the world present climatic conditions that are non-analog to those of our study area. Although conceptually more suitable for predicting species distributions across space and time than presence-absence models, profile techniques are frequently overlooked because of their inability to fit flexible envelopes. Here, we demonstrate that alpha-shapes are a transparent and intuitive profile-type technique that has this flexibility.