The cumulative niche approach: A framework to assess the performance of ecological niche model projections.

Ecological Niche Models (ENMs) are often used to project species distributions within alien ranges and in future climatic scenarios. However, ENMs depend on species-environment equilibrium, which may be absent for actively expanding species. We present a novel framework to estimate whether species have reached environmental equilibrium in their native and alien ranges. The method is based on the estimation of niche breadth with the accumulation of species occurrences. An asymptote will indicate exhaustive knowledge of the realised niches. We demonstrate the CNA framework for 26 species of mammals, amphibians, and birds. Possible outcomes of the framework include: (1) There is enough data to quantify the native and alien realised niches, allowing us to calculate niche expansion between the native and alien ranges, also indicating that ENMs can be reliably projected to new environmental conditions. (2) The data in the native range is not adequate but an asymptote is reached in the alien realised niche, indicating low confidence in our ability to evaluate niche expansion in the alien range but high confidence in model projections to new environmental conditions within the alien range. (3) There is enough data to quantify the native realised niche, but not enough knowledge about the alien realised niche, hindering the reliability of projections beyond sampled conditions. (4) Both the native and alien ranges do not reach an asymptote, and thus few robust conclusions about the species' niche or future projections can be made. Our framework can be used to detect species' environmental equilibrium in both the native and alien ranges, to quantify changes in the realised niche during the invasion processes, and to estimate the likely accuracy of model projections to new environmental conditions.