Aggregating projections of species distributions for 2071–2100

After projecting species habitat distribution under climate change scenarios selected by the k-means approach, we summarized the range of projections using the weighted average approach. Because the size of clusters was heterogeneous, we also weighted the future probabilities of occurrence by the number of scenarios in each cluster, to avoid an over-representation of climate change scenarios from small clusters. Future projections of species habitat distributions obtained under the climate change scenarios selected by the k-means algorithm were thus double-weighted, according to Eq (1), where x¯* is the weighted average of probabilities of future occurrence for a given pixel, x_ij is the probability of future occurrence obtained under the statistical model i coupled with the climate change scenario j for the same pixel, AUC_i is the AUC of the statistical model i, n is the total number of calibrated statistical models (here, n = 140), nk_j is the number of climate change scenarios in the cluster j, and k is the total number of selected clusters.

As one of our objectives was to compare outcomes from the k-means algorithm with those obtained from the full set of 27 climate change scenarios, we also weighted averaged future species habitat distributions projected under the 27 climate change scenarios. These probabilities of occurrence were simple-weighted by the AUC of their corresponding models.

We transformed consensual future probabilities of occurrence in a presence/absence form, as had been done for consensual probabilities of occurrence for the reference period by using the transformation thresholds calculated for the reference period. This allowed us calculating the percentage of grid cells projected to be gained (i.e. the number of cells where the species was absent during the reference period but will potentially be present in the future if it colonizes newly available climatic habitat, divided by the total number of cells where it was present during the reference period) or lost (i.e. the number of cells where the species was present during the reference period but will potentially be absent in the future, divided by the total number of cells where it was present during the reference period) by a given species. We assumed for this exercise an unlimited dispersal scenario.