2.3.4. Maxent Models

We built ENMs using the maximum entropy modelling approach, Maxent ver. 3.4.1 (http://biodiversityinformatics.amnh.org/open\_source/maxent/) [50]. This algorithm usually provides an excellent predictive approach compared with other modelling methods and is especially suited to deal with scarce presence-only data [51–54]. Since this technique relies on a generative rather than a discriminative approach, it performs well when the amount of training data is limited. Because our study area was small, we trained models using data from the entire European territory to account for a more comprehensive niche representation.

We carried out an ENM for each of the taxa identified in the cave by charcoal analysis using three steps: (1) we ran current models using presence records and the bioclimatic variables selected as described above; (2) we carried out paleoclimate models projecting current distribution in the LGM scenarios; and (3) we again ran paleoclimate models projecting current distribution in the LGM scenarios, but only for some taxa selected in Step 2. Unlike the previous model, here, we added the potential distribution map of the best-represented taxon in the study area using it as an "bioclimatic variables".

From the Maxent's setting panel, we selected the following options: random seed; remove duplicate presence records; write plot data; regularisation multiplier (fixed at 1) [50]; 1000 maximum iterations, 10,000 background points, cloglog format (this output appears to be most appropriate for estimating the probability of presence) [54,55]; and, finally, we used a 20-replicate effect with cross-validation run type. This run type makes it possible to replicate n-sample sets removing one locality at a time [22,56]. We fixed to 1 the default regularisation value as this is based on the different performances recorded across a range of taxonomic groups [57]. The remaining model values were set to default values [22,58].

For each species, the average final map had a cloglog output format with suitability values from 0 (unsuitable habitat) to 1 (suitable habitat). The 10th percentile (the value above which the model classifies correctly 90% of the training locations) was selected as the threshold value for defining the species' presence. This is a conservative value commonly applied to ecological niche modelling studies, particularly those relying on datasets collected over a long time by different observers and methods [22,56,58,59]. We used this threshold to reclassify our model into binary presence/absence maps.

We generated the paleoclimate models using the same climatic variables above described. These models were trained with all occurrences collected, and projected to Europe in the LGM (23,000–18,000 years BP). We developed the paleoclimate models using the most used LGM scenarios: CCSM4 [19,60,61]. Projecting ENMs to regions other than those where models were calibrated, or to past or future times is a common approach to make inferences such as forecasting the spreading of alien organisms, providing paleo-reconstructions or predicting distributional patterns in future epochs [62,63]. In order to project to new area models calibrated elsewhere, whether in the current epoch or in the LGM, variables in the projection area must meet a condition of environmental similarity to the environmental data used for training the model. Therefore, we first ascertained that this condition occurred by inspecting the Multivariate Environmental Similarity Surfaces (MESS) generated by Maxent [64,65].
