Model training and model selection
Maxent v3.4.3 (Phillips et al. 2017) was used through ENMeval v2 (Kass et al. 2021) to train the models for this study. Before model comparisons, I first selected the optimal model complexity for each approach (STA, T01, T05, T10) by running and testing 500 combinations of feature classes (linear, linear-quadratic, hinge, linear-quadratic-hinge, linear-quadratic-hinge-product) and regularization multipliers (0.1 to 5, steps of 0.1). The selection of the best model in each approach was based on the lowest corrected Akaike Information Criterion (AICc), as it provides a measure to balance model complexity and predictability (Warren and Seifert 2011). To account for the elongated distribution of the occurrences along the Sierra Madre Oriental, occurrence and background data were divided into four spatial bins for cross-validation using a latitudinal block partition. Validation metrics, specifically the average Area under the Curve (AUC), the continuous Boyce Index (CBI), and the 10thpercentile of training omission rate (OR), were used to quantify the performance of the selected model in each approach. The AUC values range from 0 to 1, with values closer to 1 indicating better model performance. Similarly, the CBI values range from -1 to 1, with values closer to 1 indicating a better model performance (Hirzel et al. 2006). On the other hand, the OR ranges from 0 to 1, and a lower value indicates a better prediction of the occurrences.