## 6 Conclusions  
After the application of the different advanced statistical models, it has become clear that it is necessary to apply validation with a real inventory of slope instabilities triggered by earthquakes to ensure reliability and objectivity. However, machine learning methods provide good approximations in terms of co-seismic landslide occurrence. In addition, the use of principal components shows significantly better results in terms of statistical accuracy.  
Relevant variables for predicting co-seismic landslide susceptibility include orientation, Newmark displacement, landform, curvature, roughness, PGA, Arias intensity, and lithology. The recursive feature elimination (SET-3) was shown to be adequate as a variable selection method (predictor), while the Boruta model and simulated annealing selection methods (SET-1 and SET-4, respectively) showed poor performance.  
In terms of statistical accuracy, artificial neural network (ANN), random forest (RF), and support vector machine with radial basis functions (SVMR) are the best models. However, when compared to the actual location of slope instabilities, RF shows poor results, while ANN and SVMR, both using principal components, are the optimal ones (high success rate values) for developing co-seismic landslide susceptibility maps. Neverthe  
Figure 10: Comparison between the best models in terms of co-seismic slope instability susceptibility and the best model obtained using the physical-based methodology in [27]. Landslide hazard ranges: very low (0–20%), low (21–40%), moderate (41–60%), high (61–80%), and very high (81–100%). Location of this sector in the total study area is shown in Figure 1.  
less, compared with physical-based methods, the use of the SVMR model (without using principal components) shows a similar prediction in relation to co-seismic landslides.  
The use of machine learning or physical-based models depends on the quality and quantity of data, as well as the available time. For small areas with limited but high-quality data, physical-based methods are recommended. On the other hand, for regional areas with lower-quality data, physical-based methods are not as accurate as machine learning methods. However, machine learning models require a high quantity of data, which is the main limitation when implementing such models.  
The results are of interest to society because they allow the establishment of effective and resilient land planning and hazard management strategies in active seismic areas to minimize the damage of future co-seismic landslides.  
Conceptualization, [PERSON], [PERSON] and [PERSON]; methodology, [PERSON], [PERSON] and [PERSON]; software, [PERSON]; validation, [PERSON] and [PERSON]; formal analysis, [PERSON], [PERSON] and [PERSON]; investigation, [PERSON], [PERSON] and [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and [PERSON]; visualization, [PERSON], [PERSON] and [PERSON]; supervision, [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research was partially supported by the research project PID2021-124155 NB-C31 from the Spanish Investigation Agency and the research group \"Planetary Geodynamics, Active Tectonics and Related Hazards\", UCM-910368 of the Complutense University of Madrid.  
Not applicable.  
The data that support the findings of this study are available upon request from the corresponding authors.  
We are very grateful for the comments and suggestions provided by the reviewers and editor, as they have certainly contributed to a significant improvement in this paper.  
The authors declare no conflict of interest.