## 4 Discussion
### Why Should Multi-Year Studies Be Favored?  
Only 28% of the comparisons for the study of temporal variability showed a significant difference on HaDaily pseudo-medians while 71% were significant for the study of spatial variability (Figure 3). This would suggest that spatial variability would be more important than temporal variability. However, the largest undetected difference on tests of temporal variability is more than twice as large as on tests of spatial variability (1.25 versus 0.58, see Tables 1 and 3-5). Pseudo-median differences are therefore equally important for the temporal variability but they seem to be less easily detected. As underlined in [122], it would be appropriate to overlook the dichotomy between \"significant\" and \"not significant\" and focus on comparing results between them. Furthermore, an insignificant \(p\)-value may result from a large variability within the serie studied and does not necessarily mean that the tested hypothesis is true [123]. In our study case, on Anglas for the 2018 versus 2019 comparison, the pseudo-median is 1.25 h and is framed by the confidence interval \([0.17;2.17]\) (Table 5); this difference, although statistically insignificant after FDR correction, is biologically relevant. Furthermore, tests indicating estimators that correspond to almost 25% of HaDailyref can be considered biologically relevant; here this concerns the differences 2018 versus 2019 on NH and 2017 versus 2019 on SL. Thus, there were appreciable biological inter-annual variability on all studied localities.  
The pseudo-medians of the calculated difference series represented up to half of the reference daily activity time (from 1.08 to 2.25 h (Table 5) in regard to HaDailyref = 4.5 h). These differences were associated with very various persistence indices depending on the year. For example, for the SH locality, the index indicated an extinction probability of 0.125 in 2017 and activity time safety margins of 34.65 and 7.20 h in 2018 and 2019 (Table 2). Conducting the study only in 2017 would have encouraged habitat protection policies while conducting it only in 2018 or 2019 would have indicated that populations would be maintained. Moreover, the average persistence index over the three years was 1.020 \(\pm\) 0.140, which did not exclude the possibility of local population extinction in this locality. The same result was observed in the SL locality, the average index was 1.038 \(\pm\) 0.096. Averaging persistence indices over several years allows a better assessment of the risk of local extinction. Indeed, if only one year is unfavorable, knowing that adults are capable of reproducing every year [92], this year will not be representative of the population fate. In our study case, in 2019, the heatwave from 22-25 July [124] was observed on all nine records, operative temperatures exceeding the upper critical lethal temperature CTmax at all locations studied except NH (Figure A2). Inversely, during the coldwave that occurred from 27-31 July [124], operative temperatures dropped below CTmin. Low altitude localities (\(\sim\)2050 m) were more impacted than the Peyreget peak localities (Figure A2). These excessively high or low temperatures force individuals to remain in their shelters for a longer period of time, which could explain, for instance, lower activity times than in 2018 (Table 2). Thus, our results highlight the importance of considering inter-annual variability in biodiversity conservation studies.