3- Power analysis on real ibex trends in GPNP
We randomly sampled 112,000 total time intervals each of a specified length (5, 10, 15 or 20 years) from the original dataset of Alpine ibex counts in GPNP and estimated the population trend with a Generalized Linear Model (GLM) for the Poisson distribution. If a trend was detected (with P<0.05) in the target interval using the full number of sectors (complete trend), we randomly selected n sectors (with 1 < n < 38) and estimated again the trend using only the sum of the individuals counted in the n sectors (sample trend). We compared the two trends and, following Wauchope et al. (2019), classified the sample trend as matching or opposing the complete trend, missed (sample counts that did not detect the complete trend) or false trends (sample counts that erroneously detected a stable complete trend). As for our simulations, we considered the sample trend correct in magnitude if the difference with the complete trend was of 0.02 or lower (2% error each year). The procedure was repeated 1,000 times for each possible number of sampled sectors (1 to 38) and we assessed the statistical power as the proportion of samples in which the sample trend matched the complete trend, in terms of direction (increase or decrease in the population) or magnitude, with a threshold power of 0.8 (80%). All the analyses were performed in R, version 4.1.3 (R Core Team 2022) with the code provided in supplementary materials.