DISCUSSION
Our results show that sample counts can be adequate to monitor population trends of mountain ungulates in a large area. Sampling half of the total area allowed us to correctly identify medium to strong population trends. In addition, in most of the cases in which sample counts were not able to estimate the population trend, also complete counts failed in detecting the direction or magnitude of the trend. The retrospective power analysis confirmed our results, as the trends historically estimated with complete counts would have been inferred equally well, with a sufficient statistical power, using sample counts with only half of the sectors monitored. Given that the results obtained with sample counts are very similar to those obtained with a complete count, we suggest that sample counts (in particular monitoring half of the target area) can be used as a viable alternative when monitoring trends, hence allowing for important, cost-effective improvements in the monitoring of wild animals of conservation interest. Time and budget constraints can indeed disincentivize wildlife managers to implement monitoring programs (McDonald-Madden et al. 2010), while potentially reducing the survey effort could lead to undertake monitoring projects that are otherwise impossible to perform.
In the case of Alpine ibex, the species is currently monitored throughout its entire area of extent in the Alps without a standardized protocol and, while in GPNP a long time series is available, the lack of data in many other areas makes impossible to draw reliable conclusions about the population trends (Brambilla et al. 2020a). Reducing the costs of monitoring by using sample counts, could therefore be of critical importance to allow more conservation and management authorities to perform periodic counts. Assessing population trends in Alpine ibex is essential as the species may be sensitive to future declines (Toïgo et al. 2020) because of low recolonization rates, low genetic diversity and high inbreeding levels (Biebach and Keller 2009, Brambilla et al. 2014, 2020b) and heat-sensitivity (Aublet et al. 2008, Mason et al. 2017, Semenzato et al. 2021) in an environment that suffers strong global warming effects (Giorgi 2006, Gobiet et al. 2014, Rogora et al. 2018). However, as the reliability of sample counts depends on the variability between years and sectors, wildlife managers must carefully evaluate the expected reliability of censuses in their specific case.
Sample counts can also be useful to perform a quick and highly cost-effective preliminary monitoring in new areas to collect information on the status of a population in the short term, as we showed that the direction of a strong trend over 10 years can be detected even with very few sectors sampled (less than 5 out of 38). For instance, the method can be useful to detect recovery after epidemic outbreaks with high mortality, common in mountain ungulates as the Alpine ibex (Giacometti et al. 2002, Garnier et al. 2016, Pérez et al. 2021), or to identify a strong response after management actions such as reintroductions (Giacometti 1991, Stüwe and Nievergelt 1991, Brambilla et al. 2020a).
However, if there are sufficient resources, sampling the entire area may still be preferable than using sample counts. Sampling all sectors, indeed, reduced the occurrence of errors in trend detection that, even if at a low frequency, were present with sample counts. Furthermore, sampling the entire area would allow for less biased abundance estimates, as shown in our results and as pointed out by Sutherland (2006). An accurate estimate of population size is important for instance to measure carrying capacity (Holzgang 1997, Terry Bowyer et al. 2014) or for management purposes such as reintroductions (Peracino and Bassano 1990) and hunting (e.g., Carvalho et al. 2018). Therefore, conservation authorities must weigh up the costs and benefits of using sample counts, using them to reliably detect population trends at a lower cost or performing complete counts to measure abundance with higher financial effort but also reduced errors in the estimation of trends and abundance.
We also showed that neither sample counts nor complete counts could reliably monitor the magnitude of short-term trends and that for such analysis at least 15 or 20 years of censuses data are needed. This result is consistent with several other studies pointing out that more than 10 years are required to draw reliable conclusions on population trends (e.g., Gerber et al. 1999, Hatch 2003, White 2019). Long-term wildlife monitoring projects are indeed of critical importance for conservation (Nichols and Williams 2006, Magurran et al. 2010, Giron-Nava et al. 2017), but series of yearly counts are lacking for most mountain ungulates (Singh and Milner-Gulland 2011, Brambilla et al. 2020a, Nuttall et al. 2022). Therefore, we further recommend that stakeholders plan long-term monitoring projects to correctly evaluate population dynamics at a local and global scale. Sample counts, that proved in this study to be as reliable as complete counts in detecting the long-term trends if half of the sectors are sampled, can constitute a viable method to reduce the required census effort for such projects, but further studies are needed before they can also be applied in abundance estimations.
Our results show that the strongest constraint for accurate trend estimations is the variability between years, for which Alpine ibex in GPNP showed a coefficient of variation around 0.05 in the last 65 years. Keith et al. (2015) found that, among nine species of terrestrial mammals for which population trend was estimated counting the total number of individuals in a specified area (mostly Cricetidae and Muridae), the mean variability between years was 0.052, and Saiga tatarica , the only ungulate species in the study, showed a yearly variation of 0.058. Therefore, sample counts would likely have been efficient for estimating the trend also in those species and other with similar trend variation over time. Under a greater variability, estimating the population dynamics could be subject to severe errors even with complete counts and especially for weak trends, as also pointed out by other studies (Wilson et al. 2011, Rhodes and Jonzén 2011, Rueda-Cediel et al. 2015).
In general, in Keith et al. (2015) species with lower yearly variation of abundance were mostly those with a higher generation time (coefficient of variation was 0.088 for species that give birth to a new generation within 2 years and 0.026 for species with longer generation time, with a mean variability of 0.014 if the generation length was higher than 5 years). Species with a long life-history can indeed show less extreme yearly abundance fluctuations, as for example they are slower to react to fast environmental changes (Berteaux et al. 2004). However, White (2019) showed that life history traits (such as generation length) have only a very weak influence on the minimum time required to accurately monitor the species, while time series characteristics (e.g., trend strength) seems to be a much more important driver. Our results could therefore potentially be relevant to any animal species with a sufficient generation length (possibly more than 2 years), but the applicability to other species with a different life-history must be tested.
In our simulations, sampling half of the sectors allowed to achieve a sufficient statistical power even with high values for cvs and cvd. A large number of species is likely to exhibit a trend variability between sectors in the range we used in our simulations (i.e., 0.05-0.20): Weiser et al. (2019) reported a sector-specific variation between 0.05 and 0.1 in many species of different taxa (from 0.02 to 0.024 in small mammals). Additionally, the wide range of cvd we used in the simulations (0.1-0.5) suggests that our results can be expanded to many study areas in which spatial variation of parameters that affect detectability is high.
We also show that the overall detectability in the target area did not have any effect on the statistical power, thus trend estimation could be performed with cost-effective methods such as block counts, that are believed to underestimate population size (Loison et al. 2006, Morellet et al. 2007, Corlatti et al. 2015). In such case, the costs of trend estimations could be further reduced by the use of block counts instead of other techniques, that account for imperfect detection but require a higher field or data analysis effort, such as Capture-Mark-Resight (Schwarz and Seber 1999) or Distance Sampling (Buckland et al. 2001). Besides, also several sources of errors in abundance estimation, such as underestimations of group size (Vallecillo et al. 2021) or missed detection of small groups (Samuel and Pollock 1981), could possibly be ignored while performing sample counts to estimate direction and magnitude of population trends. Our results about detectability are in contrast to other studies, for which a low detectability critically influenced the ability of detecting a trend (e.g. Newson et al. 2013, Ficetola et al. 2018, Sanz-Pérez et al. 2020). However, some of these studies included the possibility of sites with very few animals and a detectability (p) close to zero (e.g. abundance of 7.5 per site and p=0.05 in Ficetola et al. 2018), thus analyzed the situation in which no animals were detected in most of the sites. This phenomenon, not present in our Alpine ibex population where the population per sector was higher, could have been therefore the major cause of a difficult trend estimation in such studies. Besides, in other of the above mentioned researches, the detectability was also variable across the sites (e.g. Sanz-Pérez et al. 2020), and such effect could have been the actual driver of a difficult trend estimation, rather than the value of detectability, as we show here.
When using sample counts, the monitoring costs can be further reduced by performing censuses only in the sectors with the highest abundance (that can be easier to sample). However, as the method of sector selection had a weak effect on statistical power of trend estimations, also selecting sectors based on other needs could lead to a reliable analysis. This result is in contrast with Fournier et al. (2019) who claimed that counting in the best sites (i.e., those with the highest abundance) leads to detect false trends (Fournier et al. 2019). However, as also pointed out by Fournier and colleagues, not every real population exhibits this bias. The advantage of selecting the most abundant sectors however disappears if abundance is estimated instead of the population trend, with a considerable overestimation compared to a random sector selection.