INTRODUCTION
Monitoring population dynamics is a key goal for conservationists, as it allows to investigate the effects of ecological variability on wildlife populations (Jacobson et al. 2004, Jonas et al. 2008, Mignatti et al. 2012), to quantify the efficacy of management interventions (Hinkson and Richter 2016, Saunders et al. 2018) and to evaluate the conservation status of a species (Vors and Boyce 2009, Brambilla et al. 2020a). For instance, the assessment of population trends is used in the IUCN framework to evaluate the risk of extinction of a species, which under criterion A (IUCN 2022) is considered threatened if it suffered a population decline of 30% or more over the last 10 years or three generations.
Trends in abundance are generally estimated through multiple counts over time (Magurran et al. 2010), but this process implicates several challenges and can be subject to different sources of errors (Yoccoz et al. 2001). Indeed, the true long-term population trends are often hidden by short-term random fluctuations, due to demographic stochasticity and environmental year-to-year variability (McCain et al. 2016). Surveys too limited in time can therefore fail to identify the sign and magnitude of a population trend (Wauchope et al. 2019). Moreover, population dynamics can also vary across sites, with different subpopulations exhibiting different trends (Urquhart 2012). If this variability is not taken into account, biases in determining the real population trend can easily arise (Palmer 1993, Weiser et al. 2019, Fournier et al. 2019). Finally, imperfect detection during counts (Lahoz-Monfort et al. 2014, Kellner and Swihart 2014) can influence the ability to detect population trends (Kéry et al. 2009, Ficetola et al. 2018, Wood et al. 2019). The design of population monitoring programs should try to minimize the above mentioned potential biases, but also reduce survey costs in order to make long term monitoring financially sustainable (Caughlan and Oakley 2001, White 2019). Power analysis is the tool generally used to quantify the minimum sampling effort required to correctly detect the true population trend (Gerrodette 1987, Taylor and Gerrodette 1993, Thomas 1997, Vallecillo et al. 2021). In a power analysis, multiple replicates of the data are built, either with simulations or subsets of real measures, and the statistical power is estimated as the proportion of replicates in which a statistical model fitted to the data is able to detect the change in population size over time (Steidl and Thomas 2001). Many authors have used power analysis to estimate the minimum number of years required in a monitoring project to detect a significant trend (Luymes and Chow-Fraser 2019, Wauchope et al. 2019), showing that a minimum of 5-35 years is needed depending on the species (Reynolds et al. 2011, White 2019). However, fewer studies considered the use of censuses conducted only in a sample of the target area (defined here as sample counts) in monitoring population trends and estimated the proportion of sites of the total area required to detect trends with similar power to total counts. Sample counts have been described as imprecise (Stoddard et al. 1998, Yoccoz et al. 2001), as it has been shown for instance that a limited number of sites generally enables detection of only strong declines in the population (Sewell et al. 2012, Wagner et al. 2022), unless the species is particularly abundant and easy to detect (Ficetola et al. 2018). However, the reliability of a particular sampling design (such as sample counts) to detect population dynamics is strictly linked to the study system (White 2019, Weiser et al. 2019) and the efficacy of sampling only a portion of the target area to monitor trends needs therefore to be analyzed for each system.
Monitoring certain taxa such as mountain ungulates, can present several technical constraints due to difficult terrain, climatic conditions, remote habitats and required logistics (Singh and Milner-Gulland 2011). Mountain ungulates are usually counted with helicopter censuses (Gonzalez-Voyer et al. 2001, Rice et al. 2009) or ground counts (Jacobson et al. 2004, Largo et al. 2008, Suryawanshi et al. 2012), but both these methods require big financial and human efforts, especially in large areas and rough terrain conditions. Reducing the effort in terms of time or number of surveyed sectors, while maintaining enough power to detects trends, is therefore of critical importance in monitoring species living in remote areas (Lindenmayer and Likens 2010).
In some cases, the survey effort can be reduced by sampling the population less often (interval sampling), for instance every 3 or 5 years as suggested by some authors (Urquhart et al. 1998, Singh and Milner-Gulland 2011, Reynolds et al. 2011). However, interval sampling has proved to be less effective than sampling every year in detecting the magnitude of a trend (e.g. Wauchope et al. 2019) and could therefore not be adequate if the goal is to analyze the drivers of population dynamics in a long-term monitoring project or for endangered species for which declines must be detected quickly in order to provide appropriate conservation strategies. Consequently, surveying only a sample of the target area every year could be the only viable and cost-effective alternative. To the best of our knowledge, a complete assessment of the statistical power of sample counts for monitoring has not been performed before.
In this study, we investigated the reliability of sample counts in estimating population trends, using as a case study the Alpine ibex (Capra ibex ) population of Gran Paradiso National Park (GPNP, North-West Italian Alps), for which an exceptionally long-term series of 65 years of count data, collected with block counts over the whole territory of the Park, is available (Jacobson et al., 2004; Mignatti et al., 2012). With a real-case range of parameters, we simulated populations under various scenarios of abundance trends over 10 and 20 years and calculated the power of population models based on sample counts in detecting the real trend. We also estimated the minimum proportion of sectors (count areas in which the Park is divided) needed to correctly detect the population trend of Alpine ibex population in the whole area from which the samples are drawn. Moreover, we explored the effect of different strategies for selecting which sectors to monitor: i) random selection each year; ii) random selection in the first year, then the same sectors are surveyed each of the following years and iii) biased selection towards the sectors with the highest abundance. We also included different magnitudes of both trend variability between years and sectors and variability of detection probability, a phenomenon that heavily affects the species and possibly leads to severe underestimates of abundance (Gaillard et al. 2003, Morellet et al. 2007, Largo et al. 2008).
Finally, we tested the predictions obtained with simulations analyzing the real count data collected in GPNP over the last 65 years and comparing trends estimated from the entire area with trend estimations that would have been obtained from sample counts.