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.