Introduction
Density estimation is a cornerstone of wildlife research and
conservation. Spatially explicit capture-recapture methods (SCR), or
capture-mark-recapture more broadly, are a well-established approach to
estimating abundance and density (Efford, 2004; Royle & Young, 2008;
Tourani, 2021). Traditionally in SCR, individuals are assumed to be
identifiable and independent, but many species may not meet or adhere to
these assumptions. Individuals may be unidentifiable (i.e., ‘unmarked’)
for reasons including uninformative visual appearances from non-invasive
sampling techniques such as camera traps, or the high costs of genetic
approaches for obtaining identity (Cheng et al., 2017; Gilbert et al.,
2021). The independence assumption may also be unmet because many
species exhibit some degree of territoriality or sociality for at least
some period of their lives (Prox & Farine, 2020). Accommodating common
realities such as unmarked and non-independent individuals can be
important for avoiding biases in density estimates. Approaches using the
SCR framework have been developed that handle unidentifiability and
non-independence separately (e.g., Augustine et al., 2018; Chandler &
Royle, 2013; Emmet et al., 2021; Royle, 2004), but there are as yet no
SCR-based approaches that simultaneously accommodate both. Instead,
models for unmarked populations are applied and the non-independence is
acknowledged as a potential source of bias of unknown magnitude (e.g.,
Sun et al., 2022). However, the consequence of violating independence in
SCR-based unmarked models should be quantified because precise and
accurate density estimates are critical for determining population
status and monitoring for conservation and management.
Identities enable the assignment of detections to individuals and the
creation of individual-specific detection histories. These detection
histories are informative about detection probability, and therefore
help quantify the number of undetected individuals remaining in the
population. When some detections cannot be assigned to individuals, they
may be discarded (Tourani et al., 2020), incorporated along with
detections of marked individuals (Sollmann et al. 2013), or modeled as
having lost their identity with some probability (Jiménez et al., 2020).
Occasional misidentifications may also be accounted for (McClintock et
al., 2014; Morrison et al., 2011; Petersma et al., 2023; Rakhimberdiev
et al., 2022; Yoshizaki et al., 2009). However, if all individuals are
entirely unmarked or have few identifying marks such that their full
identities are unknown, then spatial count (SC) and spatial partial
identity models (SPIM) are two SCR-based modelling alternatives that can
be used for density estimation. For wholly unmarked populations, SC
models use the spatially correlated pattern of counts of detections
across the sampling array, based on expectations of how single,
independent individuals move on the landscape (Chandler & Royle, 2013).
When partial identity marks are available, such as the spot or stripe
pattern on one or both flanks of an animal, SPIM can probabilistically
match detections to individuals and deterministically exclude
non-matching detections from being from the same individual (Augustine
et al., 2018, 2019). Precision with SPIM generally increases with more
partial marks. SC and SPIM can be promising options for estimating
populations with low density, but become less robust as density and
individual movement increase space-use overlap among individuals and
uncertainty in identities (Augustine et al., 2019; Chandler & Royle,
2013; Ruprecht et al., 2021).
In SCR-based models, individuals and their activity centers are modelled
as outcomes of a spatial point process (Royle et al., 2013). Individuals
may be distributed non-homogenously due to habitat associations, but are
usually assumed to not interact with each other. However, in nature,
non-independence among individuals arises from interactions ranging from
avoidance and territoriality to varying degrees of temporary or
permanent grouping. We focus on grouping because it can also contribute
to difficulty in determining identities. Grouping can provide safety
from predators (Lehtonen & Jaatinen, 2016), increase foraging
efficiency (McInnes et al., 2017), and improve chances of mating (Røed
et al., 2002). Non-independence from grouping can be described with two
components: aggregation and cohesion (Bischof et al., 2020). Aggregation
describes the group size, so more individuals share the same activity
center as aggregation increases. Cohesion is the degree to which group
individuals move together, so detections of individuals become
increasingly coordinated as members become more cohesive. Developing
sampling designs that meet the independence assumption for group-living
species such as wolves (Canis lupis ), lions (Panthera
leo ), and some ungulates can be difficult, so there is growing interest
in models that account for non-independence (e.g., see Emmet et al.,
2021; Hickey & Sollmann, 2018; Reich & Gardner, 2014). Notably, Emmet
et al. (2021) developed a SCR model using a cluster point process to
estimate the size of cohesive groups as well as population abundance,
while accounting for detection heterogeneity due to group size. By
modeling non-independence among individuals, the cluster SCR model
increases the understanding of a species’ and population ecology, but
still leaves a gap in the toolkit for density estimation because it
cannot be used with unmarked individuals.
Due to the lack of SCR-based models for individuals that are both
unmarked and non-independent, unmarked models are applied and
non-independence is left unaddressed. Unmodeled correlation among
detections can compromise model inferences, but so far has only been
investigated for fully marked SCR models (Bischof et al., 2020;
López-Bao et al., 2018; Moqanaki et al., 2021). Simulations show SCR to
be relatively robust to low-to-moderate levels of aggregation and
cohesion, but the overdispersion from correlated detections and
resulting inflated precision and poor coverage of the confidence
intervals around the true value may still lead to false inferences about
population parameters. In unmarked density models, non-independence may
contribute to the issues that SC and SPIM already face: higher local
densities that increase overlap between individual space-use and
uncertainty about which detections originate from which individuals (Sun
et al. 2022). Aggregation and especially cohesion may result in fewer
apparent individuals with inflated detection probability and therefore
underestimate density, while moderate levels of cohesion could inflate
estimates of the spatial scale of individual movement (fewer individuals
being detected over a larger spatial extent than otherwise expected).
Thus, grouping would be expected to increase bias while reducing
precision and coverage. Such biased estimates could be misleading about
population density, insensitive to changes in population trajectory, and
ultimately misinform conservation and management action.
We conducted a simulation study to assess the impacts of
non-independence on SC and SPIM estimation and to identify any levels of
tolerable aggregation and cohesion in order to inform further
application of unmarked density models for ecological inference on
species and populations with non-independent movements. For a template
species, we considered boreal caribou (Rangifer tarandus ) because
it is an unmarked and grouping species of conservation concern in Canada
(Festa-Bianchet et al., 2011; Hervieux et al., 2013). Many caribou
populations are threatened and declining due to a combination of factors
including habitat loss from natural resource exploration (Nagy-Reis et
al., 2021), climate change (Barber et al., 2018; Bradley & Neufeld,
2012), and altered predator-prey dynamics (Burgar et al., 2019; Dickie
et al., 2017; Hervieux et al., 2014). Tracking population responses to
conservation interventions is critical to assessing populations across
landscapes and reversing the fate of the species, but their wide
distribution across remote areas makes it difficult to collect
individual detection histories for SCR (McFarlane et al., 2020). As
such, there has been interest using camera trapping and unmarked density
models to estimate caribou density (Fisher et al., 2021; Sun et al.,
2022).
A key challenge in monitoring caribou density with camera traps is that
caribou violate requirements of independence and identifiability for
traditional SCR approaches. Caribou form temporary multi-age herds or
associations throughout the year (Body et al., 2015) and present
challenges to visual identification, although they can be partially
identified based on visible sex attributes and the number of antler
points on both sexes. We conducted simulations using SCR, SC, and SPIM
to estimate populations under varying levels of aggregation and
cohesion. We also varied the number of partial identity marks to assess
how non-independence interacts with the amount of available identity
information in SPIM. Using SCR with known identities as a reference for
comparison, we expected SCR to perform best and SPIM to outperform SC as
aggregation and cohesion increase due to the availability of partial
identities for assigning individuals to detections (Figure 1).
Ultimately, the objective was to assess the reliability of SC and SPIM
approaches for estimating densities of populations that are
simultaneously unmarked and non-independent.