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.