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Animal movement affects interpretation of occupancy models from camera-trap surveys of unmarked animals
Abstract
Occupancy models are increasingly applied to data from wildlife camera-trap (CT) surveys to estimate distribution, habitat use, or relative abundance of unmarked animals. Fundamental to the occupancy modeling framework is the temporal pattern of detections at camera stations, which is influenced by animal population density and the speed and scale of animal movement. How these factors interact with CT sampling designs to affect the interpretation of occupancy parameter estimates is unclear. We developed a simple yet ecologically relevant animal movement simulation to create CT detections for animal populations varying in movement rate, home range area, and population density. We also varied CT sampling design by the duration of sampling and the density of CTs in our simulated domain. A single-species occupancy model was fitted to simulated detection histories, and model-estimated probabilities of occupancy were compared to the asymptotic proportion of area occupied (PAO), calculated as the union of all simulated home ranges. Occupancy model parameter estimates were sensitive to simulated movement and sampling scenarios. Occupancy models overestimated asymptotic PAO when a low population density of simulated animals moved quickly over large home ranges and this positive bias was insensitive to sampling duration. Conversely, asymptotic PAO was underestimated when simulated animals moved slowly in large- or intermediately sized home ranges. This negative bias decreased with increasing sampling duration and a lower density of CTs. Our results emphasize that the interpretation of occupancy models depends on the underlying processes driving CT detections, specifically animal movement and population density, and that model estimates may not reliably reflect variation in these processes. We recommend carefully defining occupancy if it is applied to CT data in order to better match sampling and analytical frameworks to the ecology of sampled wildlife species.
Introduction
Remote detectors, such as camera traps (CT), have become widely used in combination with analytical approaches for assessing unmarked populations, such as occupancy modeling (O'Brien et al. 2010, O'Connell and Bailey 2011, Burton et al. 2015). Although initially developed for a specific set of sampling conditions (i.e., repeated samples of sites closed to changes in occupancy; MacKenzie et al. 2002, MacKenzie and Nichols 2004), occupancy models have now been applied to a wide array of sampling designs to make inferences about population distribution, habitat use, and relative abundance (Bailey et al. 2014, Kellner and Swihart 2014). However, many studies applying occupancy models to CT data have not explicitly considered how the underlying patterns of animal movement and population density affect both the area occupied by an animal population and the probability of detection at CTs (Burton et al. 2015). There is thus a need to evaluate whether inferences from occupancy models applied to CT data are robust to variation in animal movement and population density.
Occupancy models estimate the proportion of sites at which a species occurs, ѱ, while simultaneously estimating the probability of detection, P, through repeated surveys of each site (MacKenzie et al. 2002, 2006, Bailey et al. 2014). Assuming the occupancy status of sites is closed such that animals do not move into and out of sites between repeated surveys, detectability is estimated from the frequency of detections per site. The proportion of sites with at least one detection (termed naïve occupancy by Mackenzie et al. 2006) is adjusted using P to estimate ѱ. In CT surveys of mobile animals, a “site” in reality is the camera's detection zone, which normally covers only a very small portion of an individual animal's home range. The occupancy status of sites is therefore not closed over the duration of repeated sampling, and in practice, researchers relax the assumption of site closure (Mackenzie et al. 2004). It is instead assumed that animals move into and out of a site at random and occupancy is interpreted as the proportion of sampled sites used by the species (Kendall 1999, MacKenzie et al. 2004, Mackenzie and Royle 2005). Efford and Dawson (2012) pointed out that in addition to lack of closure, CTs in continuous habitat are point detectors (i.e., not plots or quadrats) that sample the proportion of area occupied (PAO; Mackenzie and Royle 2005), rather than the proportion of sites occupied.
The PAO emerges dynamically over time as animals move across their home range such that occupied locations are used only temporarily. Therefore, detection/non-detection data from CTs (naïve occupancy) are a sample of the PAO, reflecting only the proportion of area used during the sampling period (Efford and Dawson 2012). Estimating the full PAO requires an estimate of the probability a CT will be used during sampling, which is attempted through occupancy models using the record of repeat visits to a CT. The probability of use of a CT during sampling, termed availability for detection (Mordecai et al. 2011), is analogous to P in conventional occupancy modeling in that it informs the model with respect to all the detectors the sampled population will eventually occupy but did not use during sampling (MacKenzie et al. 2006, Nichols et al. 2008). As such, Efford and Dawson (2012) concluded that model estimates of occupancy from point samples in continuous habitat should be interpreted as the full proportion of area used by all individual animals after completely using their home ranges, termed “asymptotic” PAO. Asymptotic PAO estimated from CTs is the product of population density and home range area (HRA) and can be interpreted as the probability that a CT is in at least one home range (Efford and Dawson 2012, Linkie et al. 2013).
MacKenzie et al. (2002) demonstrated through simulations that some combinations of occupancy and detectability lead to bias and imprecision in model estimates of occupancy. In particular, when detectability <0.3, estimates of occupancy were positively biased when simulated occupancy was <0.7 and negatively biased when simulated occupancy was >0.9. Therefore, unbiased and precise estimates of asymptotic PAO from CTs require adequate detectability, which, if detection in the CT detection zone is close to one, is primarily a function of a species' availability for detection (i.e., use of the detection zone). Assuming the area of the detection zone is constant and animals are equally likely to use any part of the study area, the probability of an individual passing through the detection zone is determined by the length of the sampling duration and the speed and range of animal movement (Rowcliffe et al. 2008). For a population, the probability of any individual passing through a detection zone is a function of the number of animals whose home ranges overlap the CT (i.e., population density; Royle and Nichols 2003, Guillera-Arroita et al. 2011, Efford and Dawson 2012). Finally, both animal movement and population density interact with the configuration of CTs to influence the probability of detection (Efford and Dawson 2012).
Despite recognition of widespread variation in animal densities and movement over space and time, both within and between species (Duncan et al. 2015, Efford et al. 2016), the consequences of such variation for the performance of occupancy models using CT data have not been assessed. In this study, we sought to determine how animal movement and population density interact with the sampling design of CT surveys to affect the performance of occupancy model parameter estimates. We began by testing the hypothesis that the area used during sampling is adequately estimated by naïve occupancy (i.e., no model-based correction of detectability). We then tested how animal population density, movement rate, and HRA affect the accuracy and precision of estimates of the asymptotic PAO from occupancy models. Finally, we explored how the sampling duration and spatial distribution of camera arrays interacted with the above factors to affect the bias and precision of occupancy estimates. In order to measure accuracy, we compared model estimates of occupancy using our simulated CT detections to the true PAO by simulated animals (i.e., asymptotic PAO; Efford and Dawson 2012, Latif et al. 2015).
Methods
Animal movement simulations
(1)Here, I is an indicator function (valued either 1 or 0, depending on the validity of the expression in parentheses), β is the home range center attraction parameter, and the denominator is a sum over all the cells in the domain so that the kernel sums to one. The above formulation allows us to simulate space use as it emerges from different combinations of spatially independent movement cost (α) and spatially dependent home range attraction (β∥x − x′∥2). Movement simulations were run for 3,153,600 time steps (corresponding to one full year).
Asymptotically (i.e., after long enough time), the above movement model gives rise to a bivariate Gaussian utilization distribution (UD) centered on x′. The scaling parameter of this distribution, σ, is given by (4β)−0.5 and is equivalent to the Royle et al.'s (2014) spatial capture–recapture scaling parameter. This can be shown by considering the squared distance from the home range center as a habitat feature that is being selected against and hence the term 
as the habitat selection function governing the movement process. Based on the theoretical work by Moorcroft and Barnett (2008) and more recently by Avgar et al. (2016), asymptotic UD should scale linearly with the square of the underlying habitat selection function (as long as movement capacity is much shorter than the scale of habitat variation) and hence the above-stated relationship between σ and β. Alternatively, our model can be viewed as a discrete approximation of a circular bivariate Ornstein-Uhlenbeck model (often used to model animal ranging behavior; Blackwell 1997), which has a well-known Gaussian steady-state solution (Signer et al. 2017).
By defining a cutoff value at which we truncate asymptotic UD, we can translate the microscale movement process governed by Eq. 1, to a macroscale steady-state HRA. For a cutoff value of 0.01 used here (including 99% of the UD within the home range), asymptotic HRA is approximately 14.4676·β−0.5 m. The value of α is inversely related to the animal's movement rate and will determine how fast the UD approaches its steady state. To facilitate biological interpretation, we convert α into the spatially independent probability that the animal will move within a single time step, 
. Since the centroids of neighboring hexagonal cells in our simulation are ~10 m apart, and a single step's duration is 10 s, μ is the mean maximal speed (in m/s). Note that, once speed is measured at a coarser temporal resolution (e.g., displacement per hour), it is bound to be much smaller than μ as our simulated animals lack directional persistence (and hence often backtrack) and their movement is biased toward their home range center.
Occupancy models
A small subset of hexagonal cells in the simulation domain were designated as CTs (with a detection area of 100 m2), and a detection event was recorded whenever a simulated animal was present in a camera cell (i.e., we assumed P = 1 once an animal entered the detection zone). Cameras were evenly spaced across the domain (Fig. 1). Camera-trap data used in occupancy models are discretized into presence/absence detection histories using a sampling occasion (the duration of a single repeat sample at a detector) that typically varies from one day to two weeks (Burton et al. 2015). To emulate realistic CT studies, we created detection histories from the movement simulations to estimate occupancy with a sampling occasion of one week (60,480 simulation time steps). We treated occupancy and detectability as constant across all detectors (i.e., no site covariates), and detectability as constant across sampling occasions, and we estimated the probabilities of occupancy (
) and detectability (P) by maximizing the likelihood:
(2)where nt is the number of detectors at which the species was detected at sampling occasion t out of T total sampling occasions, s is the number of detectors at which the species was detected at least once, and S is the total number of detectors (MacKenzie et al. 2002). All modeling was implemented in R package UNMARKED (R Core Team 2016).
(3)Effects of movement, population density, sampling duration, and camera density on occupancy estimation
In order to reflect plausible values for real species, we assigned simulation parameter values based on HRAs reported in previous CT studies (Burton et al. 2015) and a review of studies that reported both speed and HRA for a range of mammal species (Appendix S1: Table S1). For all analysis, we discarded the first 1,576,800 steps (6 months) of each movement simulation to remove any effects of the initial conditions. To test our first prediction that naïve occupancy measured by CTs reflects the PAO during sampling, we compared the proportion of CT cells used during the second 6 months of sampling to the total proportion of cells used during the same period. For all remaining analyses, we compared model estimates of occupancy to the asymptotic PAO or the proportion of cells inside at least one animal home range (Efford and Dawson 2012, Linkie et al. 2013). To this aim, we calculated the proportion of CT cells within a distance from home range centers corresponding to the radius of 99% of the asymptotic home range UD.
To test the effect of movement and population density on occupancy model inference, we discretized detections at all hexagonal cells from 183 d (6 months) of sampling into detection histories across weekly sampling occasions. To mitigate the effect of camera spacing, we uniformly spaced cameras using the mean home range diameter in each scenario, calculated as the minimum convex polygon encompassing each simulated trajectory. Note that for fast-moving animals occupying small home ranges (i.e., with large β), the observed HRA rapidly approaches asymptotic HRA, whereas for slow-moving animals or animals occupying large HRAs, the short-term HRA may be much smaller than asymptotic HRA (Table 1). We varied densities (N = 10, 100, 500, 1000) within the constant domain according to HRA for two reasons. Firstly, to maintain biological relevance, we only simulated animal populations with realistic densities given home range sizes and therefore decreased densities with increasing HRA (Table 2). Secondly, by not simulating either many large home ranges or few small home ranges, we did not model occupancy when the asymptotic PAO was near either 1 or 0, which results in detections at every CT or bias due to low sample size, respectively (Guillera-Arroita et al. 2010). We tested the effect of sampling duration by comparing the preceding analysis to replicated analyses with durations of 30 and 90 d. Our three sampling durations therefore resulted in 4-, 13-, or 26-week-long repeated sampling occasions, respectively.
| Scenario parameters | Realized values | ||
|---|---|---|---|
| Asymptotic home range area (km2) | Movement rate | Home range area (km2) | Movement rate (m/h) |
|
Small HRA = 1 |
Slow μ = 0.1 |
0.76–0.98 | 55–58 |
|
Fast μ = 1 |
0.99–0.99 | 162–171 | |
|
Intermediate HRA = 10 |
Slow μ = 0.1 |
3.1–8.1 | 56–58 |
|
Fast μ = 1 |
7.9–9.7 | 175–183 | |
|
Large HRA = 100 |
Slow μ = 0.1 |
4.8–33.4 | 56–58 |
|
Fast μ = 1 |
23.4–85.1 | 176–186 | |
Notes
- Simulation HRA values (1, 10, 100) correspond to the asymptotic area of an individual's home range—the value that would emerge after long enough time. The observed values correspond to the area covered after 6 months.
| Asymptotic home range area (km2) | Abundance |
|---|---|
|
Small HRA = 1 |
1000 |
| 500 | |
|
Intermediate HRA = 10 |
500 |
| 100 | |
|
Large HRA = 100 |
100 |
| 10 |
We tested the effect of the spatial distribution of camera arrays on occupancy model inference using the above movement parameters across a range of systematic camera spacing. Here, we used one sampling duration of six months and held the total area used over that duration constant. As HRA and/or speed increased, we decreased N to hold the total proportion of area used constant at 0.5 (Table 3). We varied camera spacing across grids with distances of approximately 1, 4, and 11 km between adjacent CTs (spanning a range of spacing typical of camera-trap studies; Burton et al. 2015). As a result of this spacing, the number of cameras varied by scenario, but detection data were sampled with replacement in a bootstrap procedure (as with movement and population density analysis) to maintain equal sample sizes of cameras across scenarios.
| Asymptotic home range area (km2) | Movement rate | Density (N) |
|---|---|---|
|
Small HRA = 1 |
Slow | 891 |
| Fast | 700 | |
|
Intermediate HRA = 10 |
Slow | 234 |
| Fast | 96 | |
|
Large HRA = 100 |
Slow | 174 |
| Fast | 26 |
Note
- Density was varied across movement speeds and home range sizes to maintain the proportion of area used during six months of sampling at 0.5.
Results
Naïve occupancy and estimated detectability
As predicted, the proportion of CTs that registered a detection closely matched the proportion of area used during the sampling duration across 11 of the 12 simulated movement speed, HRA, and population density combinations (Fig. 2). The only scenario for which the naïve occupancy failed to estimate the proportion of area used during sampling was when a low population density of animals (100) moved quickly across large home ranges. Estimated detectability was in general very low, with values being >0.3 in only three of 12 scenarios (Fig. 3), reflecting low availability for detection (i.e., use of CT cell) for species with larger home ranges. In small home ranges, confidence intervals for estimated detectability overlapped or were above 0.3 for all densities and movement rates (Fig. 3).
Effect of movement and population density on occupancy estimates
The performance of occupancy models varied most consistently with variation in simulated animal home ranges, being generally poorer for larger HRA and better for smaller HRA. For large HRA and low densities (0.01/km2), occupancy estimates of the asymptotic PAO were biased and the speed of movement determined the direction of bias (Fig. 4). Fast-moving, low-density, large home range scenarios had the lowest estimate of detectability of any scenario tested (Fig. 3) and highest overestimation of the asymptotic PAO (Fig. 4) with a mean bias of 60%. Conversely, low densities of slow-moving animals in large home ranges were detected on very few CTs (Fig. 2) and the asymptotic PAO was underestimated (mean negative bias = 34%, Fig. 4). At higher densities (0.1/km2) of large HRA animals, occupancy was underestimated, particularly for slow-moving animals (mean negative bias = 52%, Fig. 4). Overall, for realistic densities of animals that move over large areas, occupancy models poorly estimated the asymptotic PAO, exhibiting either positive or negative bias depending on population density and speed.
For intermediate HRA and densities of 0.1/km2, occupancy models estimated the PAO with precision and accuracy when animals moved quickly but underestimated the PAO when animals moved slowly (mean negative bias = 55%, Fig. 4). When densities were increased to 0.5/km2 at intermediate HRA, the domain was nearly saturated and occupancy estimates were accurate when animals moved quickly, with minimal bias when animals moved slowly (mean negative bias = 16%, Fig. 4). Overall, occupancy models performed well for intermediate HRA when densities were high or animals moved quickly. For small HRA and densities over which the domain was approximately 50% occupied (0.5/km2 and 1/km2), models estimated the asymptotic PAO precisely and without bias for both movement speeds (Fig. 4).
Effect of sampling on occupancy estimates
Occupancy model estimates of the asymptotic PAO were more sensitive to the speed and range of animal movement and population density than to the sampling duration. In general, negative bias decreased with increasing sampling duration, particularly for larger home ranges and slower movement rates (Fig. 5). Occupancy estimates were insensitive to sampling duration when HRA was small (Fig. 5). The density of CTs had very little effect on the precision and accuracy of asymptotic PAO estimates (Fig. 6). Only the lowest density of cameras exhibited marginally improved estimates of asymptotic PAO when animals moved over medium or large home ranges (Fig. 6).
Discussion
By modeling occupancy from CT data generated using various animal movement parameters and sampling designs, we exposed bias in occupancy estimates of the asymptotic PAO by mobile animals in continuous habitat. When animals occupied large- and medium-sized home ranges, low detection rates and the resulting low estimates of detectability generated bias in occupancy estimates, with the direction of this bias depending on animal population density and movement speed. At low population densities, CTs overlapped fewer home ranges and were less likely to be visited by more than one animal. Fast-moving animals in large home ranges were less likely to re-visit a given CT but more likely to visit new CTs, leading to higher naïve occupancy but lower detectability (due to few repeat detections across sampling occasions) and thus positively biased estimates of occupancy, (consistent with previous simulation studies (MacKenzie et al. 2002). This combination of low population density and fast, far-ranging movement is typical of many larger mammal species targeted by CT surveys for conservation applications (e.g., Mace et al. 2008, O'Brien et al. 2010, Ahumada et al. 2011). At high densities, each CT more likely overlaps multiple home ranges such that few re-visits by fast-moving individuals are counterbalanced by an increase in the probability of other individuals visiting a given CT. Under these conditions, detectability is not likely to be underestimated, regardless of speed. But detectability can be overestimated if animals move slowly, which, in combination with low naïve occupancy, resulted in underestimated asymptotic PAO.
Occupancy estimates for scenarios with small home ranges closely matched the simulated asymptotic PAO. In this case, animals covered home ranges quickly, particularly when moving fast. As a result, animals more frequently re-visited CTs within their home range and were less likely to visit new CTs (as small home ranges overlapped few), such that estimated detection was higher (>0.3 in two out of four scenarios), and both naïve and model-estimated occupancy matched the asymptotic PAO (Figs. 3, 4).
The effect of sampling design on the performance of occupancy estimates was smaller than the effect of animal movement and population density in our simulations. Increased sampling duration generally decreased the bias of occupancy estimates for animals with large and intermediate HRAs, corroborating the observed effect of increased number of sampling occasion shown by MacKenzie et al. (2002). However, estimates for slow-moving or low population density animals with large and medium HRAs were not accurate even after 6 months of sampling. Varying the spacing of CTs (and hence the spatial intensity of sampling) by an order of magnitude had only minor influence on the accuracy of model estimates of detectability and occupancy. However, when animals moved over large home ranges and CT spacing was small, larger spacing of CTs resulted in a marginal improvement in model estimates of asymptotic PAO. When CTs were spaced farther apart, there were fewer CTs per home range, potentially reducing both detections and estimates of detectability, and consequently, the negative bias in occupancy estimates of asymptotic PAO. We suggest this issue could be mitigated by spacing (or aggregating) CTs at a scale that matches the target species HRA.
Our results provide important insight on interpretation of occupancy from point detectors such as CTs. By simulating movement, we have shown that detection/non-detection data from point detectors reflect the area used by the species during sampling and model-estimated occupancy roughly reflects asymptotic PAO with bias due to animal movement over large or intermediate home ranges. We therefore corroborate Efford and Dawson's (2012) conclusion that estimates of occupancy from CT data should be interpreted as the asymptotic PAO. This interpretation is distinct from the common practice of using occupancy modeling to estimate the proportion of researcher-defined larger sites (e.g., Fuller et al. 2016) around the CT that are occupied (Karanth et al. 2011, O'Connell and Bailey 2011, Burton et al. 2015). As the area of sites increases beyond the area of the CT detection zone, the mismatch between the proportion of those sites that are occupied and the asymptotic PAO increases (MacKenzie et al. 2006, Efford and Dawson 2012). In addition, the probability of a home range overlapping a site but not the CT that is sampling that site increases with site area, driving an increasing mismatch between the real and estimated proportion of sites occupied.
Implications for wildlife monitoring
Monitoring programs are increasingly using CTs in combination with occupancy modeling in efforts to assess changes in populations over time or space, often for multiple species (O'Brien et al. 2010, Ahumada et al. 2011, O'Connell and Bailey 2011, Rich et al. 2017, Steenweg et al. 2017). In our simulated scenarios, performance of estimates varied considerably with animal movement. This variability should be of concern to monitoring programs. For example, if movement rates vary across seasons or years, or between habitats, rates of detection and resulting occupancy estimates will change, whereas the asymptotic PAO may not. Such movement variation has been observed in many species including grizzly bears (Graham and Stenhouse 2014) and woodland caribou (Avgar et al. 2013). Under such conditions, HRA is likely to change as well, further confounding estimates of the asymptotic PAO. Therefore, when comparing estimates of occupancy across strata such as season or habitat, researchers should account for potential changes in movement across strata. While this seems a daunting task, our results suggest it may be perilous to ignore.
Our results also highlight that variation in animal movement may limit the use of occupancy models of CT data as an indicator of abundance (Mackenzie and Royle 2005, Efford and Dawson 2012). As expected (Gaston et al. 2000), asymptotic PAO was positively related to population density in our simulations; however, the CT-based occupancy estimates only roughly approximated changes in density (Fig. 3). Further, the ability of occupancy models to reliably track density depended on the speed and range of animal movement. This could be particularly problematic if movement parameters vary with density. When a species' movement rate increases with decreasing density, as has been documented in several species such as roe deer (Panzacchi et al. 2009) and tigers (Efford et al. 2016), estimates of the asymptotic PAO will be increasingly overestimated with decreasing density and underestimated with increasing density, potentially masking true changes in population trends. Clearly, these issues also apply when CTs are deployed to assess the occupancy of multiple species that vary significantly in movement and density, as is increasingly common (Burton et al. 2015, Beaudrot et al. 2016, Rich et al. 2017). In fact, our results suggest that using CTs to compare occupancy dynamics across a range of species varying greatly in density and movement behavior may not be appropriate, which has strong implications for the current state of practice.
Addressing the effects of animal movement and population density on occupancy estimates
Strategies for dealing with bias in occupancy estimation imposed by animal movement may include changes to sampling design. For surveying animals with large HRA, including more than one CT per sampling site and linking within-site cameras in multi-scale occupancy models may hold promise for increasing detectability and more explicitly modeling availability for detection (Nichols et al. 2008, Mordecai et al. 2011). Nevertheless, explicitly incorporating animal movement into sampling (e.g., telemetry) and modeling may be required for reliable inferences (Rowcliffe et al. 2016). Deploying attractants such as scent lure can increase detections at CTs (Burton 2014). However, further work is needed to determine whether attractants at CTs can increase detections beyond small scales sufficiently for the large HRA scenarios for which low detections contributed to biased estimates of occupancy.
We evaluated the relatively simple single-season, single-species occupancy model originally proposed by Mackenzie et al. (2002), for which probabilities of detection and occupancy are assumed to be constant over space and time. Incorporating more heterogeneity into the simulated landscape, animal movements, and CT placements (e.g., high- and low-quality habitat patches), and testing occupancy models that incorporate spatial and/or temporal covariates (MacKenzie et al. 2002, 2006) are worthwhile directions for further research. Incorporating covariates into occupancy models of CT data is often used to examine a species' intensity of use of certain habitats (Burton et al. 2015). Further work examining how animal movement and density affect such interpretations is warranted. Occupancy model variants that incorporate heterogeneity in detectability due to variation in abundance (e.g., Royle and Nichols 2003) or allow for temporary immigration/emigration of sites (Kéry et al. 2009) should also be explored in this context. Nevertheless, applying more complex models does not negate the need to carefully define the interpretation of model parameters in relation to ecological processes (e.g., movement, population density).
Extending the relatively simple movement model used in our simulations is another important area for future research. Our model simulated animal movements from one cell to the next without any directional persistence. This influenced detection rates, as an animal moving with directional persistence is less likely to remain in one area by chance (either lingering near the CT or away from it) and is more likely to realize its asymptotic home range within the observation period. Including non-random movements in simulations, such as habitat selection or linear movement along trails, and responses to CT protocols (e.g., attractants, trap shyness) would also be expected to have important effects on detection rates. However, we do not see an a priori reason to expect occupancy models to perform more consistently in the face of such variations in animal movement behavior. In addition, we acknowledge that the bias we observed in the occupancy estimates is likely sensitive to our measure of the asymptotic PAO. For instance, negative bias would have been reduced and positive bias increased had we defined PAO using only 95% of the simulated UD rather than 99%.
We assumed perfect detection inside our 10 × 10 m CT grid cells (simulated detection zone) because of our focus on understanding the effect of movement in and out of the detection zone on estimates of detectability and occupancy. In practice, detectability within the detection zone will be affected by factors such as vegetation, temperature, body size, and speed and location of movement relative to the CT field of view (Rowcliffe et al. 2008). However, we suggest that these sources of imperfect detection will typically be less important than movement in many CT surveys and more easily controlled (e.g., by clearing vegetation, restricting inference to a single species). However, further work evaluating variation in both movement and detectability within the detection zone is warranted.
Ultimately, new analytical approaches for CT data may be warranted. Individual animal positions are inherently correlated in space and time; consequently, detections at a CT form a time series that often is characterized by multiple detection events over short intervals, followed by long periods with no events. The common practice of analyzing the CT time series as independent detections at a much coarser resolution (e.g., detections grouped within daily or weekly sampling occasions) erodes the information embedded in these spatiotemporal patterns (Efford 2004). On the other hand, defining short sampling occasions often leads to zero-inflation and hence frequent model convergence failures. We did not explicitly evaluate the effect of sampling occasion, but we suggest that this trade-off deserves further investigation. It may be possible to reduce bias in occupancy estimates using modeling approaches that include information on spatial and temporal autocorrelation in CT detections (Guillera-Arroita et al. 2011).
Conclusions
Our assessment revealed that occupancy model estimates from CT surveys in continuous habitat are not accurate over several realistic combinations of animal movement rate, HRA, and population density. Furthermore, the bias and imprecision in occupancy estimates was not consistent across sampling duration or CT spacing. The increased popularity of modeling occupancy of species detection/non-detection data collected using CTs is due in part to the relative ease with which such data can be collected and the models fit. However, in many situations, supplementary information on the number of animals and their movement behavior may be needed to reliably estimate occupancy. This potentially reduces the utility of occupancy modeling for CT surveys of mobile animals, especially when surveys span conditions in which abundance and movement are expected to vary, as in multispecies surveys or long-term monitoring. We therefore recommend that researchers carefully consider their study system, sampling design, and analytical assumptions before applying occupancy models to CT data. When occupancy models are used, we urge researchers to explicitly define the occupancy and detectability parameters in light of their sampling framework and the expected ecological characteristics of their study species and system. Whereas recent development of CT methods and occupancy models certainly represents key advances in wildlife methodology, ecologists can never grow complacent in the face of ecological complexities, and we look forward to continued advances in the effort to reliably assess animal distribution and abundance.
Acknowledgments
This study was partially funded by the Natural Sciences and Engineering Research Council of Canada (Grant ID SFR1451). TA gratefully acknowledges support by the Banting postdoctoral fellowships. We thank Robin Steenweg and Andrew Ladle for their comments on the manuscript and discussions regarding concepts. Thanks also to Erin Bayne for helpful guidance on the project. We thank the Ecosphere associate editors and anonymous reviewers for their help directing the manuscript. Simulation data will be archived online through the University of Alberta (https://dataverse.library.ualberta.ca/) upon publication.
