Integrating telemetry data into spatial capture–recapture modifies inferences on multi‐scale resource selection

The long shadow of woody encroachment: An integrated approach to modeling grassland songbird habitat

Animals must track resources over relatively fine spatial and temporal scales, particularly in disturbance-mediated systems like grasslands. Grassland birds respond to habitat heterogeneity by dispersing among sites within and between years, yet we know little about how they make post-dispersal settlement decisions. Many methods exist to quantify the resource selection of mobile taxa, but the habitat data used in these models are frequently not collected at the same location or time that individuals were present. This spatiotemporal misalignment may lead to incorrect interpretations and adverse conservation outcomes, particularly in dynamic systems. To investigate the extent to which spatially and temporally dynamic vegetation conditions and topography drive grassland bird settlement decisions, we integrated multiple data sources from our study site to predict slope, vegetation height, and multiple metrics of vegetation cover at any point in space and time within the temporal and spatial scope of our study. We paired these predictions with avian mark-resight data for 8 years at the Konza Prairie Biological Station in NE Kansas to evaluate territory selection for Grasshopper Sparrows (Ammodramus savannarum), Dickcissels (Spiza americana), and Eastern Meadowlarks (Sturnella magna). Each species selected different types and amounts of herbaceous vegetation cover, but all three species preferred relatively flat areas with less than 6% shrub cover and less than 1% tree cover. We evaluated several scenarios of woody vegetation removal and found that, with a targeted approach, the simulated removal of just one isolated tree in the uplands created up to 14 ha of grassland bird habitat. This study supports growing evidence that small amounts of woody encroachment can fragment landscapes, augmenting conservation threats to grassland systems. Conversely, these results demonstrate that drastic increases in bird habitat area could be achieved through relatively efficient management interventions. The results and approaches reported pave the way for more efficient conservation efforts in grasslands and other systems through spatiotemporal alignment of habitat with animal behaviors and simulated impacts of management interventions.

Improved inferences about landscape connectivity from spatial capture-recapture by integration of a movement model

Understanding how broad-scale patterns in animal populations emerge from individual-level processes is an enduring challenge in ecology that requires investigation at multiple scales and perspectives. Complementary to this need for diverse approaches is the recent focus on integrated modeling in statistical ecology. Population-level processes represent the core of spatial capture-recapture (SCR), with many methodological extensions that have been motivated by standing ecological theory and data-integration opportunities. The extent to which these recent advances offer inferential improvements can be limited by the data requirements for quantifying individual-level processes. This is especially true for SCR models that use non-Euclidean distance to relax the restrictive assumption that individual space use is stationary and symmetrical to make inferences about landscape connectivity. To meet the challenges of scale and data quality, we propose integrating an explicit movement model with non-Euclidean SCR for joint estimation of a shared cost parameter between individual and population processes. Here, we define a movement kernel for step selection that uses "ecological distance" instead of Euclidean distance to quantify availability for each movement step in terms of landscape cost. We compare performance of our integrated model to that of existing SCR models using realistic animal movement simulations and data collected on black bears. We demonstrate that an integrated approach offers improvements both in terms of bias and precision in estimating the shared cost parameter over models fit to spatial encounters alone. Simulations suggest these gains were only realized when step lengths were small relative to home range size, and estimates of density were insensitive to whether or not an integrated approach was used. By combining the fine spatiotemporal scale of individual movement processes with the estimation of population density in SCR, integrated approaches such as the one we develop here have the potential to unify the fields of movement, population, and landscape ecology and improve our understanding of landscape connectivity.

Integrated animal movement and spatial capture-recapture models: Simulation, implementation, and inference

Over the last decade, spatial capture-recapture (SCR) models have become widespread for estimating demographic parameters in ecological studies. However, the underlying assumptions about animal movement and space use are often not realistic. This is a missed opportunity because interesting ecological questions related to animal space use, habitat selection, and behavior cannot be addressed with most SCR models, despite the fact that the data collected in SCR studies - individual animals observed at specific locations and times - can provide a rich source of information about these processes and how they relate to demographic rates. We developed SCR models that integrated more complex movement processes that are typically inferred from telemetry data, including a simple random walk, correlated random walk (i.e., short-term directional persistence), and habitat-driven Langevin diffusion. We demonstrated how to formulate, simulate from, and fit these models with standard SCR data using data-augmented Bayesian analysis methods. We evaluated their performance through a simulation study, in which we varied the detection, movement, and resource selection parameters. We also examined different numbers of sampling occasions and assessed performance gains when including auxiliary location data collected from telemetered individuals. Across all scenarios, the integrated SCR movement models performed well in terms of abundance, detection, and movement parameter estimation. We found little difference in bias for the simple random walk model when reducing the number of sampling occasions from T = 25 to T = 15. We found some bias in movement parameter estimates under several of the correlated random walk scenarios, but incorporating auxiliary location data improved parameter estimates and significantly improved mixing during model fitting. The Langevin movement model was able to recover resource selection parameters from standard SCR data, which is particularly appealing because it explicitly links the individual-level movement process with habitat selection and population density. We focused on closed population models, but the movement models developed here can be extended to open SCR models. The movement process models could also be easily extended to accommodate additional "building blocks" of random walks, such as central tendency (e.g., territoriality) or multiple movement behavior states, thereby providing a flexible and coherent framework for linking animal movement behavior to population dynamics, density, and distribution.

An integrated path for spatial capture-recapture and animal movement modeling

Ecologists and conservation biologists increasingly rely on spatial capture-recapture (SCR) and movement modeling to study animal populations. Historically, SCR has focused on population-level processes (e.g., vital rates, abundance, density, and distribution), whereas animal movement modeling has focused on the behavior of individuals (e.g., activity budgets, resource selection, migration). Even though animal movement is clearly a driver of population-level patterns and dynamics, technical and conceptual developments to date have not forged a firm link between the two fields. Instead, movement modeling has typically focused on the individual level without providing a coherent scaling from individual- to population-level processes, whereas SCR has typically focused on the population level while greatly simplifying the movement processes that give rise to the observations underlying these models. In our view, the integration of SCR and animal movement modeling has tremendous potential for allowing ecologists to scale up from individuals to populations and advancing the types of inferences that can be made at the intersection of population, movement, and landscape ecology. Properly accounting for complex animal movement processes can also potentially reduce bias in estimators of population-level parameters, thereby improving inferences that are critical for species conservation and management. This introductory article to the Special Feature reviews recent advances in SCR and animal movement modeling, establishes a common notation, highlights potential advantages of linking individual-level (Lagrangian) movements to population-level (Eulerian) processes, and outlines a general conceptual framework for the integration of movement and SCR models. We then identify important avenues for future research, including key challenges and potential pitfalls in the developments and applications that lie ahead.

Modeling abundance, distribution, movement and space use with camera and telemetry data

Studies of animal abundance and distribution are often conducted independently of research on movement, despite the important links between processes. Movement can cause rapid changes in spatial variation in density, and movement influences detection probability and therefore estimates of abundance from inferential methods such as spatial capture-recapture (SCR). Technological developments including camera traps and GPS telemetry have opened new opportunities for studying animal demography and movement, yet statistical models for these two data types have largely developed along parallel tracks. We present a hierarchical model in which both datasets are conditioned on a movement process for a clearly defined population. We fitted the model to data from 60 camera traps and 23,572 GPS telemetry locations collected on 17 male white-tailed deer in the Big Cypress National Preserve, Florida, USA during July 2015. Telemetry data were collected on a 3-4 h acquisition schedule, and we modeled the movement paths of all individuals in the region with a Ornstein-Uhlenbeck process that included individual-specific random effects. Two of the 17 deer with GPS collars were detected on cameras. An additional 20 male deer without collars were detected on cameras and individually identified based on their unique antler characteristics. Abundance was 126 (95% CI: 88-177) in the 228 km² region, only slightly higher than estimated using a standard SCR model: 119 (84-168). The standard SCR model, however, was unable to describe individual heterogeneity in movement rates and space use as revealed by the joint model. Joint modeling allowed the telemetry data to inform the movement model and the SCR encounter model, while leveraging information in the camera data to inform abundance, distribution and movement. Unlike most existing methods for population-level inference on movement, the joint SCR-movement model can yield unbiased inferences even if non-uniform sampling is used to deploy transmitters. Potential extensions of the model include the addition of resource selection parameters, and relaxation of the closure assumption when interest lies in survival and recruitment. These developments would contribute to the emerging holistic framework for the study of animal ecology, one that uses modern technology and spatio-temporal statistics to learn about interactions between behavior and demography.

Modeling spatiotemporal abundance and movement dynamics using an integrated spatial capture-recapture movement model

Animal movement is a fundamental ecological process affecting the survival and reproduction of individuals, the structure of populations, and the dynamics of communities. Methods to quantify animal movement and spatiotemporal abundances, however, are generally separate and therefore omit linkages between individual-level and population-level processes. We describe an integrated spatial capture-recapture (SCR) movement model to jointly estimate (1) the number and distribution of individuals in a defined spatial region and (2) movement of those individuals through time. We applied our model to a study of polar bears (Ursus maritimus) in a 28,125 km² survey area of the eastern Chukchi Sea, USA in 2015 that incorporated capture-recapture and telemetry data. In simulation studies, the model provided unbiased estimates of movement, abundance, and detection parameters using a bivariate normal random walk and correlated random walk movement process. Our case study provided detailed evidence of directional movement persistence for both male and female bears, where individuals regularly traversed areas larger than the survey area during the 36-day study period. Scaling from individual- to population-level inferences, we found that densities varied from <0.75 bears/625 km² grid cell/day in nearshore cells to 1.6-2.5 bears/grid cell/day for cells surrounded by sea ice. Daily abundance estimates ranged from 53 to 69 bears, with no trend across days. The cumulative number of unique bears that used the survey area increased through time due to movements into and out of the area, resulting in an estimated 171 individuals using the survey area during the study (95% credible interval 124-250). Abundance estimates were similar to a previous multiyear integrated population model using capture-recapture and telemetry data (2008-2016; Regehr et al., Scientific Reports 8:16780, 2018). Overall, the SCR-movement model successfully quantified both individual- and population-level space use, including the effects of landscape characteristics on movement, abundance, and detection, while linking the movement and abundance processes to directly estimate density within a prescribed spatial region and temporal period. Integrated SCR-movement models provide a generalizable approach to incorporate greater movement realism into population dynamics and link movement to emergent properties including spatiotemporal densities and abundances.

Confronting spatial capture-recapture models with realistic animal movement simulations

Spatial capture-recapture (SCR) models have emerged as a robust method to estimate the population density of mobile animals. However, model evaluation has generally been based on data simulated from simplified representations of animal space use. Here, we generated data from animal movement simulated from a mechanistic individual-based model, in which movement emerges from the individual's response to a changing environment (i.e., from the bottom-up), driven by key ecological processes (e.g., resource memory and territoriality). We drew individual detection data from simulated movement trajectories and fitted detection data sets to a basic, resource selection and transience SCR model, as well as their variants accounting for resource-driven heterogeneity in density and detectability. Across all SCR models, abundance estimates were robust to multiple, but low-degree violations of the specified movement processes (e.g., resource selection). SCR models also successfully captured the positive effect of resource quality on density. However, covariate models failed to capture the finer scale effect of resource quality on detectability and space use, which may be a consequence of the low temporal resolution of SCR data sets and/or model misspecification. We show that home-range size is challenging to infer from the scale parameter alone, compounded by reliance on conventional measures of "true" home-range size that are highly sensitive to sampling regime. Additionally, we found the transience model challenging to fit, probably due to data sparsity and violation of the assumption of normally distributed inter-occasion movement of activity centers, suggesting that further development of the model is required for general applicability. Our results showed that further integration of complex movement into SCR models may not be necessary for population estimates of abundance when the level of individual heterogeneity induced by the underlying movement process is low, but appears warranted in terms of accurately revealing finer scale patterns of ecological and movement processes. Further investigation into whether this holds true in populations with other types of realistic movement characteristics is merited. Our study provides a framework to generate realistic SCR data sets to develop and evaluate more complex movement processes in SCR models.

Occupancy data improves parameter precision in spatial capture-recapture models

Population size is one of the basic demographic parameters for species management and conservation. Among different estimation methods, spatially explicit capture-recapture (SCR) models allow the estimation of population density in a framework that has been greatly developed in recent years. The use of automated detection devices, such as camera traps, has impressively extended SCR studies for individually identifiable species. However, its application to unmarked/partially marked species remains challenging, and no specific method has been widely used. We fitted an SCR-integrated model (SCR-IM) to stone marten Martes foina data, a species for which only some individuals are individually recognizable by natural marks, and estimate population size based on integration of three submodels: (1) individual capture histories from live capture and transponder tagging; (2) detection/nondetection or "occupancy" data using camera traps in a bigger area to extend the geographic scope of capture-recapture data; and (3) telemetry data from a set of tagged individuals. We estimated a stone marten density of 0.352 (SD: 0.081) individuals/km2. We simulated four dilution scenarios of occupancy data to study the variation in the coefficient of variation in population size estimates. We also used simulations with similar characteristics as the stone marten case study, comparing the accuracy and precision obtained from SCR-IM and SCR, to understand how submodels' integration affects the posterior distributions of estimated parameters. Based on our simulations, we found that population size estimates using SCR-IM are more accurate and precise. In our stone marten case study, the SCR-IM density estimation increased the precision by 37% when compared to the standard SCR model as regards to the coefficient of variation. This model has high potential to be used for species in which individual recognition by natural markings is not possible, therefore limiting the need to rely on invasive sampling procedures.

Monitoring partially marked populations using camera and telemetry data

Long-term monitoring is an important component of effective wildlife conservation. However, many methods for estimating density are too costly or difficult to implement over large spatial and temporal extents. Recently developed spatial mark-resight (SMR) models are increasingly being applied as a cost-effective method to estimate density when data include detections of both marked and unmarked individuals. We developed a generalized SMR model that can accommodate long-term camera data and auxiliary telemetry data for improved spatiotemporal inference in monitoring efforts. The model can be applied in two stages, with detection parameters estimated in the first stage using telemetry data and camera detections of instrumented individuals. Density is estimated in the second stage using camera data, with all individuals treated as unmarked. Serial correlation in detection and density parameters is accounted for using time-series models. The two-stage approach reduces computational demands and facilitates the application to large data sets from long-term monitoring initiatives. We applied the model to 3 years (2015-2017) of white-tailed deer (Odocoileus virginianus) data collected in three study areas of the Big Cypress Basin, Florida, USA. In total, 59 females marked with ear tags and fitted with GPS-telemetry collars were detected along with unmarked females on 180 remote cameras. Most of the temporal variation in density was driven by seasonal fluctuations, but one study area exhibited a slight population decline during the monitoring period. Modern technologies such as camera traps provide novel possibilities for long-term monitoring, but the resulting massive data sets, which are subject to unique sources of observation error, have posed analytical challenges. The two-stage spatial mark-resight framework provides a solution with lower computational demands than joint SMR models, allowing for easier implementation in practice. In addition, after detection parameters have been estimated, the model may be used to estimate density even if no synchronous auxiliary information on marked individuals is available, which is often the case in long-term monitoring.

A review of spatial capture-recapture: Ecological insights, limitations, and prospects

First described by Efford (2004), spatial capture-recapture (SCR) has become a popular tool in ecology. Like traditional capture-recapture, SCR methods account for imperfect detection when estimating ecological parameters. In addition, SCR methods use the information inherent in the spatial configuration of individual detections, thereby allowing spatially explicit estimation of population parameters, such as abundance, survival, and recruitment. Paired with advances in noninvasive survey methods, SCR has been applied to a wide range of species across different habitats, allowing for population- and landscape-level inferences with direct consequences for conservation and management. I conduct a literature review of SCR studies published since the first description of the method and provide an overview of their scope in terms of the ecological questions answered with this tool, taxonomic groups targeted, geography, spatio-temporal extent of analyses, and data collection methods. In addition, I review approaches for analytical implementation and provide an overview of parameters targeted by SCR studies and conclude with current limitations and future directions in SCR methods.

Estimating the movements of terrestrial animal populations using broad-scale occurrence data

As human and automated sensor networks collect increasingly massive volumes of animal observations, new opportunities have arisen to use these data to infer or track species movements. Sources of broad scale occurrence datasets include crowdsourced databases, such as eBird and iNaturalist, weather surveillance radars, and passive automated sensors including acoustic monitoring units and camera trap networks. Such data resources represent static observations, typically at the species level, at a given location. Nonetheless, by combining multiple observations across many locations and times it is possible to infer spatially continuous population-level movements. Population-level movement characterizes the aggregated movement of individuals comprising a population, such as range contractions, expansions, climate tracking, or migration, that can result from physical, behavioral, or demographic processes. A desire to model population movements from such forms of occurrence data has led to an evolving field that has created new analytical and statistical approaches that can account for spatial and temporal sampling bias in the observations. The insights generated from the growth of population-level movement research can complement the insights from focal tracking studies, and elucidate mechanisms driving changes in population distributions at potentially larger spatial and temporal scales. This review will summarize current broad-scale occurrence datasets, discuss the latest approaches for utilizing them in population-level movement analyses, and highlight studies where such analyses have provided ecological insights. We outline the conceptual approaches and common methodological steps to infer movements from spatially distributed occurrence data that currently exist for terrestrial animals, though similar approaches may be applicable to plants, freshwater, or marine organisms.

Factors predicting habitat use by leopards in human-altered landscapes

Transformed landscapes caused by human activity leave remnant patches of natural habitat for wildlife. The persistence of species in the face of such transformation depends on individuals’ ability to adapt to novel habitat, and to secure resources and reproductive opportunities despite habitat alterations. The leopard, Panthera pardus, is the last free-roaming top carnivore in South Africa whose high trophic status and wide-ranging movements make them an effective focal species in conservation planning. Using location data from leopards, we investigated key correlates of habitat selection in human-altered landscapes at two spatial scales. We compared sex-related differences and predicted how conspecific home range locations influenced habitat selection. Leopards avoided human-altered landscapes more strongly at the large spatial scale, where both sexes selected core areas near formally protected areas. Conspecific home range locations had a strong positive effect at both spatial scales for males, while for females, conspecifics explained fine-scale habitat selection by selecting areas near neighboring females. Spatial scale, sex-related differences, and conspecific location play roles in habitat selection for solitary felids and have implications for conservation planning and management. Excluding these factors may result in inappropriate species management policies.

Experimental evaluation of spatial capture-recapture study design

A principal challenge impeding strong inference in analyses of wild populations is the lack of robust and long-term data sets. Recent advancements in analytical tools used in wildlife science may increase our ability to integrate smaller data sets and enhance the statistical power of population estimates. One such advancement, the development of spatial capture-recapture (SCR) methods, explicitly accounts for differences in spatial study designs, making it possible to equate multiple study designs in one analysis. SCR has been shown to be robust to variation in design as long as minimal sampling guidance is adhered to. However, these expectations are based on simulation and have yet to be evaluated in wild populations. Here we conduct a rigorously designed field experiment by manipulating the arrangement of artificial cover objects (ACOs) used to collect data on red-backed salamanders (Plethodon cinereus) to empirically evaluate the effects of design configuration on inference made using SCR. Our results suggest that, using SCR, estimates of space use and detectability are sensitive to study design configuration, namely the spacing and extent of the array, and that caution is warranted when assigning biological interpretation to these parameters. However, estimates of population density remain robust to design except when the configuration of detectors grossly violates existing recommendations.

An open spatial capture-recapture model for estimating density, movement, and population dynamics from line-transect surveys

The purpose of many wildlife population studies is to estimate density, movement, or demographic parameters. Linking these parameters to covariates, such as habitat features, provides additional ecological insight and can be used to make predictions for management purposes. Line-transect surveys, combined with distance sampling methods, are often used to estimate density at discrete points in time, whereas capture-recapture methods are used to estimate movement and other demographic parameters. Recently, open population spatial capture-recapture models have been developed, which simultaneously estimate density and demographic parameters, but have been made available only for data collected from a fixed array of detectors and have not incorporated the effects of habitat covariates. We developed a spatial capture-recapture model that can be applied to line-transect survey data by modeling detection probability in a manner analogous to distance sampling. We extend this model to a) estimate demographic parameters using an open population framework and b) model variation in density and space use as a function of habitat covariates. The model is illustrated using simulated data and aerial line-transect survey data for North Atlantic right whales in the southeastern United States, which also demonstrates the ability to integrate data from multiple survey platforms and accommodate differences between strata or demographic groups. When individuals detected from line-transect surveys can be uniquely identified, our model can be used to simultaneously make inference on factors that influence spatial and temporal variation in density, movement, and population dynamics.

Low wolverine (Gulo gulo) density in a national park complex of the Canadian Rocky Mountains

Large carnivores are sensitive to human-caused extirpation due to large home ranges, low population densities, and low reproductive rates. Protected areas help maintain populations by acting as sources, but human-caused mortality, habitat displacement, and edge effects occurring at protected area boundaries may reduce that function. The national parks Banff, Yoho, and Kootenay in the Canadian Rocky Mountains are refugia for large carnivores, including wolverines (Gulo gulo (Linnaeus, 1758)). Despite growing conservation concern, empirical baseline population data for wolverines remain scarce throughout their range, including most of Canada. We hypothesized (i) that in these national parks, wolverine density matched values expected for high-quality habitat, and (ii) that edge effects decreased density towards park boundaries. We conducted systematic non-invasive genetic sampling surveys covering >7000 km2 (2011 and 2013). Using spatial capture–recapture models, we estimated mean (±SE) female (1.5 ± 0.3 and 1.4 ± 0.3 wolverine/1000 km2), male (1.8 ± 0.4 and 1.5 ± 0.3 wolverine/1000 km2), and combined (3.3 ± 0.5 and 3.0 ± 0.4 wolverine/1000 km2) densities for 2011 and 2013, respectively. These estimates were lower than predictions based on density extrapolation from nearby high-quality habitat, and density decreased towards park boundaries. To benefit the population, we recommend creating buffer zones around parks that protect female habitat and prohibit harvest.

Spatial density estimates of Eurasian lynx (Lynx lynx) in the French Jura and Vosges Mountains

Obtaining estimates of animal population density is a key step in providing sound conservation and management strategies for wildlife. For many large carnivores however, estimating density is difficult because these species are elusive and wide-ranging. Here, we focus on providing the first density estimates of the Eurasian lynx (Lynx lynx) in the French Jura and Vosges mountains. We sampled a total of 413 camera trapping sites (with two cameras per site) between January 2011 and April 2016 in seven study areas across seven counties of the French Jura and Vosges mountains. We obtained 592 lynx detections over 19,035 trap days in the Jura mountains and 0 detection over 6,804 trap days in the Vosges mountains. Based on coat patterns, we identified a total number of 92 unique individuals from photographs, including 16 females, 13 males, and 63 individuals of unknown sex. Using spatial capture-recapture (SCR) models, we estimated abundance in the study areas between 5 (SE = 0.1) and 29 (0.2) lynx and density between 0.24 (SE = 0.02) and 0.91 (SE = 0.03) lynx per 100 km2. We also provide a comparison with nonspatial density estimates and discuss the observed discrepancies. Our study is yet another example of the advantage of combining SCR methods and noninvasive sampling techniques to estimate density for elusive and wide-ranging species, like large carnivores. While the estimated densities in the French Jura mountains are comparable to other lynx populations in Europe, the fact that we detected no lynx in the Vosges mountains is alarming. Connectivity should be encouraged between the French Jura mountains, the Vosges mountains, and the Palatinate Forest in Germany where a reintroduction program is currently ongoing. Our density estimates will help in setting a baseline conservation status for the lynx population in France.

Simulation-based validation of spatial capture-recapture models: A case study using mountain lions

Spatial capture-recapture (SCR) models have improved the ability to estimate densities of rare and elusive animals. However, SCR models have seldom been validated even as model formulations diversify and expand to incorporate new sampling methods and/or additional sources of information on model parameters. Information on the relationship between encounter probabilities, sources of additional information, and the reliability of density estimates, is rare but crucial to assessing reliability of SCR-based estimates. We used a simulation-based approach that incorporated prior empirical work to assess the accuracy and precision of density estimates from SCR models using spatially unstructured sampling. To assess the consequences of sparse data and potential sources of bias, we simulated data under six scenarios corresponding to three different levels of search effort and two levels of correlation between search effort and animal density. We then estimated density for each scenario using four models that included increasing amounts of information from harvested individuals and telemetry to evaluate the impact of additional sources of information. Model results were sensitive to the quantity of available information: density estimates based on low search effort were biased high and imprecise, whereas estimates based on high search effort were unbiased and precise. A correlation between search effort and animal density resulted in a positive bias in density estimates, though the bias decreased with increasingly informative datasets. Adding information from harvested individuals and telemetered individuals improved density estimates based on low and moderate effort but had negligible impact for datasets resulting from high effort. We demonstrated that density estimates from SCR models using spatially unstructured sampling are reliable when sufficient information is provided. Accurate density estimates can result if empirical-based simulations such as those presented here are used to develop study designs with appropriate amounts of effort and information sources.