- Methodology article
- Open Access
Accounting for location uncertainty in azimuthal telemetry data improves ecological inference
- Brian D. Gerber^{1, 2}Email authorView ORCID ID profile,
- Mevin B. Hooten^{3},
- Christopher P. Peck^{1},
- Mindy B. Rice^{4},
- James H. Gammonley^{4},
- Anthony D. Apa^{5} and
- Amy J. Davis^{6}
- Received: 2 April 2018
- Accepted: 21 June 2018
- Published: 25 July 2018
Abstract
Background
Characterizing animal space use is critical for understanding ecological relationships. Animal telemetry technology has revolutionized the fields of ecology and conservation biology by providing high quality spatial data on animal movement. Radio-telemetry with very high frequency (VHF) radio signals continues to be a useful technology because of its low cost, miniaturization, and low battery requirements. Despite a number of statistical developments synthetically integrating animal location estimation and uncertainty with spatial process models using satellite telemetry data, we are unaware of similar developments for azimuthal telemetry data. As such, there are few statistical options to handle these unique data and no synthetic framework for modeling animal location uncertainty and accounting for it in ecological models.
We developed a hierarchical modeling framework to provide robust animal location estimates from one or more intersecting or non-intersecting azimuths. We used our azimuthal telemetry model (ATM) to account for azimuthal uncertainty with covariates and propagate location uncertainty into spatial ecological models. We evaluate the ATM with commonly used estimators (Lenth (1981) maximum likelihood and M-Estimators) using simulation. We also provide illustrative empirical examples, demonstrating the impact of ignoring location uncertainty within home range and resource selection analyses. We further use simulation to better understand the relationship among location uncertainty, spatial covariate autocorrelation, and resource selection inference.
Results
We found the ATM to have good performance in estimating locations and the only model that has appropriate measures of coverage. Ignoring animal location uncertainty when estimating resource selection or home ranges can have pernicious effects on ecological inference. Home range estimates can be overly confident and conservative when ignoring location uncertainty and resource selection coefficients can lead to incorrect inference and over confidence in the magnitude of selection. Furthermore, our simulation study clarified that incorporating location uncertainty helps reduce bias in resource selection coefficients across all levels of covariate spatial autocorrelation.
Conclusion
The ATM can accommodate one or more azimuths when estimating animal locations, regardless of how they intersect; this ensures that all data collected are used for ecological inference. Our findings and model development have important implications for interpreting historical analyses using this type of data and the future design of radio-telemetry studies.
Keywords
- Home range
- Location uncertainty
- Radio-telemetry
- Radio
- Resource selection function
- Telemetry
- VHF
Background
Understanding animal space-use and its implications for population and community dynamics is a central component of ecology and conservation biology [1, 2]. Coupling environmental characteristics of where animals are found (and not found) provides important insights into species-habitat relationships, which is fundamental to understanding a species’s ecological niche [3]. For vagile animals, characterizing space-use during different life-history stages can help elucidate stage-specific habitat area requirements, dispersal patterns, or site-fidelity associations. Perhaps two of the most common objectives related to animal space-use are describing the home range [4] area and configuration and how animals selectively use spatially-explicit resources relative to their availability (i.e., resource selection functions (RSF); [2, 5]). RSFs provide insights into how landscape features affect animal behavior and habitat associations, and thus potentially limiting factors on population dynamics. Generally, animal spatial relationships provide critical information to land-use planners and conservation decision makers, making it vital that inferences are made correctly.
The need to understand animal spatial relationships has led to the increasing refinement and utility of telemetry devices [6]. Traditional telemetry data were solely collected using VHF (“very high frequency”) radio signals to track individual animals with radio tags; VHF radio-telemetry started around the mid-1960s and is still often employed. Location data are often collected by observers recording azimuths in the direction of the radio signal from known locations, but also by direct observation after walking up to a radio-tagged animal. The use of azimuths is attractive because it can reduce disturbance to the animal and also can reduce observer effort and thus increase the number of locations possible. Azimuths are often made using hand-held receivers, but also vehicle mounted receivers, or fixed towers [7]. A limitation of VHF telemetry is that there is a maximum distance to which animals can be detected, such that animals that leave the area may never be found, and large movements may be missed, thus possibly mischaracterizing the home range. This limitation can be alleviated by attaching VHF technology to a fixed wing aircraft and homing in on animal locations. However, the major limitation of VHF telemetry is that obtaining azimuths or locations requires considerable effort by the researcher, thus generally leading to limited spatial datasets. Modern telemetry technology used to track animals over large spatial areas and obtain extensive datasets is done by using Argos satellites, the global positioning system (GPS), or cell phone tower technology. While these newer forms of telemetry data can be beneficial, radio-telemetry devices are still relatively inexpensive. Radio technology also typically have low energy requirements, which allows for miniaturized and long-lasting devices to be fixed to small and volant animals for obtaining high spatial resolution data with minimal risk to incurring costs on survival and movement [8]. More so, digital VHF is quickly becoming an important way to monitor the movements of small-bodied species at regional scales [9]. This technology does not rely on directional signaling, but instead signals detected at radio towers.
It is well recognized that spatial locations from telemetry devices are not without error and estimation uncertainty [10, 11]. Observed locations contain measurement errors, or deviations between the recorded telemetry location and the true location of the animal. The magnitude of these deviations and the shape or structure of spatial location uncertainty is often specific to the type of telemetry technology [12] and the environmental conditions [7, 10, 13, 14]. Failing to account for location uncertainty can have pernicious impacts on spatial analyses of animal resource selection [15, 16], distribution [17], and movement modeling [2, 18, 19]. We are careful to distinguish between measurement error and location uncertainty. Location uncertainty is commonly referred to as error, which often implies additive and Gaussian uncertainty, neither of which are usually true for animal spatial analyses. While telemetry location uncertainty may sometimes be modeled as a multivariate Gaussian process [20], it is often much more complex [12]. In contrast, measurement error is explicitly the deviation between truth and the observed data, such as an azimuth or location.
Recent model developments focusing on satellite-based telemetry data (e.g., GPS, Argos) have highlighted the importance of appropriately characterizing location uncertainty using hierarchical modeling techniques to synthetically incorporate uncertainty into ecological process models (e.g., RSF: [21]; Movement analyses: [22, 23]). These developments have been in part to accommodate complex data structures due to the high density of location data that are obtained with these technologies, necessitating models that account for autocorrelation through movement processes. Similar developments that address the unique issues of azimuthal telemetry data do not exist. Since VHF telemetry data are mostly collected at coarse temporal scales with only a few locations per animal per day, the data structure is simpler and more likely meets the independence assumptions of commonly used ecological models. However, regardless of the quantity of data or type of telemetry technology, characterizing uncertainty is paramount for proper ecological inference and is flexibly handled by hierarchical modeling [2].
In fact, there have been few model developments to improve animal location estimation or uncertainty in the recent decades [24, 25]. Standard practice is to analyze azimuthal data using Lenth’s (1981) maximum likelihood estimator (MLE) or weighted MLE (M-estimators) to reduce the influence of outliers. The estimators are implemented in the software LOCATE [26] and LOAS (Ecological Software Solutions LLC, Sacramento, California). Spatial location estimates are then commonly used in a secondary ecological model, in which the location uncertainty is ignored and possibly unreported [15, 27, 28]. More so, location estimates may also be dropped due to estimation issues, thus a loss of information, or the magnitude of the uncertainty is used to define the scale of inference, rather than the ecological question [15, 27, 28]. These approaches raise several concerns.
Foremost is that these practices degrade ecological inference by disregarding uncertainty, censoring data, or altering the scale of inference. Second, uncertainty from Lenth’s MLE or M-estimators are commonly defined using confidence ellipses based on the assumption of asymptotic normality [7]. Assuming the uncertainty is strictly elliptical (e.g., multivariate Gaussian) may be overly restrictive and thus misrepresenting the true uncertainty. Empirical evidence indicates that 95% confidence ellipses of Lenth’s MLE or M-estimators cover the true location much less than 95% of the time (between 39% and 70%; [7]). There are also concerns raised by Lenth (1981) over the validity of the variance-covariance matrix of the M-estimators. Last, additional improvements could add flexibility in how researchers approach the design of radio-telemetry studies. For example, Lenth’s estimators cannot estimate locations when azimuths do not intersect, or estimate uncertainty when only two azimuths are collected. It is also possible for the estimator to fail with three or more azimuths, resulting in the use of a secondary estimator (i.e., a component-wise average of all azimuthal intersections) that has no measure of uncertainty or robust statistical properties.
Furthermore, it is well known that radio-signal direction can be influenced by many factors, including vegetation, terrain, animal movement, observer experience, and the distance between the observer and the animal [6, 7]. To accommodate these factors, standard practice has been to test observers taking azimuths on known locations of a radio-signal to experimentally quantify telemetry error. Observer error can then be applied to estimate location uncertainty via error polygons and confidence ellipses [28]. If field trials obtain data across known influencing factors, a model can be developed to incorporate variation in telemetry error for these conditions [29]. However, field trials will always be limited in their ability to anticipate all combinations of influential factors when collecting radio-telemetry data. Also, there are inconsistent recommendations in the literature regarding how best to estimate location uncertainty ([7]; i.e., Error polygons vs. Lenth’s confidence ellipses). We developed an approach that accommodates pre-existing data sources, where field trials may not be available; if these data are available, they can be incorporated.
We developed hierarchical azimuthal telemetry models (ATM) that estimate animal locations with uncertainty, which can be synthetically propagated into spatial ecological models. We first describe a novel Bayesian ATM, which models azimuthal uncertainty using covariates. Second, we evaluate the ATM and Lenth’s estimators under a variety of study designs; model development is motivated by a VHF telemetry study on the threatened Gunnison sage-grouse (Centrocercus minimus; [30]), which we use to setup the simulation and explore observer effects using the ATM. Third, we develop hierarchical spatial models for azimuthal data, including a home range and RSF analysis, which we fit to azimuthal data collected on the Gunnison sage-grouse; see Additional file 1 for species background information and study details. Last, we examine how ignoring location uncertainty can affect ecological inference through these empirical examples, but also more generally by conducting an RSF simulation.
Methods
Azimuthal telemetry model (ATM)
or perhaps include terrain complexity or habitat structure at observer locations to model radio-signal bounce and general site-level variability.
We fit the ATM using a Markov chain Monte Carlo (MCMC) algorithm written in R and C++ ([32]; see Additional file 3; an R package, ‘razimtuh’ can be downloaded at https://github.com/cppeck/razimuth). A specialized MCMC algorithm was preferred over using Bayesian model fitting software, such as JAGS (Just Another Gibbs Sample), to ensure computational efficiency and reliability for all sizes of data. First, we fit simulated data to examine a wide range of conditions, including one or more intersecting or non-interesting azimuths. Second, using the Gunnison sage-grouse telemetry data from two observers, we fit the ATM (Eqs. 1 and 2) to investigate possible group-level differences in κ between observers and variation within observers.
Radio-telemetry simulation
We evaluated the performance of the ATM and Lenth’s MLE and M-estimators (Andrews and Huber) along with a simple component-wise average of intersections. We did so by simulating known location data under two common radio-telemetry study designs (road and encircle) and a more variable approach (random). Under the random design, each observer location was defined by a random azimuth from the true animal location sampled uniformly from −π to π and the distance was sampled randomly from the empirical distances estimated from the Gunnison sage-grouse data (Additional file 2: Figure S2). Under the encircle design, the initial observer location is sampled the same as the random design, but subsequent observer locations are sampled uniformly from 30−60° from the previous observer location and true animal location; each observer distance is also randomly sampled from the sage-grouse distance distribution. In effect, this places observers such that they encircle the animal location. Last, the road design constrains the observer locations to a linear feature, thus limiting the angular differences among azimuths. For each design, we considered scenarios of 3 or 4 azimuths per location and moderate and high azimuth uncertainty (κ = 100 or 25, respectively). Simulation algorithms are provided in Additional file 3 and R code in Additional file 4. The ATM, assuming a homogeneous κ, was fit using MCMC and posterior properties were based on 50,000 iterations. Lenth’s MLE and M-estimators were fit using Lenth’s original algorithms [24]. Lenth’s MLE was also fit using the R package ‘sigloc’ [33]. sigloc is the only R package we are aware of that estimates Lenth’s MLE, but it does not use the algorithm suggested by Lenth (1981), but rather a quasi-Newton optimization algorithm which Lenth (1981) suggested avoiding.
Spatial models for azimuthal data
Home range
evaluated at locations of interest c≡(c_{1},c_{2})^{′}, choice of kernel function g (·), and bandwidth parameters b_{1} and b_{2} (which we constrain as b_{1}=b_{2}). The result is a posterior distribution of the 95% home range isopleth, which could be used to further derive a posterior distribution of the home range area, thus fully incorporating all uncertainties in our estimate. We fit the ATM and derived a convex hull and kernel density home range for six individual Gunnison sage-grouse for different seasons (breeding and summer) across all years of available data (2005-2010). We compared these results with home range estimates using estimated locations from Lenth’s MLE, thus ignoring location uncertainty.
Resource selection analysis
We fit the ATM-RSF model to the same individual Gunnison sage-grouse from the home-range analysis using data from the summer months (16 July to 30 September, from 2005 to 2009). We use these individuals as exemplars to compare estimated regression coefficients from the ATM-RSF with estimates from the same RSF, but we assumed location estimates from Lenth’s MLE are known without uncertainty. We include six common spatial variables to model resource selection of the Gunnison sage-grouse (Additional file 1; [30]): road density, distance to highway, distance to wetlands, distance to conservation easements, elevation, and vegetation classification (i.e., grassland, agriculture). In addition to including both categorical and continuous spatial covariates, the variables include a highly variable topographic variable (i.e., elevation) and more smoothly continuous measures of distance to features. The structure of each type and how variable values are from neighboring locations could differently impact RSF inference by the scale and shape of animal location uncertainties [36].
We assumed uniform spatial availability (f_{A}(·)) for an individual animal in two ways: 1) by defining a large study area region and 2) by using the convex hull of all locations (μ_{li}). The first focuses on a first-order selection process within the broader landscape and the second focuses on the second-order selection process within an individual’s area of use [37]. In addition to producing fundamentally different inference for resource selection, the location uncertainty affects each process differently. For the study area region, resource selection is subject to only location uncertainty, whereas for convex hull availability for an individual, resource selection is subject to both location and availability uncertainty.
For a more general understanding, we conducted a simulation to explore the connection among location uncertainty, covariate spatial heterogeneity, and ecological inference in RSF analyses. Previous work has demonstrated that the size of telemetry error and the resolution and heterogeneity of spatial covariates can affect the quality of ecological inference from RSFs [36]; we further this understanding by examining how varying levels of spatial autocorrelation of a continuous and categorical covariate at different sample sizes and spatial resolution affects RSF coefficients when incorporating and ignoring location uncertainty, compared to knowing the true locations. Specifically, we simulated animal location data (N_{locations}= 50, 200) that coincide with covariate values of low, moderate, and high spatial autocorrelation, defined using a Gaussian random field (covariates at 25 m or 100 m resolution; Additional file 5). Observations were three azimuths per location, simulated under a random design (Additional file 3), with moderate azimuthal uncertainty (κ= 50). We fit these data with 1) the ATM-RSF, and 2) a typical RSF model that used location estimates from Lenth’s (1981) MLE, ignoring location uncertainty. We compared coefficient estimates from these approaches across simulations with that of fitting an RSF where the true locations are known, providing a reference to the best case scenario for these data.
Results
ATM
Radio-telemetry simulation
Simulation findings comparing the azimuthal telemetry model (ATM) with the average of the component-wise azimuth intersections (simple) and Lenth (1981) maximum likelihood estimator (Lenth, sigloc) and M-estimators (Andrews, Huber)
κ=100 | κ=25 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Simple | sigloc | Lenth | Huber | Andrews | ATM | Simple | sigloc | Lenth | Huber | Andrews | ATM | ||
Encircle design comparison: | |||||||||||||
n_{θ}=3 | \(n_{\hat {\boldsymbol {\mu }}}\) | 600 | 597 | 600 | 600 | 600 | 600 | 600 | 581 | 598 | 600 | 600 | 600 |
d_{0.5} (m) | 22.4 | 20.8 | 20.5 | 20.4 | 20.4 | 21.0 | 45.3 | 43.6 | 42.7 | 42.8 | 43.5 | 42.8 | |
Coverage | – | 0.430 | 0.432 | 0.432 | 0.433 | 0.888 | – | 0.422 | 0.425 | 0.423 | 0.435 | 0.858 | |
n_{θ}=4 | \(n_{\hat {\boldsymbol {\mu }}}\) | 600 | 539 | 600 | 600 | 600 | 600 | 600 | 470 | 592 | 595 | 599 | 600 |
d_{0.5} (m) | 9.9 | 9.3 | 8.7 | 8.7 | 8.8 | 8.7 | 19.2 | 19.6 | 17.5 | 17.6 | 17.4 | 17.5 | |
Coverage | – | 0.575 | 0.592 | 0.585 | 0.592 | 0.923 | – | 0.553 | 0.542 | 0.538 | 0.541 | 0.917 | |
Random design comparison: | |||||||||||||
n_{θ}=3 | \(n_{\hat {\boldsymbol {\mu }}}\) | 600 | 533 | 595 | 593 | 593 | 600 | 600 | 439 | 564 | 561 | 566 | 600 |
d_{0.5} (m) | 32.6 | 32.2 | 25.1 | 25.1 | 25.3 | 25.0 | 62.9 | 75.1 | 54.2 | 53.4 | 53.7 | 55.6 | |
Coverage | – | 0.403 | 0.418 | 0.417 | 0.417 | 0.883 | – | 0.328 | 0.348 | 0.348 | 0.352 | 0.850 | |
n_{θ}=4 | \(n_{\hat {\boldsymbol {\mu }}}\) | 600 | 454 | 594 | 594 | 598 | 600 | 600 | 367 | 573 | 573 | 579 | 600 |
d_{0.5} (m) | 14.2 | 13.0 | 9.9 | 10.0 | 9.9 | 10.0 | 25.3 | 34.0 | 19.5 | 19.6 | 20.0 | 20.3 | |
Coverage | – | 0.559 | 0.581 | 0.567 | 0.572 | 0.920 | – | 0.526 | 0.560 | 0.550 | 0.556 | 0.912 | |
Road design comparison: | |||||||||||||
n_{θ}=3 | \(n_{\hat {\boldsymbol {\mu }}}\) | 600 | 499 | 593 | 593 | 597 | 600 | 600 | 409 | 573 | 571 | 576 | 600 |
d_{0.5} (m) | 56.7 | 44.4 | 39.0 | 39.0 | 38.5 | 40.5 | 95.5 | 110.4 | 85.1 | 84.6 | 83.9 | 86.4 | |
Coverage | – | 0.397 | 0.418 | 0.418 | 0.412 | 0.877 | – | 0.296 | 0.316 | 0.310 | 0.312 | 0.822 | |
n_{θ}=4 | \(n_{\hat {\boldsymbol {\mu }}}\) | 600 | 443 | 600 | 600 | 600 | 600 | 600 | 316 | 592 | 593 | 595 | 600 |
d_{0.5} (m) | 53.8 | 33.4 | 26.9 | 27.7 | 28.1 | 26.5 | 90.3 | 83.5 | 54.6 | 54.8 | 55.2 | 55.8 | |
Coverage | – | 0.580 | 0.618 | 0.595 | 0.588 | 0.923 | – | 0.487 | 0.561 | 0.543 | 0.545 | 0.883 |
Spatial models for azimuthal data
Discussion
Our model developments have important implications for interpreting historical radio-telemetry data analyses and to study designs for future research projects. While state-of-the-art tracking technologies (e.g., GPS) are increasingly used, animal telemetry via VHF radio is still widely used and will likely continue due to its lower cost and miniaturization [8]. The development of the ATM addresses several complicating factors when dealing with azimuthal data. Foremost is that our model appropriately characterizes azimuthal telemetry uncertainty and allows the uncertainty to synthetically be propagated into spatial models. Appropriately accounting for uncertainties in ecological inference is needed to ensure appropriate inference ([21, 38]; Figs. 3, 4, and 6). The ATM illustrates that the magnitude and shape of location uncertainty from azimuthal telemetry data is complex and highly variable. Previous methods have led to over confidence in the precision of animal locations, the certainty in resource selection, and the size of home ranges.
A current condition of the ATM is that the researcher is required to set a maximum distance in which an animal may be reliably detected. However, alternative prior specifications (e.g., multivariate Gaussian) can be used, but the computational benefits of the Uniform prior imply that posterior distributions are more quickly and fully explored, thus facilitating algorithm convergence. To set the maximum distance, we suggest knowledge of the study area and experience of the researcher should be employed, because the distance will largely depend on the terrain complexity and the behavior of the animal. Field trials can be conducted as part of the study, where a transmitter is placed in known locations and observers attempt to detect the radio signal at increasing distances. Field trials could even be conducted jointly while sampling animals, without the knowledge of the observer, thereby efficiently collecting data on known locations to be used as information for modeling. It should be clear though, the prior has limited influence when typical radio-telemetry data are collected, such that three or more azimuths are taken in a way that they all intersect. The prior will be more important with only 1-2 azimuths and more so if the two azimuths do not intersect. In these cases, the researcher should consider the absolute maximum distance the animal could likely be from the observer, given the surrounding terrain complexity. The maximum distance may likely be different for every location an azimuth is taken. For example, this distance will be quite different if locating a ring-tailed cat (Bassariscus astutus) in a desert canyon or flat. The location uncertainty will also depend on how κ is being modeled. Because one azimuth provides very little information for estimating κ, sharing information about κ across spatial locations will help determine how narrow or wide the uncertainty should be around the single azimuth.
Modeling κ is a major benefit of the ATM, because it overcomes the issue of limited experimental field trials by allowing telemetry uncertainty to be directly modeled, therefore accounting for telemetry uncertainty in location estimates. Researchers may allow for heterogeneity in κ across multi-dimensions, such as across observers, individual animals, spatial or temporal regions, or specific spatial covariates. If the goal is to minimize location uncertainty, we found that it is prudent to encircle the animal, as well as obtain more than three azimuths (Fig. 1d, Table 1, Additional file 2: Figure S3). However, the optimal study design will ultimately depend on the questions being considered (e.g., home range vs. RSF study); researchers can pair the ATM with spatial models to identify optimal study designs that minimize logistical costs and maximizing model performance, something that was not previously possible.
Throughout, we have considered situations where an animal is at a specified location, and our goal is to estimate the animal location via azimuths from known observer locations. Of course animals do not always stay in one place for long, and thus it is important to consider the total amount of time it takes to get the first and last azimuth. Ideally, the amount of time will be short, but this time depends entirely on the species being studied and the season and time of day. If an animal does move during the time period azimuths are taken, it is likely several azimuths will poorly intersect each other, such that the location uncertainty will be fairly large, which is appropriate. A future extension of the ATM could incorporate an animal movement process linked to the amount of time taken in between azimuths, thus properly accounting for this issue. Researchers should be especially concerned of potential bias due to animal movement in situations when only two azimuths are taken and a long time has elapsed between them. Movement is of less concern with only one azimuth and many azimuths will likely help determine whether an animal is moving.
Another concern in radio-telemetry is the issue of signal bounce, in which the radio signal bounces off geographic features, obscuring the direction to the animal. The ATM could be used to model this effect by including terrain complexity as a covariate for κ, as long as these azimuths were included as data. It is common to exclude azimuths that may be due to signal bounce. An alternative approach would be to extend the ATM akin to the M-estimators proposed by Length (1981) to identify and remove outliers.
We found the affects of location uncertainty on ecological inference are not straightforward. Our RSF investigation demonstrated how the affect of location uncertainty on parameter estimates depends on the definition of availability [39], whether covariates were categorical or continuous, and the degree of spatial autocorrelation in the covariate. Our simulation clarified that incorporating location uncertainty helps reduce bias in RSF coefficients across all levels of covariate spatial autocorrelation. Previous RSF studies that used azimuthal data and ignored the location uncertainty should be viewed cautiously. Furthermore, our home range results suggest that previous studies that ignored location uncertainty could have been conservative in their estimate of home range areas; ignoring location uncertainty can strongly affect the shape and size of home range estimates.
The ATM may be useful beyond the contexts we have considered. For example, the ATM may be applied to directional frequency analysis and recording sonobuoys of recorded azimuths to whale vocalizations or use azimuths to estimate buoy drift [40]. Locating animals by vocalization direction in a spatial-capture recapture framework may also be a potential utility of the ATM [41]. More generally, the ATM may be useful for acoustic vector sensor data to identify the location of noise sources [42].
Conclusion
Methodology using azimuthal data has received much less attention than satellite-based telemetry technologies, despite it being a common source of data for small and volant wild animals. More so, it was the sole type of spatial data for wildlife telemetry studies for many decades. We found previous methods using azimuthal data likely led to poor inference, due to disregarding data and ignoring location uncertainty. Specifically, RSF coefficients could be biased and home ranges overly conservative. We also found location estimation and uncertainty is improved using the ATM framework, which can be used to model location uncertainty and has not been possible previously. Most importantly, the ATM can be integrated with spatial ecological models to account for location uncertainty and thus reduce potential biases. Furthermore, the ATM provides considerable flexibility in the design of radio-telemetry studies because it can estimate animal locations from any number of intersecting or non-intersecting azimuths. Future radio-telemetry studies should use the ATM to consider design tradeoffs in an optimal design framework.
Declarations
Acknowledgments
Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. The findings and conclusions of the U.S. Fish and Wildlife Service employees in this article are their own and do not necessarily represent the views of the U.S. Fish and Wildlife Service. M. L. Phillips led the Gunnison sage-grouse field data collection effort. We are grateful for the reviews by B. Sandercock and an anonymous reviewer.
Funding
Funding was provided by CPW 1701 and NSF DMS 1614392 awards.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request. All data generated or analysed during this study are included in this published article [and its supplementary information files].
Authors’ contributions
BDG, MBH, CPP, MBR, JHG, ADA, and AJD conceived ideas for this manuscript. BDG, MBH, and CPP designed the statistical framework and fit the data. BDG led the writing. All authors contributed to critical editing of previous drafts and gave final approval for publication.
Ethics approval and consent to participate
Trapping and handling protocols were approved by the Colorado Parks and Wildlife Animal Care and Use Committee (permit number 02-2005).
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
- Kernohan BJ, Gitzen RA, Millspaugh JJ. Analysis of animal space use and movements In: Millspaugh J, Marzluff JM, editors. Radio tracking and animal populations. San Diego: Academic Press: 2001. p. 125–66.Google Scholar
- Hooten MB, Johnson DS, McClintock BT, Morales J. Animal Movement: Statistical Models for Telemetry Data.Boca Raton: Chapman & Hall/CRC; 2017.View ArticleGoogle Scholar
- Hutchinson GE. Concluding remarks. Cold Spring Harb Symp Quant Biol. 1957; 22:415–27.View ArticleGoogle Scholar
- Burt WH. Territoriality and home range concepts as applied to mammals. J Mammal. 1943; 24:346–52.View ArticleGoogle Scholar
- Manly BFL, McDonald L, Thomas D, McDonald TL, Erickson WP. Resource Selection by Animals: Statistical Design and Analysis for Field Studies.London: Kluwer Press; 2002.Google Scholar
- Millspaugh J, Marzluff JM. Radio Tracking and Animal Populations.San Diego: Academic Press; 2001.View ArticleGoogle Scholar
- White GC, Garrott RA. Analysis of Wildlife Radio-Tracking Data.San Diego: Elsevier; 1990.Google Scholar
- Ponchon A, Gremillet D, Doligez B, Chambert T, Tveraa T, Gonzàlez-Solìs J, Boulinier T. Tracking prospecting movements involved in breeding habitat selection: insights, pitfalls and perspectives. Methods Ecol Evol. 2013; 4:143–50.View ArticleGoogle Scholar
- Loring PH, Griffin CR, Sievert PR, Spiegel CS. Comparing satellite and digital radio telemetry to estimate space and habitat use of American Oystercatchers (Haematopus palliatus) in Massachusetts, USA. Waterbirds. 2017; 40:19–31.View ArticleGoogle Scholar
- Frair JL, Nielsen SE, Merrill EH, Lele SR, Boyce MS, Munro RH, Stenhouse GB, Beyer HL. Removing GPS collar bias in habitat selection studies. J Appl Eco. 2004; 41:201–12.View ArticleGoogle Scholar
- Patterson TA, Thomas L, Wilcox C, Ovaskainen O, Matthiopoulos J. State-space models of individual animal movement. Trends Ecol Evol. 2008; 23:87–94.View ArticlePubMedGoogle Scholar
- Costa DP, Robinson PW, Arnould JP, Harrison AL, Simmons SE, Hassrick JL, et al.Accuracy of ARGOS locations of pinnipeds at-sea estimated using Fastloc GPS. PloS ONE. 2010; 5:e8677.View ArticlePubMedPubMed CentralGoogle Scholar
- Gantz GF, Stoddart LC, Knowlton FF. Accuracy of aerial telemetry locations in mountainous terrain. J Wildl Manag. 2006; 70:1809–12.View ArticleGoogle Scholar
- Rettie WJ, McLoughlin PD. Overcoming radiotelemetry bias in habitat-selection studies. Can J Zool. 1999; 77(8):1175–84.View ArticleGoogle Scholar
- Montgomery RA, Roloff GJ, Ver Hoef JM, Millspaugh JJ. Can we accurately characterize wildlife resource use when telemetry data are imprecise?J Wildl Manag. 2010; 74:1917–25.View ArticleGoogle Scholar
- Moorehouse AT, Boyce MS. Deviance from truth: Telemetry location errors erode both precision and accuracy of habitat-selection models. Wildl Soc Bull. 2013; 37:596–602.Google Scholar
- Hefley TJ, Baasch DM, Tyre AJ, Blankenship EE. Correction of location errors for presence-only species distribution models. Methods Ecol Evol. 2014; 5:207–14.View ArticleGoogle Scholar
- Jerde CL, Visscher DR. GPS measurement error influences on movement model parameterization. Ecol Appl. 2005; 15:806–10.View ArticleGoogle Scholar
- Jonsen ID, Flemming JM, Myers RA. Robust state-space modeling of animal movement data. Ecology. 2005; 86:2874–80.View ArticleGoogle Scholar
- Johnson DS, London JM, Lea MA, Durban JW. Continuous-time random walk model for animal telemetry data. Ecology. 2008; 89:1208–15.View ArticlePubMedGoogle Scholar
- Brost BM, Hooten MB, Hanks EM, Small RJ. Animal movement constraints improve resource selection inference in the presence of telemetry error. Ecology. 2015; 96:2590–7.View ArticlePubMedGoogle Scholar
- Buderman FE, Hooten MB, Ivan JS, Shenk TM. A functional model for characterizing long-distance movement behaviour. Methods Ecol Evol. 2016; 7:264–73.View ArticleGoogle Scholar
- McClintock BT, London JM, Cameron MF, Boveng PL. Modelling animal movement using the Argos satellite telemetry location error ellipse. Methods Ecol Evol. 2015; 6:266–77.View ArticleGoogle Scholar
- Lenth RV. On finding the source of a signal. Technometrics. 1981; 23:149–54.View ArticleGoogle Scholar
- Guttorp P, Lockhart RA. Finding the location of a signal: A Bayesian analysis. J Am Stat Assoc. 1988; 83:322–30.View ArticleGoogle Scholar
- Nams VO. Locate II: User’s guide.Truro: Pacer; 2000.Google Scholar
- Saltz D. Reporting error measures in radio location by triangulation: a review. J Wildl Manag. 1994; 58:181–4.View ArticleGoogle Scholar
- Withey JC, Bloxton TD, Marzluff JM. Effects of tagging and location error in wildlife radiotelemetry studies In: Millspaugh J, Marzluff JM, editors. Radio tracking and animal populations. Academic Press: 2001. p. 43–75.Google Scholar
- Pace III RM, Weeks Jr HP. A nonlinear weighted least-squares estimator for radiotracking via triangulation. J Wildl Manag. 1990; 5:304–10.Google Scholar
- Rice M, Apa AD, Wiechman L. The importance of seasonal resource selection when managing a threatened species: targeting conservation actions within critical habitat designations for the Gunnison sage-grouse. Wildl Res. 2017; 44:407–17.View ArticleGoogle Scholar
- Mardia KV, Jupp PE. Directional Statistics.Chichester: Wiley; 1972.Google Scholar
- R Development Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2017. http://www.r-project.org/.Google Scholar
- Sergey S. Berg. sigloc: Signal Location Estimation. R Package version 0.0.4. 2014.Google Scholar
- Laver PN, Kelly MJ. A critical review of home range studies. J Wildl Manag. 2008; 72:290–8.View ArticleGoogle Scholar
- Hooten MB, Buderman FE, Brost BM, Hanks EM, Ivan JS. Hierarchical animal movement models for population-level inference. Environmetrics. 2016; 27:322–33.View ArticleGoogle Scholar
- Montgomery RA, Roloff GJ, Hoef JMV. Implications of ignoring telemetry error on inference in wildlife resource use models. J Wildl Manag. 2011; 75:702–8.View ArticleGoogle Scholar
- Johnson DH. The comparison of usage and availability measurements for evaluating resource preference. Ecology. 1980; 61:65–71.View ArticleGoogle Scholar
- Hobbs NT, Hooten MB. Bayesian models: a statistical primer for ecologists.Princeton University Press; 2015.Google Scholar
- Hooten MB, Hanks EM, Johnson DS, Alldredge MW. Reconciling resource utilization and resource selection functions. J Anim Ecol. 82:1146–54.Google Scholar
- Miller BS, Wotherspoon S, Rankin S, Calderan S, Leaper R, Keating JL. Estimating drift of directional sonobuoys from acoustic bearings. J Acoust Soc Am. 2018; 143(1):EL25–EL30.View ArticlePubMedGoogle Scholar
- Kidney D, Rawson BM, Borchers DL, Stevenson BC, Marques TA, Thomas L. An efficient acoustic density estimation method with human detectors applied to gibbons in Cambodia. PloS one. 2016; 11(5):e0155066.View ArticlePubMedPubMed CentralGoogle Scholar
- Haege M. Acoustic vector sensors: Principles, applications, and practical experience. J Acoust Soc Am. 2015; 138(3):1767–1767.View ArticleGoogle Scholar