Resolving issues of imprecise and habitat-biased locations in ecological analyses using GPS telemetry data

Abstract

Global positioning system (GPS) technologies collect unprecedented volumes of animal location data, providing ever greater insight into animal behaviour. Despite a certain degree of inherent imprecision and bias in GPS locations, little synthesis regarding the predominant causes of these errors, their implications for ecological analysis or solutions exists. Terrestrial deployments report 37 per cent or less non-random data loss and location precision 30 m or less on average, with canopy closure having the predominant effect, and animal behaviour interacting with local habitat conditions to affect errors in unpredictable ways. Home-range estimates appear generally robust to contemporary levels of location imprecision and bias, whereas movement paths and inferences of habitat selection may readily become misleading. There is a critical need for greater understanding of the additive or compounding effects of location imprecision, fix-rate bias, and, in the case of resource selection, map error on ecological insights. Technological advances will help, but at present analysts have a suite of ad hoc statistical corrections and modelling approaches available—tools that vary greatly in analytical complexity and utility. The success of these solutions depends critically on understanding the error-inducing mechanisms, and the biggest gap in our current understanding involves species-specific behavioural effects on GPS performance.

1. Introduction

Radio-collars and other platforms equipped with global positioning systems (GPS) document animal activity under cloak of darkness and inclement weather conditions, providing a continuous record of animal locations that remains unobtainable using traditional technologies such as very high-frequency (VHF) devices (White & Garrott 1990; Beyer & Haufler 1994; Rogers et al. 1996; Tomkiewicz et al. 2010). The systematic and frequent recording of animal locations by on-board GPS units facilitates greater resolution in the study of habitat selection (Johnson et al. 2002b; Boyce et al. 2003), deeper insight into animal movements (Morales et al. 2004; Frair et al. 2005; Fryxell et al. 2008), and novel investigations into animal behaviour (e.g. Anderson & Lindzey 2003; Merrill et al. 2010). Although GPS applications have transformed contemporary wildlife studies (Hebblewhite & Haydon 2010), the technology comes with its problems. High up-front unit costs, rare but catastrophic equipment failures (i.e. computer glitches or failed breakaway devices), and trade-offs between GPS location collection intervals and unit longevity lead generally to fewer monitored individuals and shorter study durations compared with VHF-based studies (Johnson et al. 2002a; Gau et al. 2004; Hebblewhite et al. 2007). Moreover, decreasing the interval between recorded locations increases the level of autocorrelation in the resulting data. As a result, analysts of GPS telemetry data face even greater challenges for deriving population-level inferences (Lindberg & Walker 2007; Fieberg et al. 2010).

Fundamentally, instruments imply measurement errors (Cagnacci et al. 2010). Problems inherent to both VHF and GPS devices are spatial imprecision and potential biases in the locations acquired. The accuracy of GPS locations do not typically include a directional bias (Moen et al. 1996; Sager-Fradkin et al. 2007), but are subject to variability in precision measured as the distribution of differences between the true (central) location and GPS-estimated locations. Therefore, we use ‘precision’ or ‘measurement error’ rather than ‘accuracy’ when addressing the distribution of spatial error in GPS locations. Precision on the order of 200–600 m has been reported for locations of VHF devices acquired via triangulation and homing (White & Garrott 1986; Marzluff et al. 1994; Zimmerman & Powell 1995). In contrast, measurement errors of 100 m or less were reported for early model GPS collars between their first deployment in the mid-1990s and the removal of selective availability in 2000 (Rempel et al. 1995; Rogers et al. 1996), after which time a precision of 10–28 m has consistently been observed (D'Eon et al. 2002; Cain et al. 2005; Hansen & Riggs 2008). Nevertheless, large measurement errors (up to several km) intermittently occur even with contemporary GPS devices (e.g. Villepique et al. 2008), which complicate analyses using these data. Moreover, with GPS devices, biases occur when locations are more likely to be obtained under certain environmental conditions. Failed locations are not unique to GPS devices, with inclement weather, darkness and poor access to areas reducing our ability to detect VHF devices (White & Garrott 1990; Keating et al. 1991; Moen et al. 1996; North & Reynolds 1996). Such conditions are generally study specific and difficult to quantify in VHF-based studies. In contrast, local habitat conditions predictably influence the ability of GPS devices to acquire satellite signals, thus systematically biasing the set of locations acquired but also making it possible to quantify the biasing mechanism so as to employ statistical corrections (D'Eon 2003; Frair et al. 2004). For clarity, we reserve the term ‘bias’ for the bias in acquiring a GPS location rather than as a component of spatial error in the locations acquired. We refer to bias and measurement error collectively as ‘GPS errors’.

GPS technology poses unique opportunities for wildlife studies, but proper statistical inference requires attention be paid to the inherently autocorrelated, spatially imprecise and habitat-biased locations acquired by current systems (but see the emerging technologies in Tomkiewicz et al. 2010). Fieberg et al. (2010) focus exclusively on the implications of correlated data and review contemporary solutions. Herein, we review the magnitude and source of contemporary GPS errors; consider the implications of these errors in studies of animal resource selection, movements and home range; and summarize the toolbox of solutions available to data analysts. Lastly, we chart ongoing needs for research on GPS errors in animal ecology. Note that we limit this review to studies employing devices reliant on the NAVSTAR GPS satellite system and deployed mainly on terrestrial species (Rodgers et al. 1996), because the range of systems (e.g. Loran, Argos) and their inherent errors are too great to succinctly summarize here. Nevertheless, the analytical issues and solutions discussed are generally adaptable to these other systems as well.

2. Types, magnitude and causes of gps errors

Problems associated with animal-borne GPS devices have been elucidated using three primary methods: stationary tests, controlled mobile tests and returns from free-ranging animals. With stationary tests, devices are typically affixed 0.5–1.5 m above ground to simulate the neck height of standing animals, or placed on the ground (with collar designs placed upright or on their sides) to simulate bedded animals. These devices attempt to acquire locations (or ‘fixes’) at a pre-determined temporal interval (usually every 5 min to 2 h) and are left in place for a given period of time (usually 24 h or more). The number of successful fixes (stored locations) divided by the number attempted yields the fix rate, and the precision of locations is quantified as the average distance between each estimated location and the ‘true’ location of the device (the latter determined using fixed geodetic markers, differential-correction or a large-sample average). For optimal performance, tests should deploy GPS devices on a medium that mimics the ground-plane of an animals' body (e.g. balloon filled with saline solution). Stationary tests are particularly useful because they remove vagaries arising when devices are deployed on animals, can be replicated across a range of spatial and temporal variation, and are readily comparable among study sites and time periods. By contrast, mobile device tests affix a GPS device to a human, vehicle or tame animal generally moving at a speed of approximately 3–10 kph, with ‘true’ locations estimated by following the moving device with a hand-held unit. Such studies provide unique insights into motion effects on GPS performance, but are less comparable across species, study sites and time periods, and represent a limited range of behaviour and ecological conditions compared with free-ranging animals. Finally, returns from free-ranging animals yield fix rates and some information on location precision (e.g. proportion of locations in the more precise ‘three-dimensional’ mode), but the conditions causing GPS errors cannot be directly assessed unless animals are also physically observed by researchers (see Heard et al. 2008). Free-ranging animal returns are least comparable among species, study areas and time periods, but nonetheless provide information critical to understanding animal behaviour and refining controlled tests.

We know from stationary tests that canopy closure (Moen et al. 1996; D'Eon et al. 2002; Frair et al. 2004; Cargnelutti et al. 2007; Hebblewhite et al. 2007; Sager-Fradkin et al. 2007; Heard et al. 2008), topographic complexity (D'Eon et al. 2002; Frair et al. 2004; Cain et al. 2005; Hebblewhite et al. 2007), device orientation (Moen et al. 1996; D'Eon & Delparte 2005; Sager-Fradkin et al. 2007; Heard et al. 2008; Jiang et al. 2008), scheduled fix interval (Cain et al. 2005) and device make/model (Frair et al. 2004; Hebblewhite et al. 2007) consistently influence both fix rate and location precision (table 1). Less consistently, researchers have observed diurnal (Sager-Fradkin et al. 2007, but see Graves & Waller 2006), seasonal (Sager-Fradkin et al. 2007) and tree height or density effects (Rempel et al. 1995; Rumble & Lindzey 1997; Dussault et al. 1999). The effects of canopy closure on GPS errors remain predominant, reducing fix rates up to 37 per cent and location precision by 12–17 m on average (table 1). Canopy closure may interact with local terrain complexity resulting in even greater errors (D'Eon et al. 2002; Frair et al. 2004; Hebblewhite et al. 2007; Hansen & Riggs 2008). Excluding canopy effects, terrain complexity alone may result in an 8 per cent or less reduction in fix rates and 10–13 m measurement error on average (D'Eon et al. 2002; Cain et al. 2005). Collar orientation alone tends to have a negligible effect on GPS errors in open areas, but can reduce fix rates up to 80 per cent and location precision as much as 17 m under dense canopy cover (Heard et al. 2008; Jiang et al. 2008). Cain et al. (2005) observed that reducing the frequency with which locations were collected, from every 15–30 min to every 6–13 h, reduced fix rates up to 8 per cent without affecting location precision. Finally, GPS hardware and software varies among manufacturers and manufacturing cycles, with earlier models, e.g. Lotek GPS1000, exhibiting 10–30% data loss and 60 m measurement error on average across various canopy and terrain conditions (Rempel et al. 1995; Moen et al. 1996; Dussault et al. 2001). Contemporary models (Lotek 2200 and 3300, Televilt Simplex, ATS, Telonics) exhibit data losses from 1 to 24 per cent and measurement errors less than 28 m on average (table 1).

Table 1.

Summary of GPS fix rates and measurement errors reported by stationary tests of wildlife monitoring devices in terrestrial environments. Reported values are the range of mean values reported across the studies indicated.

	effects on
variable	fix rate reduction (%)	measurement error (m)
canopy closurea,b
0–40%	1–10c,d,e,f,g,h,i,j,k	7–13c,e,h
41–70%	1–25c,d,e,f,g,h,i,k	16c,e
>70%	2–37c,d,e,f,g,h,i,j,k	19–30c,e,h
topography (available sky)l,m
>60% AS	0–1c,n	0–5c,n
30–60% AS	1–2c,n	5–7c,n
<30% AS	4–8c,n	10–13c,n
collar orientation
0–45°	0–6o,g	3–6o
90° (above ground)	1–16o,i	10o
90° (on ground)l	16–80d,g
135–180°	12–24o	17o,p
fix interval
0.5 h	1n	no effectn
1 h	3n
4 h	6n
6+ h	8n
collar brand, modelq
Lotek 1000	10–30i,r,s	60s
Lotek 2200L	4–14e,j	13e
Lotek 3300	1–7e,h,j,k,p	14–28e,h,k,p
Televilt Simplex	6–24j,d,g
ATS	3–5c,j	11c,o
Telonics (3580)	4n	10n

^aEffects observed to vary with collar brand and model (Frair et al. 2004; Hansen & Riggs 2008).

^bEffects observed to vary with terrain complexity (Sager-Fradkin et al. 2007).

^cD'Eon et al. (2002).

^dSager-Fradkin et al. (2007).

^eHansen & Riggs (2008).

^fFrair et al. (2004).

^gHeard et al. (2008).

^hCargnelutti et al. (2007).

ⁱMoen et al. (1996).

^jHebblewhite et al. (2007).

^kLewis et al. (2007).

^lEffects observed to vary with canopy closure (Jiang et al. 2008; Sager-Fradkin et al. 2007; Heard et al. 2008).

^mOther terrain variables influencing collar errors include topographic position (Hebblewhite et al. 2007), aspect (Hebblewhite et al. 2007) and per cent slope (Frair et al. 2004; Hebblewhite et al. 2007).

ⁿCain et al. (2005).

^oD'Eon & Delparte (2005).

^pJiang et al. (2008).

^qAveraged across canopy cover and terrain conditions.

^rDussault et al. (1999).

^sRempel et al. (1995).

Stationary tests have also been used to explore the effects of satellite number and configuration on location precision. With each acquired location, GPS devices store additional information on the number of satellites used in the location solution, and an index to satellite geometry based on a dilution of precision (DOP) metric. Lower DOP values indicate wider satellite spacing, and tests reveal a general, albeit noisy, trend of decreasing spatial precision with increasing DOP values (Moen et al. 1996; Lewis et al. 2007) Along with DOP, GPS devices record whether the solution is in two-dimensional (based on three satellites) versus three-dimensional mode (based on four or more satellites, which includes a correction based on device elevation). On average, two-dimensional locations exhibit less precision (≤ 36 m) than three-dimensional locations (≤ 12 m; Moen et al. 1996; D'Eon et al. 2002; Graves & Waller 2006; Lewis et al. 2007; Sager-Fradkin et al. 2007; Jiang et al. 2008), and researchers recommend separate consideration of these two classes of data when choosing to censor locations, as we shall consider in depth later. In addition to biasing whether a location is collected or not, canopy closure and terrain ruggedness explained 52–71% of the variation in mean measurement error, proportion of locations collected in a three-dimensional mode, and mean DOP values in stationary device tests (Lewis et al. 2007), with canopy closure having the greatest explanatory power.

Controlled mobile tests are rare, and their results less consistent than stationary tests, nonetheless their insights into the effects of animal behaviour and mobility on GPS performance are compelling. Bowman et al. (2000) observed that fix rates were reduced by up to 20 per cent when captive white-tailed deer (Odocoileus virginianus) were bedded compared to when they were standing or moving. Observations of captive moose (Alces alces) and white-tailed deer indicated no significant differences in either fix rate or location precision when animals were moving compared to when the animals remained stationary (Moen et al. 1996; Bowman et al. 2000); however, both of these studies were conducted using older model GPS devices that had lower baseline precision and fix rates compared with contemporary models (but see back-pack trial of Edenius 1997). More recently, Cargnelutti et al. (2007) fitted an English setter with a GPS collar and observed lower fix rates but no differences in location precision when the animal was moving compared with stationary tests. An interaction between movement and forest cover was observed by Jiang et al. (2008) using devices affixed to a vehicle moving approximately 10 kph. Jiang et al. (2008) documented reductions in both fix rates and the proportion of fixes in a three-dimensional mode when moving through forest but not through open areas.

Importantly, fix rates recovered from free-ranging mammals wearing GPS collars averaged 5–33% lower than stationary collar tests (Biggs et al. 2001; Cain et al. 2005; Hebblewhite & Merrill 2007; Lewis et al. 2007; Sager-Fradkin et al. 2007). From terrestrial studies of various large mammal species and collar brands since 2001, researchers have observed fix rates in the range of 43–99% (Gau et al. 2004; Graves & Waller 2006; Hebblewhite et al. 2007; Lewis et al. 2007; Sager-Fradkin et al. 2007; Brooks et al. 2008; Heard et al. 2008) that tend to vary both diurnally (Biggs et al. 2001; Graves & Waller 2006; Sager-Fradkin et al. 2007; Heard et al. 2008) and seasonally (Dussault et al. 1999; Sager-Fradkin et al. 2007, but see D'Eon & Serrouya 2005). Some temporal variation may be accounted for by satellite configuration and leaf-drop, but these effects have generally been trivial in stationary collar tests (e.g. Frair et al. 2004). The strong diurnal and seasonal forcing in fix rates observed for free-ranging animals is probably driven by animal behaviour and habitat choices. For example, Graves & Waller (2006) determined that fix rates for grizzly bears (Ursus arctos) were positively correlated with movement rate, which conflicts with the mobile device tests reported previously, and was not explained by variation in local satellite availability. Graves & Waller (2006) presumed this to be a function of collar orientation (largely vertical when bears were moving, and horizontal when resting) rather than an effect of movement per se. Using aerial telemetry, Heard et al. (2008) observed that bears tended to rest under forest cover and actively forage in open areas. Stationary tests revealed an interaction between collar position (on the ground to simulate bedding) and canopy cover that, when combined with the diurnal activity patterns of bears, explained the low fix rates observed for free-ranging bears (Heard et al. 2008). These studies demonstrate how combining visual observations of animal activity with stationary tests forges strong linkages among animal behaviour and GPS performance. Where possible more such studies are needed to understand the generality of animal behaviour effects on GPS errors.

Negative correlations between fix rates and grizzly bear body size (neck circumference, girth and weight) have also been observed (Graves & Waller 2006). This may have resulted from improperly fitted collars, which are not one size fits all but tailored specifically to a small range of neck circumferences. Moreover, in their study female bears were smaller than male bears, and sex-specific behavioural differences also could have played a role in GPS functioning. We caution that differences according to body size within a species may not translate to differences among species because discrepancies in habitat selection would probably confound interpretation of body size effects on GPS performance (see also Hebblewhite et al. 2007).

3. Implications of gps errors and the toolbox of solutions for ecological analyses

(a). Resource selection

Statistical detection of whether animals select or avoid certain conditions (White & Garrott 1986; Nams 1989; Rettie & McLoughlin 1999; Frair et al. 2004; Visscher 2006; Johnson & Gillingham 2008), the apparent magnitude of selection or avoidance (Frair et al. 2004; Visscher 2006; Johnson & Gillingham 2008) and the predictive ability of statistical models (Johnson & Gillingham 2008) are sensitive to both spatial imprecision and habitat biases in GPS location data. The magnitude of observed effects depends on the magnitude of imprecision and bias, GPS sampling interval, landscape grain (i.e. minimum mapping unit), habitat patchiness and the ecology of the species under study. Generally speaking, rare habitat types are subject to false negatives (type-II errors), whereas common types are subject to false positives (type-I errors). However, McKenzie et al. (2009) observed high type-I error rates for the use of linear habitat features, such as trails, which may not be rare per se but represent patches of small spatial extent with high amounts of edge. Changes in coefficients of selection generally become statistically important given biased data losses in the range of 10–25% (D'Eon 2003; Frair et al. 2004; Johnson & Gillingham 2008; Nielson et al. 2009). The effects of location imprecision, namely misclassifying the habitat type within which locations occur, are exacerbated by the size and interspersion of vegetation types (or habitat patches), and animal preference for edges (White & Garrott 1986; Nams 1989; Rettie & McLoughlin 1999; Visscher 2006; Johnson & Gillingham 2008). Given patch sizes that are smaller than the average location error, selection coefficients tend towards zero (White & Garrott 1986; Rettie & McLoughlin 1999; Johnson & Gillingham 2008). The effects of location imprecision and fix-rate bias on selection coefficients also are exacerbated by strong selection for a habitat or cover type, which is a function of both animal preference and habitat rarity (Frair et al. 2004; Visscher 2006; Johnson & Gillingham 2008). We know of only one study comparing the direct effects of both location imprecision and fix-rate bias on selection coefficients (Johnson & Gillingham 2008). In this simulation study, coefficients deviated significantly from ‘truth’ given spatial imprecision of 200 m or more or fix-rate bias of 25 per cent or more, each evaluated while holding the other type of error constant (at zero). Interestingly, Johnson & Gillingham (2008) further tested the effect of classification accuracy in the original habitat map on selection coefficients, and noted statistically significant differences given misclassification rates of 10 per cent or more. Overall classification accuracy rates for Landsat-derived habitat data typically range approximately 60–90% (Stehman et al. 2003; Wickham et al. 2004; Mayaux et al. 2006), profoundly constraining the ecological question pursued and, by extension, the level of spatial precision required in animal locations. Further study is needed to explore how general these patterns are as well as to quantify the additive or compounding effects of location imprecision, fix-rate bias and map accuracy on inferences of selection. Moreover, attention needs to be paid to the gross mismatch between the fine-scale, temporally dynamic animal locations and the coarse-scale, static habitat maps we relate those locations to (Urbano et al. 2010).

To our knowledge there has been no solution proposed for overcoming both fix-rate bias and location imprecision in a single analysis. Recommendations for dealing with imprecise locations in studies of resource selection have included smoothing habitat maps by lumping rare cover types to increase patch sizes relative to location imprecision (but at the expense of resolution of inference), calculating proximity to all habitat types rather than assigning each location to a single habitat type (Conner et al. 2003, but see Dussault et al. 2005; Conner et al. 2005), censoring locations that occur on the edge of patches (which could eliminate large numbers of locations and introduce bias for edge-dependent species; Zimmerman & Powell 1995) or removal based on a DOP cutoff (which also may result in large and habitat-biased data losses; Rempel & Rodgers 1997; Lewis et al. 2007), buffering locations to replace points with areas of potential use (Kufeld et al. 1987; Rettie & McLoughlin 1999), buffering small-extent (high-edge) landscape features as a function of both location precision and width of the feature (McKenzie et al. 2009), resampling from a fitted or assumed error distribution to quantify uncertainty in misclassification rates (Nams 1989; Samuel & Kenow 1992; Kenow et al. 2001; Visscher 2006) or producing selection estimates that are weighted by misclassification rates (Nams 1989; Findholt et al. 2002; table 2). Whether replacing points with areas or resampling within error polygons, buffers introduce noise by including habitats that may not influence animal behaviour, and thereby reduce one's ability to statistically detect selection (Rettie & McLoughlin 1999). Exponential, bivariate normal, or bivariate Laplace distributions better reflect known distributions of spatial imprecision in GPS locations (Visscher 2006; McKenzie et al. 2009), and their use should introduce less noise compared with a uniform error distribution when buffering either animal locations or landscape features.

Table 2.

Summary of proposed solutions for imprecise and biased missing locations in ecological analyses using GPS telemetry data.

proposed solution	description	benefits	considerations
increase sample sizesa,b	reduce location interval, or increase duration or number of animals monitored to acquire more locations	reduces standard errors around estimates, increases statistical powera	habitat-dependent bias and spatial imprecision not removedc
smooth habitat maps	lump rare types to increase patch size relative to measurement error	reduces misclassification of habitats used	reduces resolution of inference. does not account for biased missing data
censor edge locations	remove locations occurring on the edge of habitat patches	reduces misclassification of habitats used	potentially eliminates large numbers of locations, and introduces bias, especially for edge-dependent species
increase location accuracy by
differential correction	store ephemeris data with locations, post-process locations to reduce imprecision using base station data collected simultaneously with animal-borne device	reduces measurement error to within 5 m on averaged	reduces battery storage capacity, post-processing labor intensive, base station must be within 400 kmd; does not fully remove canopy-induced errorse
DOP-based screening	remove data above DOP threshold, consider different thresholds for two-dimensional and three-dimensional locationsd,f	removes grossly imprecise locations, reducing 95% circular error probable values, but does not improve mean location precision per sef	habitat-dependent error not removedc, bias potentially exacerbatedf; reduces sample sizes, and interrupts continuous path recordg; should be conducted prior to modelling Pfix for sample weighting or iterative simulation (see below)
smooth animal paths by
censoring inaccurate locations	buffer displacement between pairs of locations separated by 1 time lag (buffer representing location imprecision), remove intervening location if within bufferh	straightens tortuous pathsh	appropriate buffer difficult to specify, varies with habitat and behaviour; removing locations reduces sample samples sizes and disrupts continuous path trajectoryg
fitting spline to trajectory	fit spline through point trajectoryh	removes fine-scale jitter from path; interpolates information to areas between acquired fixes assuming straight-line travel between fixes	continuous line no longer corresponds to original path sampling intervalsh; can introduce error into accurate locations; path must be re-segmented to estimate turn angle and step length
resampling fix intervals	specify fix interval based on animal movement propensity, GPS location precision, and average habitat patch sizei	minimizes falsely concluding animal movementg, and misclassification of patch usei	longer fix intervals will reduce sample size, potentially reduce fix ratesj, and may underestimate total daily movement
removing resting bouts	identify periods of animal inactivity using activity sensors, movement rates, or predictive models	step length and turn angle distributions more accurate, based on actual moves	resting confounded with fine-scale foraging behaviour, may underestimate total movement and time spent active
resample locations within error polygons	buffer locations by predicted level of imprecision, generate random sample of locations within buffer; can model location imprecision ∼ f(collar, time, canopy cover, terrain conditions, and animal activity)	reduces misclassification rates; untested for reducing coefficient bias or errors in predictive success of models; may be readily combined with iterative simulation for missed fixes	distribution of error for re-sampling should be bivariate normalk or bivariate laplacel (uniform distribution introduces excessive noisem)
buffer habitat ‘patch’ by location imprecision	buffer linear or other small-extent (high edge) patches, e.g. roads, ∼f(GPS precision and width of habitat feature)l	reduces type-I errors with little sacrifice of type-II errors	error distribution of Lotek 3300_s followed bivariate laplace distribution under conifer coverl; need broader testing by habitat type and collar brand; does not correct for missing locations
replace points with areas	use location precision to define area used by animal, analyse composition of area rather than habitat at pointsc,n or simulate points to calculate misclassification ratesa,o,k,n	corrects relative ranking of habitats used, and direction of effectsc	buffers include noise and reduce ability to detect selectionc; applicable only for categorical variables
apply sample weights
to missing locations	adjust the influence of acquired locations so as to represent lost data. Model Pfix ∼ f(collar, time, canopy cover, terrain conditions, animal activity), and use 1/Pfix as sample weightp,s,t	reduces type-II errors and corrects coefficient bias when estimating habitat selection given correctly specified bias modelp. Can produce unbiased home range estimateu	developing bias model requires independent field surveysp,q,r, and bias mechanism may include hard-to-specify animal behaviourf. May not be available for all statistical routines, e.g. conditional logistic regression except by weighting the log-likelihood for each location. ‘Resamples’ in environmental not geographical space
to inaccurate locations	generate random points within error polygon to estimate habitat mis- classification rate (i.e. bias matrix), invert and use to weight collected observationsa,o,k,n	provides more reasonable estimate of uncertainty around habitat use estimates. Effects vary given degree of habitat fragmentation	improper error distribution can exacerbate noise or introduce bias; effects vary given degree of habitat fragmentation
complete trajectories by
dead-reckoning	record speed, heading, and depth from known position (could be release site or GPS location) to project path in areas where physical location not observablee	accurate in marine systems where speed and depth recorded accuratelye; might be used to infer animal path over short distances where GPS imprecision has largest effect	subject to bias from skewed device attachments (miscalibaration) and drift; accurately measuring effective move distance difficult in terrestrial systems, but promisinge
Brownian bridges	estimate probability of occurrence in area between collected GPS points as a function of diffusive spreadv	accounts for measurement error when estimating certainty of area used by animal	assumes random direction and constant rate of movement between known locations
iterative simulation	Model Pfix as ∼f(habitat, collar brand make, time, season, animal behaviour); use Pfix to iteratively replace missing locations within domain bounded by adjacent fixes to complete animal paths; replicate due to uncertainty in simulation process, combine results using multiple imputation techniquesp	reduces type-II errors and coefficient biasp; adaptable to various analytical approaches, including conditional logistic models, animal movement and home range models; physically replaces location in geographical and environmental space, and at time of missing location	fix acquisition model requires independent field study, and effects of animal behaviour difficult to parameterize; processing can be laborious; can be extended to include solution for imprecise locations by also resampling with error polygons when completing paths
simultaneously model data and process
occupancy approach	simultaneous estimation of selection and detection given selection using maximum likelihood approachw	does not require independent model for Pfix; efficient estimator of selection given probability of detection; provides individual-based model of detection and selection	accounts for missed fix effect, but does not address measurement error
state-space models	simultaneous estimation of observation and process model using Bayesian approachx,y	relies on previous information of location bias and imprecision; efficient estimator of complex animal behaviour given noisy data; can model missing and imprecise dataz	complex analytical machinery
data-cloning	maximum likelihood alternative to Bayesian state-space models that relies on data replicationaa,ab	same as for state-space models	same as state-space models

^aNams (1989); ^bDussault et al. (1999); ^cRettie & McLoughlin (1999); ^dRempel & Rodgers (1997); ^eWilson et al. (2007); ^fLewis et al. (2007); ^gJerde & Visscher (2005); ^hDeCesare et al. (2005); ⁱSwain et al. (2008); ^jCain et al. (2005); ^kKenow et al. (2001); ^lMcKenzie et al. (2009); ^mVisscher (2006); ⁿMoen et al. (1996); ^oSamuel & Kenow (1992); ^pFrair et al. (2004); ^qHebblewhite et al. (2007); ^rD'Eon et al. (2002); ^sD'Eon (2003); ^tJohnson et al. (1998); ^uHorne et al. (2007b); ^vHorne et al. (2007a); ^wNielson et al. (2009); ^xMorales et al. (2004); ^yJonsen et al. (2005); ^zPatterson et al. (2008); ^aaLele et al. (2007); ^abPonciano et al. (2009).

Censoring locations to improve the overall precision of the dataset is commonly employed, and begins with careful screening of implausible locations (e.g. a single location far outside the normal animal range requiring extraordinary speed). Lewis et al. (2007) showed that censoring based on values of positional DOP (PDOP) removes some grossly imprecise locations, effectively reducing the circular error probable (CEP; the radius of a circle containing a given percentage of locations assuming a bivariate normal distribution), but without reducing the average location precision per se. Depending on the choice of PDOP cutoff and the magnitude of location imprecision, the proportion of data removed by screening could be as large as 80 per cent (D'Eon & Delparte 2005; Lewis et al. 2007). Lewis et al. (2007) recommend screening only two-dimensional locations, and by removing two-dimensional locations having PDOP more than 5 they reduced 95 per cent CEP values (CEP_0.95) from 106.8 to 79.2 m while removing only 5.5 per cent of the locations. The same rule applied to free-ranging black bears (Ursus americanus) resulted in an 8.6 per cent data reduction on average, for an overall data retention rate of 80–90%, which we note falls within the range at which statistical errors manifest in resource selection studies. Importantly, given that canopy closure and terrain influence location precision, the intentional removal of imprecise locations occurs at the expense of increasing habitat-biased data loss.

Recommended solutions for the problems of biased missing locations have included sample weighting (Johnson et al. 1998; D'Eon 2003; Frair et al. 2004) and iterative simulation (Frair et al. 2004; table 2), both of which require a spatially predictive model for the probability of a GPS device successfully acquiring a fix (P_fix). With sample weighting, each acquired location is adjusted by 1/P_fix, such that hard-to-acquire locations exert greater influence on model results. Sample weighting does not physically alter sample sizes by duplicating records or putting locations back in geographical space (sensu Aarts et al. 2008), i.e. the physical x, y and z (or depth) coordinates of a given missing location. Rather, by inflating the influence of hard-to-acquire locations weighting corrects for missing locations in environmental space (sensu Aarts et al. 2008), i.e. as a function of the suite of biotic and abiotic variables influencing P_fix. As such, adjusting the weight of each successfully acquired location may not account for the diurnal and seasonal forcing apparent in free-ranging animal location data unless the P_fix model includes covariates to capture those effects (e.g. see Sager-Fradkin et al. 2007). In the alternative approach, iterative simulation, a new location is probabilistically added to the dataset (based on P_fix) within the geographical realm of the missing location to complete multiple realizations of ‘true’ animal paths, with each realization analysed independently, and the results of multiple realizations combined using multiple imputation techniques (Frair et al. 2004). Related developments include the use of Brownian bridge models to reconstruct paths between locations based on a random walk process (Horne et al. 2007a; table 2). Such simulation approaches are more technically involved than sample weighting, but also may prove more advantageous because they provide corrections in both environmental and geographical space, and thus implicitly account for potential interactions between animal behaviour and local habitat conditions. Both iterative simulation and sample weighting approaches have been shown to reduce type-II error rates and correct biases in coefficient values (Frair et al. 2004, but see D'Eon 2003; Sager-Fradkin et al. 2007).

Models of P_fix can be developed from stationary device tests (e.g. Frair et al. 2004; Hebblewhite et al. 2007), or from analysis of areas of successful and unsuccessful fixes during monitoring of free-ranging animals (e.g. Graves & Waller 2006). The former approach can be time-consuming, and requires replication across a range of environmental conditions. Even among devices of the same brand and manufacturing cycle, moderate variation in canopy and terrain conditions can affect the magnitude of missed fixes (e.g. Frair et al. 2004; Hebblewhite et al. 2007). Thus, P_fix models should be developed specific to the study area, time period, device make/model and fix schedule that characterize data collection from free-ranging animals. If data-screening based on PDOP is employed, censoring should be done prior to estimating the P_fix model so as to account for the full extent of habitat-biased data loss. The Graves & Waller (2006) approach has the potential advantage of implicitly accounting for animal behaviour when estimating P_fix, although the precise coordinates of a failed location attempt may often be unknown and, consequently, only coarse habitat effects might be evaluated. Moreover, the specific behaviour will also probably be unknown, therefore this approach could not illuminate the relative effects of behaviour versus local habitat on GPS functioning. Nevertheless, individual-based models of P_fix may implicitly rather than explicitly account for the interactive effects of animal behaviour and local habitat variation on GPS performance. Formal testing is required to evaluate how such a P_fix model performs when used for statistical corrections in selection models. An alternative to the stand-alone P_fix model was recently proposed by Nielson et al. (2009), where only GPS data collected from a free-ranging animal were used to independently estimate models for: (i) resource selection, and (ii) animal detection given selection in a manner similar to patch-occupancy models (table 2). The Nielson et al. (2009) method also requires a larger landscape grain, but successfully corrected selection coefficients given up to 50 per cent biased data loss. This approach is adaptable to conditional sampling designs and movement models that may not allow for location specific weights. More complicated model structures, such as hierarchical models, are not yet readily available, but population-level inference might instead be obtained using a two-stage approach as detailed in Fieberg et al. (2010).

To our knowledge there has been no comprehensive approach proposed to correct for both imprecise and biased missing locations in resource selection models. Iterative simulation seemingly provides the most flexible solution as it can be applied to sampling designs that do not allow location-specific weights, is adaptable to movement modelling approaches, and, importantly, replacing missing locations (Frair et al. 2004) and resampling imprecise locations (Samuel & Kenow 1992) might readily be accomplished simultaneously to complete realizations of animal paths that account for both types of error. Additional research is required to determine whether such an approach might sufficiently account for the interactive effects of animal behaviour and local habitat interactions in resource selection studies, or whether additional detail specific to animal behaviour needs to be included in P_fix models.

(b). Animal movements

Fundamental to models of animal movements are statistical distributions of move distance and direction (Turchin 1998). Using GPS-based locations, the distance moved, or step length (SL), requires two consecutive fixes, whereas the direction moved, or turn angle (TA), requires three consecutive fixes. If we assume the probability of a single fix, P, to be independent and identically distributed (ignoring issues of fix-rate bias), then the probability of recording a SL and TA is P² and P³, respectively (Jerde & Visscher 2005), indicating that movement data may remain scarce even given relatively high fix rates. Moreover, SL and TA distributions are inherently noisy, a problem exacerbated by location imprecision. From a study design perspective, it is critical to consider measurement error in animal locations within the context of the magnitude of animal movement (Jerde & Visscher 2005). For a more general, rather than species-specific perspective, it is useful to speak in terms of error standard deviations (s.d.) rather than absolute distance errors (both scaled in the same units). For example, given , then the s.d. = 10 m and 5 error s.d.'s = 50 m absolute error. Using simulations, Jerde & Visscher (2005) showed that the observed SL is positively biased given very short moves (actual SL < 0.5 error s.d.), and given SL < 5 error s.d. it is difficult to conclude whether the animal has moved at all. Thus, assuming a location precision of ± 25 m, consecutive GPS fixes must be more than 125 m apart to reliably infer that the animal had moved. In their simulation, the effect of location imprecision became negligible given very large moves (SL > 100 error s.d.; Jerde & Visscher 2005; see also Ganskopp & Johnson 2007). Nevertheless, when combining sequences of SL's into longer movement paths, GPS-induced ‘jitter’ may increase the apparent tortuosity of animal paths (DeCesare et al. 2005), leading to an overestimate of the cumulative distance travelled (Kauhala & Tiilikainen 2002; DeCesare et al. 2005; Jerde & Visscher 2005; Ganskopp & Johnson 2007), and eroding the biological signal in the animal trajectory (Bradshaw et al. 2007).

Location imprecision has a relatively greater effect on estimates of TA versus SL, potentially causing analysts to conclude a directional bias in animal movement when actual SLs are short. In two different simulation studies (Jerde & Visscher 2005; Hurford 2009), analysts observed that TA estimates were routinely off by more than 160° when either SL making up the trio of consecutive fixes was short (SL < 0.5 error s.d.). However, with two consecutive SLs that were moderately long (SL > 5 error s.d.), TA estimates were routinely within 60° (Jerde & Visscher 2005), and on average the mean of the TA distribution approached the true mean (Hurford 2009). The effect of location imprecision on TA estimates also varies with the magnitude of the turn itself. For example, for wolves (Canis lupus), estimating an accurate TA required a minimum SL ≥ 1.03 error s.d. when the true TA was 90° but a SL ≥ 1.66 error s.d. when the true TA was 180° (Hurford 2009).

Resting bouts recorded by GPS devices are another potential source of large errors in movement analyses because a SL and TA will be estimated even when an animal remains stationary during the sampling interval (e.g. Ganskopp & Johnson 2007). Resting bouts have been identified using activity sensors combined with GPS (Pépin et al. 2004; Ungar et al. 2005; Schwager et al. 2007), minimum distance or acceleration thresholds (Frair et al. 2005; Ganskopp & Johnson 2007), or combinations of activity sensors, movements and other variables (Ungar et al. 2005; Ganskopp & Johnson 2007; Van Moorter et al. 2010). Once identified, resting bouts might be excluded, or treated differently, for analyses of animal movements. But we note that resting bouts and fine-scale foraging activities are often confounded when based on GPS-derived data (Pépin et al. 2004; Ungar et al. 2005).

Researchers generally recommend strategically setting fix intervals a priori (at the study-design phase) or temporally resampling collar data so as to ensure sufficient movement relative to location imprecision during each sampling interval (Jerde & Visscher 2005; Bradshaw et al. 2007; Ganskopp & Johnson 2007; table 2). For example, Jerde & Visscher (2005) considered elk having an average rate of movement of 2.5 m min⁻¹ (approx. 150 m h⁻¹) and a GPS location imprecision of ± 20 m (at 1 s.d.; D'Eon et al. 2002), and concluded that elk locations more than 100–120 m apart would be required to yield accurate movement information. As such, collecting locations on a sub-hourly interval would not yield informative data on elk movements, whereas a 1 h or more interval might prove optimal. Obviously, very infrequent fix intervals may grossly underestimate total movement (Mills et al. 2006), or miss short-duration but long-distance forays. Thus, previous knowledge on species movement behaviour and the precision of GPS locations is the key to proper study design. Should fine-scale movements (below the resolution of GPS precision) be of particular interest, one might employ differential correction to improve location precision to within a few meters (e.g. Ganskopp & Johnson 2007), or seek alternative approaches to mapping animal movements between GPS fixes, such as using a Brownian Bridge (Horne et al. 2007a; see also Lonergan et al. 2009 for interpolation of Argos paths) or incorporating dead-reckoning technologies such as those commonly employed in marine applications (Wilson et al. 2007). Additional approaches to reduce the effects of location imprecision involve smoothing animal paths, either mechanistically such as by censoring out the ‘jitter’ caused by GPS imprecision, or phenomenologically such as by fitting a spline through the trajectory of locations (DeCesare et al. 2005; table 2). Using a straight-line test path and a hand-held GPS, DeCesare et al. (2005) identified that under high canopy conditions, a location at time t + 1 that deviated less than 7.98 m from the straight line connecting the locations acquired at time t and t + 2 was probably due to location error (given a 2 s sampling interval), and used this observation to censor locations. Although we have not yet seen these techniques applied to ecological questions for free-ranging animals, these approaches are akin to the process suggested by Turchin (1998) in which biological moves are extracted from recorded animal paths. The larger conceptual issue of discriminating between biological moves (animal choices) and empirical steps (simply connecting the dots) is beyond the scope of this review (but see Hebblewhite & Haydon 2010).

Too often the complexity of studying animal movements has led researchers to overlook the problems associated with data acquisition, especially the compounding effects of fix-rate bias and measurement error, and interactions between animal behaviour and the performance of GPS devices (see Brooks et al. 2008; Heard et al. 2008). One especially promising area of enquiry includes state-space models (table 2), which couples a probabilistic model of the sampling process (the observation model) with a mechanistic model for animal movement (the process model; Patterson et al. 2008). In this approach an animal's future ‘state’, be that a spatial location or a behavioural mode (e.g. resting, foraging, migrating), is predicted as a function of its current state (using a Markovian process) weighted by the likelihood of observing the data (e.g. Forester et al. 2007, who modelled the effects of autocorrelation on the observation process). Although state-space models can accommodate the effects of both biased missing data and measurement error in the locations acquired (Patterson et al. 2008), we know of no empirical examples doing so for the study of animal movements using GPS-based locations (but see Jonsen et al. (2005) for an approach focused on Argos sampling errors; and Clark & Bjørnsad (2004) for a population time-series analogue). The analytical complexity of state-space models remains non-trivial, and although the conceptual and technical machinery may exist, these approaches are not readily accessible to most applied ecologists.

(c). Home ranges

The large number of fixes required to capture seasonal patterns of space use by animals (Girard et al. 2006), and the even more frequent fixes required to capture brief but long-distance forays (Mills et al. 2006; Kochanny et al. 2009), can be difficult to acquire using traditional radiotelemetry techniques. Thus, GPS devices provide an unprecedented ability to quantify animal home-range patterns (see Kie et al. 2010). Although location imprecision can influence estimates of home-range size and shape, as well as the relative location of peaks and valleys of the utility distribution (Kauhala & Tiilikainen 2002; Moser & Garton 2007; Börger et al. 2008), estimates of animal home ranges nevertheless appear largely robust to contemporary levels of GPS measurement error. Moser & Garton (2007) used a volume of intersection (VI) statistic (0 indicating no overlap and 1 indicating identical distributions) to compare home-range estimates using accurate and ‘jittered’ locations achieved via simulation. As expected, VI values increased with increasing sample sizes and decreased with the magnitude of location imprecision, with the effects on fixed kernel home-range estimates mediated to some degree by home-range size. Using an error ratio (ER) = median location precision (CEP_0.5)/home-range area (A), where CEP_0.5 and A are expressed in similar units (e.g. km and km²), Moser & Garton (2007) demonstrated that the impact of location imprecision on home-range estimates was negligible given an ER < 0.1. This means that for an animal whose home-range averages 100 km², GPS locations having a median precision ≤ 940 m will yield accurate home-range estimates (likewise an average home size of 10 km² requires a median GPS precision of 94 m or less for accurate estimates). Thus, the home ranges of animals large enough to carry GPS devices are expected to be generally unaffected by contemporary levels of measurement error in the recorded locations. For comparative studies, Börger et al. (2006) suggested using an average measure of location precision within individual home ranges as a covariate to control for individual- and spatially varying GPS positional error.

Biased missing data, on the other hand, has the potential to severely bias estimates of home-range size and utility distributions (Horne et al. 2007b), depending upon the magnitude of fix-rate bias and its spatial variability. Horne et al. (2007b) suggested that spatially uniform fix rates, even if they are low, would not influence home-range estimates, but that estimates could become inaccurate when the probability of acquiring a fix either covers a broad range of values (e.g. 0.5–1.0), or when low observation rates are aggregated within one part of the home range. As such, smaller home ranges composed of relatively few homogeneous patches may be more influenced by fix-rate bias than larger, more heterogeneous home ranges. Horne et al. (2007b) detailed a sample weighting approach, where locations are weighted by 1/P_fix (similar to the approach for resource selection studies), which provided robust home-range estimates (see also Fieberg 2007; table 2). Applying the approach to telemetry data, Horne et al. (2007b) observed greater discrepancies between corrected and uncorrected home-range estimates for mule deer (O. hemionus) than black bear, with the latter species occupying larger and more heterogeneous home ranges.

The impact of fix-rate bias also varied among home-range estimators, with differences between corrected (by sample weighting) and uncorrected estimates (the ‘true’ home-range being unknown) of −0.25 per cent to +10 per cent for a bivariate normal model, −14.2 per cent to +19.2 per cent for a 2-mode bivariate normal mixture model, and −18.4 per cent to +16.8 per cent for a fixed-kernel home-range model (Horne et al. 2007b). One problem with P_fix models is their failure to account for particularly low collar returns under some environmental conditions (e.g. D'Eon 2003; Frair et al. 2004), and thus weighting alone may be insufficient to overcome large data losses in geographical space. The iterative simulation approach detailed by Frair et al. (2004) might thus provide a more robust alternative for home-range estimators.

4. Conclusions and future directions

Animal location data acquired by GPS devices are indeed plentiful, and becoming increasingly precise, but nevertheless pose challenges for analyses of resource selection and space use by animals. In terrestrial deployments we can be certain that closed canopies and steep terrain interfere with satellite signals, inducing habitat-biased errors that include both missing and spatially imprecise animal locations. These errors can muddy inferences of habitat and space use by animals, but can also be overcome to varying degree a priori via proper study design (e.g. considering GPS imprecision in light of animal movement behaviour and the resolution of environmental data), or, alternatively, by employing any number of ad hoc statistical corrections. Researchers consistently neglect to explicitly consider GPS errors during the study-design phase, and typically conduct no corrections (justifying this because of high fix rates), or correct for one or the other type of error without recognizing that errors propagate. That is, we collectively overlook the additive or compounding effects of location imprecision, fix-rate bias and, in the case of resource selection, the perhaps even more egregious problem of map inaccuracy on statistical inferences. It was our intention with this review to provide clarity on these issues so as to improve study designs and, by extension, the veracity of ecological insights gained from GPS-based location data. Nevertheless, more work is needed to understand how animal behaviour affects GPS functionality, along with more rigorous testing of solutions that address the combined effects of location imprecision and fix-rate bias in ecological analyses. In light of these issues, two analytical approaches seem particularly appealing: (i) iterative simulation to complete animal paths, combined with spatial resampling of locations prior to analysing patterns in the data, and (ii) state-space models that simultaneously model the observation process as well as the ecological process of interest. In contrast to sample weighting, these approaches show promise for resolving GPS problems in geographical as well as environmental space, implicitly including animal behaviour in the analytical solution. Yet, these approaches remain underused due in large part to their non-trivial levels of complexity. We commend authors who provide scripts, code and workshops to make these approaches more accessible to ecologists. It remains unclear, however, whether ever-increasing analytical complexity is really necessary to account for GPS errors in ecological analyses. Perhaps censoring gross positional errors based on PDOP values and weighting hard-to-acquire locations provides an equally satisfying solution. As technologies continue to improve, GPS errors will diminish. But rather than assume GPS location data to be hunky-dory and without error, or to immediately invest in potentially expensive and complicated solutions, we suggest that analysts might benefit most by testing the sensitivity of their models to the probable causes and magnitudes of GPS errors specific to their collar brand, study area, species and ecological question.