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- Materials and methods
Recent integration of global positioning systems (GPS) into devices for tracking animals has extended our ability to monitor movements of free-ranging species over a broad range of spatial and temporal conditions. Despite improvements in this technology two types of errors remain inherent in animal location data collected by GPS telemetry, namely spatial inaccuracy in the locations acquired and missing data in the form of failed location attempts. The first type of error is not unique to GPS telemetry and its effect on apparent habitat selection has been well considered (White & Garrott 1986; Nams 1989). In particular, location inaccuracy can lead to misclassification of habitat use dependent upon the magnitude of location error and the degree of landscape heterogeneity. Location inaccuracy may be of less concern because the intentional degradation of satellite signals (selective availability) ceased in May 2000 and errors are reported to be ≤ 31 m 95% of the time (D’Eon et al. 2002), which is comparable to the resolution of most habitat maps. To counteract potential misclassification problems, one might resample locations within error polygons (Nams 1989; Samuel & Kenow 1992; Kenow et al. 2001) or replace point data with areas (buffers) around points (Kufeld, Bowden & Siperek 1987; Rettie & McLoughlin 1999).
The second type of error, missing data, has largely been ignored even though it may have a more profound effect on inferences of habitat selection than inaccurate locations (Johnson et al. 1998). Missing locations equate to a loss of information, the implications being reduced efficiency and potential bias in the parameters estimated by habitat selection models (Little & Schenker 1995). Bias is likely in GPS telemetry studies because failed location attempts do not occur randomly but systematically. Previous work has shown that canopy type (Moen et al. 1996; Moen, Pastor & Cohen 1997), percentage canopy cover (Rempel, Rodgers & Abraham 1995; Rumble & Lindzey 1997; D’Eon et al. 2002), tree density (Rumble & Lindzey 1997), tree height (Rempel & Rodgers 1997; Dussault et al. 1999) and tree basal area (Rempel, Rodgers & Abraham 1995; Rumble & Lindzey 1997) can affect the acquisition of GPS locations. For example, GPS collars have been shown to be 3·8 times less likely to acquire a location under a tall forest canopy (> 15 m height) than in treeless areas (Rempel & Rodgers 1997). In mountainous study areas, terrain conditions can interact with forest canopy cover to reduce location acquisition further (D’Eon et al. 2002). There are also predictable temporal effects due to the presence or absence of deciduous leaves (Dussault et al. 1999; Moen, Pastor & Cohen 1997) and a changing satellite constellation throughout the day (Moen, Pastor & Cohen 1997). A simulation experiment demonstrated that animal locations biased to approximate GPS error led to type II errors (failure to detect significant selection) and incorrect conclusions of selection vs. avoidance (Rettie & McLoughlin 1999). The magnitude of effects observed by Rettie & McLoughlin (1999) depended on the level of data loss, how often the animal used biased vegetation types, and the degree of spatial association among vegetation types.
Despite documentation of GPS bias, and strong recommendations for bias corrections (Rumble & Lindzey 1997; Johnson et al. 1998; Dussault et al. 1999), most statistical analyses of habitat selection continue to ignore the effects biased data may have on subsequent inferences. One suggested method for reducing these effects, in addition to the effects of spatial inaccuracy, is to measure the areal extent of each habitat type within buffers around point locations rather than the habitat type at each location (Kufeld, Bowden & Siperek 1987; Rettie & McLoughlin 1999). Using this approach, Rettie & McLoughlin (1999) were better able to identify selection vs. avoidance accurately because buffers captured portions of biased habitat types that the acquired set of locations did not. However, buffers added sampling error by including ‘noise’, habitats that may not affect animal behaviour, and thus their power to detect significant selection of certain habitats was reduced. Buffers therefore fail to solve the problems caused by biased missing data. Because missing GPS locations may be largely predictable, a more direct approach is to model the missing data mechanism and correct for bias statistically.
In this study, we modelled the effects of collar brand, forest structure, season, terrain and time of day on the probability of acquiring a GPS-collar location using field data. Using this model, we removed locations incrementally from an unbiased set of animal locations at two temporal sampling intensities (6- and 1-h locations). We identified the level of data loss at which coefficients in habitat selection models differed from unbiased estimates. Resource selection functions (RSF; Manly et al. 2002) were used to quantify selection patterns. Alternative methods exist for assessing selection, e.g. compositional analysis (Aebischer, Robertson & Kenward 1993), but we are most familiar with RSF techniques and focus solely on these. We chose a sampling design consistent with a third-order selection process (Johnson 1980), where used sites (animal locations) are compared with available sites (random locations) within the animal's home range, because this design is common to selection studies. We compared model coefficients produced using unbiased and biased data to determine how habitat-induced data loss affected the direction (selection vs. avoidance), magnitude (coefficient value) and strength (significance level) of selection. Finally, we evaluated the effectiveness of two bias-correction methods, sample weighting and iterative simulation, at removing bias from RSF coefficients. Sample weighting is a deterministic process in which the influence of each location in the data set is weighted by the inverse probability of having acquired that location (Little 1986; Kish 1992; Pfeffermann 1993). The alternative approach, iterative simulation, involves repeatedly simulating plausible spatial coordinates for each missing location and using multiple imputation methods to combine simulation results into a single model (Rubin 1987; Schafer 1999). Both techniques require a bias estimate for every location in the landscape, which we produced using field trials and data held in a geographical information system (GIS).
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- Materials and methods
The results from our collar tests generally agreed with previous studies in that acquisition of GPS locations was lowest under dense forest canopies, taller trees and during the summer months (Moen, Pastor & Cohen 1997; Rempel & Rodgers 1997; Dussault et al. 1999; D’Eon et al. 2002). Unlike D’Eon et al. (2002), we found significant differences by time of day. Nevertheless, time was not a variable in our highest-ranked models and its effect on habitat selection therefore was not evaluated by our tests. We did not detect an effect of open canopy forests (< 60% canopy closure) or mixed deciduous–coniferous forest cover on location acquisition, possibly because the latter type tended to have a layered canopy with an ‘open’ overstorey. Terrain variables were not significant by themselves, possibly due in part to the coarse resolution of our digital elevation model. However, interactions between closed canopy forest types and percentage slope suggested that the reduction in canopy interference down-slope outweighed the potentially increased blockage of satellites up-slope due to terrain. Uncertainty among our highest-ranked models indicated that season also had important effects on GPS bias. For simplicity we did not include an effect of season in our tests but we have observed acquisition rates to vary by season for collars recovered from free-ranging wapiti, and therefore a model including season may be necessary to compensate appropriately for GPS bias in field studies. Finally, differences in acquisition rates between collar brands may reflect, in large part, different years in which the collars were manufactured, i.e. Televilt collars were produced in 1999 and Lotek collars produced in 2001, because other researchers have reported that collar performance has improved over the years (Rempel & Rodgers 1997; Dussault et al. 1999).
We conclude that a GPS bias model should be produced specific to the collars employed in a given study, the specific conditions and seasons under study, and preferably produced using a sampling interval consistent with that of the free-ranging collars to be corrected. Further, animal behaviour has been shown to affect collar performance (Moen et al. 1996; Bowman et al. 2000) and collars that provide information on animal activity may additionally improve our ability to model acquisition error. We caution against extrapolating our GPS bias model to areas outside the east-central Rocky Mountains and foothills of Alberta because poorly fit models may introduce bias or cause excessive variation in parameter estimates (Robins, Rotnitzky & Zhao 1994). We concur with D’Eon et al. (2002) that unexplained or random error is a large cause of the data missing from GPS collars but, nevertheless, we have demonstrated that even a small bias resulting in small losses of data can influence our assessment of resource selection by animals.
Habitat-induced bias in animal locations acquired by GPS collars can result in type II errors and biased RSF coefficients. Several factors influenced the extent of these errors. First, rarity of certain vegetation types made them susceptible to type II errors. Similar observations have been reported by White & Garrott (1986) and Rettie & McLoughlin (1999). The two rare types, deciduous and mixed forest, were similar in extent (11% and 8% of the landscape, respectively) but deciduous forest was used slightly less (16% vs. 21%). The lower apparent strength of selection for deciduous forest (P = 0·042) compared with mixed forest (P = 0·008), combined with the large and negative effect of deciduous forest cover on GPS location acquisition, was sufficient to cause type II errors in this type given relatively small data losses (10%). Secondly, interactions among variables indicated that GPS-induced bias in one variable can influence conclusions about an animal's selection of another resource. For example, we observed that the biased loss of locations from closed conifer forest probably caused type II errors in the distance to trail variable because the wapiti more frequently used areas near trails when under a closed conifer canopy compared with other vegetation types. Thirdly, even though closed conifer and deciduous forest had similar coefficients in the GPS bias model (Table 3), we did not observe an equivalent bias in RSF coefficients for these variables because the magnitude of use of each type of forest by the wapiti differed. Our understanding of this effect, however, differs from the simulations conducted by Rettie & McLoughlin (1999). Here closed conifer forest was the most extensive vegetation type (58% of the landscape) and was used 2·3 times more than deciduous forest, thus bias related to wapiti use of conifer forest occurred at least twice as often as for use of deciduous forest. Therefore, the magnitude of the modelled bias alone may not be sufficient to anticipate the full influence of biased data loss.
How well our corrections reduced the effects of GPS bias depended on how effectively each approach ‘replaced’ missing locations. Simulation increased sample sizes to their original level, thereby reducing type II errors in the rare deciduous forest type and, when combined with α= 0·10, reducing more type II errors overall than sample weighting. However, simulation placed locations on the landscape randomly with respect to trails and was thus less effective than sample weighting at removing type II errors from the distance to nearest trail variable. Sample weighting effectively ‘resampled’ existing animal locations, which in this case were not distributed randomly with respect to trails. Refinements to the spatial domain for imputations, e.g. limiting location replacements to within a buffer around the straight-line displacement between the last and next known locations, may better conserve the selection patterns of the animal under study and are worthy of further investigation. Further, the GPS sampling intensity affected both the magnitude of coefficient bias and how well corrections performed. Both techniques effectively eliminated bias from closed conifer forest coefficients without introducing bias into any other variables. The extreme condition we tested of frequent sampling (1-h locations) and large data losses (30% reduction) limited our ability to correct coefficients. However, we have observed that location rates generally increase as relocation intervals shorten and thus this extreme is unlikely to be achieved in field studies.
The most suitable approach for bias correction will depend on the design for assessing resource selection. For widely roaming animals or infrequent location schedules, sample weighting may be preferable because simulating locations within a large spatial domain may introduce an unreasonable amount of sampling error, especially in heterogeneous landscapes. Further, sample weighting may perform better than simulation when covariates are distance based (Conner, Smith & Burger 2003). Note that when sample weights are applied, a weight of one should be assigned to all influential and outlying data points to avoid unduly inflating the influence of these locations when estimating coefficients (Little & Schenker 1995). However, sample weighting may not be applicable for certain designs, such as conditional fixed-effects logistic regression, where weights cannot be applied to individual observations (Stata Corporation 2001a). For designs that temporally constrain availability (Arthur et al. 1996; Cooper & Millspaugh 1999; Hjermann 2000; Compton, Rhymer & McCollough 2002), iterative simulation may be more desirable as corrections are constrained to the time and area of the missed location. Further, location inaccuracy may be of concern to sample weighting as weights are applied to the GPS location rather than the true location of the animal. Our simulation routine could be adapted as part of a resampling method similar to Kenow et al. (2001) to account for GPS bias due to both location uncertainty and failed location attempts. Using multiple imputation techniques to combine simulation results would also be appropriate when correcting for inaccurate locations. Note that simulations should not be conducted on long sequences of missing data that occur due to random malfunction rather than GPS bias. For example, we rarely observed gaps between successful locations of greater than 8 h for Lotek collars and, thus, we used 8 h as a cut-off for corrections. Finally, both techniques support the use of point data, which overcome the limitations imposed by the use of buffers (Rettie & McLoughlin 1999). However, we have not tested the effects of bias or our corrections under any sampling design other than using logistic regression to detect a third-order selection process. We encourage exploration of bias and corrections when using any other sampling design.
Despite the increased sample sizes and increased spatial accuracy of animal locations obtained by GPS collars, inherent biases in this technology remain an evolving challenge for their users. Large-scale studies across heterogeneous landscapes may suffer unequal sample sizes among individuals due to the local effects of GPS bias. Rarification of data to investigate resource selection for specific behaviours, e.g. small- vs. large-scale movements (Johnson et al. 2002), or for certain time periods, e.g. day vs. night, will restrict sample sizes potentially to within the range for which we observed pervasive type II errors and coefficient bias. Further, researchers will adapt their questions to take advantage of improving technologies and, thus, sampling intervals will become increasingly shorter to the extent allowed by battery capacity. In so doing, coefficient bias may become more problematic rather than less so over time. The bias correction techniques we present can be used to overcome many of these issues; however, large sample tests across a broad range of conditions may be necessary to understand the stability of the patterns we observed.