Does perspective matter? A case study comparing Eulerian and Lagrangian estimates of common murre (Uria aalge) distributions

Abstract Studies estimating species' distributions require information about animal locations in space and time. Location data can be collected using surveys within a predetermined frame of reference (i.e., Eulerian sampling) or from animal‐borne tracking devices (i.e., Lagrangian sampling). Integration of observations obtained from Eulerian and Lagrangian perspectives can provide insights into animal movement and habitat use. However, contemporaneous data from both perspectives are rarely available, making examination of biases associated with each sampling approach difficult. We compared distributions of a mobile seabird observed concurrently from ship, aerial, and satellite tag surveys during May, June, and July 2012 in the northern California Current. We calculated utilization distributions to quantify and compare variability in common murre (Uria aalge) space use and examine how sampling perspective and platform influence observed patterns. Spatial distributions of murres were similar in May, regardless of sampling perspective. Greatest densities occurred in coastal waters off southern Washington and northern Oregon, near large murre colonies and the mouth of the Columbia River. Density distributions of murres estimated from ship and aerial surveys in June and July were similar to those observed in May, whereas distributions of satellite‐tagged murres in June and July indicated northward movement into British Columbia, Canada, resulting in different patterns observed from Eulerian and Lagrangian perspectives. These results suggest that the population of murres observed in the northern California Current during spring and summer includes relatively stationary individuals attending breeding colonies and nonstationary, vagile adults and subadults. Given the expected growth of telemetry studies and advances in survey technology (e.g., unmanned aerial systems), these results highlight the importance of considering methodological approaches, spatial extent, and synopticity of distribution data sets prior to integrating data from different sampling perspectives.


| INTRODUC TI ON
Distribution and abundance data of mobile species are useful for identifying important foraging, migration, and breeding habitats MacArthur, 1972). Data can be obtained from observations collected during surveys within a predetermined frame of reference (i.e., Eulerian sampling) or by sampling discrete locations estimated using animal-borne tracking devices (i.e., Lagrangian sampling; Rutz & Hays, 2009, Tremblay et al., 2009. Eulerian survey designs sample at x-y coordinates at predetermined stations or along contiguous transects, often replicated through time. The primary objective of Eulerian sampling approaches is to obtain information about animal distribution and abundance in a predefined area and time period. In the ocean, vessel-based Eulerian surveys regularly use direct sightings to quantify the distributions of marine mammals (Ainley, Dugger, Toniolo, & Gaffney, 2007;Ballance & Pitman, 1998;Keiper, Ainley, Allen, & Harvey, 2005) and seabirds Ballance, Pitman, & Reilly, 1997). Ships can survey coastal and offshore ecosystems for relatively long (i.e., weeks to months) periods across hundreds to thousands of kilometers, and simultaneously sample in situ abiotic and biotic factors including seawater temperature, chlorophyll concentration, and prey species abundance and composition, which allows quantification of animalhabitat relationships (Ainley, Ribic, & Woehler, 2012;Fiedler et al., 1998). However, ships are slow relative to the movement of mobile species including seabirds, and the flux of birds into or out of a survey area, as well as vessel avoidance or attraction by some species, may bias distribution and abundance estimates by convoluting spatial patterns with the passage of time (van Franeker, 1994;Wahl & Heinemann, 1979). Aerial surveys (e.g., airplanes and drones) are another Eulerian sampling approach that sample along transects in a relatively short (i.e., hours to days) period and, because the movement of seabirds is slow relative to an aircraft, provide a synoptic estimate of species distribution and abundance (Briggs, Tyler, & Lewis, 1985a;Buckland et al., 2001;Certain & Bretagnolle, 2008).
Aircraft can survey areas often inaccessible to ships (e.g., nearshore shallow habitats and ice fields), but may not be able to transit as far offshore to survey pelagic habitats beyond the continental shelf (Henkel, Ford, Tyler, & Davis, 2007;Hodgson, Baylis, Mott, Herrod, & Clarke, 2016). Accordingly, ship-based and aerial survey data are limited by the spatial and temporal extent and sampling resolution of the survey (Watanuki et al., 2016). Species detectability can also be an issue, as smaller, rare, or cryptic species may not be accurately represented in a data set (Barbraud & Thiebot, 2009;Monk, 2014).
Further, for many species, breeding status, sex, and age of individual seabirds cannot be discerned from sighting data, constraining most analyses to the population level. Despite these limitations, transect surveys from ships transiting the world's oceans were an early and significant contributor to studies of pelagic seabird distributions (Brown, 1980;Murphy, 1936;Wynne-Edwards, 1935), and ship and aircraft surveys continue to be an important component of seabird research (Ainley et al., 2009;Certain & Bretagnolle, 2008;Hunt et al., 2018).
In contrast to Eulerian approaches, Lagrangian survey designs track seabirds through space and time using data logging or tracking devices attached to individuals (Burger & Shaffer, 2008;Hart & Hyrenbach, 2009;Hooker, Biuw, McConnell, Miller, & Sparling, 2007). Satellite-linked tags that provide near-real-time, continuous, and independent sampling are a common tool for Lagrangian sampling (Adams, MacLeod, Suryan, Hyrenbach, & Harvey, 2012;Hatch, Meyers, Mulcahy, & Douglas, 2000). Depending on mobility of the species, a Lagrangian sampling approach may increase the spatial extent and resolution of the survey area compared with an Eulerian perspective (Block, Costa, Boehlert, & Kochevar, 2002). Fine-scale (i.e., 1-10 km) movements of individuals can be measured with satellite tags and then matched as closely as possible to remotely sensed, modeled, or in situ environmental data to gain insights on correlations between movement and habitat use (Adams & Flora, 2010;Phillips, Horne, Adams, & Zamon, 2018).
As the number of Eulerian and Lagrangian studies of marine mammals and seabirds increases (Block et al., 2016;Drew, Piatt, & Renner, 2015), efforts to combine data from these two perspectives have increased. This is due in part to the potential to expand spatial and temporal sampling scales, which could enhance studies of species' distributions and inform conservation efforts (Fujioka et al., 2014;Watanuki et al., 2016). Data from Eulerian and Lagrangian perspectives or platforms may be complementary, but integration can be complicated by biases inherent in data collected from different sampling approaches, including a mismatch in spatiotemporal sampling coverage. Concurrent and spatially overlapping data from both Eulerian and Lagrangian perspectives are rare, consequently differences in species distribution patterns attributable to sampling perspective are difficult to evaluate.
We used contemporaneous data from Eulerian and Lagrangian surveys to examine whether sampling perspective or platform influences estimates of a seabird's distribution. We quantified and compared common murre (Uria aalge) density distributions observed during May, June, and July 2012 from ship, aerial, and satellite telemetry surveys in the northern California Current. Murres are one of the most numerous seabird species along the west coast of North America (Briggs, Tyler, Lewis, & Carlson, 1987;Carter et al., 2001;Thomas & Lyons, 2017), with ~532,000 individuals attending colonies and breeding along the Oregon and Washington coasts during spring and summer (April-August; Naughton, Pitkin, Lowe, So, & Strong, 2007;Speich & Wahl, 1989). Nesting adult murres are central place foragers that search for prey within ~100 km of their colony (Davoren, Montevecchi, & Anderson, 2003;Decker & Hunt, 1996;Hatch et al., 2000). Thus, the expected movement constraints of murres and the availability of concurrent ship, plane, and telemetry data sets allowed us to compare spatial patterns of murres observed during the breeding season using different sampling perspectives and platforms.

| ME THODS
All sampling was conducted in continental shelf waters along the northern Oregon and Washington coasts, with a focus near the mouth of the Columbia River and colonies adjacent to this geographic feature.

| Ship-based surveys
We used ship-based data from an ongoing ecosystem research program examining the ocean ecology of salmon off the Washington and Oregon coasts (Brodeur, Myers, & Helle, 2003). Using standard strip transect survey methods (Tasker, Jones, Dixon, & Blake, 1984) Table 1).

| Aerial surveys
We used data from aerial surveys of the northern California  Table 1). Transects flown during A-1 were spaced 13.9 km apart and extended 72.4-km offshore, whereas A-2 included a mix of broad survey transects (27.8-km spacing, up to 93.6-km offshore) and two focal-area surveys (each with ten, 25-km-long parallel transect lines spaced 6 km apart) nested within the broad survey transects (Adams et al., 2014;Figure 2). For this study, we treated counts of murres obtained during the two July surveys as one survey for analyses (i.e., all transects were analyzed together) unless otherwise noted. were programmed to transmit every 60 s for 4 hr in the morning (08:00-12:00 hours) and 4 hr in the evening (14:00-18:00 hours), which coincided with Eulerian surveys that were conducted during daylight hours. Locations of individual birds were determined using the ARGOS system (www.argos-system.org; CLS, 2013) and archived via the Satellite Tracking and Analysis Tool (STAT; Coyne & Godley, 2005). To resolve tag attachment or instrument failure, we removed data from tags that did not transmit for more than 2 weeks, had intermittent transmissions (e.g., 5-day gap in transmissions), or showed evidence of halted movement (i.e., when median daily movements fell below the 95% confidence interval of average movement of birds for the sampling year; S. Loredo pers. comm.). To maximize location accuracy, all ARGOS location class data (LC-3 through LC-B, excluding LC-Z) were filtered using speed, distance, and angle, resulting in a nominal spatial accuracy of 3 km (mfilter function in R package argosfilter, Freitas, Lydersen, Fedak, & Kovacs, 2008; for full details see Phillips et al., 2018). We also plotted all tag locations in

| Data analysis
For the two Eulerian data sets, we first compared overall density of murres observed during ship and aerial surveys. We calculated densities of murres observed during ship-based surveys by dividing the total number of murres counted in 3-km bins (~10-min increments) by the strip area searched (0.9 km 2 ) to obtain murres/ km 2 . Similarly, we calculated densities of murres observed during aerial surveys by dividing the total number of murres counted in 2.4-km bins (~1-min increments) by the strip area (either 0.18 km 2 [one observer] or 0.36 km 2 [two observers]) to obtain murres/km 2 .
To determine whether mean densities differed within data sets, we compared densities observed during S-1 and S-2, and A-1 and A-2 using t tests (Zar, 1999). To determine whether offshore distribution patterns varied by survey method, we evaluated histograms of the frequency of murres observed as a function of distance from shore.
We removed the focal-area survey data from S-2 histogram plots as these transects did not extend beyond 25 km of shore.
Because absolute densities cannot be estimated from locations of satellite-tagged murres, we calculated Brownian bridge utilization distributions (Horne, Garton, Krone, & Lewis, 2007) to estimate each tagged murre's probability of occurrence using the kernelbb function in R package adehabitat (Calenge, 2006). A utilization distribution (UD) is a probability distribution that gives the probability density that an animal is found at a given point in space. It is estimated by sampling the location of individuals in space through time.
The Brownian bridge UD approach provides an estimate of space use from animal trajectories with serial autocorrelation of relocations (Horne et al., 2007). We created an overall 99% UD for all 12 murres by first calculating 99% UDs for each individual bird (i.e., 99% cumulative probability that an individual murre would be present in all 3-km 2 cells) and then proportionately weighting the individual UD by its tracking duration (i.e., tracking days per individual divided by total tracking days for all individuals) and summing with the rest of the individually weighted UDs. The overall UD represents a summed probability density surface of tagged murre space use during the full duration of tag transmissions, with a spatial resolution of 3 km 2 .
Because UD values are calculated from a population of individuals and have a spatial context, they are similar to mapped densities and can be compared. To estimate concurrent tagged murre distributions during each ship or aerial survey, we calculated separate UDs of tagged murres during each survey time period, using the full spatial extent of tag locations. For the ship surveys, this included a UD during 30 May-3 June (S-1; n = 10 tagged birds, n = 233 locations) and 21 June-28 June (S-2; n = 8 tagged birds, n = 298 locations).
To compare with the aerial surveys, we calculated a UD on 19 May (A-1; n = 12 tagged birds, n = 60 locations) and on 1 and 4 July (A-2; n = 8 tagged birds, n = 157 locations). Because telemetry data were available for the periods before, between, and after each ship or aerial survey, we calculated separate UDs during these periods to determine whether tagged murre distributions were different earlier or later in the season when Eulerian survey data were unavailable.
Finally, the distance from shore of satellite-tagged murre locations was tabulated and plotted to compare with offshore distributions of murres observed during ship and aerial surveys.
To compare distributions of murres observed from ship and aerial surveys with the satellite telemetry-derived UDs, we created interpolated, continuous-surface density distributions using the kernel interpolation with barriers tool in ArcMap 10.3. Kernel density estimation (KDE) is a simple nonparametric statistical technique TA B L E 1 Description of ship, plane, and satellite telemetry-based data collections for common murres (Uria aalge) in 2012 including sampling perspective and platform type, survey identity, date range, duration, track length, and total sightings or tag locations used for analyses that estimates a real-valued function as the weighted average of neighboring observed data (Worton, 1989). The weight is defined by the kernel, such that closer points are given greater weights, and smoothness is set by the kernel bandwidth (Worton, 1989

| Ship-based surveys
We counted a total of 428 murres during 43.4 km 2 of survey effort during S-1 and 749 murres during 78.8 km 2 of survey effort during S-2 (Table 1). Murres were found across most of the extent of ship surveys (4.7-44.8 km from shore), with greatest numbers of individuals occurring between 10 and 20 km of shore ( Figure 3).

| Aerial surveys
We counted a total of 618 murres during 45.1 km 2 of survey effort during A-1 and 880 murres during 162.5 km 2 of survey effort during A-2 (Table 1). During aerial surveys, we observed murres between 0.3 and 50 km from shore ( Figure 3). The offshore distribution of murres during A-1 was primarily between 5 and 25 km from shore, with greatest numbers of individual murres located 10-15 km from shore. During A-2, most murres occurred within 5 km of shore.
Mean densities did not differ between A-1 (13.7 murres/km 2 ) and A

| Lagrangian sampling
We tracked satellite-tagged murres for an average of 54.2 ± 21.9 days (mean ± SD) between early May and early July. Tracking duration ranged from 18 to 73 days, with 7 of 12 (58%) tags transmitting for ≥63 days (Table 1). Fifty-eight percent (n = 7) of tagged murres were female, 33% (n = 4) were male, and the sex of one murre could not be determined. Most murre locations occurred within 5-10 km from shore (range: 3-76 km), and were closer to shore than murres  (Figure 6a, c). Spatial overlap between the 99% UD and the full kernel density surface (KD) during S-1 was 35%, and 25% of core use areas (50% UD and KD) overlapped. The geographic mean centers of gravity (CGs) were 37 km apart. A similar spatial distribution of tagged murres was observed during the 16 days between ship surveys S-1 and S-2, although the UD revealed that some tagged murres shifted north during this period into Canadian waters along the west coast of Vancouver Island (Figure 5c). During S-2, tagged murres were more broadly distributed throughout Washington coastal waters, with greatest spatial use near Grays Harbor (Figure 6b, d).
Overlap between the 99% UD and the full KD during S-2 was 30%, and 27% of core use areas overlapped. The CGs were separated by

| D ISCUSS I ON
We used concurrent data from ships, planes, and satellite telemetry to illustrate that seabird distributions inferred from independent, F I G U R E 3 Distribution of common murre (Uria aalge) distances from shore during ship (S-1, S-2) and broad aerial surveys (A-1, A-2), and satellite telemetry tag locations during each ship or aerial survey. Dashed vertical lines indicate the offshore extent of each ship or aerial survey. During A-2, the plane surveyed 94-km offshore, but the x-axis was truncated because no murres were observed more than 75 km from shore contemporaneous data sets can indicate similar high-use areas, Meares and Tillamook Head (Carter et al., 2001;Naughton et al., 2007). This is not surprising given that the study period coincided with the breeding season for murres (April-August), a time when both breeding and nonbreeding murres aggregate on the water near colonies before and after foraging bouts (Ainley, Nettleship, Carter, & Storey, 2002;Zador & Piatt, 1999). Regardless of latitude, all murres occurred primarily within 0-25 km of the coast, with tagged murre locations generally occurring closer (3-5 km) to shore than murres observed during ship surveys, which did not survey in shallow water within ~5 km of shore due to hull draft.
Aerial surveys revealed nearshore distributions of murres more similar to the telemetry data, particularly during A-2. Consistently similar densities of murres observed from ship and aerial surveys during May, June, and July demonstrate that large numbers of murres occupy the northern California Current during spring and summer, and that both Eulerian methods can effectively survey the regional distribution of this relatively large-bodied, coastal seabird (Briggs, Tyler, & Lewis, 1985b;Henkel et al., 2007). Satellite telemetry results during the early part of the study indicated similar spatial distributions of murres across independent data sets, River, which is a productive area that supports a variety of prey fish for seabirds and attracts murres (Litz, Emmett, Bentley, Claiborne, & Barceló, 2013;Phillips et al., 2017). The consistent occurrence of murre aggregations near the mouth of the Columbia River, and the relative ease of capturing murres from the water, is the primary reason that all of the at-sea captures and tag deployments during the study occurred in this area. There are no active murre colonies along the coast between the mouth of the Columbia River and Grays Harbor, so our results suggest that murres observed in this area were breeding birds that commuted at least 60 km north from large colonies in northern Oregon or moved a minimum of 50-100 km south from colonies along the Washington coast (e.g., Bodelteh Islands, Grenville Arch Rock; Thomas & Lyons, 2017). Alternatively, as the telemetry data suggest, murres observed in this area may not be associated with a colony (i.e., nonbreeders) and therefore able to continually occupy productive waters near the river mouth without returning to coastal colonies.
Although the data from May suggest that common murres in the ing adults, or failed breeders because these groups exhibit greater dispersals away from colonies than breeding birds (Hatch et al., 2000). Alternatively, the unexpected mobility could indicate that tagging caused individuals to change their movement and/or breeding behavior (see Phillips et al., 2018 for a discussion).
While regional densities of murres observed from ship and aerial surveys were similar during the study period, and the surveys were relatively synchronous, the differences in survey timing and spatial resolution may explain fine-scale disparities in spatial patterns (van Franeker, 1994;Ronconi & Burger, 2009;Ryan & Cooper, 1989). Ship surveys were designed to sample the entire coast from central Oregon to northern Washington, and transects were separated by 35-90 km, which allowed for observations of murre densities across a wider range of the northern California Current but also may have obscured higher-resolution variability. In comparison, the aerial surveys were more limited in their overall latitudinal extent but the greater number of more closely spaced transects, especially the focal-area surveys which were only 6 km apart, may have captured higher-resolution variability in hourly and daily murre distributions than in ship surveys. Murres are known to aggregate near convergent fronts formed along the boundary between fresh and saltwater near the mouth of the Columbia River (Phillips et al., 2018), where prey fish distributions are also concentrated (Litz et al., 2013;Phillips et al., 2017). Variation in Columbia River plume circulation and the formation of convergent fronts occur at temporal periods of hours to days (Jay, Pan, Orton, & Horner-Devine, 2009;Jay, Zaron, & Pan, 2010), which is often not detectable at the sampling resolu- we captured birds at sea, rather than at a colony, breeding status prior to tagging is unknown. There were no major differences in the sex ratio of tagged murres and their movement patterns, suggesting a somewhat random sample, but whether murres segregate at sea in relation to age or breeding status, or colony of origin, is unknown.
Future research on this topic would provide important insight on murre conservation and management in the northern California Current (Thomas & Lyons, 2017). Tracking a small number of individuals can lead to large variability in observed habitat use (Fossette et al., 2014;Hays et al., 2016;Lindberg & Walker, 2007), and sample size may have also influenced the observed results. Of the 12 murres tagged, one flew to California, and five flew to Canada. To better understand the spatial and temporal extent of tagged animal distributions, Lindberg and Walker (2007)   , and therefore offer potentially more opportunities for ecological studies. Aerial surveys, however, can accomplish a survey in a much smaller amount of time, are not as limited by sea surface conditions and ocean depth, and may capture higher-resolution variation in density distributions.
In comparison, a Lagrangian perspective using satellite telemetry enables a much larger spatiotemporal sampling range compared to Eulerian surveys, allowing for a more extensive analysis of habitat use throughout a seabird's potential range. However, these results demonstrate that data from satellite telemetry of birds captured and tagged at sea may not be representative of the full population of interest (Priddel et al., 2014), and space use may not be necessarily related to actual density at sea . By collecting and comparing concurrent data from three independent platforms, we ters observed from either perspective use the same general habitat, but that tagged birds were concentrated nearshore where larger vessels could not survey (c.f., Watanuki et al., 2016). Whether observed differences in spatial distributions of shearwaters were related solely to a spatiotemporal mismatch in sampling coverage, or possibly to differential habitat use or prey availability, remains unknown.
Efforts to combine Eulerian and Lagrangian perspectives using seabird counts within quantitative models have been conducted (Hyrenbach, Keiper, Allen, Ainley, & Anderson, 2006;Louzao et al., 2009;Yamamoto et al., 2015), and methods continue to be refined (Watanuki et al., 2016). Development of separate habitat models using data from each sampling perspective, and then comparing and integrating results across models, presents a powerful tool to quantify factors influencing marine mammal and seabird distributions and habitat use (Watanuki et al., 2016). This integrative approach has facilitated ongoing efforts to identify and delineate marine protected areas for multiple mobile marine predators (Ballard, Jongsomjit, Veloz, & Ainley, 2012;Camphuysen, Shamoun-Baranes, Bouten, & Garthe, 2012;Perrow et al., 2015), as well as dynamic ocean management approaches (Hazen et al., ,2018Maxwell et al., 2015). This type of habitat modeling could be a useful next step for the data presented here, especially in combination with Eulerian survey data from areas used by tagged murres in California and British Columbia to provide a comprehensive analysis of common murre spatial distributions along the west coast. Given the expected growth of telemetry studies (Hart & Hyrenbach, 2009) and efforts to integrate independent data sets (Watanuki et al., 2016), our results serve as a case study on how sampling perspective and choice of platform can influence spatiotemporal observations of species distributions. Overton, and two anonymous reviewers. Reference to trade names or commercial products does not imply endorsement by the U.S.

ACK N OWLED G M ENTS
Government.

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
This study was conceived and designed by EMP, JA, and JEZ. Data were collected by EMP, JA, JEZ, and JJF. EMP conducted data analyses with assistance from JA, JEZ, JJF, and JKH. JA, JEZ, JJF, and JKH contributed to writing the manuscript with EMP. EMP edited the final manuscript, and all authors approve of its submission.