DOI: 10.5061/dryad.zgmsbccpj
title: Distance sampling: Comparing walked transects and road transects for rock ptarmigan densities and population trends

description: We compared population trends for rock ptarmigan (Lagopus muta) densities
 (2003‒2019) derived from walked transects and driven road transects in
 Mosfellsheiði and Slétta in southwest and northeast Iceland, respectively.
 The walked transects were laid out according to a random rule.
 Convenience-based road transects could give biased population density
 estimates if roads affect the distribution of ptarmigan. We used distance
 sampling to compare density estimates provided by the two survey types.
 Our results showed that road transects were more than five times faster to
 conduct than walked transects. Estimated ptarmigan density changed in
 synchrony for the two survey methods in both study areas. Mean density
 estimates in Mosfellsheiði were similar for the two survey methods (walked
 transects 1.6 males × km-2, 95% CI 1.4‒1.8; road transects 1.7 males ×
 km-2, 95% CI 1.4‒2.0), but not in Slétta, where density estimates for road
 transects were significantly lower (walked transects 5.2 males × km-2, 95%
 CI 4.7‒5.7; road transects 3.2 males × km-2, 95% CI 2.8‒3.7). Density
 estimates from the Slétta road transects were biased low because parts of
 the road intersected areas that ptarmigan did not occupy. This bias was
 remedied, at least partially, by considering the area of non-habitats
 within the surveyed belt by applying multipliers in the distance analysis.
 Collectively, our results demonstrate that road-based surveys and distance
 sampling can provide an economical means for estimating density and annual
 population trends for open country grouse (Tetraonini) like ptarmigan.
 Still, density estimates can be biased without proper consideration for
 survey design.
description: <strong>Study area</strong>
   Our study occurred in two distinct
 areas, one in southwest Iceland called Mosfellsheiði (N64.13591,
 W21.44585) and the other in northeast Iceland called Slétta (N66.4683,
 W16.476; Fig. 1). The linear distance between the two areas is 360 km. The
 Mosfellsheiði study area (210 km2) is 15 km from the coast and has
 altitudes ranging from 200 to 400 m above sea level. The Slétta study area
 (50 km2) is close to the coast, and altitudes range from sea level to
 approximately 40 m above sea level. The landscape on Slétta is best
 described as flat or gently undulating; on Mosfellsheiði, the ground is
 less flat, with low ridges and shallow depressions between them. Both
 study areas are treeless. The habitat types on Mosfellsheiði were more
 variable than those on Slétta. The dominant habitat types on Mosfellsheiði
 were mosslands (57%) and heathlands (23%), but other components included
 lava fields (7%), wetlands (7%), and fell fields, moraines, and sands
 (combined 4%). The dominant habitat types on Slétta were heathlands (89%).
 Other habitat types of importance were fell fields, moraines and sands
 (3%), lakes (3%), and farmland (3%) (we used a digital map of habitat
 types to calculate the relative importance of habitat types; Icelandic
 Institute of Natural History n.d.-b).  
 <strong>Walked and Driven
 Transects</strong>  
 In Iceland, ptarmigan have traditionally been surveyed in
 spring from late April to late May, when the birds are in their breeding
 territories. The territories are spaced across the landscape, and males
 are confined to their territories throughout a ca.  8-week period from
 late April to early June (Gardarsson 1988). Surveys are conducted either
 early in the morning (04:00–11:00) or late in the afternoon (16:00–23:00)
 when ptarmigan are most active (Nielsen et al. 2004). Surveys target male
 ptarmigan because they have much greater detectability than females in
 spring. Males retain their white winter plumage during the first 3–4 weeks
 of the territorial period, making this the best time to observe them (Fig.
 2). Males become more difficult to detect after mid-May when their
 behavior and plumage change (Montgomerie et al. 2001).
   Ptarmigan have been surveyed in
 Iceland using road transects since 1999 (Nielsen et al. 2004). Roads
 selected for surveying are primarily secondary roads that traverse
 ptarmigan breeding habitats and are passable in spring. The Slétta road
 survey route was started in 1999 and is 22.4 km long. The Mosfellsheiði
 road survey route was started in 2003 and is 43.6 km long (Fig. 1). For
 the distance analysis, we divided the road survey routes into 1-km
 transects, but some end transects were either slightly longer or shorter
 than 1 km. This was done to measure encounter rate variance. To evaluate
 whether road surveys yielded unbiased estimates of ptarmigan density, we
 initiated walked surveys in 2003 along parallel transects randomly
 superimposed on the two study areas, Slétta and Mosfellsheiði. However,
 this design turned out to be inefficient as too much time was spent by
 observers walking between transects. In 2004, we adopted transects
 arranged in a zig-zag pattern, as suggested by Buckland et al. (2001, p.
 235), and randomly located them across the study areas, which eliminated
 wasted time spent walking between transects (Fig. 1). Walked transects had
 starting or ending points on the road transects or adjacent roads.
 Starting/ending points were separated by 2 km and 3 km at Slétta and
 Mosfellsheiði, respectively. The length of the walked transects across the
 country from the roads was set to cover the areas traversed by the road
 transects. The walked surveys in the two study areas were last done in
 2019, but the road surveys continued.  
 One observer conducted ptarmigan surveys along the walked
 transects. The observer used a GPS receiver to find the starting point of
 the transect, stay on the transect line, and navigate to the endpoint of
 the transect. We had starting and ending times for each transect surveyed
 but not for individual observations made. During the survey, the observer
 walked at an even speed and looked for ptarmigan on both sides of the
 transect. Binoculars were used to aid in the detection of ptarmigan. The
 perpendicular distance between each male ptarmigan and the transect line
 was measured using a laser range finder (Leica LRF 800 and Leica
 Rangemaster 900, both give measurements within the range of 10‒800 m), or
 estimated if the range finder did not provide a measure. If the bird was
 first seen ahead of the observer, measurement was not taken until the bird
 was perpendicular to the line, and if the bird moved in the meantime, the
 measurement was to the place where it was first observed.
   Ptarmigan surveys were conducted on
 road transects on Mosfellsheiði by a single driver-observer, whereas an
 assistant often accompanied the driver at Slétta. We drove field vehicles
 slowly along the road (20–30 km per hour), with intermittent stops to look
 for birds. Perpendicular distances of all grouse observations to the
 transect were recorded as described for the walked transects. In addition,
 the geographic coordinates of the observation points and observation time
 were recorded using a GPS receiver.  
 The area surveyed by the two methods on Slétta was 46 km2
 combined for a truncation distance of 400 m. The survey areas of the road
 and walked transects overlapped by 7 km2 or 15%. The area surveyed by the
 two methods on Mosfellsheiði was 90 km2 combined for a truncation distance
 of 325 m. The road and the walked transects overlap was 6 km2 or
 7%.  
 <strong>Analyses</strong>
   For the analysis, we followed
 recommendations from Buckland et al. (2001), Marques et al. (2007), and
 Hawkshaw et al. (2017). First, we made frequency histograms of distance
 data for each of the four site × type surveys. The maximum detection
 distances for Slétta road transects and walked transects were 650 m and
 850 m, and for Mosfellsheiði road transects and walked transects, 595 m
 and 800 m, respectively. There was evidence of rounding distances to
 favored values, close to the transect line and further out. However, it
 was believed that this would not influence the analysis results, and the
 data was not grouped into distance intervals for analysis. All the
 histograms indicated a long tail of larger distances, and we
 distance-truncated the data sets before analysis (Buckland et al. 2001).
 Exploratory analysis with different truncation values indicated that 400 m
 was an adequate truncation point for both Slétta walked transects and road
 transects and 325 m for both Mosfellsheiði walked transects and road
 transects.   We conducted an
 exploratory analysis of four potential covariates that we a priori
 considered could affect the detectability of ptarmigan, namely observer
 (Fig. 3A), period (Fig. 3B), date (Fig. 3C), and time (Fig. 3D). Observer
 and period were parameterized as factor covariates. To be included in our
 analysis, each factor had at least 60 observations. For walked transects,
 we aggregated all observations from observers with less than 60
 observations to one category (called NN). Accordingly, there were five
 observer IDs used for both Slétta and Mosfellsheiði. We could not use
 observer as a covariate for the road transects on Mosfellsheiði and Slétta
 as the same person was responsible for most of the observations at each
 site; observations made by others were less than 60. There was a clear
 difference in distance distributions by the observers for walked transects
 on Mosfellsheiði and Slétta (Fig. 3A). Therefore, we kept the observer
 covariate (OBS) in our subsequent analysis. Due to small sample sizes
 during each year, we could not evaluate yearly differences in detection
 probability. Instead, we evaluated whether detection probability varied
 over three defined periods: period 1 = 2003-2008, period 2 = 2009-2014,
 and period 3 = 2015-2019. There was a clear difference in distance
 distributions by period for all four survey cases (Fig. 3B). Therefore, we
 kept the period covariate (PER) in our subsequent analysis.
   We expected that the survey date would
 affect the detectability of ptarmigan, i.e., detectability would become
 more difficult at later dates because of phenological changes in
 territorial behavior and molt of ptarmigan males. We used the Pearson
 correlation coefficient (PCC) to check for a correlation between distance
 observations and survey date among the four survey cases. Only the Slétta
 walked transects showed a significant negative correlation (p value of PCC
 &lt; 0.05; Fig. 3C). However, distance models that included date,
 input as Julian day, as a covariate would not converge, so we eliminated
 date from further consideration. We also expected that observation time
 would affect the detectability of ptarmigan, i.e., detectability would be
 highest early in the morning and again late in the afternoon but lowest
 during the middle of the day (Fig. 3D). We used PCC to check for a
 correlation between distance observations and observation time for morning
 observations (observations made before 12:00), and again for afternoon
 observations (observations made after 14:00). For road transects we had
 the exact time for each observation. For walked transects, we used the
 mid-time between start and finish times in our analysis. Of the eight
 comparisons, only two were significant (p &lt; 0.05): the Slétta
 walked transects showed the expected morning pattern, a linear decline in
 detections from early morning towards noon, and only the Mosfellsheiði
 walked transects showed the expected afternoon pattern, a linear increase
 in detections from early afternoon towards evening. Because of the diurnal
 relationship's non-linear nature and the weak pattern, we decided not
 to include observation time as a covariate in our analysis.
   We fit and evaluated distance sampling
 models using the conventional distance sampling engine (CDS) and the
 multiple covariate distance sampling engine (MCDS) in Distance 7.5 Release
 2 (Thomas et al. 2010). The minimum sample size of 60–80 observations
 needed to adequately model a robust detection function (Buckland et al.
 2001) excluded the possibility of obtaining a separate function for each
 year for the walked and the road transects on Slétta and Mosfellsheiði.
 Instead, we modelled standard detection functions across all years for
 each case. We used observation year to post-stratify the data, allowing us
 to estimate each year's density. The key functions and series
 expansions that we tested were: 1) uniform + cosine; 2) uniform + simple
 polynomial; 3) half-normal + cosine; 4) half-normal + Hermite polynomial;
 5) hazard-rate + cosine; and 6) hazard-rate + simple polynomial. Note that
 uniform key functions are not allowed in the MCDS engine. We compared 14
 candidate models for the walked transects, including eight with covariates
 (OBS and PER). [LM1] [ÓN2] We could not model OBS + PER because of sample
 size issues (n &lt; 60 for some combinations). We compared 10
 candidate models for the road transects, including four models with the
 PER covariate. The resulting functions had to comply with assumptions
 regarding their shape. The detection function should 1) monotonically
 decrease because detection probability cannot increase moving away from
 the centerline, and 2) have a “shoulder” at low distance values (Buckland
 et al. 2001). The Distance software provides the results of Cramer-von
 Mises and Kolmogorov Smirnov goodness-of-fit tests for the different
 models. We used the minimization of the Akaike Information Criterion (AIC)
 (Akaike 1974) to select among the candidate models (Greenwood 2023). We
 considered models to be parsimonious if they were within 2 AIC units from
 the highest-ranking model.  Among the parsimonious candidate models, we
 selected the “best” model based on what is called the principle of
 parsimony. Namely, simpler models are better if everything else is close
 to equal. [LM3] [ÓN4]    The
 roads were not straight lines, and sharp bends reduced the area surveyed.
 Also, for Slétta, the western part of the road survey routes (11 transect
 legs; 11 km in total length) was on the periphery of the ptarmigan
 habitat; the road divided survey areas into heath (i.e., ptarmigan
 habitat) on one side of the road and non-habitat characterized by
 intertidal zone, ocean, coastal lagoons, and gravel flats on the other
 side. At Mosfellsheiði, the roads always traversed the ptarmigan habitat,
 although some sharp bends in the roads reduced the survey area covered. To
 account for both these effects, we used multipliers applied to the density
 estimation function (Buckland et al. 2001, pp. 57‒58). For the Slétta road
 transects, the multiplier was 1.429 to account for 30% of the total area
 within the 400 m truncation distance was non-habitat according to GIS
 analysis. For the Mosfellsheiði road transects, it was 1.02 to account for
 a 2% reduction in the area surveyed because of sharp bends, according to
 GIS analysis. We also analyzed the Slétta road transect data by censoring
 the 11 legs on the periphery (see above) and using the multiplier 1.053 to
 account for 5% of the total area within the 400 m truncation distance was
 non-habitat.  
 <strong>Data exploration and comparison of the time
 series</strong>   Data
 exploration, plots, and statistical tests were performed with R version
 4.0.2 (R Core Team 2020). We used a cross-correlation function to study
 whether population trends derived by walked and road transects changed in
 synchrony. We used a z-test to compare the average annual estimated
 densities between the two survey methods at each site (Buckland et al.
 2001, pp. 84‒85) with the BSDA package in R (Arnholt and Evans 2023). All
 cartographic data analysis was performed using the software ArcMap 10.8.2
 by Esri, Inc. (http://www.esri.com). The maps (Fig. 1) were made in ArcMap
 and using the habitat map of Iceland as a background (for download of the
 Iceland habitat map, see: https://atlas.lmi.is/NI_Data/); all graphs were
 created in Statistica version 13 by Dell, Inc.
 (software.dell.com).  
 [LM1]You did not address in your revision or respond to the
 reviewer’s comments regarding the consideration of only univariate
 models.  The reviewer suggested you consider multivariate additive models
 which can improve inference on the support of covariate effects.  Was your
 choice to only consider univariate models in your candidate set due to a
 sample size issue?  Regardless, please add a sentence justifying your
 univariate approach.  
  [ÓN2]This was a sample size issue. We intended to do it for
 OBS+PER but had too few observations for some of the  OBS combinations
 (&lt;60 observations) when broken down according to
 period.
description: # Distance sampling: Comparing walked transects and road transects for
 rock ptarmigan densities and population trends
 [https://doi.org/10.5061/dryad.zgmsbccpj](https://doi.org/10.5061/dryad.zgmsbccpj) ## Description of the data and file structure Spring surveys of territorial ptarmigan males have been used to derive annual densities in Iceland. These counts were started in the early 1960s using the territory mapping method on designated plots, but since 1999, walked and road (driven) transects have been included, applying the distance sampling technique to collect and analyze the transect data. While the territory mapping method assumes the detection of all individuals on the designated plot, distance sampling considers variable detection probabilities based on the distance from the transect and other covariates. Road transects for ptarmigan are less demanding than walked transects. Still, they may break one of the basic assumptions of distance sampling, namely random spacing of transects, and roads could potentially affect the distribution of the targeted species. The constraints on monitoring ptarmigan densities on a distribution-wide basis in Iceland are time, money, and personnel. Currently, 2200 km of road transects are surveyed annually for ptarmigan (Icelandic Institute of Natural History, unpublished data); conducting walked surveys at randomly selected off-road transects on this scale is unrealistic. To evaluate the suitability of road-based surveys for estimating unbiased trends in ptarmigan population size, we compared annual densities derived from road transects and walked transects in Iceland from 2003–2019. Specifically, our objectives were to 1) estimate and compare annual densities and temporal trends of ptarmigan estimated from off-road walked transects and driven road-based transects occurring at two distinct study areas, and 2) assess evidence of ptarmigan avoidance of roads, and 3) compare the effort required for walked and road survey protocols. ### Files and variables #### File: Effort\_minutes\_per\_km.csv **Description:**  ##### Variables * Area: There are two survey areas, Slétta (Sle) in the northeast of Iceland and Mosfellsheiði (Mos) in the southwest of Iceland * Platform: road means that the data relates to a road survey where observations were made from a car, walked relates to walked transects laid out according to Distance protocol * Walked_Transects: this is the id of the different walked transects, for road transects we only have time for the total transects, not the different segments. * Length (km): this is the length of the different walked transects and total length of the road transects * Year: relates to the different years of the study * DurationMinutes: this is the total time in minutes it took to complete the survey * Min per km: here are minutes per km walked or driven #### File: Mos\_road.csv **Description:** The results from a road survey for rock ptarmigan males on Mosfellsheiði, southwest Iceland, 2003-2019 ##### Variables * Multiplier: is the multiplier used in the Distance analysis * SurveyType: Mos_road implies that this is a road survey from Mosfellsheiði * Year: year of survey * Period: the survey years 2003-2019 were split into three periods: period 1 = 2003-2008, period 2 = 2009-2014, and period 3 = 2015-2019 * TransectID: Is the ID of the different transects * Line length (km): The length of the transect in km * Perp distance (m):  The perpendicular distance in m of the male rock ptarmigan from transect * DecDate: Date of survey. Before analysis, we transformed the “date” variables to decimal values. We first transformed the variable to Julian date and then divided that value by the number of days in the year. * DecTime: Time of observation. Before analysis, we transformed the “time of day” to decimal values. For “time of day” we used the HH:MM format in Microsoft Excel and converted the values to numeric. * Observer: The IDs of the different observers * Note: Empty cells for Perp distance (m), DecDate, DecTime, Observer, are transect lines that were done/counted but no ptarmigan were observed. #### File: Mos\_walked.csv **Description:** The results from a walked survey for rock ptarmigan males on Mosfellsheiði, southwest Iceland, 2003-2019 ##### Variables * Multiplier: not used * SurveyType: Mos_walked implies that it is a walked survey from Mosfellsheiði * Year: Year of survey * Period: the survey years 2003-2019 were split into three periods: period 1 = 2003-2008, period 2 = 2009-2014, and period 3 = 2015-2019 * TransectID: Is the ID of the different transects * Line length (km): The length of the transect in km * Perp distance (m):  The perpendicular distance in m of the male rock ptarmigan from transect * Dec Date: Date of survey. Before analysis, we transformed the “date” variables to decimal values. We first transformed the variable to Julian date and then divided that value by the number of days in the year. * Dec Time:  Time of observation. Before analysis, we transformed the “time of day” to decimal values. For “time of day” we used the HH:MM format in Microsoft Excel and converted the values to numeric. * Observer: The IDs of the different observers * Note: Empty cells for Perp distance (m), DecDate, DecTime, Observer, are transect lines that were done/counted but no ptarmigan were observed. #### File: Sle\_road.csv **Description:** The results from a road survey for rock ptarmigan males on Slétta, northeast Iceland, 2003-2019 ##### Variables * Multiplier: is the multiplier used in the Distance analysis * SurveyType: Sle_road implies that this is a road survey from Slétta * Year: Year of survey * period: the survey years 2003-2019 were split into three periods: period 1 = 2003-2008, period 2 = 2009-2014, and period 3 = 2015-2019 * TransectID: those are the IDs of the different transects * Line length (km): The length of the transect in km * Perp distance (m): The perpendicular distance in m of the male rock ptarmigan from transect * DecDate: Date of survey. Before analysis, we transformed the “date” variables to decimal values. We first transformed the variable to Julian date and then divided that value by the number of days in the year. * DecTime: Time of observation. Before analysis, we transformed the “time of day” to decimal values. For “time of day” we used the HH:MM format in Microsoft Excel and converted the values to numeric. * Observer: The IDs of the different observers * Note: Empty cells for Perp distance (m), DecDate, DecTime, Observer, are transect lines that were done/counted but no ptarmigan were observed. #### File: Sle\_walked.csv **Description:** The results from a walked survey for rock ptarmigan males on Slétta, northeast Iceland, 2003-2019 ##### Variables * Multiplier: not used * SurveyType: Sle_walked implies that this is a walked survey from Slétta * Year: Year of survey * Period: the survey years 2003-2019 were split into three periods: period 1 = 2003-2008, period 2 = 2009-2014, and period 3 = 2015-2019 * TransectID: Is the ID of the different transects * Line length (km): The length of the transect in km * Perp distance (m):  The perpendicular distance in m of the male rock ptarmigan from transect * Dec Date: Date of survey. Before analysis, we transformed the “date” variables to decimal values. We first transformed the variable to Julian date and then divided that value by the number of days in the year. * Dec Time:  Time of observation. Before analysis, we transformed the “time of day” to decimal values. For “time of day” we used the HH:MM format in Microsoft Excel and converted the values to numeric. * Observer:  The IDs of the different observers * Note: Empty cells for Perp distance (m), DecDate, DecTime, Observer, are transect lines that were done/counted but no ptarmigan were observed. #### File: Sle\_road\_censored.csv **Description:**  The results from a road survey for rock ptarmigan males on Slétta, northeast Iceland, 2003-2019, here the first 10 legs of the road transect were censored (not included) otherwise the data set is identical to Sle_road.csv ##### Variables * Multiplier: is the multiplier used in the Distance analysis * ID: Sle_road_censored implies that this is a road survey from Slétta * SurveyType: Sle_road implies that this is a road survey from Slétta * Year: Year of survey * TransectID: Is the ID of the different transects * Line length (km): The length of the transect in km * Perp distance (m): The perpendicular distance in m of the male rock ptarmigan from transect * DecDate: Date of survey. Before analysis, we transformed the “date” variables to decimal values. We first transformed the variable to Julian date and then divided that value by the number of days in the year. * DecTime:   Time of observation. Before analysis, we transformed the “time of day” to decimal values. For “time of day” we used the HH:MM format in Microsoft Excel and converted the values to numeric. * Observer: The IDs of the different observers * Note: Empty cells for Perp distance (m), DecDate, DecTime, Observer, are transect lines that were done/counted but no ptarmigan were observed. ## Code/software We fit and evaluated distance sampling models using the conventional distance sampling engine (CDS) and the multiple covariate distance sampling engine (MCDS) in Distance 7.5 Release 2 (Thomas et al. 2010). Thomas, L., Buckland, S. T., Rexstad, E. A., Laake, J. L., Strindberg, S., Hedley, S. L., Bishop, J. R. B., Marques, T. A. and Burnham, K. P. 2010. Distance software: design and analysis of distance sampling surveys for estimating population size. – Journal of Applied Ecology 47(1): 5–14. [https://doi.org/10.1111/j.1365-2664.2009.01737.x](https://doi.org/10.1111/j.1365-2664.2009.01737.x)