Distance sampling: Comparing walked transects and road transects for rock ptarmigan densities and population trends

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.

Methods
Study area

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).

Walked and Driven Transects

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%.

Analyses

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 < 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 < 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 < 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.

Data exploration and comparison of the time series

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 (<60 observations) when broken down according to period.