https://doi.org/10.5061/dryad.wwpzgmstj

Description of the data and file structure

Data set for Distance Sampling Analysis

Descriptions

The data is as follows:

Region: This is a grouping of the data according to the stratification analysis employed.

Area: This measures the entire visual area available for survey in square kilometres.

Line transect: These are the individual square transects which were surveyed, each transect given a unique letter code.  Each transect was a four sided 1km square which matched that of the grid system used on the observer’s GPS device, was followed repeatedly each year.

Line length: This is the recorded actual distance surveyed in kilometres.  The distance is sometimes greater than 4km, because the surveyor navigated around or though deep cloughs and valleys. 

Perp distance*: This is the distance to the mountain hare, from the transect line, in metres.  This was derived by measuring the distance from the observer to the mountain hare with a laser range finder, taking an angle using an angle board attached to a compass, and then using trigonometry to calculate distance to transect line.

Cluster size*: This is the number of mountain hares observed at each encounter. 

NOTE: Empty cells are deliberate and represent zero values: Cluster size and Perp distance.  These are deliberately empty since Software Distance cannot accept zero value for cluster size estimation and would report errors.

Data for habitat classes: These indicate how each transect and its associated mountain hare observations were allocated to a map of six different habitat classes characteristic of English uplands.  These were: acid grassland, grouse moor bog, grouse moor heath, restored bog, unrestored bog, and unmanaged dwarf shrub heath. 

The dataset is always the same.

However, it is configured differently to accomplish the distance sampling analyses in three ways:

1. by year  
2. by habitat class
3. by habitat and by year

Therefore, the observation data is identical between the three files. However, data structure and transect identifications are cut differently between them to enable these three analyses. All data reconciles between the three, i.e., observations and transect lengths.  

Software

The files have been sorted to enable uploading into Software Distance. The analysis used version 7.3

Details are at the University of St. Andrews website.

https://distancesampling.org

Note that Software Distance has some different estimators from those of the R package of Distance. E.g., Software Distance uses a distance/size biased cluster size estimator.  All analyses we conducted were with Software Distance.

To load up the data, select the columns according to the requirements of Software Distance. Any alterations to the files may result in errors. Data  headings are as follows, with the first row showing:

1/. By year

Use file 2017_TO_2024_BY_YEAR_ONLY_BMH_250217.csv

2/. By habitat class

Use file 2017_TO_2024_BY_YEAR_BY_HABITAT_BMH_250217.csv

3/. By  habitat class and by year

Use file 2017_TO_2024_BY_MEAN_HABITAT_BMH_250217.csv

Analyses

We analysed our data with DISTANCE v.7.3 (Thomas et al. 2010), using different data filtering and model selections. We assessed different truncation distances and bin widths. We compared detection models with three key functions: uniform, half-normal, and hazard rate, with cosine or polynomial expansion terms (Buckland et al. 2001 47; Williams & Thomas 2007). We assessed the suitability of assumptions and models using histograms, quantile-quantile plots, χ2 goodness of fit statistics, and the fit of the detection function close to the transect line g(0). We compared and sought simple models with few parameters, lower AIC values between models using the same data selection, higher χ2 goodness of fit statistics and lower detection probability cv values (Buckland et al. 2001).

For stratification, the global detection function was applied, with encounter rate, cluster size and density varying by strata in three ways: (1) by year, pooled within each year, without habitat information; (2) by habitat class, mean values for all eight years together; (3) by habitat and by years i.e. 6 habitats over 8 years = 48 strata. Each stratification analysis used the same data, allocating transects, transect distances and observations to the different strata definitions.   Parameter estimates were compared, with 95% confidence intervals. Density comparisons between pairwise combinations of the strata of habitat classes for 2017-2024 were made using the t-statistic which applies the Satterthwaite approximation, accounting for unequal sample sizes (Buckland et al. 2001: 84-86) and considers the lack of independence of data arising from using a common detection function between strata. We evaluated significance with a Bonferonni corrected p-value and also calculated effect sizes (Field et al. 2012: 57-58).

References

Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., & Thomas, L. (Eds.) 2001. Introduction to distance sampling. Oxford University Press

Field, A., Miles, J. & Field, Z. 2012. Discovering statistics with R. SAGE Publications. London.

Thomas, L., Buckland, S. T., Rexstad, E. A., Laake, J. L., Strindberg, S., Hedley, S. L., Bishop, J. R. B., Marques, T. A., & Burnham, K. P. 2010. Distance software: Design and analysis of distance sampling surveys for estimating population size. Journal of Applied Ecology, 47, 5–14.

https://doi.org/10.1111/j.1365-2664.2009.01737.x

Williams, R., & Thomas, L. (2007). Distribution and abundance of marine mammals in the coastal waters of British Columbia, Canada. Journal of Cetacean Resource Management. 9(1):15-28

Usage notes

Microsoft Excel can be used to read the .csv files.

Software Distance can be used to conduct distance sampling analysis on the .csv files.