DOI: 10.5061/dryad.wwpzgmstj
title: Data from: Seven year decline of mountain hare abundance in the Peak District, England

description: In England the mountain hare is found only in the Peak District, and is a
 remnant population surviving from translocations from Scotland during the
 1870s, of the genetically distinct subspecies Lepus timidus
 scoticus.  Population monitoring undertaken by Manchester
 Metropolitan University and Queen’s University Belfast began in 2017,
 continuing to 2021.  Subsequently, monitoring was conducted by
 Natural England, during 2022-2024, reporting for two sites, Bleaklow and
 Margery Hill, previously shown having the highest densities of mountain
 hares.  Standardised survey and analytical techniques remained
 identical to previous monitoring, enabling evaluation of change in
 absolute estimates of hare density from 2017-2024. Using distance sampling
 analysis, results showed a statistically significant decline of density
 from 2017=15.9 hares km-2 (95% CI 10.4-24.4) to 2024=6.7 hares
 km-2  (95% CI 3.9-11.5) (p-value = 0.0001). When stratifying by
 habitat class, highest densities of hares km-2 were found on restored
 blanket bog (27.9) and statistically significantly higher than all other
 surveyed habitat classes: acid grassland (9.0), grouse moor bog (9.3),
 grouse moor heather (8.3), unrestored bog (19.3)  and unmanaged
 dwarf shrub heath (4.0).  All habitat classes showed declines,
 the largest were on grouse moors. For the two combined survey sites the
 2024 absolute population abundance was estimated at 542 individuals (95%
 CI 315-929). Extrapolating to the wider Peak District the whole population
 abundance was estimated to have declined from 3,562 individuals (95%
 2,291-5,624 CI ) to 1,038 individuals (95% CI 604-1,765).  Were
 this trajectory to continue, the mountain hare would likely disappear from
 England within the next few years. The causes of decline since 2017 are
 unknown. Lagomorph population sizes can fluctuate substantially owing to
 parasite mechanisms.  Mountain hares persist better on restored
 blanket bog areas.  Overall the population is small and
 declining, exhibiting increased extinction risk and meriting conservation.
description: We have submitted our observation data, gathered from 2017 to
 2024 by walking by daytime a fixed series of transects repeated in winter
 each year and recording observations to mountain hares on two locations:
 Bleaklow and Margery Hill in the Peak District, England, UK, with distance
 sampling principles.  Please refer to the leading text
 book Introduction to Distance Sampling by Buckland et al. 2001 for
 extensive information on this approach.
description: # Data from: Seven year decline of mountain hare abundance in the Peak
 District, England
 [https://doi.org/10.5061/dryad.wwpzgmstj](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](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 | Region | Area | Line transect | Line length | Perp distance | Cluster size | | :----- | :---- | :------------ | :---------- | :------------ | :----------- | | 2017 | 80.83 | BBM | 4.99 | 27 | 1 | 2/. By habitat class Use file 2017_TO_2024_BY_YEAR_BY_HABITAT_BMH_250217.csv | Region | Area | Line transect | Line length | Perp distance | Cluster size | | :----- | :--- | :------------------------ | :---------- | :------------ | :----------- | | ACID | 8.54 | BLEAKLOW\_HS \_ACID\_2021 | 0.1 | 28 | 1 | 3/. By  habitat class and by year Use file 2017_TO_2024_BY_MEAN_HABITAT_BMH_250217.csv | Region | Area | Line transect | Line length | Perp distance | Cluster size | | :--------- | :--- | :----------------------- | :---------- | :------------ | :----------- | | 2017\_ACID | 8.54 | BLEAKLOW\_RC\_ACID\_2017 | 0.83 | 325 | 1 | **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, *χ*2 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 *χ*2 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](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.