Statistical methods

Choice of start date and time period

The standard start year for most NGC series is 1961, corresponding to the formal start of the NGC. In addition, for mammals under the Tracking Mammals Partnership, summary trends were also evaluated for the most recent 25-year period and from 1995. The 25-year period is a standard component in the UK Biodiversity Action Plan listing procedure (Anon. 1994, 1995) and in the evaluation of avian conservation status (e.g. Eaton et al. 2009). The year 1995 is when the British Trust for Ornithology and many other members of the Tracking Mammals Partnership began their mammal monitoring schemes, so provides a standard period for comparisons between schemes.

Statistical procedure

For each species, analysis is based on all annual shoot returns greater than zero. Shoots contributing only one year's data were omitted. Statistical analysis followed the approach adopted by Whitlock et al. (2003) and was carried out using the GenStat statistical computer package (Lawes Agricultural Trust, Rothamsted). For each species, bag data were analysed using a generalised linear model (McCulloch & Nelder 1996) with a Poisson error distribution and logarithmic link function, with shoot and year as factors and the logarithm of shoot area as an offset variable. For most species, the start year for the series of bag data was taken as 1961, but for several species the it had to be moved forward because of insufficient sites in early years (five contributing sites in any one year was a minimum requirement). The year coefficients were exponentiated to give an index of bag size on the arithmetic scale. All index values were relative to the start year, which had a value of 1. To obtain index values for the standard Tracking Mammals Partnership period starting in 1995, the index values from the full analysis were recalibrated by dividing by the 1995 value. The 95% confidence intervals around the index values were obtained by bootstrapping at the shoot level: for each of 199 bootstrap runs, shoots equal in number to the original sample were selected at random with replacement and a new set of indices obtained as described above (Efron & Tibshirani 1986). For each year, the 95% confidence limits were taken as the lower and upper 95th percentiles of the distribution of all 200 index values.

To measure the percentage change between the first and last years of each time period, a generalized additive model (GAM, Hastie & Tibshirani 1990) was fitted to the bag indices with one degree of freedom per decade or part-decade, then the percentage change calculated from the GAM fitted values for the first and last years. The 95% confidence limits were obtained by fitting GAMs to each bootstrap sample, calculating the percentage change, and selecting the lower and upper 95th percentiles of the 200 values that resulted. If the 95% confidence interval did not include zero, then the percentage change was declared significant at P < 0.05.

Analyses were carried out for the UK as a whole. For mammals under the Tracking Mammals Partnership, analyses were also carried out for England, Scotland, Wales and Northern Ireland, and by environmental zones, in all cases where there were sufficient data. Because of the lack of data, no analyses could be carried out for Chinese Water Deer and Wild Boar.

References

  • Anon. (1994). Biodiversity: The UK Action Plan. HMSO, London.
  • Anon. (1995). Biodiversity: The UK Steering Group Report. Volume 2: Action Plans. HMSO, London.
  • Eaton,M.A., Brown,A.F., Noble,D.G., Musgrove,A.J., Hearn,R.D., Aebischer,N.J., Gibbons,D.W., Evans,A.D. & Gregory,R.D. (2009). Birds of Conservation Concern 3: the population status of birds in the United Kingdon, Channel Islands and Isle of Man. British Birds 102: 296-341.
  • Efron,B. & Tibshirani,R.J. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science 1: 54-77.
  • Hastie, T.J. & Tibshirani, R.J. (1990). Generalized Additive Models. Chapman & Hall, London.
  • McCullagh, P. & Nelder, J.A. (1996). Generalized Linear Models, 3rd edn. Chapman & Hall, London.
  • Whitlock, R.E., Aebischer, N.J. & Reynolds, J.C. (2003). The National Gamebag Census as a Tool for Monitoring Mammal Abundance in the UK. GCT Research Report to JNCC. The Game Conservancy Trust, Fordingbridge.

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