Using the Mahalanobis distance statistic with unplanned presence-only survey data for biogeographical models of species distribution and abundance: a case study of badger setts

Project-specific data for biogeographical models are often logistically impractical to collect, forcing the use of existing data from a variety of sources. Use of these data is complicated when neither absence nor an estimate of the area sampled is available, as these are requirements of most analytical techniques. We demonstrate the Mahalanobis distance statistic (D-2), which is a presence-only modelling technique and does not require information on species absence or the sampled area. We use badger (Meles meles) setts as the basis for this investigation, as their landscape associations are well understood, and survey data exist against which to compare estimates of sett distribution and abundance. England and Wales (151,403 km(2)). We used stratified random samples of sett locations, and landscape variables that are known to be important for choice of badger sett location within a geographic information system at a cell resolution of 100 x 100 m. Landscape conditions at two scales were extracted, at and around sett locations, and the D-2 was used to classify all cells in England and Wales into a sett suitability model. Comparison of this sett suitability model with known main sett densities allowed estimates of main sett density to be made across England and Wales, with associated uncertainty. The sett suitability model was shown through iterative sampling and model evaluation using independent data to be stable and accurate. Main sett density estimates were biologically plausible in comparison with previous field-derived estimates. We estimate 58,000 main setts within England and Wales, with 95% confidence intervals suggesting a value between 31,000 and 93,000. The D-2, which could be applied to other species and locations, proved useful in our context, where absence data were not available and the sampled area could not be reliably established. We were able to predict sett suitability across a large area and at a fine resolution, and to generate plausible estimates of main sett density. The final model provides valuable information on probable badger sett distribution and abundance, and may contribute to future research on the spatial ecology of badgers in England and Wales.