Rule-based habitat suitability modelling for the reintroduction of the grey wolf (Canis lupus) in Scotland

Though native to Scotland, the grey wolf (Canis lupus) was extirpated c.250 years ago as part of a global eradication drive. The global population has recently expanded, now occupying 67% of its former range. Evidence is growing that apex predators provide a range of ecological benefits, most stemming from the reduction of overgrazing by deer–something from which Scotland suffers. In this study, we build a rule-based habitat suitability model for wolves on the Scottish mainland. From existing literature, we identify the most important variables as land cover, prey density, road density and human density, and establish thresholds of suitability for each. Fuzzy membership functions are used to assign suitability values to each variable, followed by fuzzy overlay to combine all four: a novel approach to habitat suitability modelling for terrestrial mammals. Model sensitivity is tested for land cover and prey density, as these variables constitute a knowledge gap and an incomplete dataset, respectively. The Highlands and Grampian mountains emerge strongly and consistently as the most suitable areas, largely due to high negative covariance between prey density and road/human density. Sensitivity testing reveals the models are fairly robust to changes in prey density, but less robust to changes in the scoring of land cover, with the latter altering the distribution of land mainly through the 70–100% suitability range. However, in statistical significance tests, only the least and most generous versions of the model emerge as giving significantly different results. Depending on the version of the model, a contiguous area of between 10,139km2 and 18,857km2 is shown to be 80 to 100% suitable. This could be sufficient to support between 50 and 94 packs of four wolves, if the average pack range size is taken to be 200km2. We conclude that in terms of habitat availability, reintroduction should be feasible.

7 145 of habitat (34). Similarly in north-eastern USA, prey availability and not habitat type explained 72% 146 of spatial wolf population variation (16). Road density is also recognised as a crucial factor in habitat 147 suitability in multiple studies (e.g. (35,36)). This difference between American and European studies 148 suggests that either different limiting factors are at play, or that high covariance makes it hard to 149 disentangle the importance of each variable. 150 Similarly, slightly different wolf predation behaviours emerge from different European 151 studies, though wild ungulates always predominate (though see Ciucci et al. (14), for scavenging 152 behaviour on garbage dumps) (32,37). Though roe and red deer form the majority of wolf diets in 153 most European studies, some studies suggest red deer are preferred (though roe deer often still make 154 up the majority of the diet due to higher availability) (19,(38)(39)(40)(41)(42). Therefore, it is likely that in 155 Scotland, both roe and red deer would be predated, though there may be a preference for red deer 156 where they are available. Fallow and Sika deer are also found in Scotland, but little data exists for 157 wolf predation on these species (43).

158
Despite these variations across studies, land cover, prey density, road density and human 159 density emerge as the most important factors in wolf habitat suitability. As regards land cover, we 160 noted which cover types are associated with wolf presence and absence, but as regards the other three 161 variables -which are continuous rather than categorical variables -we needed to establish thresholds 162 of suitability and unsuitability. 166 recorded in the wolf ranges in Yellowstone National Park (10,21,22,37,44).

167
As regards roads, road density (km/km 2 ) is the standard metric used in studies that assess wolf 168 responses to roads (13,16,(18)(19)(20)35,36 194 output maps were combined using fuzzy overlay (Fig 2). This process was applied to six variations 9 195 in input data, to explore uncertainty and to test sensitivity.  (53,54). This "smooths" the density over a wider area, in recognition of the fact that the 239 herd will move around its range, and so the entire range may be considered to offer prey (55).   (Fig 3a, 3b, 302 3c), prey density (Fig 3d and 3e), road density (Fig 3f) and human density (Fig 3g). Land cover and 303 prey density have three and two variations respectively, as per Table 4.  (Fig 3d and 3e). The addition of a roe 310 deer baseline density in three council areas increases the suitability of the Highlands and Southern 311 Uplands. Human density (Fig 3g) is suitable for wolves across a large proportion of Scotland, but 312 suitable road densities (Fig 3f) are far more limited, again to the Highlands and Grampians.  (Table 4).

320
The area and proportion of mainland Scotland falling into each of ten equal classes of 321 suitability was calculated for each model (Table 5). This underlines the fact that the majority of 322 Scotland is unsuitable according to these models, and that this does not vary much between models.
323 There is more variation at the high suitability end of the scale, with between 0.6% and 21% of the 324 area (or between 384km 2 and 14259.5km 2 ) rated most suitable (  Our results have shown that there is a high level of covariance between three of the variables, 345 with the most suitable areas in terms of prey density, road density and human density all concentrated 346 in the same regions (Fig 3). This results in the Highlands and Grampian mountains emerging strongly 347 and consistently in Fig 4 as the areas most suitable for wolves in mainland Scotland. Though this 348 area is contiguous, it is bisected by the A82 and the many lochs of the Great Glen, which could be 349 barriers to wolf movement. Human density, prey density and road density are suitable throughout 350 this region, and the addition of roe deer to the prey density map makes little difference. This is partly 351 because in the Highlands the high densities of red deer already reach the suitability threshold, whereas 352 in the Southern Uplands, the majority of the region is excluded anyway due to high road densities. It 353 is also partly because the adjustment of the suitability thresholds upwards to account for the smaller 354 body size of roe deer (Table 3) somewhat negates the gains of including them.

355
However, the suitability of the fourth variable, i.e., land cover, depends heavily on how 356 suitable open heath and bog habitat is for wolves. It is the scoring of three land cover types in this 357 variable that make the largest difference in the fuzzy overlay maps. Though in all cases the Highlands 358 and Grampians still emerge as most suitable, differences in scoring mean they may be anywhere 359 between somewhat suitable and completely suitable (between 0.7 and 1.0).

360
In terms of sensitivity, it can thus be concluded that the model is not particularly sensitive to 361 the changes in prey density used here. However, it is somewhat sensitive to changes in land cover 362 scoring: though the regions with highest suitability do not change, their level of suitability does.

363
As regards prey density, road density, and human density, the models could be considered 364 relatively conservative. This is due to two reasons: the estimates of suitability and unsuitability 365 adopted as thresholds were conservative; and prey density is likely to be higher and more widespread 366 than the SNH's deer counts suggest, as these counts mostly only include red deer spotted in open 367 areas where and when a count is carried out. The British Deer Society's distribution survey (56) finds