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Distance-sampling methods extend the strip transect approach without assuming that all objects are detected, or that the transect width is constant (Burnham & Anderson 1984; Burnham, Anderson & Laake 1985). The basis of distance-sampling methods is to measure perpendicular or radial sighting distances of objects from random lines or points, and to estimate their density by modelling their detection function, g(x), i.e. the probability of detecting an object given that it is at distance x from the line or point. The detection function accounts for all the environmental or experimental variables that could influence the number of objects detected and is estimated for each survey. As a result, variations in visibility among sites or over years should not be a problem.
Distance-sampling methods have been used widely to determine densities from sighting data of wildlife (reviewed by Buckland et al. 1993) and have compared well with estimates derived from other methods (for mammal species: White et al. 1989; Southwell & Weaver 1993; Southwell 1994; Borralho, Rego & Vaz Pinto 1996; Péroux et al. 1997; for fox: Heydon, Reynolds & Short 2000). Theoretically, unbiased estimates of density can be obtained from distance data if three critical assumptions are met (Buckland et al. 1993): (i) objects directly on the transect line are detected with certainty; (ii) objects are detected at their initial location and do not move (or move randomly) before being detected by the observer; (iii) distance and angles are measured with accuracy. The sampling design should also ensure that the transect lines or points are placed randomly with respect to the distribution of objects. Finally, Buckland et al. (1993) suggested a sample size of at least 60–80 sightings for an adequate estimation of density.
Two main problems immediately arise when applying distance-sampling methods to spotlight counts of foxes by night. The first relates to the sampling design because spotlight counts take place along roads or trails. Using roads as transects is questionable (Buckland et al. 1993) because the habitat adjacent to the road may be unrepresentative and foxes could behave differently in their proximity. It may also be difficult to place straight line transects on roads, which potentially increases the difficulty of obtaining accurate perpendicular distance measurements (Anderson et al. 1979). The second problem relates to the behaviour of foxes, which may react before being detected. The problem of animals escaping before being detected is potentially important for mobile, terrestrial mammals (Buckland 1985; Southwell 1994; Clancy, Pople & Gibson 1997; Péroux et al. 1997) and may lead to important bias (Anderson, Burnham & Crain 1985; Burnham, Anderson & Laake 1985). The magnitude of this potential evasive movement has not been evaluated for foxes.
The aim of this study was to: (i) evaluate whether the assumptions of distance-sampling theory could be met when using spotlight counts of foxes along roads; (ii) compare density estimates obtained with line and point transects on the same sites during the same period, thereby identifying the more precise and efficient method; (iii) examine whether density estimates derived from line transects show differences in fox abundance among sites that would not have been detected by a simple encounter rate index, i.e. the number of foxes seen per kilometre, which is the common way of expressing spotlight counts of foxes along roads.
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Spotlight counts are commonly used to monitor fox abundance. However, true densities of foxes are most often unknown and few studies have demonstrated that the number of foxes seen is related to population abundance. In a few cases, winter spotlight counts have been related to a known population change due to shooting (Newsome, Parer & Catling 1989; Stahl & Migot 1990; Pech et al. 1992) or poisoning (Short et al. 1997), suggesting a good relation between spotlights counts and changes in population size. Most authors, however, have highlighted the problems associated with visibility bias, observer bias, variations in weather conditions and animal behaviour (Mahon, Banks & Dickman 1998; Edwards et al. 2000). By using distance data to estimate a detection function, distance-sampling methodology implicitly takes accounts of such variables influencing visibility and could improve simple encounter rate indices such as the number of foxes seen per kilometre.
The first aim of this study was to evaluate whether fox behaviour and field methods were compatible with the assumptions of distance-sampling theory. The examination of the distance data almost invariably showed low sighting frequencies adjacent to the road or point. This could be due to two causes: (i) some foxes directly on the road were not detected, which violates the assumption that the detection probability on the centreline line equals one; (ii) foxes move away before being detected by the observer, which violates the assumption that objects are detected at their initial location. Failure of these assumptions results in negative bias (Burnham & Anderson 1984; Burnham, Anderson & Laake 1985). In most of our data sets, the deficit of data in the first interval was followed by a peak of sightings in subsequent intervals. This suggests evasive movement of foxes. The presence of barriers such hedges alongside the road could also lead to this sighting distribution because there is a blind spot behind the barriers, the area of which diminishes with increasing distance from the road. In our case, this problem was limited by excluding all obstructed portions where visibility was < 50 m from the point or line.
The evasive movements were not too important for eight out of 12 data sets, and it was possible to fit a good model to the data using a 50-m regular grouping. In the four other data sets, the lack of data in the shortest distances was particularly pronounced and regular grouping was inadequate. This may be due to habitat characteristics. On two sites, the importance of shrub and forest cover was particularly important (> 40%) and many foxes could have been missed by just hiding on the ground at very short distances in cover. The two other sites were composed of large open fields. In these fields, foxes probably saw the spotlights and moved away long before the vehicle arrived. Some solutions have been developed for marine mammals to take account of reactive movement (Turnock & Quinn 1991) or of a detection probability that differs from one on the centreline (Borchers et al. 1998a; Borchers, Zucchini & Fewster 1998b) but these methods seem difficult to apply for foxes. In our case, we used two modelling strategies: (i) a full left truncation excluding distance data in the first 20-m interval, which accounts for the problem of missing animals near the centreline, and (ii) grouping data with an enlarged first interval, which accounts for evasive movement. A better model fit was obtained with the second strategy, although we cannot exclude the possibility that density estimates were still negatively biased if foxes were also missed.
The assumption that distances and angles are measured accurately was probably fulfilled by measuring distances with a laser telemeter and by placing the vehicle perpendicular to the initial position of the fox. The problem of angle measurements does not exist for point transect surveys, and the similarity in the density estimates obtained by the two methods in two sites supports the view that distance measurement errors were not too important.
Sampling design is central to distance-sampling methods and should ensure that lines and points are placed randomly with respect to the distribution of foxes. In this study, we defined a systematic sampling design with evenly spaced transects or points to get uniform coverage of the entire area. It is likely that this sampling design is more efficient than the single unbroken, convoluted transect route used in most spotlight count studies (Stahl & Migot 1990; Weber et al. 1991; Ralls & Eberhardt 1997; Edwards et al. 2000; Heydon, Reynolds & Short 2000; Kay et al. 2000). Our results show that most of the variance of density estimates was attributable to variance of encounter rates from one transect to another. This spatial variability cannot be taken into account when using a continuous itinerary. A 2-km transect length also facilitates the placement of straight line transects.
Two main problems still remain, however, concerning sampling design. First, spotlight counts are carried out along roads accessible by cars. As argued by Heydon, Reynolds & Short (2000), it seems the only realistic way of surveying a sufficient length of transect to obtain the required number of sightings for density estimation, but it must be assumed that roads do not constitute a special habitat for foxes. Mahon, Banks & Dickman (1998) have demonstrated a fox preference for roads over other habitats in a sand-dune desert habitat where roads constituted natural runways. In the rural areas of Europe, where the density of roads is very high and foxes are well accustomed to human presence, the situation may be different and it is unlikely that foxes would avoid the proximity of roads. Prior radio-tracking experience showed that minor roads were neither avoided nor used preferentially (Heydon, Reynolds & Short 2000). Furthermore, a vehicle travelling along roads probably causes fewer disturbances than an observer walking across fields (Borralho, Rego & Vaz Pinto 1996; Heydon, Reynolds & Short 2000).
The second, and perhaps more important, point concerning the sampling design is that spotlighting cannot be undertaken in forested areas nor in portions of transects with forest immediately adjacent to the road. In the strict sense, density estimates obtained by spotlighting relate only to foxes active at night and in open habitat. These ‘density estimates’ could better be viewed as an index of abundance but would be valid for comparisons between years or sites if the proportion of time spent by foxes in open and closed habitats did not vary in space and over time. Because foxes are strongly attracted to open areas, there is probably no major problem in rural regions with a small grain-mosaic of forested areas and open fields, where fox territories encompass open and wooded land. Most of the foxes observed during spotlight counts were hunting or foraging (Weber et al. 1991) and open field constituted the main source of Microtinea, the preferred rodent species for foxes (Macdonald 1977). Von Schantz & Liberg (1982) showed that foxes spent only 23% of their time in forested habitats and Stahl (1990) showed that the sighting frequency of tagged foxes during spotlight counts was constant between years in a small area (230 ha). There is more uncertainty in habitats with large blocks of forested areas, because some individuals may move away from open areas to forested habitats when rodents are in low density. Changes in habitat use in response to food availability and to denning have been reported for foxes (Halpin & Bissonette 1988; Phillips & Catling 1991; Lovari, Lucherini & Crema 1996). Further studies are needed, for example using radio-telemetry, to estimate the proportion of time spent in forests and to verify that this proportion does not vary in space.
The second aim of this study was to examine whether density estimates obtained with line transects differ from estimates obtained from point transects on the same study area and during the same period. In this study, line and point transects led to similar density estimates, suggesting that both methods could be used. In some regions, however, point transects may provide a more systematic and adequate sampling design than line transects, which are heavily constrained by the availability of straight roads (Péroux 1991). In closed habitats, point transects may also be the only technique logistically possible. In the type of habitat we studied, with a high density of roads, line transects offer different important advantages. Line transect density estimates were more precise because of the greater number of foxes seen, and they were more efficient because more time was spent lighting. Evasive movements by foxes also seemed to be less pronounced in line transects than in point transects, where observers had to stop their vehicle and move away from it before beginning to scan the fields. Moreover, as argued by Bollinger, Gavin & McIntyre (1988), any movement away from the observer could cause larger errors with point transect methods because the area sampled geometrically increases with distance from the observer, whereas it increases only linearly with line transects. For all these reasons and because the total number of sightings is an important point when modelling, line transects may be preferred to point transects for foxes.
The third aim of this study was to examine whether distance-sampling methods show differences of fox abundance among sites that would not have been detected by a simple encounter rate index. Density estimates ranged from 0·4 to 3·5 foxes km−2 with rather low CV, varying from 4·5% to 24·6%. Despite strong variations in the percentage of forested cover among sites, few differences were shown between effective strip widths so that density estimates and encounter rates showed the same differences among sites. This may be due to the field methods: spotlighting counts by night limit the search width of the observer, who has to focus on the shortest distances to locate the initial position of the animal. The search width may also be limited by the strength of spotlights. The principle advantage of line transects over simple encounter rate, i.e. the calculation of an effective strip width, may be of limited value when spotlighting foxes, but further studies in other types of habitats or among different observer teams are needed to confirm this conclusion.