• density estimation;
  • evasive movement;
  • line transects;
  • point transects;
  • Vulpes vulpes


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    Monitoring red fox Vulpes vulpes abundance is necessary to assess the status and management of this species and to understand predator–prey relationships. Spotlight counts are most often used for this purpose. However, comparisons between regions or over years may be questionable when using encounter rates, i.e. the number of foxes seen per kilometre. We evaluated whether distance-sampling methods, which take account of variation in visibility, could be applied to spotlight counts of foxes along roads and trails.
  • 2
    Distance-sampling methods were used at 12 contrasting sites in France in a systematic design with equally spaced transects or points. Line and point transects were simultaneously applied at two sites to find the more precise and efficient method.
  • 3
    The number of foxes seen near the centreline was always low, although some foxes may have been missed. A peak of sightings at subsequent intervals from the centreline suggested evasive movements.
  • 4
    Despite the low sighting frequency near the centreline, which may reflect a violation of distance-sampling assumptions, a good model fit was obtained for eight out of 12 data sets using a regular 50-m grouping of the distance data. Increasing the first interval to account for evasive movement improved model fit in the four other data sets. Density estimates ranged from 0·39 to 3·54 foxes km−2 (range of coefficient of variation 4·5–24·6%).
  • 5
    Point and line transects resulted in similar density estimates, but point transects were more time consuming and resulted in larger coefficients of variation due to a smaller number of foxes seen by this method. Line transects may therefore produce better estimates of fox numbers.
  • 6
    There were few differences among the effective strip width estimates between the 12 sites (range 191–286 m), thus line transect estimates may have a limited advantage over encounter rates.
  • 7
    Synthesis and applications. The systematic scheme we applied in this study improved sampling design and variance estimations and should be useful for surveying terrestrial mammals with spotlight counts. However, the location of transects along roads and in open habitats probably induced biased results. Methodological improvements are necessary before spotlight distance sampling can become a routine monitoring tool for foxes.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Foxes Vulpes vulpes L. are easily sighted by night in open fields and spotlight counts are often used to monitor their abundance (Aubert, Roboly & Migot 1988; Newsome, Parer & Catling 1989; Stahl & Migot 1990; Stahl 1990; Weber et al. 1991; Pech et al. 1992; Weber, Meia & Aubry 1994; Reynolds 1995; Ralls & Eberhardt 1997; Short et al. 1997; Brochier et al. 1999; Greentree et al. 2000; Kay et al. 2000). However, the number of sightings, even corrected by the length of transect surveyed, does not take account of possible variations either in the transect width or of fox detectability, which can vary markedly between studies and habitats. Comparisons among regions or years are then questionable.

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.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

study areas

Spotlight counts were carried out in 12 contrasting rural regions in France (Fig. 1) where previous studies had showed different fox encounter rates (Stahl & Migot 1990). In most of these regions the landscape was a mosaic of farmland and woodland areas with flat terrain. Arable lands predominated at sites A, C, E and F, while larger blocks of forest were present at sites J, L and K. Relief at sites B, G and D was undulating. Density estimates from line and point transects were compared at two sites (A and B) during one winter. The line transect method was applied on these two sites during, respectively, one (B) and two additional winters (A), and on the 10 other sites (C to L) during one winter (Table 1). Study areas were calculated by using minimum convex polygons encompassing all the transects or points, and ranged from 42 to 650 km2. The percentage of forest cover varied greatly among sites (range 7–47%; Table 1). Road density averaged 0·88 ± 0·17 km km−2 (range 0·55–1·15 km km−2). Roads were distributed uniformly within all the study areas.


Figure 1. Location of the 12 sites surveyed with line and point transect methods in France. An example of the sampling design applied for point and line transects is given for region B (winter 1999).

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Table 1.  Periods, effort, numbers of foxes seen and encounter rates (foxes/km or foxes/point) during line and point transects surveys in 12 regions of France
RegionYearPeriodTotal area (km2)Forested area (%)Number of transects (or points)Total length of transects (km)Number of repeatsTotal effort (km or points surveyed)Number of foxes seenEncounter rates (%CV)
  • *

    The same transects were used during the three winters.

  • The same area was surveyed using point transects.

  • Mean estimates over years in the same region.

A*199805–10 Jan202 7 2456·55282·6 710·25 (13·2)
A*199914–20 Jan202 7 2456·56339 600·18 (21·8)
A*200010–14 Jan202 7 2456·75283 750·26 (12·2)
AMean        0·23 (9·01)
A199805–10 Jan229 9120 points 3360 points 230·06 (24·9)
B199809–25 Feb30347 3160·06331·12810·85 (12·4)
B199920–27 Feb27646 3558·54208·21720·83 (12·6)
BMean        0·84 (8·7)
B199921-Feb28645122 points 4483 points 990·29 (16·1)
C199925–29 Jan66012 47914360·2 680·19 (18·1)
D200014–23 Feb 4236 1426·75131·61521·15 (17·1)
E200031 Jan−20 Feb 8614  830·96183·72211·20 (12·4)
F200018 Feb−02 Mar10016 1532·96197·11710·87 (22·0)
G200001–09 Feb 9026 1029·76168·8 570·34 (20·0)
H200017–26 Jan 8731 1433·86202·81410·70 (11·2)
I200027 Jan−08 Feb12418 1833·56196·71200·61 (16·2)
J200013–18 Jan11240 132961742601·49 (15·6)
K200018–25 Jan 7937 142561501380·92 (17·5)
L200004–11 Jan 6326 1429·16134·71881·40 (11·5)

sampling design

To obtain a uniform coverage of the entire area and ensure that transects were randomly placed with respect to the types of habitat, a grid of systematically spaced points was superimposed at random on a map. Spacing between points on the grid was calculated from d2 = S × 2/(K × √3), where d is the distance between two points, K the number of points and S the total area surveyed (Péroux 1991). We selected a design with 15 points 100 km−2, i.e. with ‘theoretical’ points 2·8 km apart, except in the largest study area (region C), where theoretical points were 4 km apart. Transects of about 2 km were placed on small roads and tracks as close as possible to the theoretical points. This design limited the time spent travelling from one transect to another and ensured that the problem of flushing animals from one transect to another was reduced. The ends of consecutive transects were 500 m–1 km apart. To calculate the exact length surveyed (= sampling effort), parts of transects with no visibility, i.e. with cover ≤ 50 m from the centreline, were excluded and foxes were not counted in these obstructed portions. Although a few transects were not entirely straight, it was possible to identify their centreline at all times (Fig. 1). The total number of transects at each site varied between eight and 47 (Table 1).

For point transect surveys, we chose a design with 60 points 100 km−2 corresponding to a grid of theoretical points 1·4 km apart. As for transects, points were selected as close as possible from these theoretical points. A total of about 120 points was located on each site (Fig. 1). To calculate the exact area surveyed (= sampling effort), angles of obstructed portions around each point (i.e. with cover ≤ 50 m from the point) were measured during daylight and excluded. Foxes were not counted in these obstructed portions. Transects and points were all marked in the field to ensure that the same transects and points were surveyed by various teams.

The total length, L, to survey during line transect surveys was estimated with the formula L = [b/CV(D)2] × [L0/n0] (Buckland et al. 1993). With a recommended value of b = 3, a coefficient of variation [CV(D)] for density of about 20% and an estimated encounter rate (n0/L0) varying between 0·2 and 0·5 foxes km−1, 150–375 km had to be surveyed to get 75 detections. Surveys were repeated during four to six consecutive nights at each site to reach the total length. Given that a team could only survey 30 km night−1, two to three teams operated at the same time on the largest sites (regions A, B and C) to cover the whole area. An equivalent formula was used to determine the total number of points to survey during point transects surveys (Buckland et al. 1993), with b = 3, CV(D) = 20% and an encounter rate (n0/k0) of 0·15 fox point−1. About 500 points should be surveyed to obtain 75 detections. Surveys were repeated during four nights on each site to reach a total of 480 points. Given that a team could only survey 20 points night−1, five teams worked during the same night to survey the 120 points at each site.

data collection

All spotlight counts were conducted between January and early March to estimate pre-breeding fox density. Visibility on farmlands is maximal during these months. For line transects, teams comprised one driver and two observers. The vehicle was driven at a speed of 10–15 km h−1. The observers stood upright through a sunroof, which enabled them to be ≥ 1·5 m above the ground level, and they scanned the fields with a 100 W hand-held spotlight. To minimize the risk of missing animals on the centreline, each observer surveyed only one side of the transect but frequently scanned the fields a little ahead to detect foxes running away from the approaching vehicle, while the driver surveyed the road ahead of the car. The car was stopped when shining eyes were seen. The observer located the initial position of the animal and kept track of that position before trying to identify the animal using binoculars. The vehicle was then placed perpendicular to the initial position of the fox for distance measurement. The perpendicular distance of each fox from the centre of the road was then measured using a laser telemeter (Geovid, Leica, Solms, Germany). For point transect surveys, the teams comprised one driver and one observer. Once the vehicle was stopped at a point, the driver switched the vehicle lights off, while the observer went out rapidly and quietly from the car. He scanned the fields all around the point using spotlights, first rapidly to detect the nearest animals and a second time more slowly to detect more distant animals. To limit observer bias, the observers were moved from night to night among different parts of the site. The point and line transects surveys were conducted by the same observers.

All surveys were carried out between 20:00 and 01:00. The surveys were called off when there was heavy rain or high wind. Portions of transect or points under local mist conditions during spotlight counts were recorded and excluded from the analysis and foxes were not counted. As a result, the total length surveyed could differ a little from night to night. To estimate and compare survey effort between line and point transects, the time spent preparing the survey and lighting was recorded in winter 1999 on site B.

data analysis

Estimating density using line and point transects has been thoroughly covered by Buckland et al. (1993). Densities were estimated according to the general equations D̂ = n/(2 × L × ESW) for line transects and D̂ =n/(k × π × EDR2) for point transects, where n is the number of sightings, L the total transect length, ESW the effective strip width, k the number of points surveyed and EDR the effective detection radius. The encounter rate, n/L, corresponds to the common index used to express spotlight counts. Estimates of ESW and EDR were calculated from the probability density function of the estimated detection function at zero distance for line transects or its derivative for point transects.

Line and point transect density estimates with their log-normal confidence intervals were computed with the software distance (Laake et al. 1993). Before model fitting, a truncation of the more distant data was operated. These extreme observations are difficult to model and provide little information for estimating the density function at zero distance, which is the most critical part of the curve. The truncation distance, w, was chosen for each data set so that the probability of detection g(x) was near 0·15 for line transects or near 0·10 for point transects at distance x (Buckland et al. 1993). The half-normal detection function without any expansion term was used to calculate truncation distances fulfilling the above criterion (R. Péroux, personal communication). Data were grouped a posteriori into 50-m intervals to improve model fit and to smooth out measurement inaccuracies. In the exploratory phase of the analysis, we used five a priori robust models: a uniform key function with either cosine (i.e. Fourier series) or polynomial series expansion, a half-normal key function with either cosine or Hermite polynomial series expansion, and a Hazard rate key function with cosine series expansion. Plots of model fit to histogram distance data were assessed visually to ensure a good fit of the data, especially near the centreline where the detection function should have a ‘shoulder’ (Buckland 1985). The Fourier series model fit our data sets well, gave similar density estimates compared with the other models (density estimates differed less than 15% except in one case, 23%, and were well within the 95% confidence interval for any estimate) and led to small differences in Akaike Information Criterion (AIC) (≤ 2) relative to other models. To facilitate comparisons, all the results presented in Table 2 are limited to the Fourier series detection model.

Table 2.  Estimates of fox density, effective strip width and effective distance of detection using line or point transects in 12 regions of France (Fourier series model)
RegionYearModel*Method (LT/PT)Truncation distance (m)P-value§Density (foxes km−2)Effective strip width (m)% of var(D) attributable to var(n)
EstimateCV (%)95% CIEstimateCV (%)
  • *

    Regular interval: data were grouped into 50-m intervals. Enlarged interval: the first cut-off point was set at the radius for which all flushed animals could be considered as included. Left truncation: data in the first 20-m interval were excluded.

  • LT, line transects; PT, point transects.

  • Percentage of data eliminated to the truncation point are indicated in parentheses.

  • §

    P-value corresponding to the χ2 goodness-of-fit test of the Fourier series model to the observed data set.

  • Or effective detection distance for point transects.

  • **

    Data in 250–350 intervals were pooled to improve model fit. We verified that it had no effect on density estimate.

A1998Regular intervalLT350 (2·8%)0·200·4620·20·31 0·68265·915·144·2
A1999Regular intervalLT350 (8·3%) 0·3027·60·18 0·53  70·1
A2000Regular intervalLT350 (4%) 0·4819·80·32 0·70  41·5
AmeanRegular intervalLT350 (4·9%) 0·4117·60·29 0·58   
A1998Regular intervalPT400 (13%)0·480·3728·60·21 0·65218·1 3·394·8
A1998Enlarged intervalPT400 (13%)0·130·2378·40·06 0·98274·536·612·6
A1998Left truncationPT400 (13%)0·240·2862·80·09 0·92249·728·219·6
B1998Regular intervalLT350 (1·8%)0·0012·1212·61·64 2·73196·8 2·895·2
B1999Regular intervalLT350 (6·4%) 1·9613·21·51 2·57  95·6
B1998Enlarged intervalLT350 (1·8%)0·332·1212·61·65 2·74196·2 2·795·2
B1999Enlarged intervalLT350 (6·4%) 1·9713·21·51 2·57  95·7
BmeanEnlarged intervalLT350 (3·7%) 2·064·51·70 2·51   
B1998Left truncationLT350 (1·8%)0·042·3412·41·82 3·01171·0 2·795·3
B1999Left truncationLT350 (6·4%) 2·2213·21·70 2·90  95·8
B1999Regular intervalPT350 (11%)0·201·8817·11·34 2·62209·3 4·078·5
B1999Enlarged intervalPT350 (11%)0·571·8817·11·34 2·62209·3 4·078·5
B1999Left truncationPT350 (11%)0·411·8717·31·33 2·62209·7 4·177·3
C1999Regular intervalLT450 (1·5%)0·150·3919·20·27 0·57238·1 5·492·2
D2000Regular intervalLT350 (0·7%)0·262·8617·91·96 4·18200·4 5·092·2
E**2000Regular intervalLT350 (4·1%)0·21e3·0113·12·23 4·06191·7 3·891·3
F2000Regular intervalLT450 (0%)0·0041·5424·30·94 2·54281·410·481·7
F Enlarged intervalLT450 (0%)0·271·5724·60·95 2·59276·611·079·9
F Left truncationLT450 (0%)0·0071·6125·20·96 2·68268·412·077·3
G2000Regular intervalLT300 (1·8%)0·190·8922·70·55 1·43186·810·180·1
H2000Regular intervalLT350 (2·8%)0·341·5513·51·17 2·05218·3 6·577·2
I2000Regular intervalLT350 (1·7%)0·361·2921·20·85 1·97231·813·559·3
J2000Regular intervalLT350 (1·5%)0·0033·0318·22·09 4·40242·7 9·672·2
J Enlarged intervalLT350 (1·5%)0·143·5416·02·52 4·98207·9 4·293·0
J Left truncationLT350 (1·5%)0·123·3419·02·77 4·92215·211·066·7
K2000Regular intervalLT500 (0·7%)0·881·4521·00·94 2·21316·011·868·4
L2000Regular intervalLT300 (4·3%)0·0023·4116·22·46 4·72195·810·954·9
L Enlarged intervalLT300 (4·3%)0·603·4416·22·49 4·76194·310·855·3
L Left truncationLT300 (4·3%)0·733·8117·82·68 5·43170·412·848·5

Analyses were carried out separately for each region. For each site, the distance data from a given line or point were pooled over the nights prior to analysis. For sites A and B, which were surveyed during several winters, we compared the detection function of each year to a common detection function with data pooled over the years, and selected the model with the smallest AIC value. Between-year comparisons of density estimates were made using the z-test (Buckland et al. 1993) or with the generalized χ2 statistic described by Sauer & Williams (1989) for more than two density estimates.

Theoretically, sighting frequencies should decline progressively with increasing distance from the transect centreline. If sighting frequencies are low near the centreline because animals flush from the road when the vehicle is approaching, an enlarged first interval can improve model fit to the data (Péroux et al. 1997; Heydon, Reynolds & Short 2000). However, this strategy will underestimate density if low sighting frequencies are due to animals missed near the centreline or to animals avoiding the roads or their immediate vicinity. In these situations, an alternative approach is to exclude roadside data from the analysis by selecting a left truncation point (full left truncation; Alldredge & Gates 1985). When model fit was poor due to a lack of data in the first interval, we tested (i) a full left truncation excluding data in the first 20-m interval and (ii) an enlarged first interval. For enlarged intervals, we set the first cut-off point at the radius for which all possible flushed animals (i.e. detected farther on) could be considered encompassed. To find this cut-off point, we plotted the density of sightings against the distance from transects and used the peak value of the curve as the cut-off point (Péroux et al. 1997).

Using the software distance, the variance of density is derived using the delta method (Buckland et al. 1993) and can be partitioned into two components: the detection function variance and the encounter rate variance. We examined the relative importance of the encounter rate variances in the estimation of the density variances.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Encounter rates from line transects varied between 0·18 and 1·49 foxes km−1 among sites (average = 0·83; SD = 0·44; n= 12; Table 1). At each site, coefficients of variation (CV) of the encounter rates ranged from 8·7% to 22·0% (Table 1). Encounter rates from point transects were 0·29 foxes point−1 in region B and 0·06 foxes point−1 in region A, with larger CV (16·1% and 24·9%).

modelling the detection function

Data pooling over consecutive nights led to a sufficient number of sightings to model a detection function (range 57–281), except for the 1998 point transect survey in region A (23 sightings). In this region, counts were only made during three consecutive nights due to poor weather. The truncation point varied between 300 m and 500 m. A 350-m truncation point was used in half of the data sets. With these truncation points, less than 5% of the observations were excluded for line transect data sets and 11–13% for point data sets. Sighting frequencies were generally lower near the centreline, while a peak was observed at more distant intervals (Figs 2–4). This peak of sightings was particularly pronounced in sites D, E and B. The Fourier series estimator model with a 50-m grouping provided a good fit to the distance frequencies in eight out of the 12 line transect data sets (Fig. 2). For these models, the P-value corresponding to the χ2 goodness-of-fit of the model ranged from 0·15 to 0·88 (Table 2). In the four other line transect data sets (sites F, J, L and B; Fig. 3), the lack of data in the first interval was more pronounced and model fits were poor when using a regular 50-m grouping (Table 2). For these data sets, an enlarged first interval was tested. The first cut-off point ranged from 70 m (site L) to 150 m (site F), and good model fit was then obtained (P-value = 0·13–0·60). Density estimates were higher than with a 50-m grouping procedure (range 0–16·8%) but confidence intervals (CI) overlapped (Table 2). Left truncation was also tested for these data sets. It led to higher density estimates compared with a 50-m interval grouping (range 1·7–11·7%), but a poor model fit was obtained in regions B and F. Density estimates provided by an enlarged first interval grouping were then used in further comparisons for these four data sets.


Figure 2. Number of fox sightings (50-m interval grouping) at different distances from the transect centreline in eight regions in France using the line transect method where good model fits were obtained (detection function is uniform key with cosine correction).

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Figure 3. Number of fox sightings (50-m interval grouping) at different distances from the transect centreline in four regions in France using the line transect method where poor model fits were obtained (detection function is uniform key with cosine correction).

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Figure 4. Number of fox sightings (50-m interval grouping) at different distances from the transect centreline in two regions in France using the point transect method (detection function is uniform key with cosine correction).

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At sites A and B, a common detection function was used for all years (region A: AIC = 734·5 with a common detection function, sum of AIC = 737·3 for the 3 years; region B: AIC = 1565·9 with a common detection function, sum of AIC = 1566·2 for the 2 years). Density estimates did not differ significantly between years in region A (0·46 foxes km−2 in 1998, 0·30 foxes km−2 in 1999, 0·48 foxes km−2 in 2000; χ2 = 2·58, P > 0·28) nor in region B (2·12 foxes km−2 in 1998, 1·97 foxes km−2 in 1999; z= 0·40, P= 0·69). The average density estimates and encounter rates over years were used for comparisons among sites.

comparisons of line and point transects estimates

At site A, the encounter rates were 0·25 foxes km−1 with line transects and 0·06 foxes point−1 with point transects. At site B, the encounter rates were respectively, 0·83 foxes km−1 and 0·29 foxes point−1. Density estimates were similar using point and line transects in both regions. At site A, the density estimate was 0·46 foxes km−2 (95% CI = 0·31–0·68) using line transects and 0·37 foxes km−2 (95% CI = 0·21–0·65) using point transects (z = 0·64, P= 0·55). At site B, the density estimate was 1·97 foxes km−2 (95% CI = 1·51–2·57) using line transects and 1·88 foxes km−2 (95% CI = 1·34–2·62) using point transects (z = 0·22, P= 0·83). Fewer foxes were sighted during point transect surveys, which resulted in greater coefficients of variation (site A: CV = 19·4% for line vs. 28·6% for point transects; site B: CV = 13·2% vs. 17·1%).

The survey effort was estimated in region B (300 km2). The same amount of time was spent to map, lay out and mark in the field a 60-km line transect and 122 points, i.e. 240 h, corresponding to 4 h km−1 and 2 h point−1. When excluding time spent travelling from one transect (or point) to another, 3·5 and 7·3 foxes were observed per person-hour during, respectively, line and point transect surveys, i.e. the second method was more than twice as efficient. However, the time spent sighting corresponded to 60% of the total time spent for the line transects survey vs. only 24% for the point transect survey. On average, 2·1 foxes were observed per person-hour during the line transects and 1·8 foxes per person-hour during the point transect, i.e. 16% less.

comparison of the line transects in various regions

Density estimates from the Fourier series estimator ranged from 0·39 to 3·54 foxes km−2 in the 12 study sites (CV range 4·5–24·6% in each site; Table 2). The percentage of the variance of density estimates attributable to the variance of encounter rate exceeded 75% in eight data sets and were beyond 50% in other data sets (Table 2).

Effective strip width (ESW) estimates ranged from 186·8 to 316 m (CV range 2·7–14·0%; Table 2). ESW were not related to the percentage of forested cover in the site (Spearman's coefficient correlation rs = −0·20, P= 0·54). Density estimates were mainly related to encounter rates so that the differences among sites in encounter rates resulted in similar differences in density estimates. A major influence of encounter rates on density estimates was suggested by the CV of the encounter rates calculated among sites (52·6%), which was three times bigger than the CV of ESW among sites (18·0%). The average CV of the density estimates calculated among sites was 59·3%.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

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.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We thank the officers of the Office National de la Chasse et de la Faune Sauvage who participated in this programme with their excellent fieldwork. Eveline Taran improved the English and Philippe Landry prepared maps. We are very grateful to Professor Steve Buckland and Régis Péroux for their helpful comments and suggestions that improved an earlier draft of this paper.


  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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