Recounting bias can affect abundance estimates from intensive helicopter surveys of feral goats

Keywords: aerial survey, antipredator response, Capra hircus, density, feral goat, responsive movement, ungulate, wildlife management.

Estimating population variables is a fundamental process for wildlife management and the methods used affect accuracy, precision, reliability and utility of ecological knowledge (Elton 1927; Elphick 2008; Fryxell et al. 2014). Strip and delimited and unbounded transect surveys are commonly used to aerially estimate wildlife abundance and each methodology and analysis depends on various assumptions. Transect surveys have used distance sampling (van Hensbergen et al. 1996; Walter and Hone 2003; Buckland et al. 2004), multiple observers (Rice and Harder 1977; Caughley and Grice 1982; Tracey et al. 2005; Melville et al. 2008), radio-tagging (e.g. Rice and Harder 1977; Packard et al. 1985; Ries et al. 1998), regression techniques (e.g. Caughley et al. 1976; Hone 1986), indices (e.g. Tracey et al. 2005), and comparison with independent population estimates (Short and Hone 1988; Jachmann 2002; Greene et al. 2017).

When sampling without replacement, most estimators implicitly or explicitly assume that animals are not counted more than once, nor consistently missed (e.g. distance sampling, Buckland et al. 2004), or that they are detected prior to any movement in response to the observer. Line-transect and strip-transect sampling are instantaneous methods that assume that objects are in a fixed location at the time of the survey, are all detected on the transect line and are detected at their initial location (Buckland et al. 2001, 2004; Fewster et al. 2005). Whereas plants and inanimate objects are stationary (e.g. beans, Hone 1986), animals move at various rates and directions, which instils potential responsive movement biases for animal surveys. In most transect surveys, observers or their observation platform will cause animals to move, particularly walked line transects (e.g. Southwell 1994) and low-level aerial surveys (e.g. Fleming and Tracey 2008).

In distance sampling and strip-transect sampling, movements prior to detection have been considered and accommodated (Buckland et al. 2004; Fewster et al. 2008). Borchers et al. (1998) used a capture–recapture method from two survey platforms to correct for both the failure to observe animals on the line and the effects of responsive movement. Palka and Hammond (2001) estimated the distance at which responsive movement commenced by using animal orientation, then applied a capture–recapture method separately for observations within (‘close’) and beyond (‘far’) this distance.

Responsive movement bias is assumed to be small if animals move at random and if the animal movement is slow relative to the speed of the observer (Buckland et al. 2001; Glennie et al. 2015). Most estimators will not be adversely affected if animals have an equal chance of moving into or out of a transect. However, bias can occur when animals consistently move away from observers (Palka and Hammond 2001; Linklater and Cameron 2002; Tracey and Fleming 2007) or towards observers (Palka and Hammond 2001; Cañadas et al. 2004).

Aerial surveys of wildlife are usually designed by using standard random (e.g. Choquenot 1995) or systematic (e.g. Walter and Hone 2003) sampling procedures. Systematic designs with a random start usually provide more robust estimates and are easier to implement in the field than are designs where transects are placed randomly without replacement (Buckland et al. 2015) A common practice is to saturate the study area with a grid of transects and select a subset randomly without replacement (Choquenot 1995; Pople et al. 1998a; Fleming et al. 2000). However, in both designs, transects are typically flown consecutively from one edge of the study site to the other to reduce ferry time and operational costs (e.g. Tracey et al. 2005). In such situations, assumptions are likely to be violated by individuals flushing unidirectionally between transects.

We could find only one reference relating to animal movements into other sampled areas after detection or the passage of observers or observation platforms (Terletzky and Koons (2016) found 4.4% mean duplicate observations of GPS-collared bison, Bison bison, aerially surveyed with topography-following flight paths), and none investigating potential positive survey bias or cumulative bias with subsequent passes. Here, we sought to investigate the possibility of recounting bias in helicopter counts of feral goats (Capra hircus) and used independent ground observations to quantify any such biases.

The study site with a high density of feral goats was chosen near the Coolah Tops National Park (−32°0′S, 149°58′E) in central-eastern New South Wales, Australia. The region has high rainfall (739 mm average annual rainfall, s.e. = 23.2, n = 55 years) and medium to high elevation (620–1190 m). The topography is rugged, encompassing gorges, narrow creeklines, wide valley floors, undulating to steep hillsides, narrow ridge tops and broad plateaux. Vegetation communities ranging from open grasslands to tall forests are supported by the fertile soils derived from basalt (Banks 1998). The overstorey associations are mainly woodlands of Eucalyptus goniocalyx, E. melliodora, E. viminalis, and E. albens, and gallery forests of Casuarina cunninghamiana are interspersed. High densities of feral goats, eastern grey kangaroos (Macropus giganteus), common wallaroos (Osphranta robustus), Australian merino sheep (Ovis aries) and cattle (Bos taurus) occurred at the site.

Methods follow those described in Tracey et al. (2005) and Tracey and Fleming (2007). Between 1997 and 2002, 34 surveys were flown over the study area in either a Hughes 500 or Bell Jetranger (206B) helicopter. During surveys, the helicopter maintained an approximately constant height of 150 ft (~46 m) above ground level (agl) and a constant airspeed of 45 knots (~85 km h⁻¹). Strip transects of 100 m on each side were delimited by right-angled poles attached to the helicopter and transects were spaced 300 m apart. Doors were removed and observers, one behind the pilot and two on the passenger (double) side, looked to the side of the helicopter and forward vision was obscured for consistency of search area on the double-observer side. Subsequently, there was a blind strip of 60 m below the helicopter where animals could not be observed by on-board observers. Transects (6–14 km) were selected at random without replacement and oriented east–west, which was perpendicular to the orientation of the major valley systems, and first passes progressed from north to south. No adjacent transects were flown consecutively, so randomly selected transects that were consequently omitted on first pass were subsequently flown in a second pass from north to south. The whole site was flown in one session for each survey. Surveys were flown within 3 h of either sunrise or sunset, and each survey was sampled between 40% and 70% of the site area.

During aerial surveys, 6–12 experienced ground-based observers located, counted and monitored behaviour and movements of free-ranging goats before, during and after helicopter passes. To reduce disturbance, the ground observers, assisted by radio-telemetry, spotted herds of goats from high vantage points and approached them on foot behind cover and as quietly as possible. Observations were not conducted on the rare occasions that goats were noticeably affected by ground observers, that is, where goats exhibited any alert response to the presence of an observer. Independent behaviour data suggest that fewer than 7% of observed groups were disturbed by observers (n = 22 184, P. Fleming, unpubl. data). Because ground observers could not predict whether a particular group of goats would occur within transect areas simultaneously with survey overflights, many observations of feral goat groups were obtained (>1500), but we could use only 784 in analyses. Although macropods were aerially counted at the same time as goats, lack of local knowledge of macropod dispersion throughout the site and limited available personnel precluded deployment of observers to take simultaneous ground observations of macropods.

Observers recorded date, time and site of the observation, and the number, colour, sex and age ratio, location, activity, vegetation type, and movements of goat groups, and other variables. Horizontal distances to the helicopter from observed goats were also recorded using line-of-sight, 1:25 000 topographic maps, grid locations and a global positioning system (GPS). Prior to the helicopter being heard or becoming visible to the observer, grid locations of animals were mapped, their activity recorded, and horizontal distances were subsequently estimated with simultaneous helicopter locations that were calculated from its on-board GPS. All observations were conducted during aerial surveys and helicopters used radar altimeters to maintain a fixed height and therefore the recorded horizontal distance was directly proportional to the actual distance between the observed animals and the helicopter. When individual feral goats within a group behaved differently, the activity of most animals in the group was recorded.

Here we estimated the probability that animals once available for detection in a sampling area were available again in adjacent sample areas. This probability relies on information about the extent of responsive movement, the direction of movement, the distances between transects and the sampling design (sample intensity, transect width, distance between transects, and distance unobservable beneath the aircraft).

The probability that an animal or group is available for recounting (p_a) was estimated using the following equation:

where p_mi is the probability an animal moves to i other transects; p_si is the probability Transect i is sampled; and the maximum value for i is the maximum perpendicular distance moved divided by the distance between transects.

The probability of an animal moving into another transect (p_mi) is dependent on the transect width, the distance between the transects, the proportion of animals that move, how far they travel (d_m) and in which direction they travel (θ_m). These parameters were observed or later estimated for feral goats known from observations to be within sampled transects during surveys. We converted d_m and θ_m to the perpendicular distance moved in relation to east–west transects (d_p, Fig. 1).

Fig. 1.  Representation for calculating the perpendicular distance goats moved (d_p) from the transect during aerial surveys. Notation: d_p = (sin θ_p) d_m, where d_p = perpendicular distance moved d_m = distance moved, as recorded by ground observers, and angle θ_p is calculated using angle θ_m (direction moved, 0–360°) and the following formulae: (a) if θ_m < 90, then θ_p = 90 − θ_m; (b) if 90 < θ_m < 180, then θ_p = θ_m − 90; (c) if 180 < θ_m < 270, then θ_p = 270 − θ_m; (d) if θ_m > 270,then θ_p = θ_m − 270. Direction of helicopter travel is from left to right.

We selected a Weibull distribution for describing the relationship between the probability of goats moving into another transect (y = p_mi) and the perpendicular distance moved (x = d_p; Evans et al. 1993). This relationship was selected over the simple exponential function because its shape could be altered according to the γ-value. Scale (λ) and shape (γ) parameters were optimised using maximum log-likelihood estimation, assuming a multinomial error structure.

The probability of sampling a transect depends on survey design and the initial sampling rate. If parallel transects are sampled consecutively from one edge of the study site to the other, as is common practice (e.g. Reilly et al. 2017), only animals that move in one direction are able to be recounted. However, if multiple passes are made, or transects are sampled in a random order, the calculations of p_mi need to be adjusted, as animals that move in either direction may be available during subsequent passes.

Therefore, the sampling probability for two passes can be estimated by calculating separate probabilities for the first and second pass, where:

On the second pass, goats that moved in either direction may be available for sampling, hence

The Weibull function was used to estimate the probability that a group moved into another transect in relation to the transect spacing, i.e.

1. east–west transects were placed 300 m apart,

2. 100 m was sampled on either side of the helicopter,

3. 60 m was unavailable directly underneath the helicopter (i.e. 30 m each side of the centre line), and

4. because of 1 and 2, 40 m was unsampled between transects.

Goats were significantly more likely to move south if they were initially south of the helicopter (χ² = 16.6, d.f. = 1, P < 0.001) and more likely to move north when they were initially north of the helicopter (χ² = 16.8, d.f. = 1, P < 0.001). Combining these ratios, 64% of individual goats moved away from the helicopter and 36% moved towards it (n = 448).

For groups of goats that occurred within sampled transects, the probability of moving, p_m, decreased with the perpendicular distance travelled, d_p (Fig. 2, ). Over 60% of groups moved, but only 30% moved further than 100 m and 8% further than 400 m.

Fig. 2.  The probability that a group of goats (y) will move x distance perpendicular to the transect direction in response to intensive helicopter aerial surveys.

Because consecutive transects were omitted on the first pass, the probability of sampling an adjacent transect was 0 and probabilities of moving into more than one transect were calculated only for those animals that moved in one direction. Because the probability of goats moving was ≠1 when the perpendicular distance = 0, the Weibull function was adjusted using the observed proportion of goats moving when the helicopter was directly overhead (i.e. 0.61). The maximum recorded perpendicular distance moved was 1200 m (mean = 104 m, median = 12 m). The probabilities of goats moving (p_m) perpendicular to the helicopter were estimated using the proportion of goat groups observed; hence, these calculations assumed that the distance moved was not a function of group size (Tracey and Fleming 2007).

As goats moved unevenly in southern and northern directions relative to the helicopter, probabilities were estimated separately for each side and were weighted for direction moved according to the observed proportions (i.e. 0.64 ‘away’ and 0.36 ‘towards’). The probability of a group moving into another transect was estimated by averaging probabilities predicted for perpendicular distance moved (Fig. 2). These predicted probabilities were calculated separately for the range of distances to each adjacent transect (Table 1).

Table 1.  Predicted probabilities (p_m) of groups of goats, once available for sampling, moving to additional transects in annual abundance surveys in Coolah Tops National Park.

Assuming that transects are flown consecutively from one edge of the study site to the other, as is usually the case, the probability of animals moving into an adjacent transect occurs in only one direction. For example, if transects are flown from north to south, goats that move north will not be available in another transect. Hence the probability of animals moving south is 0.18 for goats on the northern side (1/2 of 0.36) and 0.32 for goats on the southern side (1/2 of 0.64).

We sampled all available transects and so the probability of sampling an adjacent transect (p_s) was 1. Despite sampling all transects, 100 m of every 300 m transect was unavailable (60 m underneath plus 40 m between transects), which translates to an achieved sampling rate of 67%. Using the p_a and p_m values (Table 1), and assuming that transects were sampled consecutively, the probability that a group of goats was available for recounting (p_a) would be 0.18. When estimating seasonal abundance for the whole site, we sampled 18 of 28 possible transects. Hence, the probability of sampling a transect (p_s) was 0.64 (=18/28), which translates to a sampling rate of 43% when considering the area unavailable under the aircraft and between transects. In this case, the probability that goats were available for recounting (p_a) was 0.12 (=0.64 × 0.18).

However, because consecutive transects were omitted on the first pass and sampled on a second pass, probabilities were calculated separately.

where p_m is calculated using Table 1a, p_s = 1, p_s (First pass) = 0.5

where p_m is calculated using Table 1b, p_s = 1, p_s (Second pass) = 0.5

The failure to count all animals within a defined sample area or distance classes has dominated discussions about limitations of aerial survey methods, and correction for underestimation is ubiquitous (e.g. Caughley et al. 1976; Barker 2008; Laake et al. 2008). Even when duplicate counting has been identified, estimates were still inflated to account for overall under-detection (Terletzky and Koons 2016). However, we have shown overestimation as a potential problem that needs to be designed for in aerial surveys. Although the potential for recounting animals has often been assumed to be negligible (Seber 1982; Beasom et al. 1986; Linklater and Cameron 2002) or not considered because of small movements (e.g. Lethbridge et al. 2019), our results showed that under intensive sampling, movement between transects can be substantial (here 18–21%, depending on sampling rate) and, consequently, can cause large overestimates of density and abundance.

Assuming that animal movement is independent of the observer, bias from that movement is related to the distance animals travel during survey passage (Glennie et al. 2015). Negative bias in line-transect and strip sampling is smaller when mean animal speed is less than observer speed and larger when animal speed is greater than observer speed (Glennie et al. 2015). However, animal movement is not independent of observers and flight responses to observers and observer platforms are common (Clancy et al. 1997; Stankowich 2008), particularly among large herbivorous prey animals such as ungulates and macropods (e.g. Krausman et al. 1986; Pople et al. 1998b; Grigg et al. 1999; Tracey and Fleming 2007). We also showed that the direction of feral goat movements was not uniform.

The distance ungulates travel in response to aerial disturbance, and hence the potential for recounting, is difficult to compare across studies because elevation, aircraft speed, distance to the aircraft and type of aerial activity are widely varied and, in some cases, not reported. During very low-flying helicopter surveys (10–15 m agl), Beasom et al. (1986) reported resightings of marked white-tailed deer (Odocoileus virginianus) between 0% and 13% of total deer seen. Intensive sampling resulted in multiple sightings of individual deer, but it was concluded that this rendered total counts less conservative (Beasom et al. 1986). However, the proportion of marked deer in the population was not reported, and only 26–40% of deer were observed. Hence, the reported figure of 13% for a 100% sampling intensity would indicate that a higher proportion was actually available for recounting (i.e. between 33% and 50%). The low altitudes flown (e.g. DeYoung et al. 1989) and the recorded flushing behaviour of ungulates in other studies (e.g. Linklater and Cameron 2002; Stankowich 2008; Glennie et al. 2015) would also suggest greater movement between transects than has been reported.

Our probability of recounting was negatively correlated with sampling rate and positively correlated with the distance feral goats moved between transects. Both correlations are likely to hold true for any intensive aerial transect survey of large mobile animals involving species with a fleeing antipredator response. Despite some species- and situation-specific flushing responses, recounting is highly unlikely in aerial surveys that have widely spaced transects (e.g. macropod surveys; Cairns et al. 1991; Pople et al. 2006; Lunney et al. 2018), and undercounting persists in those cases. However, studies that sample intensively to achieve higher accuracy in low-density populations or localised high-density populations (e.g. Melville et al. 2008; Reilly et al. 2017), and apply valid corrections for an inability to detect all animals are likely to produce positively biased estimates of density. Recounting is more likely for intensive or low-level surveys of large ungulates that flush large distances, such as, for example, caribou (Rangifer tarandus; Calef et al. 1976; Harrington and Veitch 1991), mule deer (Odocoileus hemionus; Krausman et al. 1986), and mountain goats (Oreamnos americanus; Côté 1996). Linklater and Cameron (2002) found that recounting of feral horses (Equus caballus) resulted in overestimates of 15–32% in the Kaimanawa Ranges of New Zealand. Their Hughes 500 helicopter was flown at 60 m agl and horses were reported moving 0.1–2.75 km in response to the helicopter, but their sampling intensity was maximised to achieve a census.

All the above ungulate species and feral goats are gregarious, and, although detectability is associated with groups size (e.g. Samuel and Pollock 1981; Melville et al. 2008; Tracey et al. 2008), it is possible that flight responses to human disturbance are greater in larger groups (Stankowich 2008). Unmanned aerial vehicles (UAVs) cause greater flight distances in larger groups of guanacos (Lama guanicoe) than in small groups or solitary animals (Schroeder and Panebianco 2021). Other solitary larger herbivores, including ungulates such as the Japanese serow (Capricornis crispus), might be less likely to flush great distances in response to human disturbance, particularly once cover is reached (Takada et al. 2019). Different social organisation and antipredator responses in ungulates (Jarman 1974) and macropods (Jarman 1991) might affect flushing behaviour and probability of recounting during aerial surveys, but further study is required to elucidate and quantify resultant estimation biases.

If transects are close relative to the distance that an animal can traverse in responsive movement, then the measurements of interest are the speed of the animal and the observer between successive transects, and the direction of movement. The threshold below which feral goats are more likely to flush is 150 m from the helicopter (Tracey and Fleming 2007), which is within the observable range of observers and close to the outer-strip boundary for transects sampled in our study. If the helicopter was within this distance, goats travelled further (>150–2500 m) from the point of disturbance, which has implications for the probability that animals are available for recounting. We concluded that goats did not have an equal chance of moving into or out of a transect, because those that were potentially visible moved significantly further than those that were outside the transect area. Full randomisation of transect placement, without replacement, has potential to reduce the possibility of directional responsive movement or to increase the likelihood that movements into and out of subsequent transects are homogenous: there is software available to facilitate logistically efficient random placement of transects (e.g. Marshall 2019). However, because flushing is often in response to the noise of low-level aerial survey platforms, including drones (e.g. Brunton et al. 2019), there is an increased likelihood of animals moving away from surveyed areas where transect lines randomly fall close together, thereby interfering with the assumptions of fixed location and sighting at initial locations.

Most of the few studies comparing aerial survey estimates with actual numbers confirm underestimation (Caughley 1974), for a review; e.g. Tracey et al. 2008), which suggests that recounting animals is uncommon and that conservative estimates of density prevail (e.g. Beasom et al. 1986; Lunney et al. 2018). However, as technologies, such as surveys using thermal imagery (e.g. Havens and Sharp 1998; Cox et al. 2021) and videography (e.g. Catling and Coops 2004), UAV-assisted thermal imagery surveys (e.g. Lhoest et al. 2015; Witt et al. 2020) and estimation procedures improve, elimination of recounting is of increasing importance to ensure that estimates are not positively biased, which is especially relevant under high-intensity sampling regimes.

Data are available from the authors on request.

The authors declare no conflicts of interest.

The Australian Government’s National Feral Animal Control Program – Natural Heritage Trust, and Wildlife and Exotic Disease Preparedness Program, and New South Wales Department of Primary Industries funded the research.