# Evaluation of the distance sampling technique to monitor gregarious species: A simulation exercise

Arthur Jacquemin, David Vallecillo, Matthieu Guillemain, Pierre Defos Du Rau, Jocelyn Champagnon

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## To cite this version:

Arthur Jacquemin, David Vallecillo, Matthieu Guillemain, Pierre Defos Du Rau, Jocelyn Champagnon. Evaluation of the distance sampling technique to monitor gregarious species: A simulation exercise. Wildlife Society Bulletin, 2022, 47 (1), 10.1002/wsb.1393. hal-05529304

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DOI: 10.1002/wsb.1393

EMERGING RESEARCH

WILDLIFE
SOCIETY BULLETIN

<figure><img src="image_3.png" /></figure>

THE
WILDLIFE
SOCIETY

# Evaluation of the distance sampling technique to monitor gregarious species: A simulation exercise

Arthur Jacquemin<fnref n="1" /> ID
Pierre Defos Du Rau<fnref n="2" />

David Vallecillo<fnref n="1" />
Jocelyn Champignon<fnref n="1" /> ID

Matthieu Guillemain<fnref n="2" />

## Correspondence

Arthur Jacquemin, 47 C rue du Bourg Dessus, 39140 Arlay, France.

Email: ajacq.arthur@gmail.com

## Abstract

Wildlife count data are used to provide estimates of population abundance. To quantify changes in the size of populations, it is necessary to determine the precision of abundance estimates. Ground or aerial survey methods are often intended to be a census and thus do not provide estimates of precision. One solution is to switch approaches to a different sampling and estimation procedure, such as distance sampling. Using an example of the long-term waterfowl censuses in the Camargue, a major wintering area in southern France, we used simulation to quantify the precision and cost effectiveness of transitioning to a distance sampling approach. Based on abundance and distribution data for 14 species of waterbirds (Anatidae and coot [*Fulica atra*]) in the Camargue, we evaluated 5 distance sampling scenarios with parallel line transects corresponding to 5 different sampling intensities. Our results suggested that, if the objective of counts is to estimate the abundance of all waterfowl together, switching from pseudo-total to distance sampling counts would be realistic on both statistical and financial grounds. The most advantageous scenario would correspond to a sampling effort with transect lines spaced 1,000 m apart, which would allow a coefficient of variation of 0.20 for total waterfowl abundance with a 27% increase in flight costs compared to the current method. Heterogeneity in the size of detected bird groups contributed to the variability

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2022 The Authors. *Wildlife Society Bulletin* published by Wiley Periodicals LLC on behalf of The Wildlife Society.

<footnote n="1">¹Tour du Valat, Research Institute for the Conservation of Mediterranean Wetlands, Le Sambuc, 13200, Arles, France</footnote>

<footnote n="2">²Office Français de la Biodiversité, Le Sambuc, 13200, Arles, France</footnote>
in our results, however, adjusting sampling effort from 1,750 m spaced transect to 760 m allowed reduced variation by 55%. We recommend proceeding to test flights which would allow some site-specific parameters to be refined before changing methods. However, the distance sampling method as simulated here would prove impractical to evaluate the abundance and distribution of one species alone.

### KEYWORDS

Abundance, distance sampling, monitoring, simulation, survey, total count, waterbirds

Precise population estimates are of fundamental importance in applied ecology as monitoring provides essential information about wildlife population status. Estimation of animal abundance and drivers of changes through time are commonly used as measures of population health (Lack 1954, Nichols and Hines 2002), providing the necessary data to identify which species require additional conservation attention (IUCN 2021). Regional or local counts reveal if a given area holds a significant proportion of a species' global population (Keller and Bollmann 2004). Such counts are therefore an indispensable source of information in the process of establishing protected areas (Pérez-Arteaga et al. 2005), as required by criterion 6, which considers sites as of international importance when they host more than 1% of the entire species or subspecies population (Ramsar Convention on Wetlands 2010). Such knowledge requires replicable methods for data collection to estimate trends in population abundance and spatial distribution (Ottichilo and Khaemba 2001).

Aerial surveys provide an instantaneous view of the distribution of individuals over large areas (Khaemba 2000) and allow to work at the scale of entire ecosystems, such as a lake or an entire watershed, at relatively low cost (Kingsford and Porter 1993, Kingsford 1999). Large-scale counts of this type are used for waterfowl across the globe (Silverman et al. 2013, Mundkur et al. 2017, Menkhorst et al. 2019, Kingsford et al. 2020) to inform international agreements, such as the European Union Birds Directive (European Commission 2019), the Agreement on the Conservation of African-Eurasian Migratory Waterbirds (AEWA 2019), the North American Waterfowl Management Plan (NAWMP 2018) or the Ramsar Convention (Ramsar Convention 1994).

However, inferences drawn about abundance from counts of wildlife populations are often complicated by incomplete detection of animals in that not all individuals present in the surveyed area are counted. This is commonly the case for aerial surveys, which systematically underestimate true population sizes (Dolbeer et al. 1997, Kingsford 1999, Jachmann 2002, Rodgers et al. 2005). As such, substantial effort has been devoted to developing well-designed survey protocols (Caughley 1974, Anderson 2001) and correction for detection bias in aerial surveys (Caughley and Grice 1982, Pollock and Kendall 1987). The choice of counting method is typically defined by species distribution, environmental conditions, and financial constraints and needs to produce abundance estimates of sufficient accuracy and precision to resolve underlying questions (Williams et al. 2002, Lindenmayer and Likens 2009). While some aerial counting methods seek complete coverage (Kingsford and Porter 1993), most rely on sampling (Silverman et al. 2013, Mundkur et al. 2017).

In France, the Camargue hosts a significant portion of the national waterbird population each winter (Schmaltz et al. 2020). Camargue is a site of international importance for 15 species, including coot (Fulica atra) and 7 species of Anatidae: mute swan (Cygnus olor), Eurasian wigeon (Mareca penelope), gadwall (Mareca strepera), common teal (Anas crecca), mallard (Anas platyrhynchos), northern shoveler (Spatula clypeata), red-crested pochard (Netta rufina), and common shelduck (Tadorna tadorna). The abundance and distribution of waterfowl in the Camargue is directly related to water management, and is an important feature to consider for land managers, both from the conservation (nature reserves) and hunting (public and private estates) points of view. Thus, there has been monitoring at Camargue since
1964 (Tamisier and Dehorter 1999). The available datasets from the Camargue are unique in France by their spatial and temporal coverage, and form the basis for numerous studies on waterfowl (Dehorter and Tamisier 1996, Mathevet and Tamisier 2002, Brochet et al. 2012, Vallecillo et al. 2021). Further, the mid-January counts are key information delivered to Wetlands International for the International Waterbird Census (Schmaltz et al. 2020).

From the beginning of the Camargue surveys in the mid-1960s, a total count method has been used. The decision to use the total count method was based on 2 characteristics of ducks during winter: they are gregarious and they use traditional roosting sites during the day to which they are faithful to over the season (Tamisier and Dehorter 1999). The total count method for censusing ducks in the Camargue was established by A. Tamisier in 1974 and described by Dervieux et al. (1980). Census protocols involve flying from one body of water to another, circling around each to identify and count all the groups of birds. Total count methods are commonly used to measure the number of wintering individuals (Pihl and Frikke 1992, Nilsson 2005, Laubek et al. 2019) but they have three major drawbacks: they assume that all birds are detected by the observers, they have no measure of uncertainty, and they may not be perfectly replicable—as in the Camargue where the flight path is complex, involving numerous and variable circles. Non-standardization of the sampling plan renders the counts very sensitive to the difference in counting accuracy among observers (Vallecillo et al. 2021) and spatial coverage as pilots cannot exactly repeat their predecessor's paths. Furthermore, detection probability can be influenced by survey conditions: waves, or glare from sunlight, can cause large flocks to be overlooked and create a source of bias often more impactful than distance to the observer (Certain and Bretagnolle 2008). The behavior of birds, habitat types (vegetation density), observer fatigue and experience can also affect detection probability (Krebs 1999, Buckland et al. 2001, Williams et al. 2002, Morrison et al. 2008, Conroy and Carroll 2009). Typically, lack of detection data leads to underestimation and, since total counts provide no known methodology to evaluate the extent of this bias, no information about the number of unobserved birds and precision of abundance estimates is available. The clustered distribution of waterfowl limits the use of other counting methods, making it difficult to sample by strip transect (Buckland and York 2018). An alternative could be mark-resight methods, but this is likely too costly for populations whose total abundance varies around 120,000 individuals and would be subject to resighting issues when many wetlands are vast private waterbodies.

The aim of our study was to use the Camargue example as a case study to simulate the feasibility of a switch from total count to distance sampling, on both statistical and economic grounds. Distance sampling protocols accommodate detection bias and provide confidence intervals around the estimated bird abundance. Distance sampling has been applied successfully to many bird species in different environments (Marsden 1999, Cimprich 2009, Shirkey et al. 2014), and has been shown to provide more robust estimates of population trends than relative estimates of bird densities, for example through line or point transect counts without distance recording (Norvell et al. 2003). The distance sampling methodology (Buckland et al. 2001) requires two main changes to the usual total count protocols such as the one applied in the Camargue: a new standardization of the sampling design and a measurement of the observer/group distance for each observation. The objectives of our study were to evaluate whether distance sampling would provide sufficient statistical precision in estimating the abundance of waterfowl, often scattered in numerous groups of very variable sizes, at a reasonable cost for the operators. Analytical approaches already exist to determine the line length to be surveyed depending on the accuracy required (Buckland et al. 2001). But these analytical approaches rely on a small-scale pilot study to provide an initial estimate of the encounter rate, which is unavailable for the Camargue given the large heterogeneity of waterbird distribution.

To obtain a preliminary assessment of precision, we relied on a simulation exercise, built on aerial counts of the Camargue waterbirds over recent decades. Our simulation study allowed us to test several sampling designs, with several sampling efforts. We also determined the economic costs of alternative survey configurations and the transition from the current single observer survey in a fixed wing microlight to a 2-observer survey in a light aircraft, evaluating the trade-offs among those configurations that increase precision and those that reduce financial costs.
## STUDY AREA

The Camargue is the biogeographical delta of the Rhone River which flows into the Mediterranean Sea in Southern France. The Camargue extends over 170,000 ha and the landscape includes over 60,000 ha of wetlands, the rest being farmland and saltpans in operation. Fourteen species of waterfowl were considered in this study: common coot, common teal, Eurasian wigeon, Gadwall, mallard, mute swan, northern shoveler, red-crested pochard, northern pintail (Anas acuta), greylag goose (Anser anser), common pochard (Aythya ferina), tufted duck (Aythya fuligula), Bewick's swan (Cygnus columbianus bewickii), and garganey (Spatula querquedula). The number of individuals of each species was counted by aerial survey by one observer (M. Gauthier-Clerc), every month during November through January from 2006 until 2013, over 93 polygons of 8 to 1,883 ha, which cover all water bodies of the Camargue delta (Figure 1). November, December and January are most representative of the wintering distribution of ducks, with individuals gathered in multi-species groups (Dervieux et al. 1980). We used the 24 counts performed between 2006 and 2013 for which the number of groups and their size within each polygon are available.

## METHODS

### Simulation of bird distribution

For each polygon, the number of groups and their sizes were randomly chosen from within the distribution of 1 of the 24 historical counts (Figure 2, Step 1) and randomly distributed inside the boundaries of the polygon (Figure 2, Step 2).

<figure><img src="image_4.png" /><figcaption>**FIGURE 1** Survey polygons used during the total count survey in Camargue, South of France during 1964–2021 grouped into four convex envelopes to facilitate the tracing of linear transects.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**FIGURE 2** Graphical outline used to develop simulated distance sampling count data from empirical total waterfowl survey data collected at Camargue, France during 2006–2013.</figcaption></figure>

Statistical units were not individual birds but groups of individuals. The total abundance of individuals (N) is based on the number of simulated groups (D) and the average size of these groups (S).

$$N = D \times E(S)$$

The predominance of multi-species groups in our data compelled us to not distinguish species in our analysis, which was therefore conducted for all species pooled.

To test our distance sampling protocol on various patterns of bird distribution we ran 1,000 simulations of within-polygon random cluster distribution. According to a visual interpretation of a Monte Carlo simulation (Mooney 1997) on the 2 random variables (number of groups and group size, see below), 1,000 simulations can achieve a representative result (Appendix 1).

## Sampling design

Sampling was performed within four convex envelopes gathering the main groups of water bodies, geographically separated by agriculture or other non-water habitats. The total sampling area, encompassing all 93 polygons where waterfowl were counted, was 659 km². We first tested a sampling design involving continuous, zigzag transects. Such transects have the advantage of reducing the unsampled portion of the flight by removing the non-censused path necessary to move from one transect to the next. Nevertheless, the unsampled portions are necessary for the light aircraft to turn when moving from one transect to the next and the unsampled portion does not increase significantly during parallel transects compared to zigzag ones in our situation due to the proximity of the transects (from 760 to 1,750 m, Figure 3). Therefore we opted for more traditional parallel transects, in which counting strips did not overlap and sampling effort could be adjusted by varying the distance between transects.

Using Distance 7.3 software (Thomas et al. 2010), we created five sampling intensities in our envelopes by varying the distance between parallel lines: 760 m, 1,000 m, 1,250 m, 1,500 m and 1,750 m. After discussion
<figure><img src="image_6.png" /><figcaption>**FIGURE 3** Examples of transects used in waterfowl abundance estimation simulations (Camargue, Southern France). Two of the five sampling efforts tested are illustrated (A) transects spaced 1,750 m apart; (B) transects spaced 1,000 m apart.</figcaption></figure>

with current observers we set the maximum distance at which a group could be detected (from 90 m altitude) at 380 m. The total width of 760 m (380 m on each side of the plane) therefore represents the maximum sampling effort without overlap. Buckland et al. (2001) suggested that a minimum of 60–80 groups should be detected and at least 20 different line transects are necessary; 1,750 m represents the upper inter-transect distance limit in our design to remain above this minimum number of groups detected. A transect grid was placed randomly within each envelope (Figure 3). The orientation of transects differed between envelopes. The choice of the direction of the transects within each envelope is a compromise between maximizing the number of transects to gain precision and economic constraints by minimizing the time to move between envelopes and the period of non-effort flight between transects.
Simulation of bird detection

We simulated two observers aboard a high-wing 4-seat aircraft at 90 m altitude, looking in opposite directions and perpendicularly to the direction of the plane. The probability of detecting each point (i.e., group of birds) was modelled from a half-normal function g(x, S) (Buckland et al. 2001; Figure 2, step 3).

$$g(x, S) = e^{\frac{-(\frac{x}{\sigma(\ln(S))})^2}{2\sigma(\ln(S))^2}} \quad \text{with} \quad \sigma(\ln(S)) = A1.e^{A2 \ln(S)}$$

The 2 continuous variables were x for the perpendicular distance of the point (bird cluster) from the plane and S for cluster size (number of individuals in that cluster). Variable A1 represents the effect of distance on detection probability and variable A2 the effect of cluster size (log-transformed) on such probability. As we had no information on the detection probability of birds in the Camargue, we fixed values of A1 to 2.2 and A2 to 0.22 based on a distance sampling field study (N. Carenton, unpublished data) on three of the duck species studied (northern pintail, common teal, northern shoveler). An initial value of A1 (2.2) gave us an unrealistic detection function, with an almost zero probability of detecting a group of 100 birds at a distance of 100 m (Figure 4). Thus, we doubled A1 to 4.4 to obtain a detection function closer to our expectation of the process which then gave a credible detection function (Figure 4) in accordance with detection probability suggested by Shirkey et al. (2014) for similar counts of duck groups. Apart from a distance effect on detection probability, we decided to include a group size effect because it is a major factor influencing the detection of animal flocks (Marques et al. 2007).

<figure><img src="image_7.png" /><figcaption>FIGURE 4 Half-normal functions with distance and group size effects on the probability of detecting a group of birds from a plane. We used σ parameters: A1 = 2.2 and A2 = 0.2 in (A) while (B) uses A1 = 4.4 and A2 = 0.2.</figcaption></figure>
## Distance sampling assumptions

We addressed several distance sampling assumptions in our design. First, detection probability at distance zero from the flown transect is 1. However, this condition cannot be validated in aircraft because observers cannot see directly under the plane. We addressed this assumption by using left truncation, ignoring the first 20 meters of the lateral counting area on each side of the plane transect (Alldredge and Gates 1985). The second assumption requires that individuals must not perform any movement in response to the aircraft before detection. This assumption can be violated in two ways: animals can move independently of the observer, or move in response to the observer. Here the birds are on their day roosts and tend to stay relatively static, so we considered that they do not move independently from observers. Even though some sources claim low-altitude aerial surveys higher than 60 m above ground level are generally not a significant source of disturbance to waterfowl species (Gilbert et al. 2020), we experienced that waterfowl within 120 m from the plane at an altitude of 90 m would occasionally take flight. However, specific survey techniques such as searching further along line transects to see animals before they respond can help mitigate this bias in density estimates (Buckland et al. 2005). We therefore considered that this assumption held in our system. The final assumption requires that distances are measured accurately. Under many circumstances it is impractical or even impossible to precisely measure perpendicular distances from the transect line to the birds. In such cases distance sampling can still be applied using discrete distance categories, using markers placed on the window and the struts of the plane (Buckland et al. 2001). We grouped our observations into four bands in the 380-m range observable from each side of the plane: 20-80 m, 80-160 m, 160-280 m, 280-380 m. The bands were defined such that they widen proportionally with distance.

## Distance sampling analyses

Following the procedures outlined above, we distributed clusters of birds within the Camargue landscape, applied transect grids according to each of the five alternative distance sampling designs, and simulated detection of each cluster depending on the distance to the transect and the size of the cluster (Figure 2, Step 4). As a simulation exercise, we assumed that the observers accurately determined group size (although in practice, detection during aerial surveys is often imperfect; Vallecillo et al. 2021). All clusters were assumed to have no spatial size and hence were found in only one bin.

For each of the 1,000 simulations, the distance sampling analysis was performed, estimating the number of clusters and the abundance estimates including cluster size as a covariate. As recommended by Buckland et al. (2001), for each simulation we fitted several models with three main key functions (uniform, hazard rate, half-normal) and different adjustment terms (cosine, hermite and polynomials; Figure 2, Step 5). The cluster size covariate (ln(S)) was not fitted for uniform key models and fitted without adjustment terms for hazard rate and half normal models. We retained the following fitted models in our simulations: half-normal without adjustment, half-normal with ln(S) covariate and hazard rate with ln(S) covariate. We compared detection functions and selected the model with the smallest AIC (Anderson et al. 1998). We used a chi-square analysis as an indicator of the goodness-of-fit (Appendix 2) but it was not part of the model selection process. We used package Distance 1.0.4 (Miller et al. 2019) called from R (version 3.5.1; R Core Team 2021).

## Indicators and cost analysis

We used three indicators to evaluate reliability of our simulation work. The coefficient of variation (CV) is the ratio of the standard deviation to the mean across 1,000 replicate estimates, providing information on the dispersion around the mean value. Each simulation produces a CV and we computed the mean coefficient of variation over the
1,000 simulations. Confidence interval coverage is a criterion for the correctness of the estimate; it provides the proportion of simulations with a confidence interval covering the true values. Normalized mean bias indicated whether the analysis tended to systematically overestimate or underestimate total waterfowl abundance. For each replicate the number of simulated individuals differed. We calculated the normalized mean bias from the average difference between the model estimate and the true number of simulated individuals for each of these replicates. We represented the relationship of those three metrics with sampling effort.

The distance traveled by the aircraft corresponded to the length of all cumulative transects plus the distance covered when not sampling. We distinguished two types of unsampled distance: the distance travelled between the envelopes (Figure 3) and the distance travelled from one transect to the next, which is not shown but was considered in the cost calculation. By multiplying the total flown distance with average aircraft speed (160 km/h) we obtained an estimated flight duration for each sampling effort. The cost of a flight was considered at 260€/hr (price in 2021), comprising the pilot's salary, aircraft rental and fuel costs. To the flight cost we added the cost of the two observers, valued at 1,152€ in total, comprising their travel expenses and their salary for both aerial count hours and office data processing.

RESULTS

Across the 1,000 simulations (Figure 5), the average number of bird groups detected was 297 (SD ± 29) groups with a total average abundance of 145,085 (SE ± 24,107) individuals. The minimum threshold of 60 detected groups recommended by Buckland et al. (2001) for a distance sampling analysis was systematically reached (Table 1).

<figure><img src="image_8.png" /></figure>

**FIGURE 5** Example of 1,000 simulation runs for defining the cluster distribution based on total count survey data (Camargue, Southern France) for use in our distance sampling simulation.
<table><caption>**TABLE 1** Distance sampling estimates and associated standard deviation values for the 1,000 simulated point distribution tested. Number of groups detected by the observers, average coefficient of variation (CV) of the abundance estimate, encounter rate, and group size are presented for the 5 sampling efforts assessed as well as confidence interval coverage and normalized mean bias as precision indicators.</caption><thead><tr><th>Distance between transect (m)</th><th>Detected groups</th><th>CV Abundance</th><th>Encounter Rate (groups/km)</th><th>CV Encounter Rate</th><th>CV group size</th><th>Confidence interval coverage</th><th>Normalized mean bias</th></tr></thead><tbody><tr><td>1,750</td><td>68.2 (±7.9)</td><td>0.27 (±0.13)</td><td>0.13 (±0.03)</td><td>0.25 (±0.05)</td><td>0.45 (±1.22)</td><td>0.78</td><td>-0.03</td></tr><tr><td>1,500</td><td>81.6 (±9.0)</td><td>0.24 (±0.05)</td><td>0.14 (±0.03)</td><td>0.24 (±0.05)</td><td>0.36 (±0.57)</td><td>0.87</td><td>0.004</td></tr><tr><td>1,250</td><td>97.7 (±10.13)</td><td>0.22 (±0.03)</td><td>0.14 (±0.03)</td><td>0.22 (±0.04)</td><td>0.29 (±0.32)</td><td>0.89</td><td>0.02</td></tr><tr><td>1,000</td><td>120.1 (±11.7)</td><td>0.20 (±0.03)</td><td>0.13 (±0.03)</td><td>0.20 (±0.03)</td><td>0.26 (±0.25)</td><td>0.87</td><td>-0.03</td></tr><tr><td>760</td><td>158.6 (±14.3)</td><td>0.17 (±0.02)</td><td>0.13 (±0.02)</td><td>0.17 (±0.03)</td><td>0.20 (±0.16)</td><td>0.94</td><td>-0.04</td></tr></tbody></table>

The encounter rate did not significantly differ between the five sampling intensities, but we observed a decrease in the encounter rate CV when the sampling effort increased.

For a minimum effort corresponding to 3 h 18 min and 523 km of flight, we obtained a mean CV of abundance of 0.27 (SD ± 0.13) (Table 1). Confidence intervals included the true number of individual birds in 78% of the simulation replicates. Differences between actual simulated abundances and the results of distance sampling estimates provided by the normalized mean bias suggest, however, that although the absolute error decreased with sampling effort, the tendency to overestimate and underestimate was more counterbalanced for intermediate sampling intensities. A high sampling effort (760 m between transects) and a low sampling effort (1,750 m between transects) underestimated the total abundance of individuals by -0.03 and -0.04 respectively.

Increasing sampling effort (reducing the distance between two transects), resulted in an increase in the number of kilometers flown, an expansion of flying time and an increased cost of the operation. Through the results of the CV and confidence interval coverage (Table 1) we observed that the increase of sampling effort led to a better global precision of the sampling distance estimation. This increase was not monotonous: as reflected by the flattening of the curve and spacing of points along the x-axis (Figure 6), the higher the degree of precision, the more expensive it was to gain further in precision. Our simulations indicate that the coefficient of variation of the bird counts within a range of 0.27 to 0.17 can be expected at a cost that ranges from 2002€ to 2804€ per flight (Table 2).

DISCUSSION

Our study demonstrates that if the objective of counts is to estimate the abundance of all waterfowl together, it is possible, and pertinent from a precision point of view, to switch from total counts of waterbirds at Camargue to a distance sampling approach. Distance sampling cannot provide an estimate with sufficient precision with the current budget of 1936€ per flight, but the coefficient of variation of bird abundance decreased, and therefore the precision of the estimate increased, with an increase in sampling cost. Based on the five designs evaluated, the 1,000 m transect-spacing scenario seems the most appropriate as it yields a CV close to the 0.20 value recommended for reasonable precision (Pearse et al. 2008) while being less expensive than the 760 m scenario. Switching from the current total count method to distance sampling would, however, result in an additional cost of 526€ per count (i.e. a 27% increase). Although the distance to be flown would be reduced by 410 km (currently 1,216 km for the total count; 806 km for distance sampling), this is not enough to compensate for the cost of using a more expensive aircraft
<figure><img src="image_9.png" /><figcaption>**FIGURE 6** Change in estimated coefficient of variation (CV) in waterbird abundance with distance sampling method as a function of cost. Vertical bars represent standard deviation, the red line the current cost of a total count (1936€), the blue line represents our precision objective of 0.20.</figcaption></figure>

<table><caption>**TABLE 2** Parameter estimates for the five sampling efforts evaluated relative to the estimated current total count of waterbirds in Camargue, France. Number of replicates, total distance flown (including portions of non-effort flights), flight duration, and expected cost are presented.</caption><thead><tr><th>Distance between transect (m)</th><th>Number of transects</th><th>Distance travelled (km)</th><th>Duration</th><th>Cost (€)</th></tr></thead><tbody><tr><td>Current count<sup>a</sup></td><td>-</td><td>1,216</td><td>6 h</td><td>1,936€</td></tr><tr><td>1,750</td><td>30</td><td>523</td><td>3 h 18 min</td><td>2,002€</td></tr><tr><td>1,500</td><td>36</td><td>584</td><td>3 h 36 min</td><td>2,101€</td></tr><tr><td>1,250</td><td>42</td><td>674</td><td>4 h 12 min</td><td>2,247€</td></tr><tr><td>1,000</td><td>53</td><td>806</td><td>5 h</td><td>2,462€</td></tr><tr><td>760</td><td>69</td><td>1,017</td><td>6 h 24 min</td><td>2,804€</td></tr></tbody></table>

and the staff time for two observers. It is also worth noting that the gasoline used in the envisaged high wing aircraft allowing two observers releases more CO₂ per kilometer flown than the current fixed wing microlight aircraft used for the total count, increasing substantially the environmental cost of the survey.

Generally, a CV below 0.20 yields results with reasonable precision in the context of wildlife population monitoring (Pearse et al. 2008), but the level of precision required to detect a change in population size mainly

<footnote>aTotal count method used to count waterbird in Camargue since 1974.</footnote>
depends on the magnitude of the true trend and the number of years of counting available. Given large natural year-to-year variability, a short time series may lead to inaccurate conclusions even with a small CV (McCain et al. 2016) and on average 15 years of continuous monitoring are required to identify long-term changes in abundance (White 2019). According to Gerrodette's equation (Gerrodette 1987) assuming a linear change in abundance over time, a CV of 0.20 requires 8 years to detect a 10% decline by year with a power >0.8 and 13 years for a 5% decline (Appendix 3). For population changes of 1% by year, as can be observed in the Camargue at species level (Tamisier and Dehorter 1999), the five distance sampling intensities tested do not allow detection of a change in a reasonable period of time. Since no measure of uncertainty is available for the current total count method, we cannot directly compare the two methods, however, the choice of a technique that can correct for bias from imperfect detection and does provide a measure of error around the estimates would be useful to allow wildlife biologists to accurately evaluate wildlife abundance. A distance sampling count, even with great imprecision, will therefore be more reliable than a total count without measure of uncertainty.

If, in Camargue, distance sampling makes it possible to obtain abundance values and a measure of uncertainty, it is nevertheless important to emphasize that it is less suitable for other objectives that may also be important to managers. Two other major objectives are generally achieved by total counts (and are in the Camargue system): a phenological objective and a spatial objective. The monthly annual counts (seven monthly counts from September to March) provide information on the migration and wintering phenology of each species and its evolution over time (Guillemain et al. 2021). Monthly distance sampling counts could also provide such information, with better precision, but its higher cost makes it difficult to consider seven counts per year without devoting an increased budget. Switching from total count to distance sampling may be an opportunity to revisit the number of counts required, a subject already under consideration among stakeholders involved in the Camargue survey. Indeed, three main periods can generally be distinguished during the wintering period for waterbirds: the beginning of the season (September, October) when birds are still less numerous over the delta, the peak season (November, December, January) when numbers are at their annual highest and flocks the most densely concentrated onto few day roosts, and the end of the season (February, March) when individuals tend to disperse again (Dervieux et al. 1980). Conducting only three distance sampling surveys, one for each period, would provide data covering the main periods of the non-breeding cycle. Moving from 7 to only 3 surveys per year would reduce cost, which could make it possible to carry out more expensive but more precise distance sampling surveys (i.e., a denser transect grid associated with a lower CV around the estimated total number of birds).

The other objective of the traditional counts is to provide data on the spatial distribution of ducks in the Camargue. At a local scale, spatial information currently provides estate-specific data that allow an efficient communication with specific landowners. Further, figures on the number of birds within a given area have, in the past, supported numerous works on waterbird habitat use (Allouche and Tamisier 1989, Allouche et al. 1990, Brochet et al. 2012). Distance sampling does not provide estate-scale information for each landowner, but waterbird spatial distribution can be modelled with a density surface model (Miller et al. 2013). Based on the raw aerial count data and the exact location of each group recorded during the flights, a density surface model would benefit from the systematic design of transects, contrary to the total count design which does not guarantee homogeneity of the sampling effort.

Although species-specific abundance estimates are one of the primary objectives of surveys in Camargue, our simulation results do not indicate whether or not distance sampling could achieve this goal with sufficient precision. We justify this choice by a lack of scientific literature available on species-specific detection functions for our 14 species, the large proportion of multi-specific groups in our dataset, and the fact that our study aimed at providing a proof of concept concerning the general switch from total counts to distance sampling. Considering that all individuals detected share the same detection function is an approximation. The probability of detection varies between species (Prenzlow and Lovvorn 1996, Nichols et al. 2000), especially for some species of very different size in our dataset (e.g. common teal vs. mute swan). The existence of multi-specific groups strongly complicates the treatment of the group effect, the likelihood of detecting a group of 200 individuals of a given species obviously
being very different whether these 200 individuals are in the middle of a group of 2,000 individuals of another species, or alone.

Another issue with counts at the species level is that bird numbers and the number of flocks found at the Camargue will then be lower than numbers for all bird species pooled. In a preliminary study, we attempted to apply the same procedure as above for teal only, i.e. relying on field data from real counts to simulate the distribution of teal numbers and flocks in the landscape, then applying the distance sampling procedure. Unfortunately, even for teal, a species which constitutes a large proportion of the total waterbird community in mid-winter (Guillemain et al. 2021), distance sampling yielded inconsistent results with a strong overestimation of total numbers (~80,000 instead of 40,000 individuals). We suggest this was because at the species level there could be both very large and very small flocks, with many of the small flocks remaining undetected, so that the extrapolation relied mostly on the larger flocks. The problem occurs less frequently when considering all species together, since average flock size then tends to be greater. Work remains to be done on the flock size effect on the detection functions to be able to use the distance sampling procedure efficiently at the species level. We hypothesize that during true surveys, small groups of teal would be more easily detected because they would be included in much larger multi-species groups, and thus more detectable. The specific detection of teal will then depend on the observer's ability to distinguish them among individuals of other species.

In order to get species-specific abundance estimates, observers should identify bird species without error up to 380 meters. Nevertheless, the cryptic (eclipse) plumage of several species especially in September and October, makes them practically indistinguishable from each other from a distance when they sit on the water. The way to accurately identify species is often to induce their flight in order to check species identification clues like wing pattern (for example the duck speculum, composed of the bright secondary remiges on the wing; Mouronval 2014). Such a need to get the birds airborne to allow species identification is problematic and difficult to accommodate within the line transect sampling method, because the aircraft cannot lift distant birds off the ground. A possible solution to this problem could be to deviate from transects, flying over each detected group then returning to the transect where it was left, as tested by Marques et al. (2006) in a helicopter. However, this technique can be cumbersome, creates safety concerns when using fixed wing aircraft and can considerably extend the total distance travelled, hence jeopardizing the relationship obtained here between travel distance (hence costs) and accuracy of the population estimates. The most feasible solution would be to perform a right truncation (Buckland et al. 2001) and exclude from the analysis all birds that were too far from the transect line to be flushed and identified with confidence. An alternative would be to lump individuals into groups of inseparable species as done for some dabbling ducks in the Mississippi Alluvial Valley survey (Lehnen and Krementz 2013).

Reliability of a distance-sampling simulation largely depends on the choice of the imported detection function (Buckland et al. 2001). In our study, the lack of data constrained us to use data from Africa, a questionable choice because the geographical context is very different. Experiments with artificial flocks of plastic hunting decoy ducks would be advisable in this context, such as the one performed for whooping crane (Grus americana; Strobel and Butler 2014) that measured impacts of observer experience, sun position, distance from transect, and group size on detectability. To confirm the validity of our work, we therefore recommend running distance sampling test flights to obtain a better estimation of waterfowl detection in Camargue. These test flights, if carried out on a large enough scale to avoid any bias due to the heterogeneity of the distribution of the birds, could also provide a real estimate of the encounter rate. It will then be directly possible to determine the necessary sampling effort to obtain any precision objective from existing analytical approaches (Buckland et al. 2001).

The CV of abundance estimate from distance sampling depends on three factors: the variance of the encounter rate, the variance of the cluster size, and the variance of the detection function (Buckland et al. 2001). Our results reveal encounter rate remains constant as sampling effort increases, but the CV decreases (Table 1), probably reflecting a better distribution of the observed individuals between the different replicates. For group size estimation, we can observe very high CVs for low sampling intensities. A small number of encounters, such as 68 for the 1,750 m spacing scenario, renders the estimates very sensitive to extreme values. In this case a sample not very
representative of the global population can easily lead to a major error in the distance sampling estimate. Such sensitivity decreases with the number of groups encountered and is reflected in the CV values of group size (Table 1). It is more than halved when moving from a sampling effort of 1,750 m to 760 m, making group size a primary factor in the reduction of the overall CV. The impact of group size is also reflected by a higher selection of models accounting for the covariate group size, particularly for the highest sampling efforts (Appendix 2). We did not estimate detection function variance, but there is a significant possibility of underestimation compared to the reality where variable sampling conditions can significantly impact detection probabilities from one count to the next (Certain and Bretagnolle 2008). By combining data from multiple successive counts for the detection function selection process and the estimation of group size, we can thus base estimation on more groups and obtain a more reliable estimate. The distance sampling design suggested for the Camargue could potentially be enhanced further by pooling the three monthly counts to produce one single year-specific estimate with potentially improved precision.

Our study is based on data from past counts, which likely under-sample waterfowl numbers due to imperfect detection (Jachmann 2002, Rodgers et al. 2005). It is therefore very probable that the first results by distance sampling would provide higher numbers than those obtained so far, which should not be interpreted as an overestimation of the new technique, but only as a closer representation of reality. If the decision is made to switch to distance sampling, it will be important to go through a phase of overlap and calibration between the two methods. The transition from total count to distance sampling survey requires careful consideration, particularly in terms of maintaining the relevance of historical data that have been collected. It will require an understanding of how distance sampling estimates compare with those from traditional methods. By carrying out both methods simultaneously, it will be possible to determine a correction factor (Caughley and Grice 1982) to be applied to the values of past counts, which will allow continued benefit from the long-term time series. Despite the influence of uncertainty in the correction factor coupled with uncertainty in the abundance estimate, the 50 years of records we have in Camargue permit the detection of small trends with a relatively high CV. Moving forward, we will have to investigate whether the two count methods return data of comparable magnitude, and propose a method for determining how many times distance sampling counts and total counts would need to be carried out in duplicate to ensure compatibility of the two data sets (Hodgson et al. 2016).

## MANAGEMENT IMPLICATIONS

Distance sampling is an appealing wildlife monitoring method, and in many situations managers may consider switching from total counts to distance sampling. Our results suggest this is realistic on both statistical and financial grounds, although with some caveats. We recommend that any manager wishing to change counting method within long-term surveys goes through a preliminary simulation phase, as done here. Without such planning, they risk a potential waste of monitoring resources in ineffective and inefficient surveys (Reid 2001), remaining ignorant of the true costs of information and the potential efficiency gains afforded by a moderate increase in technical capacity.

## ACKNOWLEDGMENTS

D. Vallecillo's was funded by a grant from the Fondation François Sommer. We thank the observers of the aerial count method: J.-B. Mouronval, M. Gautier-Clerc and A. Tamisier for useful comments and discussion, provision of data on waterfowl distribution in Camargue and N. Carenton on detection function, as well as P. Roman for the practical information he provided regarding aircraft flight. We also thank N. Taylor for helpful comments and proofreading, D. Ducros who helped in the analysis of distance sampling data, A. Besnard and P. Aubry for statistical advices. We thank D. Johnson (Associate Editor), A. Knipps (Editorial Assistant), A. Tunstall (Copy Editor) and J. Levengood (Content Editor) and two anonymous reviewers for constructive comments that improved our manuscript.
# CONFLICTS OF INTEREST

The authors declare no conflicts of interest.

# ETHICS STATEMENT

No ethical information provided.

# DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

# ORCID

Arthur Jacquemin http://orcid.org/0000-0002-9661-8766

Jocelyn Champagnon http://orcid.org/0000-0003-4850-8033

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Associate Editor: D. Johnson.

**How to cite this article:** Jacquemin, A., D. Vallecillo, M. Guillemain, P. Defos Du Rau, and J. Champagnon. 2022. Evaluation of the distance sampling technique to monitor gregarious species: a simulation exercise. Wildlife Society Bulletin e1393. https://doi.org/10.1002/wsb.1393
APPENDIX 1: RESULTS OF THE MONTE CARLO SIMULATION PROCESS ON THE TOTAL ABUNDANCE. RED LINE REPRESENTS THE MEAN OF CUMULATIVE TOTAL ABUNDANCES SIMULATED, BLUE LINES THE 95% INTERVAL OF CUMULATIVE TOTAL ABUNDANCES SIMULATED

<figure><img src="image_10.png" /></figure>

APPENDIX 2: SELECTED MODELS FOR THE 1,000 SIMULATED DISTANCE SAMPLING ANALYSES CONDUCTED FOR EACH SAMPLING EFFORT SCENARIO. KEY FUNCTIONS AND ADJUSTMENTS ARE SPECIFIED, ALONG WITH THEIR POTENTIAL COVARIATE. ABSENCE OF A COVARIATE IS NOTED WITH -, SIZE CORRESPONDS TO THE SIZE OF THE GROUP. MODEL SELECTION PROPORTION ON ALL SIMULATIONS, THE P-VALUE OF THE CHI-SQUARE GOODNESS OF FIT TEST AND THEIR STANDARD DEVIATION VALUES ARE PRESENTED FOR EACH MODEL. LACK OF DEGREE OF FREEDOM DOES NOT ALLOW TO MEASURE GOODNESS OF FIT FOR HAZARD RATE FUNCTION

<table><thead><tr><th>Distance between transect (m)</th><th>Key function + adjustment</th><th>Covariate</th><th>Model selection proportion (n = 1000)</th><th>Goodness of fit P-value</th></tr></thead><tbody><tr><td>1,750</td><td>Half normal + cosine</td><td>-</td><td>0.04</td><td>0.46 (±0.28)</td></tr><tr><td>1,750</td><td>Half normal</td><td>~ln(size)</td><td>0.83</td><td>0.28 (±0.21)</td></tr><tr><td>1,750</td><td>Hazard rate</td><td>~ln(size)</td><td>0.13</td><td>-</td></tr><tr><td>1,500</td><td>Half normal + cosine</td><td>-</td><td>0.03</td><td>0.42 (±0.28)</td></tr></tbody></table>
<table><thead><tr><th>Distance between transect (m)</th><th>Key function + adjustment</th><th>Covariate</th><th>Model selection proportion (n = 1000)</th><th>Goodness of fit P-value</th></tr></thead><tbody><tr><td>1,500</td><td>Half normal</td><td>~ln(size)</td><td>0.84</td><td>0.27 (±0.20)</td></tr><tr><td>1,500</td><td>Hazard rate</td><td>~ln(size)</td><td>0.13</td><td>-</td></tr><tr><td>1,250</td><td>Half normal + cosine</td><td>-</td><td>0.01</td><td>0.36 (±0.30)</td></tr><tr><td>1,250</td><td>Half normal</td><td>~ln(size)</td><td>0.86</td><td>0.27 (±0.20)</td></tr><tr><td>1,250</td><td>Hazard rate</td><td>~ln(size)</td><td>0.13</td><td>-</td></tr><tr><td>1,000</td><td>Half normal + cosine</td><td>-</td><td>0.01</td><td>0.42 (±0.34)</td></tr><tr><td>1,000</td><td>Half normal</td><td>~ln(size)</td><td>0.86</td><td>0.26 (±0.21)</td></tr><tr><td>1,000</td><td>Hazard rate</td><td>~ln(size)</td><td>0.13</td><td>-</td></tr><tr><td>760</td><td>Half normal + cosine</td><td>-</td><td>0.00</td><td>0.13 (±0.10)</td></tr><tr><td>760</td><td>Half normal</td><td>~ln(size)</td><td>0.87</td><td>0.27 (±0.20)</td></tr><tr><td>760</td><td>Hazard rate</td><td>~ln(size)</td><td>0.13</td><td>-</td></tr></tbody></table>

APPENDIX 3: COUNTING YEARS REQUIRED TO DETECT 3 LINEAR POPULATION TRENDS (1%, 5% AND 10% DECLINE PER YEAR) FOR LEVELS OF PRECISION (COEFFICIENT OF VARIATION) CORRESPONDING TO OUR FIVE SAMPLING INTENSITIES

<figure><img src="image_11.png" /></figure>