Correcting Waterhole-Driven Population Biases in Arid Ecosystems: A Case Study of Oryx (Oryx gazella)

Abstract

Transect surveys and distance sampling are widely used to estimate wildlife population densities, but these methods can be biased when animals aggregate near features such as waterholes or other resources that occur along survey routes. Using empirical data from the NamibRand Nature Reserve in Namibia, we developed spatial simulations to examine how clumping of oryx (Oryx gazella) near water sources affects density and population estimates. We simulated surveys along a 50 km transect and varied the proportion of the population concentrated at waterholes (5–20%). Our analyses from the simulated surveys show that such aggregation can cause substantial positive bias, as population estimates were inflated by 67% to 967% relative to the known population size. We evaluated two correction approaches: censoring observations and transect segments near waterholes and redistributing animals from waterholes across the landscape. Both methods reduced bias when applied to our simulated survey data, but censoring was simpler and consistently produced more accurate estimates. These findings demonstrate that nonrandom animal distributions near linear survey features can severely compromise distance sampling assumptions. Accounting for such biases is essential for producing reliable population estimates, particularly in arid and semi-arid systems where wildlife strongly congregates around limited water sources.

1. Introduction

Wildlife management actions typically require a relatively accurate estimate of the number of animals in a region [1]. For example, density and population size estimates may be used in semi-arid regions to assess carrying capacity of the forage resource in rangelands. Managers may also use estimates of population size to assess trends over time to understand the mechanisms for population dynamics.

One popular method to estimate population sizes is line transect surveys and distance sampling techniques [2]. Distance sampling assumes that animals that are closer to the transect line have a higher probability of being seen than animals farther from the survey route due to the relative proximity to the observers [3,4]. The perpendicular distance to each animal observed along the transect is recorded, and once the survey is completed, these estimated distances are compiled to develop a detection function for that species and landscape. The detection function mathematically models the probability of observing an individual as a function of its perpendicular distance from the transect line. The shape of the detection function is critical, as it allows for an estimate of how many animals were present but not detected along the survey route. Through distance sampling and subsequent analyses, natural resource managers can obtain an unbiased estimate of density and population size for the species of interest on their landscape [5,6].

However, a unique problem arises in dry regions that may violate an underlying assumption of transect surveys [3,7]. Distance sampling methods assume the transect line is placed randomly in respect to the distribution of objects [4], but this is not always the case. Transect survey lines often double as desolate roads used for servicing artificial waterholes, which are crucial to the survival of wildlife species in dry landscapes such as those in Namibia and other regions in southern Africa [8]. Because these transect lines are unable to be randomly placed with respect to the wildlife on the landscape, due to a lack of resources, time, and manpower, surveyors must utilize the roads that are already in place that connect to surrounding waterholes. The waterholes affect the dynamics of the ecosystem and lead to a nonrandom concentration of animals near the water source; we note that other resources such as sites for supplemental feeding would result in the same issue. Observers conducting the transect survey have a much higher probability of observing these large concentrations of wildlife immediately on the transect line than if they were away from the waterhole. Thus, the recorded observations from distance surveys in these locations reflect many individuals that are close to the transect line, which has the potential to overestimate, or positively bias, the overall density estimate for the species [7].

Line transect surveys have been compared to other survey types including point surveys [7,9], strip surveys [2], and track surveys [10], but there is limited information available on assessments of biases that result from concentrations of animals near the transect line due to nonrandom transect placement. One such study conducted in Virginia, USA in 2014 found that white-tailed deer (Odocoileus virginianus) population densities were likely to be positively biased when using distance surveys along roads due to the roads’ nonrandom placement with respect to the target species and landscape [11]. The scenario we examine in southern Africa has similar potential for bias, but with one unique difference: waterholes cause an attraction of animals to the transect line at specific locations rather than along the entire transect.

Line transect surveys are typically the chosen wildlife survey method due to the relative ease with which they can be conducted and their ability to estimate population sizes for multiple species that are visible on open landscapes. Although analyses based on distance sampling are robust and can account for many sources of error [4], factors such as the use of nonrandom transect routes when conducting distance surveys on pre-established roads can result in biases [12]. Again, these biases can occur due to the violation of the distance sampling assumption that transects are placed randomly with respect to the objects and landscape. Because it is difficult to assess bias in field-based studies, landscape simulations have been used in the past to evaluate biases related to distribution of habitat and animal movements [13,14].

The purpose of this study was to quantify the magnitude of sampling bias caused by nonrandom transects with respect to resources such as waterholes and to evaluate practical solutions for wildlife managers. To achieve this, we used oryx (Oryx gazella) as a model species to simulate populations on virtual landscapes with and without waterholes. By focusing on the unique challenges of arid environments—where waterholes attract wildlife to specific locations along the very roads used as survey transects—we aimed to identify and test correction methods that provide more reliable population estimates. We predicted that waterhole-driven clumping would significantly violate distance sampling assumptions, leading to an overestimation of density, and that our proposed correction methods would effectively mitigate this positive bias.

2. Materials and Methods

2.1. Study Area

Our study and simulation model was based on empirical data (Figure 1) collected at the NamibRand Nature Reserve, covering 172,200 hectares (1722 sq. km) in southwest Namibia (latitude: −24.999825, longitude: 16.000376) [15]. The reserve staff use distance sampling during the annual game count to survey 10 transect routes by road, each with a length of approximately 50–60 km. The landscapes at NamibRand are managed to minimize human impacts on the reserve and roads are minimized to protect fragile soil surfaces along the Namib Desert. The landscape and terrain consist of savanna grasslands, sand and gravel plains, inselbergs, small mountain ranges, and vegetated dune belts. While the landscape and terrain do differ slightly on the reserve, we assume the same pattern of detectability for the entire transect survey area for the purposes of this study.

Namibia experienced severe drought conditions from 2013 to 2019, with annual precipitation levels under the yearly average by 92–296 mm each year except 2014 [16]. During drought conditions, managers of the reserve are especially aware of the importance of density estimates for grazing wildlife species to plan for forage availability as it decreases with the lack of precipitation. NamibRand is home to a variety of animal and plant species that are native to southern Africa with oryx and springbok (Antidorcas marsupialis) as the most prevalent animal species [15].

2.2. Analysis of Empirical Data

We needed to establish real-world oryx densities and detection probabilities (the probability of a surveyor detecting an oryx at a given distance from the survey transect) based on actual wildlife surveys to use in our simulations. We used oryx sightings from the 2016 game count at NamibRand to estimate density and determine the best model with which to describe detection probabilities of oryx. Surveys for wildlife are conducted each year during late May; transect lines are driven starting 30 min after sunrise. Each management zone has a different survey crew which determines the distance from the transect by trained estimation without binoculars. We analyzed the oryx data (n = 1778 observations across the entire reserve) using four detection models in Program DISTANCE [17]: half-normal, uniform, hazard rate, and negative exponential decay curves. We allowed for a cosine adjustment term on the four detection models and used AIC [7,18] to determine the model that best described the distribution of observations away from the transect line. The negative exponential decay model most closely represented the detection of oryx in the 2016 game count. We then used the negative exponential model in the analyses of our simulated survey data to establish patterns of detection probability and to estimate density and population size.

2.3. Simulation Methods

Our simulations involved two steps. First, we created a population of oryx on the simulated landscape using a Microsoft Excel spreadsheet (v. 2016) in which each line of the spreadsheet was an individual animal. Columns provided information about the distance of each animal from the transect and the animal’s detection status (detected/not detected). In the real scenario on which we based our study, the actual population size is not known; however, in these simulations we were able to set our own values and then modify them in ways to determine which outcome was the most closely aligned with the original value. With that knowledge, we simulated a population of 750 oryx data points, based on the number of oryx seen within 500 m along transects in each management zone (Figure 2) at NamibRand during the 2016 game count. Thus, our simulated populations were similar to the real-life scenario being modeled given the length and width of our simulation. Although oryx are often sighted in groups, we simplified our model and distributed individuals on the landscape.

Our simulated landscape was 1000 m wide and 50 km long (5000 ha), with a transect straight through the middle (500 m width on each side; Figure 2) to mimic a single management zone surveyed at NamibRand. We randomly assigned each oryx a location with a perpendicular distance away from the transect (x-value) and a position along the transect (y-value).

The second step in our simulation was to conduct a survey. We used the detection probabilities from the 2016 game count data to set discrete regions with increasing distance from the transect and decreasing levels of detection probability on our own landscape. We assigned individual animals that were on the transect line a detection probability of 1.0 due to the underlying assumption of distance sampling that objects directly on the line are detected with certainty [4,17,19].

The probability of detecting an oryx in our simulated survey declined in 100 m intervals until we hit the maximum distance of 500 m away from the transect. Based on the negative exponential detection probability model established with the analyses of empirical data, the detection probabilities and their respective distances in our simulation model were: 0.88 for 1–100 m, 0.70 for 100–200 m, 0.58 for 200–300 m, 0.45 for 300–400 m, and 0.35 for 400–500 m. We determined which of the simulated animals were “seen” by observers in our model by comparing each of the 750 individuals’ zone-specific detection probability with a randomly generated number between 0 and 1.0. If the random number was less than the detection probability assigned to each individual, we categorized it as observed. We imported the animals that were observed and their respective x-values (perpendicular distance from transect) into Program DISTANCE. This initial analysis from a landscape with no waterholes and no intentional clumping provided a baseline (S0) of estimated populations sizes and animal densities.

This initial control (S0) simulated survey without waterholes and clumped animals resulted in a satisfactory (<10% difference) estimate of the simulated known population size (750 individuals); therefore, we proceeded with adjustments to the simulation to assess potential for bias caused by clumping at the waterhole. We then simulated a new landscape with two waterholes located at 12.5 km and 37.5 km along the 50 km transect (Figure 2). We used trigonometry to calculate the distance of each oryx to the waterholes in the initial simulation.

We created three different scenarios to simulate in which the closest 5%, 10%, and 20% of data points were moved to their respective waterhole (simulations S5, S10, and S20, respectively). We created this gradient of waterhole use to represent the variability in drinking and grazing behavior that may exist in different real-life scenarios. We assigned the selected individuals a new perpendicular distance of zero meters and a detection probability of 1.0. As in the real-life scenario, the waterholes in the simulation are directly along the transect line with all animals at the waterhole detected. Individuals not at the waterholes maintained their same detection status as in the first simulation, and we imported each of the new simulation sets into Program DISTANCE to estimate population sizes and densities. We defined bias in the population size estimate as the difference between the estimate from the initial control simulation (S0, no waterholes or clumping) and the population size estimates resulting from the simulations with waterholes. In this way, we were able to evaluate the influence of levels of clumping on bias in population size estimates.

We used only one simulation to compare the S0, S5, S10, and S20 scenarios (Figure 3) because we were using large sample sizes of simulated animals to establish the distribution of detected animals in each scenario. Our population size estimates from each scenario should be interpreted as a relative representation for the scenario, as our approach does not provide information about the variability that could result from each scenario. However, we anticipated very little change in the overall distribution of simulated animals and density estimates because of our robust sample size. Instead, our goal for this modeling exercise was to assess the relative difference between scenarios.

2.4. Correction Methods

We then explored ways to correct for the bias caused by clumping of animals at waterholes during surveys. Our two correction methods were to (1) censor data from the survey section near waterholes or (2) redistribute the concentrated animals to where they might have been located in the absence of the attraction of the waterhole. The censor method is currently in use in some areas of Namibia, as it combats the violation of the distance sampling assumption of nonrandom transect placement by eliminating that nonrandom data, and we proposed the redistribution method as an attempt to still account for those individuals in the total count. Given the positioning of the transects as roads, it is not feasible to modify their placement on the landscape to follow the assumption of distance sampling in which transects are randomly placed with regard to individuals on the landscape. With that in mind, we redistributed these individuals at random locations across the landscape in an attempt to best represent the assumption of random transect placement given the constraints on the setup.

We implemented the censor method by removing the animals observed at the waterholes as well as the transect lengths corresponding to those sections of survey route from where the simulated animals were pulled to clump near the waterhole. We imported the new data into Program DISTANCE and recorded the population estimates and densities. This process was completed for the simulated distributions of animals in the S5, S10, and S20 scenarios, which resulted in censor scenarios S5-C, S10-C, and S20-C.

We moved all animals from the waterhole in the S5, S10, and S20 scenarios to new, random distances from the transect line to implement the redistribution correction method. After redistribution, individual animals were determined to be detected based on the same detection probabilities used for our base simulations. We imported these new data sets into Program DISTANCE, performed the analysis, and recorded the resulting population and density estimates for redistribution scenarios S5-R, S10-R, and S20-R. Our last step was to compare results from the two correction methods to determine which method led to population estimates that were the most similar to the initial simulation data (S0) from a landscape without waterholes.

3. Results

Our density analysis from the baseline simulation (S0) with 750 oryx and no waterholes resulted in 452 of the 750 oryx observed with a resulting population estimate of 798 individuals (95% CI: 698–912; density estimate = 0.160/ha, 95% CI: 0.140–0.182). The true population size was only 6.7% (48 individuals) different from our estimate and within its 95% confidence interval. Our scenarios with animals clumped at waterholes confirmed the alterations of the distribution of animals (Figure 3), which led to bias in the estimates of density and population size. Our estimates were positively biased at levels of 67.1%, 603.9%, and 966.8% (5%, 10%, and 20% of the individuals moved to waterholes; S5, S10, S20) higher than the known population size of 750, respectively (

Table 1. Comparison of density (individuals/ha) and population size from simulated scenarios of oryx (Oryx gazella) in a hypothetical 5000-ha (5-sq. km) management zone using distance sampling. Scenarios include baseline with no waterholes (S0), 5% clumping at waterholes (S5), 10% (S10), and 20% (S20), as well as comparisons with two correction methods: censor (C) and redistribution (R). Confidence intervals for population size are 95% intervals, and bias is indicated as a % difference in population estimate relative to the known population size of 750 oryx in each simulation.

Simulation Set	Density Estimate (Individuals/ha)	Population Estimate (Individuals)	Lower Confidence Interval	Upper Confidence Interval	Bias
S0	0.160	798	698	912	6.7%
S5	0.251	1253	1053	1490	67.1%
S5-C	0.144	719	626	825	−4.1%
S5-R	0.138	688	601	789	−8.3%
S10	1.056	5279	4243	6568	603.9%
S10-C	0.148	740	643	851	−1.3%
S10-R	0.140	699	610	801	−6.8%
S20	1.600	8001	6837	9362	966.8%
S20-C	0.140	698	600	811	−6.9%
S20-R	0.132	662	574	763	−11.7%

).

Our censor correction method applied to S5, S10, and S20 resulted in population estimates within 4.1%, 1.3%, and 6.9% of the true population size, while the redistribution method provided estimates that were within 8.3%, 6.8%, and 11.7% of the true size (Table 1). For all six of the correction simulations, the distributions of animals used for analysis were similar to the S0 scenario’s distribution (Figure 3 and Figures S1 and S2). Further, the true population size of 750 oryx fell within the 95% confidence interval of population size from the corrected simulations. For comparison, none of the confidence intervals for estimates of population size from the uncorrected simulations S5, S10, and S20 included the true value of 750 oryx (Table 1).

4. Discussion

4.1. Bias

Our concern about potential bias in population size estimates was supported by the positive bias in population estimates that resulted from the S5, S10, and S20 simulations. However, the population estimates were even more inaccurate than we had anticipated. In all three cases, the resulting populations were overestimated by at least 50%. The structure of data collected during 2016 at NamibRand did not allow us to determine the proportion of oryx present at waterholes during the surveys; however, all animals at waterholes were ≤50 m from the road transect (Figure 1). Approximately 20% of all detections in the 2016 survey were in the ≤50 m distance bin. From our field observations on the survey, we estimate that one-quarter of those animals were detected at waterholes during the survey. Therefore, we believe the S5 simulation (5% of the animals in the management zone) would be the most realistic in terms of number of animals that would be concentrated at a waterhole at a given period.

Although the S5 simulation is the least biased of the S5, S10, and S20 simulations, managers under the S5 scenario would be led to believe they have 67% more individuals than reality if our simulations mirror true conditions. Managers in southern Africa are acutely aware of the need for unbiased estimates to guide decision-making. Biologists reported a need to account for negative bias in population estimates of blue duikers (Philantomba monticola) in the Democratic Republic of the Congo during surveys in which the species avoided the survey transect lines [20], the opposite problem of our study. In Namibia’s Etosha National Park, located approximately 750 km north of the NamibRand reserve, managers compared survey methodology to ensure unbiased information for black rhinoceros (Diceros bicomis bicomis) [21].

4.2. Model Performance

We were satisfied that population size estimates from our baseline scenario were only 6.7% more than the known simulated population size (Table 1). We suspect the difference was due to our use of discrete detection probabilities, which simplified our simulation process. Although the application of distance sampling in the field has unique challenges depending on the characteristics of target species [22,23], our model’s landscape and simulations allowed us to assess bias relative to a known population size. Such a comparison is not possible with field-based experiments, as the true density and population size is not known.

We note that our results and relative levels of bias are specific to our simulated system and the detection function we used. However, we based our simulations on empirical data and an established detection function for real observations, which allow general inference from our simulated results to similar situations in the environment. We simulated a range of 5% to 20% of the population found clumped at waterholes during surveys because the extent of clumping may vary with location, species, and environmental conditions. The level of clumping for most populations is unlikely to exceed 10–20% of the overall population of similar species in dry landscapes because of the need to balance water needs with foraging access and predator avoidance [24]. The percentage of clumping in each scenario did lead to changes in bias in our results, so land managers can use the scenario that most closely represents their real-life situation. An alternative setup that could have been utilized rather than clumping based on the percentage of total population could have been identifying points that were within a certain radius of the waterhole and shifting them closer by a predetermined distance. While this setup may have been more realistic than clumping based on percentages, the overall concept and outcome would still have demonstrated our result of positive bias when distance sampling; therefore, we selected the more simplified setup for our simulation.

4.3. Correction Methods

Our results suggest that the censor method provided the most accurate estimates of density and population size. Both methods we used resulted in impressive reductions in biases found in the uncorrected analyses, but the censor method was the simplest to implement in addition to having the least bias. In application to the real world at NamibRand Nature Reserve, the censor method can be easily accomplished by removing sightings of oryx and reducing the associated transect length from any survey section that contains a waterhole (Figure 2B). Our redistribution techniques were simple, although perhaps less realistic than redistribution of individual animals based on probability functions. However, our goal was to find techniques that could be used by managers to correct for biases in density estimates. Although our redistribution method effectively reduced bias in density estimates, we suggest that managers use the censor method as a relatively simple way to correct for and remove the bias created by clumped animals at waterholes that we confirmed with our analyses.

The use of the censor method during the distance sampling analysis would not prohibit a manager from using that data for other purposes. The length of transect removed in our simulations was never more than 20% of the overall transect length. The loss of data represents a potential tradeoff between higher uncertainty in the density estimate (wider 95% confidence intervals) and reduction in bias that our simulations suggested as an outcome. Density estimation is based on a sample of detected individuals [6,7], and the censor method reduces the sample in an unbiased fashion by eliminating all data from zones surrounding waterholes. We realize that oryx were abundant at the study site on which we based on simulations; the uncertainty of a density estimate from surveys of species with low population size may be impacted by the removal of data from portions of the survey route. The problem can be solved by adding additional transect lengths [4].

5. Conclusions

Our study highlights a critical methodological vulnerability in arid-zone surveys: when waterholes coincide with survey routes, the resulting clumping of wildlife like oryx can inflate population estimates by nearly ten-fold. By testing these dynamics on simulated landscapes based on the NamibRand Nature Reserve, we confirmed that the censoring of waterhole-adjacent data simply and effectively mitigates this bias, bringing estimates to within 7% of the true population size. For managers in southern Africa who rely on these counts to understand population dynamics and resource allocation, adopting these correction methods is not just a statistical preference, but a necessity for making accurate inferences about ecosystem health and carrying capacity.