Simulation Modeling to Assess Line Transect Distance Sampling Under a Range of Translocation Scenarios

Conservation translocation (referred to herein as translocation) is the intentional relocation of organisms from one area to another, to produce a positive conservation outcome (IUCN 2013; Seddon et al. 2014). The conservation goals of translocations can be the reintroduction to sites where organisms have become extirpated (Hunter et al. 2020), reinforcement of existing populations that are below their potential carrying capacity (Pille et al. 2018), and assisted colonization where organisms are introduced to areas outside of their native range (Bouma et al. 2020). In addition, mitigation-driven translocation has been used as a tool to reduce direct mortalities typically brought about by human activities, such as development (Germano et al. 2015). Translocation can serve as an important management technique that has quantifiable value for conservation science, resource management, and public engagement (Parker 2008).

For translocation programs to be successful, it is critical to understand whether recipient sites adequately support translocated populations over time (Fischer and Lindenmayer 2000). Postrelease monitoring is crucial for understanding translocation success, and it provides important empirical data to guide subsequent translocation efforts (Ewen et al. 2014). A common approach to measuring translocation successes is to monitor population abundance and density as indicators of population stability or growth. Some example methods include the use of visual encounter surveys and N-mixture occupancy models (Fitzgerald et al. 2015), using census data to calculate population growth rates (Johnson et al. 2018), and mark–recapture surveys with survival models (Tapia et al. 2021). Line-transect distance sampling (LTDS; Buckland et al. 2001) is a common method for estimating population density and abundance that accounts for nondetection of some animals during the survey. For a comprehensive explanation of distance sampling techniques, see Buckland et al. (2005); however, in brief, LTDS uses a sample of perpendicular distances between detected objects (e.g., target species) and transect lines, fit to a detection function (the probability of detection as a function of increasing distance away from the line) to estimate density or abundance.

Turtle and tortoise species are frequent targets of translocation programs globally because their populations are rapidly declining due to a myriad of threats (Stanford et al. 2020) and their life history traits make them well suited to handle the stresses of translocation (Gibbons 1987). Some examples include repatriation of Egyptian tortoises Testudo kleinmanni in Egypt (Attum et al. 2007); reintroduction (Bertolero et al. 2007) and reinforcement (Pille et al. 2018) of Hermann’s tortoise Testudo hermanni populations in Spain and France, respectively; introduction of big-headed turtles Platysternon megacephalum in southern China (Shen et al. 2010); and assisted colonization for western swamp turtles Pseudemydura umbrina in Western Australia (Bouma et al. 2020). Within the United States, mitigation-driven translocation is frequently implemented to counteract the negative effects of development projects. Common examples include the Mojave Desert tortoise Gopherus agassizii (Brand et al. 2016; Dickson et al. 2019) and gopher tortoise Gopherus polyphemus (Tuberville et al. 2005; Bauder et al. 2014). In response to habitat loss and ongoing development throughout Florida, USA, wildlife managers are now permitting and regulating the mitigation-driven translocation of gopher tortoises. In Florida, the permanent translocation of more than 85,000 gopher tortoises from development sites was undertaken between 2009 and 2022 (Candidate Conservation Agreement 2023). Initiation of the translocation program was solely as a method to avoid entombment of individuals in their burrows, but since 2012 it has had the additional long-term goal of creating independently viable gopher tortoise populations throughout their range in the state (Florida Fish and Wildlife Conservation Commission 2012, 2023).

It is important to monitor newly created gopher tortoise populations to assess whether translocation results in stable and viable long-term populations. Line transect distance sampling has often been used to estimate the density and abundance of tortoises (Smith et al. 2009a; Castellón et al. 2015; Allison and McLuckie 2018; Zylstra et al. 2023) and marine turtles (Bovery and Wyneken 2015; Barco et al. 2018). Despite clear evidence that LTDS is an efficient method for monitoring natural gopher tortoise populations (Smith et al. 2009a; Stober and Smith 2010; Castellón et al. 2015), the translocation program in Florida currently uses belt transects (also referred to as strip transects) with burrow scoping (use of a video camera scope to determine whether the burrow is occupied by a tortoise) for population monitoring at recipient sites, which do not account for imperfect detection and can potentially lead to inaccurate estimates of population trends (Florida Fish and Wildlife Conservation Commission 2023). This is because belt transects assume that all objects within the belt are detected, which is highly unlikely (Smith et al. 2009a; Glennie et al. 2015). Line transect distance sampling methods have not yet been adopted to monitor translocated gopher tortoise populations because, as described below, the process of translocation may also result in LTDS assumption violations regarding the spatial distribution of newly created populations.

Translocation of gopher tortoises (and other organisms) into recipient sites presents several unique sampling challenges that do not typically occur within natural populations. Soft-release techniques are often used to help translocated animals acclimate to their new environment and to decrease dispersal from release sites (Tuberville et al. 2005). Gopher tortoises are soft released into outdoor pens, typically constructed using silt fencing, for 6–12 mo; after which, the pen fences are removed (Florida Fish and Wildlife Conservation Commission 2023). This creates a challenge for subsequent monitoring because translocated tortoises tend to cluster along the pen edges, resulting in higher densities along the edges than elsewhere (Hinderle et al. 2014). This occurs because the translocated tortoises, attempting to disperse away from release sites, are intercepted by the pen fences where they dig burrows (Figure 1). This clustering of burrows can persist for many years after the fences are removed, violating the LTDS assumption that animals are independently distributed across a site. This assumption is especially important as it relates to the spatial arrangement of transect lines relative to the locations of burrow clusters (Buckland et al. 2005).

Recipient sites can also differ substantially in boundary shapes, acreage, size and arrangement of soft-release pens, habitat heterogeneity, and the number of resident individuals already at the site, each of which could potentially influence LTDS outcomes. Differences in vegetation structure and the age-class distribution of the tortoise population can also influence the distance at which tortoises and burrows can be detected because dense or tall vegetation can create visual obstructions that impede detection, and the smaller burrows of younger tortoises are less detectable than larger burrows. These influences of vegetation and the animal size-class distribution have been demonstrated for natural (i.e., nontranslocated) gopher tortoise populations (Howze and Smith 2019; Gaya et al. 2022) and other forest-dwelling species, such as lizards (Rosa et al. 2022). The efficacy of LTDS under translocation conditions has not been evaluated. Our goal was to investigate whether LTDS can provide accurate and precise estimates of gopher tortoise population density under a wide range of site, population, and sampling conditions that typify gopher tortoise populations made up largely of translocated individuals. Our approach centers around simulating realistic spatial scenarios of resident and translocated tortoise populations at recipient sites with a range of conditions to test the flexibility and accuracy of LTDS methods for estimating the density of translocated populations.

At the time of this analysis, there were few burrow survey datasets of entire recipient sites in Florida. Simulation was therefore the only way to produce realistic representations of gopher tortoise burrow distributions. We provide code to generate all simulation scenarios (see Text S1, Supplemental Material). We created scenarios of 10 known differences in spatial characteristics of recipient sites and population structure of gopher tortoise populations; we then simulated LTDS surveys of these populations by using different sampling strategies to assess the accuracy and precision of the density estimates they produced (Figure 2). The Florida Fish and Wildlife Conservation Commission uses habitat acreage within their calculations for stocking density at recipient sites (Florida Fish and Wildlife Conservation Commission 2023). We therefore maintained this framework for our own simulations and refer to site areas in acres throughout. We constructed the recipient site, tortoise population, and sampling strategy scenarios by using a set of 10 characteristics, each with two or three possible conditions. These characteristics included spatial attributes of the recipient sites (size, shape, percentage suitable habitat, and pen size); properties of the tortoise populations (tortoise density, size-class distribution, and degree of clustering); sets of sampling strategy alternatives (transect direction, number of observers conducting the survey); and a range of detection scales, modeled to represent different levels of visibility due to differences in vegetation structure (Figure 2).

The total area of a recipient site consists of both the area of habitat that is suitable for tortoises (the permitted area that is surveyed) and the nonsurveyed area of nonhabitat. We simulated populations by generating burrows across the sites occupied by resident tortoises, occupied by translocated tortoises, or unoccupied. We populated each site with the maximum number of tortoises allowable, based on the permitted area of habitat at the recipient site and the number of tortoises permitted per acre. We distributed the burrows of resident tortoises randomly, according to a uniform distribution, throughout the permitted area of habitat, whereas we placed burrows of translocated tortoises inside soft-release pens, with an 80% probability of occupying the area within 5 m of a pen edge, but otherwise distributed randomly (determined via a panel of gopher tortoise experts). We designed this preferential placement of translocated tortoises to replicate clustering of burrows along pen edges, as observed at real-world recipient sites (Figure 1).

Line transect distance sampling protocols for gopher tortoise monitoring focus on the detection of burrows, followed by use of a video camera scope to determine whether the burrow is occupied by a tortoise (Nomani et al. 2008). Burrow occupancy rates can vary considerably within and among both sites and populations, and burrows that are considered active (those with evidence of tortoise activity, such as feces and footprints) or inactive (no evidence of activity) can either be occupied or not. For example, Nomani et al. (2008) found a 50% occupancy rate for active burrows and 4% occupancy for inactive burrows; in addition, Auffenberg and Franz (1982) reported an occupancy rate of 61.4% for active and inactive burrows combined, whereas Stober and Smith (2010) found that occupancy varied from 18 to 31% among sites. We therefore drew burrow occupancy rates from a uniform distribution between 0.2 and 0.8 in an effort to incorporate this level of variation across sites. We simulated this occupancy by populating the site with occupied burrows and producing nonoccupied burrows based on the occupancy rate (i.e., an occupancy rate of 0.2 [20%] would result in five times as many “extra” burrows distributed across the landscape). Within actual LTDS surveys in the field, the discovery of a gopher tortoise above ground is equivalent to finding an occupied burrow and can be treated as so.

Habitat patch size and shape can influence the degree of spatial aggregation at pen edges by translocated tortoises. We simulated three habitat area conditions: 40, 400, and 4,000 acres (∼0.16, ∼1.62, and ∼16.19 km²; Figure 2A). These are a realistic range of sizes because a recipient site must contain at least 40 acres of contiguous upland habitat for consideration as a long-term protected recipient site (Florida Fish and Wildlife Conservation Commission 2023), and 4,000 acres was a suitable upper limit based on review of permit applications and expert opinion. Thus, most real-world recipient sites would fall within this range of sizes. We also simulated two patch shape conditions: regular (square sites) and irregular (equal size with a greater perimeter: area ratio; Figure 2B). Tortoise distribution is also influenced by the percentage and spatial arrangement of habitat within a recipient site. We created three recipient site scenarios with differing percentage of habitat available: 100, 60, and 20% habitat. All habitat scenarios consisted of the same habitat area, such that we inflated the total recipient site area to accommodate nonhabitat (e.g. 60% percentage cover scenario with 400 acres of habitat = 660-acre recipient site; 20% habitat, 400 acres of habitat = 2,000 acre recipient site; Figure 2C). This was done because only habitat is considered for tortoise stocking within a recipient site permitting boundary; thus, the effective sampling area is comprised of only habitat (Florida Fish and Wildlife Conservation Commission 2023). We created the 60 and 20% scenarios by randomly distributing habitat patches within a full recipient site, which equaled the total permitted habitat area needed for that scenario. The size and number of pens will determine the edge : interior ratio, thereby influencing the degree of spatial aggregation of burrows at the site. We created two pen size scenarios: small pens (40 acres) and large pens (120 acres; Figure 2D) that were rectangular or square, based on where they could fit within site area and shape. For our 40-acre site size scenarios, we had a single pen encompass the entire site. For our varying habitat area scenarios, we allowed the pen area to vary between 40 and 120 acres (based on publicly available permit applications) depending on where pens could feasibly fit within the available habitat areas. We simulated enough pen area to accommodate all tortoises permitted for translocation. Under the permitting guidelines (Florida Fish and Wildlife Conservation Commission 2023), the pens may accommodate up to 1.5 times the permitted stocking density for the particular areas of the recipient site in which the enclosure is located. This always resulted in a minimum of 67% of the total habitat area needed for soft-release pens. For example, a 400-acre recipient site that is permitted for 1 tortoise/acre can receive a total of 400 tortoises, which can be stocked in the pens at a density of 1.5 tortoises/acre. This results in an area of 267 acres needed to accommodate all 400 tortoises inside the pens, which is 67% of the total site size.

We investigated the effect of the total size of tortoise populations, including resident and translocated tortoises, and the ratio between them, on LTDS density estimate accuracy. We simulated three tortoise density scenarios based on current permitting guidelines: one, two and three tortoises per acre (Figure 2E). Up to four tortoises per acre can be authorized for receipt if there is not an existing (resident) population within the permitting boundary, but it is uncommon for the entire area of a permitted recipient site to meet all the qualifications necessary to achieve this stocking density (Florida Fish and Wildlife Conservation Commission 2023). We also created two resident : translocated tortoise ratio conditions: 20 and 60% residents. Because translocated tortoises had an aggregation of burrows along pen edges (80% probability of occupying an edge), populations with higher proportions of translocated tortoises had burrow distributions with higher degrees of spatial clustering (Figure 2G). The distribution of tortoise size classes within the population may also influence the probability of detection by LTDS observers because the larger burrows of larger tortoises are easier to see (Howze and Smith 2019). We therefore addressed this potential source of bias by modeling three age-class distributions based on Folt et al. (2021): natural, juvenile skewed, and adult skewed (Figure 2F). We assigned tortoise sizes (straight-line carapace length) randomly using a normal distribution for adult tortoises (mean = 280 mm, SD = 10 mm; Ashton et al. 2007) and a uniform distribution for juvenile tortoises (50–250 mm; Folt et al. 2021). We then adjusted the detection probability for individual sizes following the method outlined by Gaya et al. (2022), which we explain in detail below.

We simulated two transect direction conditions—north-south (N-S) and northeast-southwest (NE-SW; Figure 2H)—to assess the impact of transect orientation relative to the burrows clustered along the pen fences (see below for information on transect generation). We simulated pen edges to be linear and oriented in cardinal directions, both for simplicity and because real-world fences are often linear, because they are more time- and cost-efficient to construct. Also, they typically follow roads or access points (evidenced by publicly available permit applications). Therefore, the N-S–oriented transects ran either parallel or perpendicular with the fence lines (Figure 2H), potentially resulting in oversampling of burrows if a randomly placed transect ran directly alongside a fence (where there are high densities of clustered burrows) or undersampling if none of the transects are within visible range of the linear clusters of burrows along fences. For this reason, Buckland et al. (2001) recommend avoiding sampling along (or parallel to) linear features, such as roads or fences. The NE-SW–oriented transects ran at a 45° angle to all pen edges, allowing for a more even distribution of areas where transect lines intersect pen edges.

Previous research indicates that LTDS surveys conducted by more than one observer per transect line are more efficient (Buckland et al. 2001; Stober and Smith 2010) because it widens the shoulder of the detection function and can improve the probability of perfect detection on the line, a key LTDS assumption (Buckland et al. 2001; Smith et al. 2009a, 2009b; Castellón et al. 2015). To assess this, we simulated surveys conducted by one and three observers (Figure 2I). In the three-observer condition, simulated observers maintained a distance of 2 m apart (to simulate an arms-length distance; simulated by increasing the shoulder of the detection function by 2 m). This mirrors the standard protocol (Smith et al. 2009b; Smith and Howze 2016), with the center observer walking on the transect line, focusing on detecting burrows directly on the line (and serving as primary navigators), whereas each outer observer focuses on detecting burrows between themselves and the middle observer (while also searching away from the centerline), increasing the probability of detection on and around the transect line. Gopher tortoise habitat varies widely throughout Florida (Auffenberg and Franz 1982), from dry sandhill habitats to mesic flatwoods and dense scrub. These habitat types further vary in the degree of visibility and therefore detectability of tortoise burrows. We created three conditions in which detection probability varied, as it does in the field as a function of the habitat structure. We did this by decreasing the sigma (scale parameter for a half-normal detection function [following methodology in Gaya et al. 2022]), which could represent increased vegetation obstruction, or other factors limiting detection distance in the field: sigma = 2.5, 5, and 10 m (Figure 2J).

After simulating populations with different arrangements of tortoises, burrows, and habitat (Figures 2A–2G), we sampled the simulated populations by using our various LTDS sampling strategies (Figures 2H–2J). Our sampling followed a pilot survey methodology (Smith et al. 2009b), and we therefore refer to two sets of surveys walked by observers, the data of which are combined to estimate density at a site. The first are “pilot surveys” that are a random subset of the maximum number of possible transects that can fit within the site (based on our distance between transects; see below). We refer to pilot surveys by using a delineated percentage: a 10% pilot survey indicates that only 10% of the total number of discrete transects are used for an initial survey, and a 50% means that half of the transects are walked in the pilot survey, before a subsequent effort defined below. We then used the encounter rate (distance in meters/number of occupied burrows) to calculate the distance to be walked in the subsequent survey that is needed to obtain population density and abundance estimates with a coefficient of variation (CV) less than 17% (Smith and Howze 2016). The subsequent effort needed to attain the CV less than 17% is referred to as the “follow-up survey,” a random subset of transect lines from the maximum number of possible transects. The follow-up survey transects cannot be the same as the transects walked in the pilot survey because the data from both surveys are used within the estimation model. In some instances, the effort performed in the initial pilot survey is enough to attain a CV less than 17%, particularly if the encounter rate is high. When additional effort is needed, the follow-up survey can consist of just one more transect to meet the required effort, or it may encompass up to all remaining transects.

We initially ran all simulations using a 50-m distance between transect lines and a 50% pilot survey effort; however, we found that this resulted in an unnecessary level of survey effort for the 4,000-acre scenarios and, conversely, too little effort and a high degree of variance within our 40-acre scenarios. We therefore allowed the distance between transects to increase with the size of the recipient site, based on our expectations of realistic effort for conducting a full LTDS survey (i.e., walking distance by observers). Thus, our 40-, 400-, and 4,000-acre scenarios had 25-, 50-, and 100-m distances between transect lines, respectively. All transect lines span the entire recipient site from site boundary to site boundary, spanning unpermitted nonhabitat, although we did not survey these areas. We placed the first transect at a random starting location within the first designated transect distance of the recipient site (i.e., first 25 m for 40-acre sites and first 100 m for 4,000-acre sites), with remaining transects placed systematically at the assigned distance between transects. We did not simulate any pilot survey for the 40-acre sites because initial simulations demonstrated that a target CV of 17% (Smith and Howze 2016) could only be achieved if we surveyed all the transect lines, spaced 25 m apart across the entire site. We further surveyed 50% of the maximum number of possible transects for the 400-acre pilot surveys and reduced this to 10% for the 4,000-acre scenarios. For many of the 4000-acre sites, much less effort in the pilot surveys (∼10%) was sufficient to achieve a CV less than 17% without the need for a follow-up survey. However, the encounter rate was rarely high enough in the smaller sites to achieve a CV less than 17% during a pilot survey; thus, the requirement was for observers to walk all possible transects.

We used a half-normal detection function for both of our observer scenarios; however, we maintained our highest detection probability on the line for 2 m to simulate three observers walking at approximately arms-width apart. One of the main assumptions of LTDS is that all objects on the transect line are perfectly detected (probability of detection on line = 1); however, Howze and Smith (2019) demonstrated that 100% detection on the line is not an appropriate assumption for gopher tortoise burrows, particularly for sites with dense vegetation. We therefore relaxed this assumption of perfect detection on the line within our simulations. To do this, we drew the detection probability from a uniform distribution between 0.65 and 0.95 for each simulation (i.e., combination of scenarios and replications [9,072]; see below), based on detection probabilities observed in Howze and Smith (2019) and an improbability of reaching perfect detection. We created scenarios comprising all possible combinations of recipient site, population, and sampling strategy attributes (Figure 2), thereby resulting in 3,024 scenarios. We simulated each scenario with three replicates (9,072 total simulations) to account for variation in random placement of tortoises/burrows, random draws of burrow occupancy rates, and random draws of detection probabilities on the transects.

We assessed the importance of site, population, and sampling strategy characteristics on the accuracy of density estimates by using a conditional version of the permutation importance measure from random forest analysis (Breiman 2001; Strobl et al. 2008), which performs better for datasets with categorical predictor variables (Cutler et al. 2007; Strobl et al. 2007). Random forest is a commonly used analytical technique in ecological studies, for classifying variable importance (Cutler et al. 2007; Bradter et al. 2012; Yu et al. 2021). We calculated the bias between the true tortoise density (as modeled in each simulated recipient site) and the estimated tortoise density derived from the simulated LTDS survey as ((estimated density − true density)/true density) × 100), which we assigned as the response variable in the random forest analysis. We calculated variable importance using 10,000 trees (ntree = 10,000), fixing the number of variables randomly sampled at 5 for each node (mtry = 5; Strobl et al. 2009). We assigned a P value of 0.05 (mincriterion = 0.95) for the implementation of a split in a tree (must be lower than 0.05 to implement split). We drew 10% of observations to be sampled without replacement. We present mean decrease accuracy (MDA) herein (conditional importance), a method of assessing variable importance output from random forest analysis, and it is not related to our bias measure above, which is the response variable of the analysis (see R packages and functions in Text S3, Supplemental Material).

Across all our simulations (i.e., all possible combinations of scenarios), the bias between the true densities and estimated densities were median = −17.2%, mean = −12.4% (SD = 35%). Because we relaxed one of the main assumptions of LTDS and simulated imperfect detection on the line (drawn from a uniform distribution of 0.65–0.95), results of our simulated LTDS surveys underestimated the true density of tortoises at recipient sites on average. The probability of detection on the transect line therefore substantially influenced the accuracy of the estimates. Accordingly, simulations with a relatively low detection probability had greater bias (e.g., less than 0.85 resulted in a median and mean bias of −22 and −17.6% [35.2% SD], respectively), and bias was less severe when the detection probability was closer to 1 (e.g., greater than 0.85, median = −6%, mean = −1.8%, SD = 32.2%; Figure 3).

The size of the permitted habitat area and site shape did not substantially impact results (Figure 4; Table S3, Supplemental Material [pairwise comparisons]). We observed no clear relationship between the percentage of habitat available and accuracy of our estimated tortoise density at recipient sites. The 100% habitat condition produced the most accurate results, on average; however, this was not a linear relationship. Specifically, the 20% habitat condition produced more accurate density estimates on average than the 60% condition (Figure 4; Table S1). Likewise, there was no apparent relationship between pen size and estimated accuracy, with estimates being only slightly more accurate for the 120-acre pens over the 40-acre pens (Figure 4; Table S1).

Although we recorded no substantial difference in estimation accuracy for the different conditions for each population characteristic, some relationships are discernible. Estimation accuracy increased with decreasing tortoise density, suggesting that LTDS does not perform as well in overstocked recipient sites (Figure 4; Table S1). In addition, estimation accuracy increased with increasing adult-skew in age structure (Figure 4; Table S1). Lastly, the proportion of translocated tortoises comprising the total recipient site population affected the estimation accuracy, where a lower proportion of translocated tortoises, and therefore less clustering, resulted in more accurate estimates (Figure 4; Table S1).

The number of observers greatly influenced the accuracy of LTDS density estimates (Figure 4; Table S1), where more observers led to more accurate estimates. Increasing detection distance (i.e., visibility at the site increased; or vegetation obstruction decreased) led to increased accuracy of the density estimates (Figure 4; Table S1). The direction of the transect lines also influenced the accuracy of density estimates in interesting ways. Line transect distance sampling typically performed well irrespective of transect direction, with a large proportion of model estimates having biases near 0% for both the transect direction conditions (Figure 5). However, the N-S condition produced some extreme outliers, especially overestimates—the highest bias recorded for the N-S condition was +784.1%, which is substantially higher than any estimates produced by surveys with the transects in the NE-SW orientation, with the highest recorded bias being +53.3% (Figure 5). Both conditions had a similar effect on the mean estimation accuracy; however, there is much greater variability in the N-S condition (Table S1).

The probability of detecting a burrow on the transect line was the most important predictor of density estimate accuracy based on our random forest analysis (Figure 6). Excluding probability of detection on the transect line resulted in an MDA of 109.4%. The number of observers conducting a survey was also an important variable for accurately estimating tortoise density (MDA = 18.4%), followed by detection distance (MDA = 9.9%) and site size (MDA = 6.2%). Our remaining variables had an MDA less than 3%, which were as follows in descending order of importance: transect direction (MDA = 2.5%), the density of tortoises (MDA = 2.5%), size and arrangement of pens (MDA = 2.4%), age structure (MDA = 1.9%), site shape (MDA = 1.7%), percentage of habitat (MDA = 0.9%), proportion of residents (MDA = 0.7%), and burrow occupancy rate (MDA = 0.4%; Figure 6).

We investigated how multiple variables associated with the mitigation-driven translocation of gopher tortoises affects accurate population monitoring via LTDS surveys. In general, our site and population scenarios did not substantially affect the accuracy and precision of density estimates. Rather, our sampling strategy and conditions greatly influenced estimates: transect orientation relative to linear clustering effects, number of observers, and detection distance (Figures 4I and 4J; Figure 5). Our random forest analysis highlighted that detection on the transect line was the most important variable for predicting the bias between true and estimated tortoise densities (Figure 6). We relaxed the assumption of perfect detection on the transect lines to represent more realistic field sampling conditions. Although perfect detection on the transect line is a major assumption of LTDS (Buckland et al. 2001), this is often not satisfied during field sampling (Howze and Smith 2019; Rosa et al. 2022). Meeting the main assumption of perfect detection on the line can be particularly difficult for burrowing species, where the burrows themselves are used as the object of detection (Castellón et al. 2015; Howze and Smith 2019). Burrows are often less conspicuous than the animals themselves, which increases the perception bias during surveys. We found that severe violations of this assumption biased our density estimates downward, underestimating the true densities at recipient sites. However, our LTDS survey method was reasonably robust to violation of this assumption if detection probability on the transect was greater than 0.85 (Figure 3). Evidence from desert tortoise studies suggests that translocated tortoises may spend more time outside burrows than residents, which could increase the detection probability (Farnsworth et al. 2015; Brand et al. 2016).

Although double-observer methodologies have previously been used to address imperfect detection (Allison and McLuckie 2018), particularly those that use mark–recapture distance sampling (Buckland et al. 2010; Burt et al. 2014), these methods may be less likely to succeed for burrow surveys where detection is impacted by factors such as vegetation structure (Howze and Smith 2019). Howze and Smith (2019) missed at least 96% of burrows under 12 cm within a site with dense vegetation, even with three observers walking side by side to provide triple coverage of the transect line. Our results show that population size underestimation may occur if the assumption of perfect detection on transect lines is severely violated. Adequate training of observers to improve detection of objects on the transect line is likely the most important factor for improving LTDS estimates. The consensus among the gopher tortoise experts consulted during this study was that mark–recapture distance sampling is an impractical methodology to use at Florida recipient sites, primarily due to the challenges involved with independent detections between multiple observers. However, future studies are warranted to evaluate this further, using a similar simulation study as demonstrated herein.

We introduced a novel approach to pilot survey effort based on the total habitat area to be surveyed, allowing the use of pilot survey data in deriving density estimates. Initial runs of our simulation models for the smallest (40-acre) sites demonstrated that a CV less than 17% could only be achieved by sampling all possible transects, which means for these smaller sites, observers could remove the pilot survey process from sampling and move forward surveying all transects available. Our simulation methodology also suggested that 400- and 4,000-acre sites require only 50 and 10% pilot surveys, respectively. For field surveys, this translates to sampling a random 50% subset of all possible transects for the pilot survey when the site is of medium size (∼400 acres). In other words, it is rare that less than 50% of all discrete transects would be walked to achieve a CV less than 17%, and this pilot survey can then be used to determine effort for the follow-up survey. However, in these mid- to large-sized sites, the need to perform follow-up surveys was also rare (no further effort needed after pilot survey), because of the use of pilot survey data to derive density estimates. In the 4,000-acre, high density scenarios (site size = 4,000 acres; tortoise density = 3/acre), our 10% pilot survey achieved a CV of 13.2% on average (median = 13.3%); therefore, there was not a follow-up survey after the pilot survey. Our simulations suggest that the lack of pilot survey methodology in other study systems, particularly in large, high-density recipient sites, could result in unnecessarily high effort allocation. We demonstrate that there is rarely a need for observers to walk all possible transects at a recipient site and provide a method where pilot surveys are not only used to determine overall effort but also included within overall density estimation. Simulation modeling may prove useful in assessing the impact of pilot survey methodology in future studies.

Another important finding of our investigation with regard to gopher tortoise surveys conducted at recipient sites was that clustering of tortoises along soft-release pen edges can result in extreme outliers in density estimates. This observed clustering effect caused quite severe density gradients within some scenarios, which is known to result in biased density estimates (Marques et al. 2012). Some of our density estimates that oversampled burrow clusters along pen edges were approximately eight times higher than the true density. Conversely, when we undersampled pen edges (i.e., surveys in which none of the transects adequately sampled pen edges), we sometimes underestimated tortoise densities by greater than or equal to 90% (Figure 5). However, simulated transect lines at a 45° angle to the orientation of pen edges (Figure 2H) provided a more even distribution of sampling across pen edges and prevented the circumstances in which transects missed sampling the pen edges almost entirely (Figure 5). Unique orientation of transects according to density gradients across study regions is a known solution for LTDS survey design; however, when this is not practical, those working in other study systems may want to consider a stratification approach (Thomas et al. 2010). Although our simulations are somewhat unrealistic (real pen edges would never be perfectly oriented to cardinal directions), we demonstrated that clustering effects could be addressed through appropriate survey design that provides adequate coverage of pen edges where clumped distributions are known to occur. Marques et al. (2012) provide a modeling solution and further recommendations for dealing with distance sampling approaches under evident density gradients.

Our results have direct implications for monitoring of gopher tortoise translocation recipient sites throughout Florida, and they may be applicable to monitoring of other wildlife populations that cluster along linear landscape features such as roads. For many wildlife species, roads are linear features that can spatially structure distributions and affect estimations; including gopher tortoises, which have been shown to reside along roadside habitat (Rautsaw et al. 2018). Kiffner et al. (2022) overestimated olive baboon Papio anubis densities when using roads as LTDS transects. This could be corrected by allocating transect lines across a broader representation of baboon habitat and by avoiding parallel orientation of transects with roads; however, we recognize that sampling is sometimes limited to roads due to site accessibility. Likewise, this LTDS methodology may have implications for species with affinities for railway networks (Wiącek et al. 2020), forest edges (Terraube et al. 2016), hedgerows, and linear barriers that might limit movement.

Our study also highlighted the utility of simulation modeling to develop and assess monitoring strategies. Appropriate study design is critical to the success of monitoring programs, and simulation modeling is a cost-effective method to understanding how variation in conditions may impact estimates before investing in expensive field sampling efforts that could yield biased results (Conn et al. 2016). This has been referred to as the “virtual ecologist” approach (Zurell et al. 2010) that is cost-effective and useful when empirical data are scarce or when bias is suspected (Zurell et al. 2010). In our case, census data documenting tortoise burrow distributions at recipient sites are limited. Modeling offered a pragmatic and time- and cost-efficient approach to assess the impacts of various factors that could potentially bias results.

Our results demonstrated that the LTDS method is generally flexible and robust for estimating gopher tortoise densities at recipient sites and could provide an appropriate standardized methodology for long-term monitoring. Our range of simulation conditions had negligible impact on estimates when the probability of detection on the transect lines was high and we used three observers. Detection probability on transect lines may be increased by using three observers with sufficient training and timing surveys when detection probability is high (e.g. after prescribed fires). Because soft releasing tortoises in pens can result in clustering along pen edges that can influence density estimation, careful survey design that avoids bias in transect line placement is important to minimize effects of pen edge clustering on density estimation. Managers may produce more accurate density estimates by choosing transect directions (angles) that capture the spatial heterogeneity caused by translocation and linear landscape features. Thus, LTDS may be useful for species that are subject to complex translocation conditions or exhibit a high degree of spatial clustering along linear landscape features. Future studies and monitoring regimes, particularly for translocated gopher tortoises, may find an adaptable habitat size-based pilot survey design useful for effort allocation. Simulation modeling offers the flexibility to explore the effects of various conditions on population density estimation, and Bayesian modeling offers a solution for integrating individual-level covariates, which will likely improve the applicability of LTDS to many systems with complex sampling conditions.

Please note: The Journal of Fish and Wildlife Management is not responsible for the content or functionality of any supplemental material. Queries should be directed to the corresponding author for the article.

Text S1. R code to produce all simulated scenarios, which includes simulated recipient sites that differ in spatial characteristics and gopher tortoise Gopherus polyphemus population conditions, and simulated line transect distance sampling surveys of the sites.

Available: https://doi.org/10.3996/JFWM-23-029.S2 (30 KB R File)

Text S2. R code to run the Bayesian hierarchical model that allows for inclusion of individual-level covariates. The hierarchical model is used to analyze simulated line transect distance sampling data to calculate gopher tortoise Gopherus Polyphemus density at recipient sites.

Available: https://doi.org/10.3996/JFWM-23-029.S3 (7 KB R File)

Text S3. Information for all software used to produce simulations, run the Bayesian hierarchical model, and perform random forest analysis, including R package versions, R functions, citations, and references.

Available: https://doi.org/10.3996/JFWM-23-029.S1 (47 KB DOCX)

Table S1. Simulation characteristics, the condition of each simulation characteristics, and median, mean, and standard deviation of the bias observed between the true density and the estimated density of gopher tortoises Gopherus polyphemus for each scenario (calculated as ([estimated density − true density]/true density) × 100). Letters A–J of the simulation characteristics correspond to the scenarios outlined in Figure 2.

Available: https://doi.org/10.3996/JFWM-23-029.S4 (48 KB DOCX)

We thank the Florida Fish and Wildlife Conservation Commission for funding this research. We thank Kevin J. Loope for help in running estimation models in parallel, thereby saving us considerable processing time.

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