Abundance estimation of diving animals by the double-platform line transect method

In conventional line transect theory, it is assumed that all animals on the line are detected. This article introduces an extended and generalized hazard probability model without the need for such an assumption. The proposed method needs a survey design with independent observers having the same visual region and assumes an explicit distinction of simultaneous and delayed duplicates. It can take account of random heterogeneity caused by surfacing behavior as well as systematic heterogeneity by covariate effects. Furthermore, it can be easily extended to cases in which data from incompletely independent observers are available. The abundance estimate is based on the Horvitz-Thompson estimator in unequal detectability sampling scheme. Simulation studies suggest that the proposed method has good performance. The method is applied to a real data set on Antarctic minke whales in the illustration.     

Simulated likelihood methods for complex double-platform line transect surveys

The conventional line transect approach of estimating effective search width from the perpendicular distance distribution is inappropriate in certain types of surveys, e.g., when an unknown fraction of the animals on the track line is detected, the animals can be observed only at discrete points in time, there are errors in positional measurements, and covariate heterogeneity exists in detectability. For such situations a hazard probability framework for independent observer surveys is developed. The likelihood of the data, including observed positions of both initial and subsequent observations of animals, is established under the assumption of no measurement errors. To account for measurement errors and possibly other complexities, this likelihood is modified by a function estimated from extensive simulations. This general method of simulated likelihood is explained and the methodology applied to data from a double-platform survey of minke whales in the northeastern Atlantic in 1995.     

Double-Observer Line Transect Methods: Levels of Independence

Summary .  Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark–recapture data. Like conventional mark–recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark–recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark–recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters.     

Accounting for imperfect detection of groups and individuals when estimating abundance

If animals are independently detected during surveys, many methods exist for estimating animal abundance despite detection probabilities <1. Common estimators include double‐observer models, distance sampling models and combined double‐observer and distance sampling models (known as mark‐recapture‐distance‐sampling models; MRDS). When animals reside in groups, however, the assumption of independent detection is violated. In this case, the standard approach is to account for imperfect detection of groups, while assuming that individuals within groups are detected perfectly. However, this assumption is often unsupported. We introduce an abundance estimator for grouped animals when detection of groups is imperfect and group size may be under‐counted, but not over‐counted. The estimator combines an MRDS model with an N‐mixture model to account for imperfect detection of individuals. The new MRDS‐Nmix model requires the same data as an MRDS model (independent detection histories, an estimate of distance to transect, and an estimate of group size), plus a second estimate of group size provided by the second observer. We extend the model to situations in which detection of individuals within groups declines with distance. We simulated 12 data sets and used Bayesian methods to compare the performance of the new MRDS‐Nmix model to an MRDS model. Abundance estimates generated by the MRDS‐Nmix model exhibited minimal bias and nominal coverage levels. In contrast, MRDS abundance estimates were biased low and exhibited poor coverage. Many species of conservation interest reside in groups and could benefit from an estimator that better accounts for imperfect detection. Furthermore, the ability to relax the assumption of perfect detection of individuals within detected groups may allow surveyors to re‐allocate resources toward detection of new groups instead of extensive surveys of known groups. We believe the proposed estimator is feasible because the only additional field data required are a second estimate of group size.     

The Effect of Animal Movement on Line Transect Estimates of Abundance

Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the non-linear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.     

Improving Aquatic Warbler Population Assessments by Accounting for Imperfect Detection

Monitoring programs designed to assess changes in population size over time need to account for imperfect detection and provide estimates of precision around annual abundance estimates. Especially for species dependent on conservation management, robust monitoring is essential to evaluate the effectiveness of management. Many bird species of temperate grasslands depend on specific conservation management to maintain suitable breeding habitat. One such species is the Aquatic Warbler (Acrocephalus paludicola), which breeds in open fen mires in Central Europe. Aquatic Warbler populations have so far been assessed using a complete survey that aims to enumerate all singing males over a large area. Because this approach provides no estimate of precision and does not account for observation error, detecting moderate population changes is challenging. From 2011 to 2013 we trialled a new line transect sampling monitoring design in the Biebrza valley, Poland, to estimate abundance of singing male Aquatic Warblers. We surveyed Aquatic Warblers repeatedly along 50 randomly placed 1-km transects, and used binomial mixture models to estimate abundances per transect. The repeated line transect sampling required 150 observer days, and thus less effort than the traditional ‘full count’ approach (175 observer days). Aquatic Warbler abundance was highest at intermediate water levels, and detection probability varied between years and was influenced by vegetation height. A power analysis indicated that our line transect sampling design had a power of 68% to detect a 20% population change over 10 years, whereas raw count data had a 9% power to detect the same trend. Thus, by accounting for imperfect detection we increased the power to detect population changes. We recommend to adopt the repeated line transect sampling approach for monitoring Aquatic Warblers in Poland and in other important breeding areas to monitor changes in population size and the effects of habitat management.     

Estimation of In-Water Density and Abundance of Harbor Seals

Ecologists and managers require accurate population estimates of marine mammals to assess potential anthropogenic threats to these animals. We present estimates of in-water density and abundance of a distinct stock of harbor seals (Phoca vitulina richardii) in Hood Canal, Washington, USA. We used aerial line-transect survey data collected from 2013 to 2016 to directly estimate harbor seal density and abundance in the waters of Hood Canal, a deep-water fjord in the Salish Sea. We estimated a correction factor for trackline detection probability from dive and surface time data gathered from regional seal tagging studies, and applied this factor to correct for seals missed on the trackline during surveys. We applied conventional and multiple covariate line-transect approaches in the analysis. The resulting best estimate of in-water density of harbor seals in the Hood Canal study region was 5.80 seals/km², with an estimated abundance of 2,009 seals. We did not derive a correction factor to account for the number of seals on land (i.e., hauled out). Therefore, these estimates do not reflect total stock size but provide a starting point to evaluate potential influences of anthropogenic activities, particularly those involving underwater noise, on this marine mammal stock. © 2021 The Wildlife Society.     

Line Transect Sampling of Primates: Can Animal-to-Observer Distance Methods Work?

Line transect sampling is widely used for estimating abundance of primate populations. Researchers commonly use animal-to-observer distances (AODs) in analysis, in preference to perpendicular distances from the line, which is in marked contrast with standard practice for other applications of line transect sampling. We formalize the mathematical shortcomings of approaches based on AODs, and show that they are likely to give strongly biased estimates of density. We review papers that claim good performance for the method, and explore this performance through simulations. These confirm strong bias in estimates of density using AODs. We conclude that AOD methods are conceptually flawed, and that they cannot in general provide valid estimates of density.     

Statistical Efficiency in Distance Sampling

Distance sampling is a technique for estimating the abundance of animals or other objects in a region, allowing for imperfect detection. This paper evaluates the statistical efficiency of the method when its assumptions are met, both theoretically and by simulation. The theoretical component of the paper is a derivation of the asymptotic variance penalty for the distance sampling estimator arising from uncertainty about the unknown detection parameters. This asymptotic penalty factor is tabulated for several detection functions. It is typically at least 2 but can be much higher, particularly for steeply declining detection rates. The asymptotic result relies on a model which makes the strong assumption that objects are uniformly distributed across the region. The simulation study relaxes this assumption by incorporating over-dispersion when generating object locations. Distance sampling and strip transect estimators are calculated for simulated data, for a variety of overdispersion factors, detection functions, sample sizes and strip widths. The simulation results confirm the theoretical asymptotic penalty in the non-overdispersed case. For a more realistic overdispersion factor of 2, distance sampling estimation outperforms strip transect estimation when a half-normal distance function is correctly assumed, confirming previous literature. When the hazard rate model is correctly assumed, strip transect estimators have lower mean squared error than the usual distance sampling estimator when the strip width is close enough to its optimal value (± 75% when there are 100 detections; ± 50% when there are 200 detections). Whether the ecologist can set the strip width sufficiently accurately will depend on the circumstances of each particular study.     

An Evaluation of Survey Methods for Estimating Northern Bobwhite Abundance in Southern Texas

Abstract: Distance sampling has been identified as a reliable and well-suited method for estimating northern bobwhite (Colinus virginianus) density. However, distance sampling using walked transects requires intense sampling to obtain precise estimates, thus making the technique impractical for large acreages. Researchers have addressed this limitation by either resorting to the use of indices (e.g., morning covey-call surveys) or incorporating the use of aerial surveys with distance sampling. Both approaches remain relatively untested. Our objectives were to 1) compare density estimates among morning covey-call surveys, helicopter transects, and walked transects; 2) test a critical assumption of distance sampling pertinent to helicopter surveys (i.e., all objects on line are detected); and 3) evaluate the underlying premise of morning covey-call surveys (i.e., that the no. of calling coveys correlates with bobwhite density). Our study was conducted on 3 study sites in Brooks County, Texas, USA, during October to December, 2001 to 2005. Comparisons between walked transects and morning covey-call surveys involved the entire 5-year data set, whereas helicopter transects involved only the latter 2 years. Density estimates obtained from helicopter transects were similar to walked transect estimates for both years. We documented a detection probability on the helicopter transect line of 70 ± 10.2% (% ± SE; n = 20 coveys). Morning covey-call surveys yielded similar density estimates to walked transect estimates during only 2 of 5 years, when walked transect estimates were the least accurate and precise. We detected a positive relationship (R² = 0.51; 95% CI for slope: 29.5–53.1; n = 63 observations) between covey density and number of coveys heard calling. We conclude that helicopter transects appear to be a viable alternative to walked transects for estimating density of bobwhites. Morning covey-call surveys appear to be a poor method to estimate absolute abundance and to depict general population trajectories.     

A field test of the distance sampling method using Golden‐cheeked Warblers

ABSTRACT Criteria for delisting Golden‐cheeked Warblers (Dendroica chrysoparia) include protection of sufficient breeding habitat to ensure the continued existence of 1000 to 3000 singing males in each of eight recovery regions for ≥10 consecutive years. Hence, accurate abundance estimation is an integral component in the recovery of this species. I conducted a field test to determine if the distance sampling method provided unbiased abundance estimates for Golden‐cheeked Warblers and develop recommendations to improve the accuracy of estimates by minimizing the effects of violating this method's assumptions. To determine if observers could satisfy the assumptions that birds are detected at the point with certainty and at their initial locations, I compared point‐transect sampling estimates from 2‐, 3‐, 4‐, and 5‐min time intervals to actual abundance determined by intensive territory monitoring. Point‐transect abundance estimates were 15%, 29%, 43%, and 59% greater than actual abundance (N= 156) for the 2‐, 3‐, 4‐, and 5‐min intervals, respectively. Point‐transect sampling produced unbiased estimates of Golden‐cheeked Warbler abundance when counts were limited to 2 min (N= 154–207). Abundance estimates derived from point‐transect sampling were likely greater than actual abundance because observers did not satisfy the assumption that birds were detected at their initial locations due to the frequent movements and large territory sizes of male Golden‐cheeked Warblers. To minimize the effect of movement on abundance estimates, I recommend limiting counts of singing males to 2‐min per point. Counts for other species in similar habitats with similar behavior and movement patterns also should be limited to 2 min when unbiased estimates are important and conducting field tests of the point‐transect distance sampling method is not possible.     

A combined visual and acoustic estimate of 2008 abundance,and change in abundance since 1997, for the vaquita,Phocoena sinus

A line‐transect survey for the critically endangered vaquita, Phocoena sinus, was carried out in October–November 2008, in the northern Gulf of California, Mexico. Areas with deeper water were sampled visually from a large research vessel, while shallow water areas were covered by a sailboat towing an acoustic array. Total vaquita abundance in 2008 was estimated to be 245 animals (CV = 73%, 95% CI 68–884). The 2008 estimate was 57% lower than the 1997 estimate, an average rate of decline of 7.6%/yr. Bayesian analyses found an 89% probability of decline in total population size during the 11 yr period, and a 100% probability of decline in the central part of the range. Acoustic detections were assumed to represent porpoises with an average group size of 1.9, the same as visual sightings. Based on simultaneous visual and acoustic data in a calibration area, the probability of detecting vaquitas acoustically on the trackline was estimated to be 0.41 (CV = 108%). The Refuge Area for the Protection of the Vaquita, where gill net fishing is currently banned, contained approximately 50% of the population. While animals move in and out of the Refuge Area, on average half of the population remains exposed to bycatch in artisanal gill nets.     

Hazard models for line transect surveys with independent observers

The likelihood function for data from independent observer line transect surveys is derived, and a hazard model is proposed for the situation where animals are available for detection only at discrete time points. Under the assumption that the time points of availability follow a Poisson point process, we obtain an analytical expression for the detection function. We discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions. Discrete and continuous hazard models are compared and the robustness of the discrete model is investigated. Finally, the methodology is applied to data from a survey for minke whales in the northeastern Atlantic.     

On the importance of g(0) for estimating bird population densities with standard distance-sampling: implications from a telemetry study and a literature review

Raw count data are often used to estimate bird population densities. However, such data do not consider detection probability. As an alternative, methods that model detection probability such as distance-sampling have been proposed. However, standard distance-sampling provides reliable estimates for absolute density only when the underlying assumptions are met. One of the most critical of these assumptions is that animals on a transect line or at an observation point have to be detected with certainty (the g (0) = 1 assumption). We radiotagged nine Orphean Warblers Sylvia hortensis and estimated their short-distance detection probability. Birds were radio-located in 264 cases in single bushes or trees. Their visual detection probability after a 5-min search was only 0.58 (sd = ±0.14, range = 0.38–0.80), although the observer knew the bird's location. Furthermore, we carried out a literature review to assess how the g (0) = 1 assumption is handled in practice. None of the 28 standard distance-sampling papers reviewed contained an estimation of g (0). In 57% of the papers, the g (0) = 1 assumption was not even mentioned. Nevertheless, none of the authors declared their estimates as being relative. Our empirical data show that the g (0) = 1 assumption would be severely violated for a foliage-gleaning bird species at a desert stopover site outside the breeding season. The literature review revealed that the testing of the g (0) = 1 assumption is largely ignored in practice. We strongly suggest that more attention should be paid to the testing of this key assumption, because results may not be reliable when it is violated. If it is not possible to test the g (0) = 1 assumption or g (0) is less than 1, alternative methods should be used. Another possibility is to estimate detection probability by the means of radiotagged individuals.     

Using distance sampling techniques to estimate bottlenose dolphin (Tursiops truncatus) abundance at Turneffe Atoll,Belize

Reliable abundance estimates are critical for management and conservation of coastal small cetaceans. This is particularly important in developing countries where coastal human populations are increasing, the impacts of anthropogenic activities are often unknown, and the resources necessary to assess coastal cetaceans are limited. We adapted ship‐based line transect methods to small‐boat surveys to estimate the abundance of bottlenose dolphins (Tursiops truncatus) at Turneffe Atoll, Belize. Using a systematic survey design with random start and uniform coverage, 34 dolphin clusters were sighted during small‐boat line transect surveys conducted in 2005–2006. Distance sampling methods estimated abundance at 216 individuals (CV = 27.7%, 95% CI = 126–370). Due to species rarity in the Atoll, small sample size, and potential violations in line transect assumptions, the estimate should be considered preliminary. Nevertheless, it provides up‐to‐date information on the status of a regional population in an area under increasing threat of habitat loss and prey depletion via uncontrolled development and unsustainable fishing. This information will be useful as Belize develops a new conservation initiative to create a comprehensive and resilient marine protected area system. Our study illustrates the application of distance sampling methods to small‐boat surveys to obtain abundance estimates of coastal cetaceans in a region lacking resources.     

Nondetection sampling bias in marked presence‐only data

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Distance models as a tool for modelling detection probability and density of native bumblebees

Effective monitoring of native bee populations requires accurate estimates of population size and relative abundance among habitats. Current bee survey methods, such as netting or pan trapping, may be adequate for a variety of study objectives but are limited by a failure to account for imperfect detection. Biases due to imperfect detection could result in inaccurate abundance estimates or erroneous insights about the response of bees to different environments. To gauge the potential biases of currently employed survey methods, we compared abundance estimates of bumblebees (Bombus spp.) derived from hierarchical distance sampling models (HDS) to bumblebee counts collected from fixed‐area net surveys (“net counts”) and fixed‐width transect counts (“transect counts”) at 47 early‐successional forest patches in Pennsylvania. Our HDS models indicated that detection probabilities of Bombus spp. were imperfect and varied with survey‐ and site‐covariates. Despite being conspicuous, Bombus spp. were not reliably detected beyond 5 m. Habitat associations of Bombus spp. density were similar across methods, but the strength of association with shrub cover differed between HDS and net counts. Additionally, net counts suggested sites with more grass hosted higher Bombus spp. densities whereas HDS suggested that grass cover was associated with higher detection probability but not Bombus spp. density. Density estimates generated from net counts and transect counts were 80%–89% lower than estimates generated from distance sampling. Our findings suggest that distance modelling provides a reliable method to assess Bombus spp. density and habitat associations, while accounting for imperfect detection caused by distance from observer, vegetation structure, and survey covariates. However, detection/non‐detection data collected via point‐counts, line‐transects and distance sampling for Bombus spp. are unlikely to yield species‐specific density estimates unless individuals can be identified by sight, without capture. Our results will be useful for informing the design of monitoring programs for Bombus spp. and other pollinators.     

Total Counts Versus Line Transects for Estimating Abundance of Small Gopher Tortoise Populations

Abstract: Status and trends of gopher tortoise (Gopherus polyphemus) populations are a critical information need for natural resource managers, researchers, and policy makers. Many tortoise populations are small and isolated, which can present challenges for deriving population estimates. Our objective was to compare abundance and density estimates for a small tortoise population derived using a total burrow count versus estimates obtained with line transect distance sampling (LTDS) using repeated surveys. We also compared results of the 2 survey methods using standard burrow-to-tortoise correction factors versus assessing occupancy of all burrows with a camera scope. In addition, we compared LTDS data obtained using a compass and measuring tape to define transects to those obtained using a Global Positioning System (GPS) and Personal Data Assistant (PDA) field computer to navigate transects. Line transect distance sampling with repeated surveys (both with a measuring tape and compass and with a GPS—PDA) yielded sufficient observations of tortoises to calculate population estimates. From 18% to 31% of burrows were occupied by tortoises as determined with the burrow camera. We found 25 burrows during the LTDS survey that we did not find in the total count survey, which demonstrated that the assumption of 100% detection for the total count was not met; hence, density or abundance measurements derived with this method were underestimates. We recommend using GPS—PDA technology, scoping all burrows detected, and using LTDS with repeated surveys to estimate abundance and density for small gopher tortoise populations.     

Animal Density and Track Counts: Understanding the Nature of Observations Based on Animal Movements

Counting animals to estimate their population sizes is often essential for their management and conservation. Since practitioners frequently rely on indirect observations of animals, it is important to better understand the relationship between such indirect indices and animal abundance. The Formozov-Malyshev-Pereleshin (FMP) formula provides a theoretical foundation for understanding the relationship between animal track counts and the true density of species. Although this analytical method potentially has universal applicability wherever animals are readily detectable by their tracks, it has long been unique to Russia and remains widely underappreciated. In this paper, we provide a test of the FMP formula by isolating the influence of animal travel path tortuosity (i.e., convolutedness) on track counts. We employed simulations using virtual and empirical data, in addition to a field test comparing FMP estimates with independent estimates from line transect distance sampling. We verify that track counts (total intersections between animals and transects) are determined entirely by density and daily movement distances. Hence, the FMP estimator is theoretically robust against potential biases from specific shapes or patterns of animal movement paths if transects are randomly situated with respect to those movements (i.e., the transects do not influence animals’ movements). However, detectability (the detection probability of individual animals) is not determined simply by daily travel distance but also by tortuosity, so ensuring that all intersections with transects are counted regardless of the number of individual animals that made them becomes critical for an accurate density estimate. Additionally, although tortuosity has no bearing on mean track encounter rates, it does affect encounter rate variance and therefore estimate precision. We discuss how these fundamental principles made explicit by the FMP formula have widespread implications for methods of assessing animal abundance that rely on indirect observations.     

AERIAL SURVEYS FOR COASTAL DOLPHINS: ABUNDANCE OF HECTOR'S DOLPHINS OFF THE SOUTH ISLAND WEST COAST, NEW ZEALAND

Line-transect surveys of abundance depend critically on the estimation of detection probability, which includes corrections for availability and visibility. In this aerial line-transect survey for Hector's dolphin ( Cephalorhynchus hectori ) we recorded dive times from a helicopter to estimate the proportion of time that dolphins could be seen at or near the water surface and were therefore "available" to be counted. The proportion of available sightings that were counted on transect lines was estimated by comparing sightings by two independent teams of two observers in the fixed-wing plane. The survey covered the area between Farewell Spit and Milford Sound, off the west coast of the South Island of New Zealand. Survey effort was stratified according to existing distribution data. A total of 142 separate sightings was made on 1,355 km of trackline. Average availability for fifty Hector's dolphin groups observed from the helicopter (161 dive/surface cycles) was 46.3% (CV = 4.2%). Data from the two independent observer teams indicated that 96.2% (CV = 2.3%) of the dolphin groups that were at the surface and on the trackline were seen. The abundance estimate for the South Island west coast, corrected for visibility and availability, was 5,388 Hector's dolphins (CV = 20.6%). The total population estimate for South Island Hector's dolphins is 7,270 (CV = 16.2%).