Distance sampling surveys: using components of detection and total error to select among approaches

Wildlife population estimators often require formal adjustment for imperfect detection of individuals during surveys. Conventional distance sampling (CDS) and its extensions (mark-recapture distance sampling [MRDS], temporary emigration distance sampling [TEDS]) are popular approaches for producing unbiased estimators of wildlife abundance. However, despite extensive discussion and development of distance sampling theory in the literature, deciding which of these alternatives is most appropriate for a particular scenario can be confusing. Some of this confusion may stem from an incomplete understanding of how each approach addresses the components of the detection process. Here we describe the proper application of CDS, MRDS, and TEDS approaches and use applied examples to help clarify their differing assumptions with respect to the components of the detection process. To further aid the practitioner, we summarize the differences in a decision tree that can be used to identify cases where a more complex alternative (e.g., MRDS or TEDS) may be appropriate for a given survey application. Although the more complex approaches can account for additional sources of bias, in practical applications one also must consider estimator precision. Therefore, we also review the concept of total estimator error in the context of comparing competing methods for a given application to aid in the selection of the most appropriate distance sampling approach. Finally, we detail how the use of more advanced techniques (i.e., informed priors, open-population distance sampling models, and integrated modeling approaches) can further reduce total estimator error by leveraging information from existing and ongoing data collection. By synthesizing the existing literature on CDS, MRDS, TEDS and their extensions, in conjunction with the concepts of total estimator error and the components of the detection process, we provide a comprehensive guide that can be used by the practitioner to more efficiently, effectively, and appropriately apply distance sampling in a variety of settings.     

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.     

Understanding implications of detection heterogeneity in wildlife abundance estimation

Negative bias in mark-recapture abundance estimators due to heterogeneity in detection (capture) probability is a well-known problem, but we believe most biologists do not understand why heterogeneity causes bias and how bias can be reduced. We demonstrate how heterogeneity creates dependence and bias in mark-recapture approaches to abundance estimation. In comparison, heterogeneity, and hence estimator bias, is not as problematic for distance sampling and mark-resight methods because both techniques estimate detection probabilities based on a known quantity. We show how the introduction of a known number of individuals planted into a study population prior to a mark-recapture survey can reduce bias from heterogeneity in detection probability. We provide examples with simulation and an analysis of motion-sensitive camera data from a study population of introduced eastern wild turkeys (Meleagris gallopavo silvestris) of known size with a subset of telemetered birds. In choosing a method for abundance estimation, careful consideration should be given to assumptions and how heterogeneity in detection probability can be accommodated for each application.     

Rejection of Schmidt et al.'s estimators for bear population size

Aerial distance sampling of bears to estimate population size has been used throughout many parts of Alaska. The distance sampling models are complex since they need to account for undetected bears and differences in detection probabilities. This will require covariates and mark‐recapture data. The models proposed by Schmidt et al. do not use covariates or mark‐recapture data and are inappropriate for these surveys.     

Investigating the potential use of aerial line transect surveys for estimating polar bear abundance in sea ice habitats: A case study for the Chukchi Sea

The expense of traditional capture‐recapture methods, interest in less invasive survey methods, and the circumpolar decline of polar bear (Ursus maritimus) habitat require evaluation of alternative methods for monitoring polar bear populations. Aerial line transect distance sampling (DS) surveys are thought to be a promising monitoring tool. However, low densities and few observations during a survey can result in low precision, and logistical constraints such as heavy ice and fuel and safety limitations may restrict survey coverage. We used simulations to investigate the accuracy and precision of, DS for estimating polar bear abundance in sea ice habitats, using the Chukchi Sea subpopulation as an example. Simulation parameters were informed from a recent pilot survey. Predictions from a resource selection model were used for stratification, and we compared two ratio estimators to account for areas that cannot be sampled. The ratio estimator using predictions of resource selection by polar bears allowed for extrapolation beyond sampled areas and provided results with low bias and CVs ranging from 21% to 36% when abundance was >1,000. These techniques could be applied to other DS surveys to allocate effort and potentially extrapolate estimates to include portions of the landscape that are logistically impossible to survey.     

Aerial surveys suggest long‐term stability in the seasonally ice‐free Foxe Basin (Nunavut) polar bear population

Significant information gaps exist regarding the status of polar bears, especially with respect to the impacts of climate change, across large portions of the Arctic. To obtain an updated abundance estimate for the Foxe Basin population, we conducted comprehensive aerial surveys during the 2009 and 2010 ice‐free seasons, when bears are confined to land. We sampled with mark‐recapture distance sampling protocols on inland and coastal transects and surveyed small islands and remnant ice floes. We observed 816 and 1,003 bears in 2009 and 2010, respectively. Although detection functions differed substantially between years, estimates were consistent between analytical methods and years. Averaging four estimates (two from each year) yielded 2,585 (2,096–3,189) bears, which is similar to an estimate from the 1990s. This result, along with robust cub production, suggests a stable and healthy population despite deteriorating sea ice conditions. Collectively, this and other recent on‐land surveys provide a framework for implementing aerial surveys elsewhere. Although aerial surveys do not yield estimates of vital rates or population growth, they enable more rapid and frequent monitoring than mark‐recapture. Integrating them in long‐term monitoring programs will require consideration of ancillary data to infer status and facilitate setting harvest levels.     

Integrating distance sampling survey data with population indices to separate trends in abundance and temporary immigration

Managers rely on accurate estimators of wildlife abundance and trends for management decisions. Despite the focus of contemporary wildlife science on developing methods to improve inference from wildlife surveys, legacy datasets often rely on index counts that lack information about the detection process. Data integration can be a useful tool for combining index counts with data collected under more rigorous designs (i.e., designs that account for the detection process), but care is required when datasets represent different population processes or are mismatched in space and time. This can be particularly problematic in cases where animals aggregate in response to a spatially or temporally limited resource because individuals may temporarily immigrate from outside the study area and be included in the abundance index. Abundance indices based on brown bear (Ursus arctos) feeding aggregations within coastal meadows in early summer in Lake Clark National Park and Preserve, Alaska, USA, are one such example. These indices reflect the target population (brown bears residing within the park) and temporary immigrants (i.e., bears drawn from outside the park boundary). To properly account for the effects of temporary immigration, we integrated the index data with abundance data collected via park-wide distance sampling surveys, the latter of which properly addressed the detection process. By assuming that the distance data provide inference on abundance and the index counts represent some combination of abundance and temporary immigration processes, we were able to decompose the relative contribution of each to overall trend. We estimated that the density of brown bears within our study area was 38–54 adults/1,000 km² during 2003–2019 and that abundance increased at a rate of approximately 1.4%/year. The contribution of temporary immigrants to overall trend in the index was low, so we created 3 hypothetical scenarios to more fully demonstrate how the integrated approach could be useful in situations where the composite trend in meadow counts may obscure trends in abundance (e.g., opposing trends in abundance and temporary immigration). Our work represents a conceptual advance supporting the integration of legacy index data with more rigorous data streams and is broadly applicable in cases where trends in index values may represent a mixture of population processes.     

Using citizen‐based survey data to determine densities of large mammals: a case study from Mana Pools National Park,Zimbabwe

Since 1993, members of the national wildlife society have undertaken annual surveys of large mammals in the Zambezi alluvial woodlands of Mana Pools National Park, Zimbabwe. Data are collected along 36 systematically‐arranged transects. We provide the first thorough assessment of the data from any survey within this long‐term project. The transect data from 2011 were analysed with DISTANCE software to assess if the data were suitable for determining the densities of large mammals using distance sampling techniques. Successful application of distance sampling depended on observers using printed, large‐scale, georeferenced satellite images onto which they mapped the location of animal groups detected. The assumptions of the distance sampling were well met and thus the 2011 survey provided reliable estimates of the densities of nine species of common large mammals on the Zambezi alluvium during the late dry season. Estimated density in this dry‐season concentration area varied from 3.6 km^?2 for kudu, to 204 km^?2 for impala. The precision of the estimates ranged from a coefficient of variation of 7.9% for elephant, to 25.5% for buffalo. For elephant, warthog and baboon, the morning and afternoon densities differed significantly.     

A method for estimating population sex ratio for sage‐grouse using noninvasive genetic samples

Population sex ratio is an important metric for wildlife management and conservation, but estimates can be difficult to obtain, particularly for sexually monomorphic species or for species that differ in detection probability between the sexes. Noninvasive genetic sampling (NGS) using polymerase chain reaction (PCR) has become a common method for identifying sex from sources such as hair, feathers or faeces, and is a potential source for estimating sex ratio. If, however, PCR success is sex‐biased, naively using NGS could lead to a biased sex ratio estimator. We measured PCR success rates and error rates for amplifying the W and Z chromosomes from greater sage‐grouse (Centrocercus urophasianus) faecal samples, examined how success and error rates for sex identification changed in response to faecal sample exposure time, and used simulation models to evaluate precision and bias of three sex assignment criteria for estimating population sex ratio with variable sample sizes and levels of PCR replication. We found PCR success rates were higher for females than males and that choice of sex assignment criteria influenced the bias and precision of corresponding sex ratio estimates. Our simulations demonstrate the importance of considering the interplay between the sex bias of PCR success, number of genotyping replicates, sample size, true population sex ratio and accuracy of assignment rules for designing future studies. Our results suggest that using faecal DNA for estimating the sex ratio of sage‐grouse populations has great potential and, with minor adaptations and similar marker evaluations, should be applicable to numerous species.     

Some comments on anderson and pospahala's correction of bias in line transect sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we show that the ANDERSON-POSPAHALA estimator is optimal in the sense of being the (unique) best linear unbiased estimator within the class of estimators which are linear combinations of cell frequencies, provided certain assumptions are met.     

Distance measures and optimization spaces in quantitative fatty acid signature analysis

Quantitative fatty acid signature analysis has become an important method of diet estimation in ecology, especially marine ecology. Controlled feeding trials to validate the method and estimate the calibration coefficients necessary to account for differential metabolism of individual fatty acids have been conducted with several species from diverse taxa. However, research into potential refinements of the estimation method has been limited. We compared the performance of the original method of estimating diet composition with that of five variants based on different combinations of distance measures and calibration‐coefficient transformations between prey and predator fatty acid signature spaces. Fatty acid signatures of pseudopredators were constructed using known diet mixtures of two prey data sets previously used to estimate the diets of polar bears Ursus maritimus and gray seals Halichoerus grypus, and their diets were then estimated using all six variants. In addition, previously published diets of Chukchi Sea polar bears were re‐estimated using all six methods. Our findings reveal that the selection of an estimation method can meaningfully influence estimates of diet composition. Among the pseudopredator results, which allowed evaluation of bias and precision, differences in estimator performance were rarely large, and no one estimator was universally preferred, although estimators based on the Aitchison distance measure tended to have modestly superior properties compared to estimators based on the Kullback–Leibler distance measure. However, greater differences were observed among estimated polar bear diets, most likely due to differential estimator sensitivity to assumption violations. Our results, particularly the polar bear example, suggest that additional research into estimator performance and model diagnostics is warranted.     

An open spatial capture–recapture model for estimating density,movement, and population dynamics from line‐transect surveys

The purpose of many wildlife population studies is to estimate density, movement, or demographic parameters. Linking these parameters to covariates, such as habitat features, provides additional ecological insight and can be used to make predictions for management purposes. Line‐transect surveys, combined with distance sampling methods, are often used to estimate density at discrete points in time, whereas capture–recapture methods are used to estimate movement and other demographic parameters. Recently, open population spatial capture–recapture models have been developed, which simultaneously estimate density and demographic parameters, but have been made available only for data collected from a fixed array of detectors and have not incorporated the effects of habitat covariates. We developed a spatial capture–recapture model that can be applied to line‐transect survey data by modeling detection probability in a manner analogous to distance sampling. We extend this model to a) estimate demographic parameters using an open population framework and b) model variation in density and space use as a function of habitat covariates. The model is illustrated using simulated data and aerial line‐transect survey data for North Atlantic right whales in the southeastern United States, which also demonstrates the ability to integrate data from multiple survey platforms and accommodate differences between strata or demographic groups. When individuals detected from line‐transect surveys can be uniquely identified, our model can be used to simultaneously make inference on factors that influence spatial and temporal variation in density, movement, and population dynamics.     

Bayesian estimation of group sizes for a coastal cetacean using aerial survey data

Many small cetacean, sirenian, and pinniped species aggregate in groups of large or variable size. Accurate estimation of group sizes is essential for estimating the abundance and distribution of these species, but is challenging as individuals are highly mobile and only partially visible. We developed a Bayesian approach for estimating group sizes using wide‐angle aerial photographic or video imagery. Our approach accounts for both availability and perception bias, including a new method (analogous to distance sampling) for estimating perception bias due to small image size in wide‐angle images. We demonstrate our approach through an application to aerial survey data for an endangered population of beluga whales (Delphinapterus leucas) in Cook Inlet, Alaska. Our results strengthen understanding of variation in group size estimates and allow for probabilistic statements about the size of detected groups. Aerial surveys are a standard tool for estimating the abundance and distribution of various marine mammal species. The role of aerial photographic and video data in wildlife assessment is expected to increase substantially with the widespread uptake of unmanned aerial vehicle technology. Key aspects of our approach are relevant to group size estimation for a broad range of marine mammal, seabird, other waterfowl, and terrestrial ungulate species.     

Addressing Temporal Variability in Bird Calling with Design and Estimation: A Northern Bobwhite Example

Imprecise or biased density estimates can lead to inadequate conservation action, overexploitation of game species, or lost recreational opportunities. Common approaches to estimating density of avian populations often either ignore the probability that an individual is present within the sampling area but is not available to be sampled (e.g., not vocalizing), or do not consider covariates that could influence availability. Additionally, management decisions made at the management unit scale are often informed by inadequate monitoring practices, such as limited sampling intensity. In such cases, management agencies calculate density by applying correction factors (e.g., detection probabilities estimated using empirical data from a different study system) to count data, rather than estimating a detection function directly using statistical models. We conducted a simulation study using northern bobwhite (Colinus virginianus; bobwhite) as a model species to quantify the consequences of mis-specifying avian point count models on bias and precision of density estimates. We compared bias and precision of estimates from a fully specified distance-sampling model that estimates availability and detection to 4 different mis-specified approaches, including 2 approaches to calculating density using correction factors. Using correction factors to calculate density produced estimates with low bias but relatively lower precision compared to the fully specified model (CV of density estimates at 35 sites over 5 years: fully specified = 10%, correction factors = 25% and 30%). Although the mean precision and bias of the fully specified model improved with more data (70 sites over 5 years, CV = 9%; 35 sites over 10 years, CV = 9%), precision of correction factors did not (70 sites over 5 years, CV = 22% and 27%; 35 sites over 10 years, CV = 24% and 29%). The fully specified model captured the underlying temporal variation in detection and availability. Increasing sampling duration from 5 to 10 years improved modeled estimates of growth rate, even for mis-specified models, but not derived growth rates using pre-determined detection functions. We demonstrated that conducting point counts 3 times/year at a feasible number of sites can produce relatively unbiased estimates of bobwhite density. Pre-determined detection functions can be fortuitously unbiased for certain years, but they are not a reliable method for determining density or identifying trends in density over time. © 2020 The Wildlife Society.     

Estimating density of Kirk’s dik‐dik (Madoqua kirkii Günther), impala (Aepyceros melampus Lichtenstein) and common zebra (Equus burchelli Gray) at Mpala,Laikipia District,Kenya

This study compares two methods of estimating the density of three ungulate species: Kirk’s dik‐dik, impala and common zebra, in a dry savannah ecosystem. Fixed strip width and distance sampling involving direct animal counts were used in parallel, and tested for bias and precision in two habitats. Distance sampling was the method that achieved a better balance between accuracy and precision. The differences in sightability of ungulates, according to body size, colour and habitat characteristics, are taken into account by the distance sampling method, but not by the strip method, which produced, what we suspect are, underestimates of animal density.     

基于空间结构调查的林分密度估计

利用林分空间结构抽样调查技术,采用测量抽样点到其第k株最近相邻木的距离(距离法)进行密度估计,分别选取k=4和k=6两种距离调查方法进行分析,并对Prodan、Persson、Thompson 3种不同密度估计方法的预估能力进行检验.结果表明：不同预估方法的预估能力受林木水平分布格局影响.Prodan法在均匀分布的林分中有较强的预估能力,随着分布格局聚集性增加会产生越来越大的偏差;Persson计算法在均匀及随机分布的林分中产生正偏差,但随着分布格局聚集性增加产生的相对误差接近0,预估能力增强;Thompson计算法对随机或接近随机分布的林分有较强的预估能力,而在均匀分布和聚集分布的格局中分别产生正偏差和负偏差.抽样点为49个时,选择6株木与4株木预估能力无显著差异,因此,密度估计可与选取4株相邻木的空间结构参数调查整合在一起.     

Limited sampling hampers “big data” estimation of species richness in a tropical biodiversity hotspot

Macro‐scale species richness studies often use museum specimens as their main source of information. However, such datasets are often strongly biased due to variation in sampling effort in space and time. These biases may strongly affect diversity estimates and may, thereby, obstruct solid inference on the underlying diversity drivers, as well as mislead conservation prioritization. In recent years, this has resulted in an increased focus on developing methods to correct for sampling bias. In this study, we use sample‐size‐correcting methods to examine patterns of tropical plant diversity in Ecuador, one of the most species‐rich and climatically heterogeneous biodiversity hotspots. Species richness estimates were calculated based on 205,735 georeferenced specimens of 15,788 species using the Margalef diversity index, the Chao estimator, the second‐order Jackknife and Bootstrapping resampling methods, and Hill numbers and rarefaction. Species richness was heavily correlated with sampling effort, and only rarefaction was able to remove this effect, and we recommend this method for estimation of species richness with “big data” collections.     

Incorporating Estimates of Group Size in Sightability Models for Wildlife

ABSTRACT Sightability models have been used to estimate population size of many wildlife species; however, a limitation of these models is an assumption that groups of animals observed and counted during aerial surveys are enumerated completely. Replacing these unknown counts with maximum observed counts, as is typically done, produces population size estimates that are negatively biased. This bias can be substantial depending on the degree of undercounting occurring. We first investigated a method-of-moments estimator of group sizes. We then defined a population size estimator using the method-of-moments estimator of group sizes in place of maximum counts in the traditional sightability models, thereby correcting for bias associated with undercounting group size. We also provide associated equations for calculating the variance of our estimator. This estimator is an improvement over existing sightability model techniques because it significantly reduces bias, and variance estimates provide near nominal confidence interval coverage. The data needed for this estimator can be easily collected and implemented by wildlife managers with a field crew of only 3 individuals and little additional flight or personnel time beyond the normal requirements for developing sightability models.     

Robustness of close‐kin mark–recapture estimators to dispersal limitation and spatially varying sampling probabilities

1. Close‐kin mark–recapture (CKMR) is a method for estimating abundance and vital rates from kinship relationships observed in genetic samples. CKMR inference only requires animals to be sampled once (e.g., lethally), potentially widening the scope of population‐level inference relative to traditional monitoring programs.
2. One assumption of CKMR is that, conditional on individual covariates like age, all animals have an equal probability of being sampled. However, if genetic data are collected opportunistically (e.g., via hunters or fishers), there is potential for spatial variation in sampling probability that can bias CKMR estimators, particularly when genetically related individuals stay in close proximity.
3. We used individual‐based simulation to investigate consequences of dispersal limitation and spatially biased sampling on performance of naive (nonspatial) CKMR estimators of abundance, fecundity, and adult survival. Population dynamics approximated that of a long‐lived mammal species subject to lethal sampling.
4. Naive CKMR abundance estimators were relatively unbiased when dispersal was unconstrained (i.e., complete mixing) or when sampling was random or subject to moderate levels of spatial variation. When dispersal was limited, extreme variation in spatial sampling probabilities negatively biased abundance estimates. Reproductive schedules and survival were well estimated, except for survival when adults could emigrate out of the sampled area. Incomplete mixing was readily detected using Kolmogorov–Smirnov tests.
5. Although CKMR appears promising for estimating abundance and vital rates with opportunistically collected genetic data, care is needed when dispersal limitation is coupled with spatially biased sampling. Fortunately, incomplete mixing is easily detected with adequate sample sizes. In principle, it is possible to devise and fit spatially explicit CKMR models to avoid bias under dispersal limitation, but development of such models necessitates additional complexity (and possibly additional data). We suggest using simulation studies to examine potential bias and precision of proposed modeling approaches prior to implementing a CKMR program.

     

Variance of Stratified Survey Estimators With Probability of Detection Adjustments

Abstract: Estimates of wildlife population sizes are frequently constructed by combining counts of observed animals from a stratified survey of aerial sampling units with an estimated probability of detecting animals. Unlike traditional stratified survey designs, stratum-specific estimates of population size will be correlated if a common detection model is used to adjust counts for undetected animals in all strata. We illustrate this concept in the context of aerial surveys, considering 2 cases: 1) a single-detection parameter is estimated under the assumption of constant detection probabilities, and 2) a logistic-regression model is used to estimate heterogeneous detection probabilities. Naïve estimates of variance formed by summing stratum-specific estimates of variance may result in significant bias, particularly if there are a large number of strata, if detection probabilities are small, or if estimates of detection probabilities are imprecise. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):837–844; 2008)