A Unimodal Model for Double Observer Distance Sampling Surveys.
ABSTRACT: Distance sampling is a widely used method to estimate animal population size. Most distance sampling models utilize a monotonically decreasing detection function such as a half-normal. Recent advances in distance sampling modeling allow for the incorporation of covariates into the distance model, and the elimination of the assumption of perfect detection at some fixed distance (usually the transect line) with the use of double-observer models. The assumption of full observer independence in the double-observer model is problematic, but can be addressed by using the point independence assumption which assumes there is one distance, the apex of the detection function, where the 2 observers are assumed independent. Aerially collected distance sampling data can have a unimodal shape and have been successfully modeled with a gamma detection function. Covariates in gamma detection models cause the apex of detection to shift depending upon covariate levels, making this model incompatible with the point independence assumption when using double-observer data. This paper reports a unimodal detection model based on a two-piece normal distribution that allows covariates, has only one apex, and is consistent with the point independence assumption when double-observer data are utilized. An aerial line-transect survey of black bears in Alaska illustrate how this method can be applied.
Project description: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.
Project description: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.
Project description:Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line), these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size). We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package, hierarchicalDS, to facilitate the building and fitting of these models.
Project description: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.
Project description:Probability of detection and accuracy of distance estimates in aural avian surveys may be affected by the presence of anthropogenic noise, and this may lead to inaccurate evaluations of the effects of noisy infrastructure on wildlife. We used arrays of speakers broadcasting recordings of grassland bird songs and pure tones to assess the probability of detection, and localization accuracy, by observers at sites with and without noisy oil and gas infrastructure in south-central Alberta from 2012 to 2014. Probability of detection varied with species and with speaker distance from transect line, but there were few effects of noisy infrastructure. Accuracy of distance estimates for songs and tones decreased as distance to observer increased, and distance estimation error was higher for tones at sites with infrastructure noise. Our results suggest that quiet to moderately loud anthropogenic noise may not mask detection of bird songs; however, errors in distance estimates during aural surveys may lead to inaccurate estimates of avian densities calculated using distance sampling. We recommend caution when applying distance sampling if most birds are unseen, and where ambient noise varies among treatments.
Project description:Detecting exotic plant species is essential for invasive species management. By accounting for factors likely to affect species' detection rates (e.g. survey conditions, observer experience), detectability models can help choose search methods and allocate search effort. Integrating information on species' traits can refine detectability models, and might be particularly valuable if these traits can help improve estimates of detectability where data on particular species are rare. Analysing data collected during line transect distance sampling surveys in Indonesia, we used a multi-species hierarchical distance sampling model to evaluate how plant height, leaf size, leaf shape, and survey location influenced plant species detectability in secondary tropical rainforests. Detectability of the exotic plant species increased with plant height and leaf size. Detectability varied among the different survey locations. We failed to detect a clear effect of leaf shape on detectability. This study indicates that information on traits might improve predictions about exotic species detection, which can then be used to optimise the allocation of search effort for efficient species management. The innovation of the study lies in the multi-species distance sampling model, where the distance-detection function depends on leaf traits and height. The method can be applied elsewhere, including for different traits that may be relevant in other contexts. Trait-based multispecies distance sampling can be a practical approach for sampling exotic shrubs, herbs, or grasses species in the understorey of tropical forests.
Project description:The aim of this study was to investigate the clinical value of the apex beat and two ECG voltage criteria in the detection of left ventricular hypertrophy (LVH) while considering two distances, from the heart to the inner chest wall and to the chest surface, measured by using multislice CT (MSCT). The study population consisted of 151 patients clinically judged as requiring MSCT angiography. The apex beat was palpated with patients in the supine. Sokolow-Lyon voltage and Cornell voltage to detect LVH were determined. The pattern of sustained or double apical impulse and Cornell voltage had higher specificity as an indicator of LVH than Sokolow-Lyon voltage. Furthermore, the distance to the inner chest wall was negatively correlated with left ventricular end-diastolic volume and mass. Contrarily, the distance to the chest surface was correlated with the body mass index. Multivariate analyses revealed that the pattern of sustained or double apical impulse showed a stronger association with the distance to the inner chest wall than to the chest surface, but Sokolow-Lyon voltage was associated with the distance to the chest surface. Among the screening tests for excluding patients with LVH, Cornell voltage or the apex beat would be better than Sokolow-Lyon voltage because these are less dependent on body size and have higher specificity.
Project description:Distance sampling is widely used to estimate the abundance or density of wildlife populations. Methods to estimate wildlife mortality rates have developed largely independently from distance sampling, despite the conceptual similarities between estimation of cumulative mortality and the population density of living animals. Conventional distance sampling analyses rely on the assumption that animals are distributed uniformly with respect to transects and thus require randomized placement of transects during survey design. Because mortality events are rare, however, it is often not possible to obtain precise estimates in this way without infeasible levels of effort. A great deal of wildlife data, including mortality data, is available via road-based surveys. Interpreting these data in a distance sampling framework requires accounting for the non-uniformity sampling. Additionally, analyses of opportunistic mortality data must account for the decline in carcass detectability through time. We develop several extensions to distance sampling theory to address these problems.We build mortality estimators in a hierarchical framework that integrates animal movement data, surveillance effort data, and motion-sensor camera trap data, respectively, to relax the uniformity assumption, account for spatiotemporal variation in surveillance effort, and explicitly model carcass detection and disappearance as competing ongoing processes.Analysis of simulated data showed that our estimators were unbiased and that their confidence intervals had good coverage.We also illustrate our approach on opportunistic carcass surveillance data acquired in 2010 during an anthrax outbreak in the plains zebra of Etosha National Park, Namibia.The methods developed here will allow researchers and managers to infer mortality rates from opportunistic surveillance data.
Project description:Bias introduced by detection errors is a well-documented issue for abundance and occupancy estimates of wildlife. Detection errors bias estimates of detection and abundance or occupancy in positive and negative directions, which can produce misleading results. There have been considerable design- and model-based methods to address false-negative errors, or missed detections. However, false-positive errors, or detections of individuals that are absent but counted as present because of misidentifications or double counts, are often assumed to not occur in ecological studies. The dependent double-observer survey method is a design-based approach speculated to reduce false positives because observations have the ability to be confirmed by two observers. However, whether this method reduces false positives compared to single-observer methods has not been empirically tested. We used prairie songbirds as a model system to test if a dependent double-observer method reduced false positives compared to a single-observer method. We used vocalizations of ten species to create auditory simulations and used naive and expert observers to survey these simulations using single-observer and dependent double-observer methods. False-positive rates were significantly lower using the dependent double-observer survey method in both observer groups. Expert observers reported a 3.2% false-positive rate in dependent double-observer surveys and a 9.5% false-positive rate in single-observer surveys, while naive observers reported a 39.1% false-positive rate in dependent double-observer surveys and a 49.1% false-positive rate in single-observer surveys. Misidentification errors arose in all survey scenarios and almost all species combinations. However, expert observers using the dependent double-observer method performed significantly better than other survey scenarios. Given the use of double-observer methods and the accumulating evidence that false positives occur in many survey methods across different taxa, this study is an important step forward in acknowledging and addressing false positives.
Project description:The use of counts of unmarked migrating animals to monitor long term population trends assumes independence of daily counts and a constant rate of detection. However, migratory stopovers often last days or weeks, violating the assumption of count independence. Further, a systematic change in stopover duration will result in a change in the probability of detecting individuals once, but also in the probability of detecting individuals on more than one sampling occasion. We tested how variation in stopover duration influenced accuracy and precision of population trends by simulating migration count data with known constant rate of population change and by allowing daily probability of survival (an index of stopover duration) to remain constant, or to vary randomly, cyclically, or increase linearly over time by various levels. Using simulated datasets with a systematic increase in stopover duration, we also tested whether any resulting bias in population trend could be reduced by modeling the underlying source of variation in detection, or by subsampling data to every three or five days to reduce the incidence of recounting. Mean bias in population trend did not differ significantly from zero when stopover duration remained constant or varied randomly over time, but bias and the detection of false trends increased significantly with a systematic increase in stopover duration. Importantly, an increase in stopover duration over time resulted in a compounding effect on counts due to the increased probability of detection and of recounting on subsequent sampling occasions. Under this scenario, bias in population trend could not be modeled using a covariate for stopover duration alone. Rather, to improve inference drawn about long term population change using counts of unmarked migrants, analyses must include a covariate for stopover duration, as well as incorporate sampling modifications (e.g., subsampling) to reduce the probability that individuals will be detected on more than one occasion.