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.     

Detection probability in aerial surveys of feral horses

Observation bias pervades data collected during aerial surveys of large animals, and although some sources can be mitigated with informed planning, others must be addressed using valid sampling techniques that carefully model detection probability. Nonetheless, aerial surveys are frequently employed to count large mammals without applying such methods to account for heterogeneity in visibility of animal groups on the landscape. This often leaves managers and interest groups at odds over decisions that are not adequately informed. I analyzed detection of feral horse (Equus caballus) groups by dual independent observers from 24 fixed-wing and 16 helicopter flights using mixed-effect logistic regression models to investigate potential sources of observation bias. I accounted for observer skill, population location, and aircraft type in the model structure and analyzed the effects of group size, sun effect (position related to observer), vegetation type, topography, cloud cover, percent snow cover, and observer fatigue on detection of horse groups. The most important model-averaged effects for both fixed-wing and helicopter surveys included group size (fixed-wing: odds ratio = 0.891, 95% CI = 0.850–0.935; helicopter: odds ratio = 0.640, 95% CI = 0.587–0.698) and sun effect (fixed-wing: odds ratio = 0.632, 95% CI = 0.350–1.141; helicopter: odds ratio = 0.194, 95% CI = 0.080–0.470). Observer fatigue was also an important effect in the best model for helicopter surveys, with detection probability declining after 3 hr of survey time (odds ratio = 0.278, 95% CI = 0.144–0.537). Biases arising from sun effect and observer fatigue can be mitigated by pre-flight survey design. Other sources of bias, such as those arising from group size, topography, and vegetation can only be addressed by employing valid sampling techniques such as double sampling, mark–resight (batch-marked animals), mark–recapture (uniquely marked and identifiable animals), sightability bias correction models, and line transect distance sampling; however, some of these techniques may still only partially correct for negative observation biases. © 2011 The Wildlife Society.     

A Unimodal Model for Double Observer Distance Sampling Surveys

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.     

A hierarchical modeling framework for multiple observer transect surveys

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.     

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.     

On the importance of estimating detection probabilities from at‐sea surveys of flying seabirds

The primary and accepted method used to estimate seabird densities at sea from ships is the strip transect method, designed to correct for the effect of random directional bird movement relative to that of the ship. However, this method relies on the critical assumption that all of the birds within the survey strip are detected. We used the distance sampling method from line‐transects to estimate detection probability of a number of species of flying seabirds, and to test whether distance from the ship and bird body size affected detectability. Detection probability decreased from 0.987 (SE=0.029) to 0.269 (SE=0.035) with increasing strip half‐width from 100 to 1400 m. Detection probability also varied between size‐groups of species with strip half‐width. For all size‐groups, this probability was close to 1 for strip half‐width of 100 m, but was 0.869 (SE=0.115), 0.725 (SE=0.096) and 0.693 (SE=0.091) for strip half‐width of 300 m, a typical strip width used in seabird surveys, for respectively large, medium and small size flying seabirds. For larger strip half‐width, detection probability was higher for large sized species, intermediate for medium sized species and lower for smaller sized species. For strip half‐width larger than 100 m we suggest that more attention should be paid to testing the assumption of perfect detectability, because abundance estimates may be underestimated when this assumption is violated. Finally, the effect of the speed of travel of flying seabird on the detection probability was estimated in a simulation study, which suggests that detection probability was underestimated with increasing flying speed.     

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.     

Estimating Abundance From One-Dimensional Passive Acoustic Surveys

ABSTRACT Conventional distance sampling, the most-used method of estimating animal density and abundance, requires ranges to detected individuals, which are not easily measured for vocalizations. However, in some circumstances the sequential pattern of detection of vocalizations along a transect line gives information about the range of detection. Thus, from a one-dimensional acoustic point-transect survey (i.e., records of vocalizations detected or not detected at regularly spaced listening stations) it is possible to obtain a useful estimate of density or abundance. I developed equations for estimation of density for one-dimensional surveys. Using simulations I found that for the method to have little bias when both range of detection and rate of vocalization need to be estimated, stations needed to be spaced at 30–80% of the range of detection and the rate of vocalization should be >0.7. If either the range of detection or rate of vocalization is known, conditions are relaxed, and when both parameters are known the method works well almost universally. In favorable conditions for one-dimensional methods, estimated abundances have overall errors not much larger than those from conventional line-transect distance sampling. The methods appeared useful when applied to real acoustic data from whale surveys. The techniques may also be useful in surveys with nonacoustic detection of animals.     

Response to human presence during nocturnal line transect surveys in fallow deer (<Emphasis Type="Italic">Dama dama</Emphasis>) and wild boar (<Emphasis Type="Italic">Sus scrofa</Emphasis>)

The use of line transect methodology and portable thermal imaging for ground survey of wildlife should require a good knowledge of the behavioural response of the animals to the presence of an observer, in order to take into account the potential bias in density estimate caused by deviation from the assumption that distances are recorded at the initial position. We used ten fallow deer and eight wild boar fitted with radiocollars to investigate animals’ response during simulated nocturnal line transect surveys, carried out in a Mediterranean plain forest. The experiment consisted in radiolocating a focal animal before and after an observer walked a transect nearby (<100 m). Each transect line was followed using a Global Positioning System (GPS) navigator. We carried out a total of 64 trials on fallow deer and 57 on wild boar. Results showed that despite most of the animals moved significantly in response to the observer (mean ± standard error, wild boar—95.3 ± 10.0 m; fallow deer—149.6 ± 14.2 m), the flying patterns were different in the two species: the reaction of fallow deer turned out to be more intense and directional with respect to that showed by wild boar. Although these results sound explorative, the experiment attempted here, for the first time, is relevant for an appropriate design of nocturnal distance-sampling surveys and gives information about potential bias arising from animal’s behavioural response. We believe that these first results may foster more in-deep analyses which are now made possible with the adoption of GPS technology for animal location.     

Effects of ambient noise on detectability and localization of avian songs and tones by observers in grasslands

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.     

ABUNDANCE OF SOUTHERN CALIFORNIA COASTAL BOTTLENOSE DOLPHINS ESTIMATED FROM TANDEM AERIAL SURVEYS

We describe a tandem aerial survey method for bottlenose dolphins ( Tursiops truncatus ) that uses two aircraft and independent observer teams to conduct consecutive surveys of the same coastal strip one hour apart. Alternatively, one aircraft with one observer team surveys the same coastal strip twice over several hours. Using mark-recapture analysis, we corrected survey counts for visibility bias resulting from missing dolphin groups at the surface and submerged groups. Dolphin groups were considered "recaptured" when we determined that both observer teams had detected the same group. This tandem method is highly useful for estimating abundance (and visibility bias) for species where population closure may be assumed between flights. We assumed population closure between flights and matched groups using geographic location, group size, and expected travel rates. We derive a new variance estimator of population size which incorporates group-size variability commonly encounteted in cetacean surveys. From six tandem surveys conducted from 1991 to 1994, we estimated the abundance of southern California coastal bottlenose dolphins to be between 78 (95% CI 60-102) and 271 (240-306) animals, with an average of 140 (128-154). Variability in abundance estimates is likely due to seasonal and interannual movement of animals along the California and Baja California coast. Abundance estimates from tandem surveys averaged 53% higher than dolphin counts obtained from individual survey flights, demonstrating the importance of correcting for visibility bias.     

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.     

Predicting and correcting bias caused by measurement error in line transect sampling using multiplicative error models

Line transect sampling is one of the most widely used methods for animal abundance assessment. Standard estimation methods assume certain detection on the transect, no animal movement, and no measurement errors. Failure of the assumptions can cause substantial bias. In this work, the effect of error measurement on line transect estimators is investigated. Based on considerations of the process generating the errors, a multiplicative error model is presented and a simple way of correcting estimates based on knowledge of the error distribution is proposed. Using beta models for the error distribution, the effect of errors and of the proposed correction is assessed by simulation. Adequate confidence intervals for the corrected estimates are obtained using a bootstrap variance estimate for the correction and the delta method. As noted by Chen (1998, Biometrics 54, 899-908), even unbiased estimators of the distances might lead to biased density estimators, depending on the actual error distribution. In contrast with the findings of Chen, who used an additive model, unbiased estimation of distances, given a multiplicative model, lead to overestimation of density. Some error distributions result in observed distance distributions that make efficient estimation impossible, by removing the shoulder present in the original detection function. This indicates the need to improve field methods to reduce measurement error. An application of the new methods to a real data set is presented.     

Casual movement speed but not maximal locomotor capacity predicts mate searching success

Maximal locomotor performance is often used as a proxy for fitness. Maximal speed may be important under high‐threat conditions, such as during predator escape. However, animals do not always move at a speed that reflects their maximal physiological capacities when undisturbed. The physiological factors that determine the movement speed chosen by animals, such as minimization of energy use, may be independent from maximal performance. As a result, the casual speed at which individuals move when undisturbed in a given context may better represent an individual's motivation to move. The casual speed may therefore be a better predictor of fitness in natural contexts than maximal performance capacity. We tested the hypothesis that casual movement speed rather than maximal speed predicts fitness in the golden orb‐web spider, Nephila plumipes. We measured fitness in two separate contexts, mate‐searching success and the positional rank near a female. We show that casual but not maximal locomotor speed predicted both aspects of fitness. Casual speed was linearly related to maximal speed, indicating that casual speed is determined by physiological optimization. Size and metabolic scope were not related to either maximal or chosen speeds, indicating that the supply of ATP does not limit locomotor performance in this species. Overall, our results demonstrate that locomotor performance is related to fitness, but suggest that different types of performance and not necessarily maximal physiological capacities are most relevant for particular ecologically relevant tasks.     

Abundance estimation of long-diving animals using line transect methods

Line transect sampling is one of the most widely used methods for estimating the size of wild animal populations. An assumption in standard line transect sampling is that all the animals on the trackline are detected without fail. This assumption tends to be violated for marine mammals with surfacing/diving behaviors. The detection probability on the trackline is estimated using duplicate sightings from double-platform line transect methods. The double-platform methods, however, are insufficient to estimate the abundance of long-diving animals because these animals can be completely missed while the observers pass. We developed a more flexible hazard probability model that incorporates information on surfacing/diving patterns obtained from telemetry data. The model is based on a stochastic point process and is statistically tractable. A simulation study showed that the new model provides near-unbiased abundance estimates, whereas the traditional hazard rate and hazard probability models produce considerably biased estimates. As an illustration, we applied the model to data on the Baird's beaked whale (Berardius bairdii) in the western North Pacific.     

Line transect sampling from a curving path

Cutting straight line transects through dense forest is time consuming and expensive when large areas need to be surveyed for rare or highly clustered species. We argue that existing paths or game trails may be suitable as transects for line transect sampling even though they will not, in general, run straight. Formulas and software currently used to estimate local density using perpendicular distance data can be used with closest approach distances measured from curving transects. Suitable paths or trails are those for which the minimum radius of curvature is rarely less than the width of the shoulder in the detection probability function. The use of existing paths carries the risk of bias resulting from unrepresentative sampling of available habitats, and this must be weighed against the increase in coverage available.     

Changing motivations during migration: linking movement speed to reproductive status in a migratory large mammal

A challenge in animal ecology is to link animal movement to demography. In general, reproducing and non-reproducing animals may show different movement patterns. Dramatic changes in reproductive status, such as the loss of an offspring during the course of migration, might also affect movement. Studies linking movement speed to reproductive status require individual monitoring of life-history events and hence are rare. Here, we link movement data from 98 GPS-collared female moose (Alces alces) to field observations of reproductive status and calf survival. We show that reproductive females move more quickly during migration than non-reproductive females. Further, the loss of a calf over the course of migration triggered a decrease in speed of the female. This is in contrast to what might be expected for females no longer constrained by an accompanying offspring. The observed patterns demonstrate that females of different reproductive status may have distinct movement patterns, and that the underlying motivation to move may be altered by a change in reproductive status during migration.     

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.     

哺乳类动物数量调查中的截线抽样法与逆向截线法

文本介绍了可用于哺乳动物数量调查的一种新方法--截线抽样法,并在此方法的基础上,结合我国动物调查实践,提出了逆向截线法。逆向截线法在贺兰山自然保护区马鹿数量调查中,取得了较好效果。