Bias In Density Estimates Research Articles

Accounting for sperm whale population demographics in density estimation using passive acoustic monitoring

Sperm whales Physeter macrocephalus are highly sexually dimorphic, with adult males having larger bodies, more powerful echolocation clicks, and slower echolocation clicking rates compared to females. This study introduces methods for estimating sperm whale population densities in the Gulf of Mexico (GoMex) by accounting for the population demographics using passive acoustic monitoring and reveals that ignoring the differences between demographic segments can introduce bias in density estimates. Weekly densities were estimated per 3 demographic segments: social groups consisting of adult females and their offspring, mid-size animals, and adult males. Analysis revealed that the GoMex sperm whale population is primarily composed of social groups, which account for 92 to 98% of the overall population. Mid-size animals and adult males made up a small proportion of the population and were only intermittently present. Our 7 yr GoMex density estimates, including the 2010 Deepwater Horizon (DWH) oil spill period and subsequent years, revealed demographic-specific trends. Declines found at 2 north-central GoMex sites, coupled with increases at a southeastern site, may indicate population movements and potential impacts from the 2010 DWH oil spill and elevated noise levels from anthropogenic activities in the north-central GoMex.

Reducing bias in density estimates for unmarked populations that exhibit reactive behaviour towards camera traps

Abstract Density estimates guide wildlife management, and camera traps are commonly used to estimate sizes of unmarked populations. Unfortunately, animals often alter their natural behaviour in the presence of camera traps, which may bias subsequent density estimates. We simulated 100 populations of known density to test several new and existing methods that aimed to reduce bias in density estimates from camera trap distance sampling (CTDS) and the random encounter model (REM). Within our simulated populations, we introduced different behavioural reactions including attraction towards cameras, freezing when near cameras and fleeing from cameras. CTDS and REM provided density estimates with decent coverage of confidence intervals (CTDS = 94%, REM = 87%), mean coefficient of variation (CTDS = 0.121, REM = 0.071) and minimal bias (root‐mean squared error: CTDS = 1.336, REM = 0.913) for simulated populations with no reactive behaviour. However, failure to implement a method to account for reactive behaviour resulted in low coverage, large bias and potentially imprecise density estimates when 30% of the simulated population potentially reacted by attraction to or fleeing from camera traps. We identified a corrective strategy that enhanced confidence interval coverage, increased precision and reduced bias for every behavioural reaction except when individuals potentially fled from cameras. Synthesis and applications. We provide empirically tested methods for reducing bias of density estimates. Wildlife managers requiring population estimates of animals that exhibit reactive behaviour can use our methods to reduce inaccuracy. We encourage future studies to quantify behavioural responses to camera traps and to implement, test and possibly extend our methods to reduce bias through simulation.

Inter‐population variability in movement parameters: practical implications for population density estimation

AbstractMotion‐sensitive cameras are popular as non‐invasive monitoring tools, and several methods have been developed to estimate population densities from camera data. These methods frequently rely on auxiliary movement data including the distance traveled by an individual in a day and the proportion of the day that an animal spends moving when individual recognition is not possible. The estimation of these movement parameters is time‐consuming, which could limit the applicability of cameras to estimate population density. To investigate the relevance of measuring movement parameters for the target population, we monitored 54 wildlife populations of red deer (Cervus elaphus), fallow deer (Dama dama), roe deer (Capreolus capreolus), wild boar (Sus scrofa), and red fox (Vulpes vulpes) in different seasons through Europe with cameras. We estimated 91‐day ranges and activity levels. We fitted mixed models for day range and activity level as response variables to assess if the inter‐population variability in movement was explained by a set of a priori relevant geographical, environmental, biological, and management predictors. We then explored the bias in density estimates obtained in 25 independent populations when using predicted movement data. There was high intra‐species variation in day range and activity level among species and populations. Only species explained a small proportion of this variability; other predictor variables did not. We observed bias in densities when predicting the day range and activity for independent populations. Considering the intra‐species variability in movement parameters and the consequent unacceptable bias in density estimates, we recommend that monitoring and conservation programs estimate movement parameters for the target population and survey populations from camera data for more accurate density estimates. While this increases the handling time needed to estimate densities, it is worth the cost because of the reliability of camera‐based methodologies to estimate needed movement parameters.

Assessing the effects of survey-inherent disturbance on primate detectability: Recommendations for line transect distance sampling

Habitat destruction and over-hunting are increasingly threatening the arboreal primates of Central Africa. To establish effective conservation strategies, accurate assessments of primate density, abundance, and spatial distribution are required. To date, the method of choice for primate density estimation is line transect distance sampling. However, primates fleeing human observers violate methodological assumptions, biasing the accuracy of resulting estimates. In this study, we used line transect distance sampling to study five primate species along 378 km of transects in Salonga National Park, Democratic Republic of the Congo. We tested the effect of different levels of survey-inherent disturbance (i.e., cutting) on the number of observed (i) primate groups, and (ii) individuals within groups, by counting groups at three different time lags after disturbance of the transect, (i) a minimum of 3 h, (ii) 24 h, (iii) a minimum of 3 days. We found that survey-inherent disturbance led to underestimated densities, affecting both the number of encountered groups and of observed individuals. However, the response varied between species due to species-specific ecological and behavioral features. Piliocolobus tholloni and Colobus angolenis resumed an unaltered behavior only 24 h after disturbance, while Lophocebus aterrimus, Cercopithecus ascanius, and Cercopithecus wolfi required a minimum of 10 days. To minimize bias in density estimates, future surveys using line transect distance sampling should be designed considering survey-inherent disturbance. We recommend evaluating the factors driving primate response, including habitat type, niche occupation, and hunting pressure, peculiar to the survey-specific area and primate community under study.

Distance sampling from curving transects in dense tropical forests

AbstractLine transect distance sampling is a popular method for estimating the density of animals across the tropics. The method relies on accurate measurements of the distance between an animal and a transect to model detectability. In dense tropical forests, surveys can become time‐consuming, expensive, and dangerous when randomly placed straight line transects cross landscape features such as rivers, swamps, and dense vegetation. As a result, transects often curve as an observer deviates from an ideal, straight line. Here, we examine the practical and statistical impact of these curves. We use distance sampling simulations to assess bias in density estimates based on scenarios corresponding with different methods reliant on distinct field measurements. Methods that measure the nearest distance between the animal and the curving transect produce the most reliable density estimates. Biased estimates were obtained when using methods that ignore curves, measure the distance to an ideal line (as opposed to the curve), or inaccurately calculate the area covered in the survey. Notably, these biased estimates were most severe when observation distances were short, highlighting the importance of accurate measurements in tropical forests characterized by low visibility. Given these results and the importance of reliable density estimates to conservation efforts across the tropics, we propose a method that addresses survey design, simplifies data collection, and alleviates some of the practical field challenges associated with straight line transects. We also developed an R package (CurveTransect) based on this method with functions that ensure accurate measurements and reliable density estimates in tropical forests.

Can Video Traps Reliably Detect Animals? Implications for the Density Estimation of Animals without Individual Recognition

Several statistical models have recently been developed to estimate animal density using camera trappings without individual animal recognition. However, most models assume that detection by camera traps of animals passing a specific area of the camera view is perfect. A recently developed REST model (Nakashima et al. 2018; Journal of Applied Ecology 55: 735–744) also depends on the trapping rates and staying times within a specific area. We tested whether commercial camera traps provided unbiased estimates of these parameters by conducting an experimental trial using a domestic dog in a city park in Japan. Additionally, we tested the effects of camera angle on the estimation of these parameters using the Bushnell camera. The Bushnell camera captured the dog 96% of the time, while the Ltl-Acorn camera missed about half of his passes. The staying time was underestimated by 4% using the Bushnell and overestimated by 25% using the Ltl-Acorn camera. The bias in density estimation was < 10% using the Bushnell camera. Camera angle did not affect detection probability, while the downward-angled cameras underestimated staying time due to the delayed trigger. We hope to share the results with manufacturers to make camera traps more suitable for animal density estimation.

Incorporating Animal Movement Into Distance Sampling

Distance sampling is a popular statistical method to estimate the density of wild animal populations. Conventional distance sampling represents animals as fixed points in space that are detected with an unknown probability that depends on the distance between the observer and the animal. Animal movement can cause substantial bias in density estimation. Methods to correct for responsive animal movement exist, but none account for nonresponsive movement independent of the observer. Here, an explicit animal movement model is incorporated into distance sampling, combining distance sampling survey data with animal telemetry data. Detection probability depends on the entire unobserved path the animal travels. The intractable integration over all possible animal paths is approximated by a hidden Markov model. A simulation study shows the method to be negligibly biased (<5%) in scenarios where conventional distance sampling overestimates abundance by up to 100%. The method is applied to line transect surveys (1999–2006) of spotted dolphins (Stenella attenuata) in the eastern tropical Pacific where abundance is shown to be positively biased by 21% on average, which can have substantial impact on the population dynamics estimated from these abundance estimates and on the choice of statistical methodology applied to future surveys. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Simulation-based validation of spatial capture-recapture models: A case study using mountain lions.

Spatial capture-recapture (SCR) models have improved the ability to estimate densities of rare and elusive animals. However, SCR models have seldom been validated even as model formulations diversify and expand to incorporate new sampling methods and/or additional sources of information on model parameters. Information on the relationship between encounter probabilities, sources of additional information, and the reliability of density estimates, is rare but crucial to assessing reliability of SCR-based estimates. We used a simulation-based approach that incorporated prior empirical work to assess the accuracy and precision of density estimates from SCR models using spatially unstructured sampling. To assess the consequences of sparse data and potential sources of bias, we simulated data under six scenarios corresponding to three different levels of search effort and two levels of correlation between search effort and animal density. We then estimated density for each scenario using four models that included increasing amounts of information from harvested individuals and telemetry to evaluate the impact of additional sources of information. Model results were sensitive to the quantity of available information: density estimates based on low search effort were biased high and imprecise, whereas estimates based on high search effort were unbiased and precise. A correlation between search effort and animal density resulted in a positive bias in density estimates, though the bias decreased with increasingly informative datasets. Adding information from harvested individuals and telemetered individuals improved density estimates based on low and moderate effort but had negligible impact for datasets resulting from high effort. We demonstrated that density estimates from SCR models using spatially unstructured sampling are reliable when sufficient information is provided. Accurate density estimates can result if empirical-based simulations such as those presented here are used to develop study designs with appropriate amounts of effort and information sources.

Estimating density of fin whales and beaked whales with a mix distance sampling and spatially explicit capture recapture design

Dedicated passive acoustic density estimation studies with reliable survey design are still rare. We will present one such project: DECAF-TEA (Density Estimation for Cetaceans from Acoustic Fixed sensors in Testing and Evaluation Areas), which aims to estimate the density of beaked and fin whales on the SCORE US Navy range. We consider a mixed design that can deal with both species that produce acoustics signals with relatively short propagation distances (e.g., beaked whales) and those that produce signals with long propagation distances (e.g., fin whales), via distance sampling (DS) for the former and spatially explicit capture recapture (SECR) for the later. For beaked whales, we consider pairs of 3D bearing sensors to provide estimates of 3D localizations of detected whales, and from such data estimate detectability via distance sampling. At the same time, single units might provide a way to estimate density of fin whales via SECR. In either case, cue rates will be obtained from independent sources. In the context of DS we explore the impact of measurement error on the 3D bearing estimates and how this error propagates via errors in localization all the way through to potential bias in density estimation.

Density influences accuracy of model-based estimates for a forest songbird

Golden-cheeked Warblers (Setophaga chrysoparia) are endangered songbirds that breed exclusively in the Ashe juniper (Juniperus ashei )a nd oak (Quercus spp.) woodlands of central Texas. Despite being the focus of numerous studies, we still know little about the size of the range-wide breeding population and how density varies across the spectrum of juniper co-dominated woodlands. Models that have been tested and shown to be accurate are needed to help develop management and conservation guidelines. We evaluated the accuracy and bias of density estimates from binomial mixture models, the dependent double-observer method, and distance sampling by comparing them to actual densities determined by intensive territory monitoring on plots in the Balcones Canyonlands Preserve, Austin, Texas. We found that the binomial mixture models consistently overestimated density by 1.1-3.2 times (actual density = 0.07-0.46 males/ha), and the other two models overestimated by 1.1- 29.8 times at low density and underestimated by 0.5-0.9 times at high density plots (actual density = 0.01-0.46 males/ha). The magnitude of error for all models was greatest at sites with few or no birds (<0.15 males/ha), with model performance improving as actual density increased. These non-linear relationships indicate a lack of sensitivity with respect to true changes in density. Until systematic evaluation demonstrates that models such as those we tested provide accurate and unbiased density estimates for a given species over space and time, we recommend additional field tests to validate model-based estimates. Continued model validation and refinement of point-count methods are needed until accurate estimates are obtained across the density spectrum for Golden-cheeked Warblers and other songbird species. RESUMEN. La densidad influencia la precisi´

Applying a random encounter model to estimate lion density from camera traps in Serengeti National Park, Tanzania.

The random encounter model (REM) is a novel method for estimating animal density from camera trap data without the need for individual recognition. It has never been used to estimate the density of large carnivore species, despite these being the focus of most camera trap studies worldwide. In this context, we applied the REM to estimate the density of female lions (Panthera leo) from camera traps implemented in Serengeti National Park, Tanzania, comparing estimates to reference values derived from pride census data. More specifically, we attempted to account for bias resulting from non-random camera placement at lion resting sites under isolated trees by comparing estimates derived from night versus day photographs, between dry and wet seasons, and between habitats that differ in their amount of tree cover. Overall, we recorded 169 and 163 independent photographic events of female lions from 7,608 and 12,137 camera trap days carried out in the dry season of 2010 and the wet season of 2011, respectively. Although all REM models considered over-estimated female lion density, models that considered only night-time events resulted in estimates that were much less biased relative to those based on all photographic events. We conclude that restricting REM estimation to periods and habitats in which animal movement is more likely to be random with respect to cameras can help reduce bias in estimates of density for female Serengeti lions. We highlight that accurate REM estimates will nonetheless be dependent on reliable measures of average speed of animal movement and camera detection zone dimensions. © 2015 The Authors. Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society.

Trap Array Configuration Influences Estimates and Precision of Black Bear Density and Abundance

Spatial capture-recapture (SCR) models have advanced our ability to estimate population density for wide ranging animals by explicitly incorporating individual movement. Though these models are more robust to various spatial sampling designs, few studies have empirically tested different large-scale trap configurations using SCR models. We investigated how extent of trap coverage and trap spacing affects precision and accuracy of SCR parameters, implementing models using the R package secr. We tested two trapping scenarios, one spatially extensive and one intensive, using black bear (Ursus americanus) DNA data from hair snare arrays in south-central Missouri, USA. We also examined the influence that adding a second, lower barbed-wire strand to snares had on quantity and spatial distribution of detections. We simulated trapping data to test bias in density estimates of each configuration under a range of density and detection parameter values. Field data showed that using multiple arrays with intensive snare coverage produced more detections of more individuals than extensive coverage. Consequently, density and detection parameters were more precise for the intensive design. Density was estimated as 1.7 bears per 100 km2 and was 5.5 times greater than that under extensive sampling. Abundance was 279 (95% CI = 193–406) bears in the 16,812 km2 study area. Excluding detections from the lower strand resulted in the loss of 35 detections, 14 unique bears, and the largest recorded movement between snares. All simulations showed low bias for density under both configurations. Results demonstrated that in low density populations with non-uniform distribution of population density, optimizing the tradeoff among snare spacing, coverage, and sample size is of critical importance to estimating parameters with high precision and accuracy. With limited resources, allocating available traps to multiple arrays with intensive trap spacing increased the amount of information needed to inform parameters with high precision.

Compensatory heterogeneity in spatially explicit capture-recapture data.

Spatially explicit capture-recapture methods, used widely to estimate the abundance of large carnivores, allow for movement within home ranges during sampling. Probability of detection is a decreasing function of distance from the home range center, with one parameter for magnitude and another for spatial scale. Sex-based and other differences in home range size potentially cause heterogeneity in individual detection and bias in estimates of density. The two parameters of detection have hitherto been treated as independent, but we suggest that an inverse relation is expected when detection probability depends on time spent near the detector. Variation in the spatial scale of detection is then compensated by reciprocal variation in the magnitude parameter. We define a net measure of detection ("single-detector sampling area," a(0)), and show by simulation that its coefficient of variation (CV) is a better predictor of bias than the CV of either component or the sum of their squared CVs. In an example using the grizzly bear Ursus arctos, the estimated sex variation in a(0) was small despite large variation in each component. From the simulations, the relative bias of density estimates was generally negligible (< 5%) when CV(a(0)) < 30%. Parameterization of the detection model in terms of a(0) and spatial scale can be more parsimonious and significantly aids the biological interpretation of detection parameters.

Comparison of aerial surveys and pellet‐based distance sampling methods for estimating deer density

AbstractWildlife biologists require density estimates for white‐tailed deer (Odocoileus virginianus) to facilitate management. Aerial surveys are often used to obtain density estimates, but are subject to problems necessitating the consideration of novel techniques. During winters 2008 and 2009, we estimated deer density on 6 forest preserves near Chicago, Illinois, USA, using aerial surveys and pellet‐based distance sampling (PBDS) methods to provide a comparison of these 2 density‐estimation techniques. Density estimates from aerial surveys were obtained by dividing both the raw count of deer observed on each preserve (unadjusted aerial density) and the raw count divided by 0.75 (i.e., assuming a 75% detection rate; adjusted aerial density) by the area of the preserve. We calculated deer densities from PBDS methods using Program DISTANCE 5.0 (PBDS density) and used paired t‐tests to compare density estimates between PBDS and aerial survey techniques. Unadjusted aerial density (10–29 deer/km2) and adjusted aerial density (13–39 deer/km2) estimates did not differ (t11 = −1.99–0.44, P = 0.071–0.666) from PBDS density estimates (12–36 deer/km2). We also compared costs and found PBDS (US$85/survey) was 88% cheaper than aerial surveys (US$722/survey). Problems with bias and precision exist with both methods, and managers should give them serious consideration when choosing which method to use to estimate deer densities. Given accurate pellet decay and deposition rates and a large sample size of pellet groups, PBDS may be advantageous due to less bias in density estimates, no dependence on continuous snow cover, cheaper survey costs, and no need for elaborate equipment or for professional biologists to conduct surveys. However, future research needs to address how to reduce coefficient of variations and confidence intervals for PBDS so that differences among years can be better differentiated. © 2012 The Wildlife Society.

Comparison of Pellet-Group Counting Methods to Estimate Population Density of White-Tailed Deer in a Mexican Tropical Dry Forest

Wildlife species population density estimation is important from both ecological and management perspectives. The pellet-group counting method has been used to evaluate density of the white-tailed deer ( Odocoileus virginianus). This species is an important component of human diet in tropical habitats. The objectives of this study were to: 1) compare density estimates using four methods: counts in circular plots (FSC, Fecal Standing Crop and FAR, Fecal Accumulation Rate), and counts in transects (LT, Line Transect and ST, Strip Transect); 2) simulate the effect of increased sampling effort on density and precision, and; 3) evaluate the effort required to detect changes in population density using LT. From 2006 to 2007, we intensively sampled a 1 km2quadrant in a Mexican tropical dry forest. The results indicate that all four methods produce similar mean population density estimates. However, estimates of precision were dependent on sample size which in turn was associated with the particular counting method used. In descending order of estimate precision, the methods ranked as: LT, ST, FSC, and FAR. To detect population changes of &lt; 20%, we suggest the establishment of 5 to 22 transects (LT) of 390 m during the dry season. To reduce bias in density estimation, it is important to obtain defecation and pellet decomposition rates in the study site.

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.

Underestimation of rotifer abundance a much greater problem than previously appreciated

Although rotifers are important components of aquatic food webs and suitable sampling methods have been described and tested in the peer‐reviewed literature, they are frequently overlooked or quantified with improper methods (e.g., mesh sizes ≥ 63 µm) in freshwater ecology studies. As a result, we believe that the role of rotifers in aquatic food webs and ecosystem processes remains underappreciated, and this conceptual shortfall is exacerbated by the continued use of improper sampling methodology.We examined density and biomass estimates of metazoan zooplankton in the Upper Mississippi and Missouri rivers from two sampling methods. The macrozooplankton method was designed to target cladocerans, adult and juvenile copepods, by filtering 180 L water through a 63‐µm mesh. The microzooplankton method was designed to target rotifers and copepod nauplii by filtering 18 L water through a 20‐µm mesh. The macrozooplankton method underestimated the density and biomass of common rotifers by two to three orders of magnitude, a far greater amount of error than reported in previous studies. This bias in density estimates for rotifers decreased with increasing mean length of rotifers. The microzooplankton method proved to be ineffective for quantifying cladoceran species richness or cladoceran density at the species level. We urge aquatic ecologists to match their sampling methodology with the specific goals of their study. An accurate understanding of the role of rotifers in freshwater ecosystems will only be possible when the use of appropriate methodology becomes the rule rather than the exception.

Nonparametric density deconvolution by weighted kernel estimators

Nonparametric density estimation in the presence of measurement error is considered. The usual kernel deconvolution estimator seeks to account for the contamination in the data by employing a modified kernel. In this paper a new approach based on a weighted kernel density estimator is proposed. Theoretical motivation is provided by the existence of a weight vector that perfectly counteracts the bias in density estimation without generating an excessive increase in variance. In practice a data driven method of weight selection is required. Our strategy is to minimize the discrepancy between a standard kernel estimate from the contaminated data on the one hand, and the convolution of the weighted deconvolution estimate with the measurement error density on the other hand. We consider a direct implementation of this approach, in which the weights are optimized subject to sum and non-negativity constraints, and a regularized version in which the objective function includes a ridge-type penalty. Numerical tests suggest that the weighted kernel estimation can lead to tangible improvements in performance over the usual kernel deconvolution estimator. Furthermore, weighted kernel estimates are free from the problem of negative estimation in the tails that can occur when using modified kernels. The weighted kernel approach generalizes to the case of multivariate deconvolution density estimation in a very straightforward manner.

A comparison of mark - recapture distance-sampling methods applied to aerial surveys of eastern grey kangaroos

Aerial surveys of kangaroos (Macropus spp.) in Queensland are used to make economically important judgements on the levels of viable commercial harvest. Previous analysis methods for aerial kangaroo surveys have used both mark–recapture methodologies and conventional distance-sampling analyses. Conventional distance sampling has the disadvantage that detection is assumed to be perfect on the transect line, while mark–recapture methods are notoriously sensitive to problems with unmodelled heterogeneity in capture probabilities. We introduce three methodologies for combining together mark–recapture and distance-sampling data, aimed at exploiting the strengths of both methodologies and overcoming the weaknesses. Of these methods, two are based on the assumption of full independence between observers in the mark–recapture component, and this appears to introduce more bias in density estimation than it resolves through allowing uncertain trackline detection. Both of these methods give lower density estimates than conventional distance sampling, indicating a clear failure of the independence assumption. The third method, termed point independence, appears to perform very well, giving credible density estimates and good properties in terms of goodness-of-fit and percentage coefficient of variation. Estimated densities of eastern grey kangaroos range from 21 to 36 individuals km–2, with estimated coefficients of variation between 11% and 14% and estimated trackline detection probabilities primarily between 0.7 and 0.9.

Density estimation in wildlife surveys

Abstract Several authors have recently discussed the problems with using index methods to estimate trends in population size. Some have expressed the view that index methods should virtually never be used. Others have responded by defending index methods and questioning whether better alternatives exist. We suggest that index methods are often a cost-effective component of valid wildlife monitoring but that double-sampling or another procedure that corrects for bias or establishes bounds on bias is essential. The common assertion that index methods require constant detection rates for trend estimation is mathematically incorrect; the requirement is no long-term trend in detection “ratios“ (index result/parameter of interest), a requirement that is probably approximately met by many well-designed index surveys. We urge that more attention be given to defining bird density rigorously and in ways useful to managers. Once this is done, 4 sources of bias in density estimates may be distinguished: coverage, clo...