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The effect of data analysis strategies in density estimation of mountain ungulates using distance sampling

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Abstract

Distance sampling is being extensively used to estimate the abundance of animal populations. Nevertheless, the great variety of ways in which data can be analyzed may limit comparisons due to the lack of standardization of such protocols. In this study, the influence of analytical procedures for distance sampling data on density estimates and their precision was assessed. We have used data from 21 surveys of mountain ungulates in the Iberian Peninsula, France and the Italian Alps. Data from such surveys were analyzed with the program Distance 6.0. Our analyses show that estimated density can be higher for higher levels of data truncation. We also confirm that the estimates tend to be more precise when data are analyzed without binning and without truncating. We found no evidence of size biased sampling as group size and distances were uncorrelated in most of our surveys. Despite distance sampling being a fairly robust methodology, it can be sensitive to some data analysis strategies.

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... Transects were done by walking on the unpaved roads distributed across the study area ( Fig. 1). Transects were carried out at dawn or dusk when ungulates are more active (Pérez et al. 2014). For each transect, we recorded the observed species and number of individuals. ...
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... To date, several methods with different precisions were used to estimate abundance of mountain ungulate populations, including distance sampling, mark-resight, and block counts (e.g. Corlatti et al. 2015;Pérez et al. 2015). However, estimates of densities in inaccessible mountain landscapes with heterogeneous habitats and low detectability rates are very scarce (e.g. ...
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... In order to be properly managed, aquaculture companies require accurate data of the abundance, biomass and average weight of the fish farmed in their facilities. The more accurate these data are, the better the decision-making for the fish farm will be in terms of feed requirements, growth rate and food conversion calculations, medication administration, early detection of fish losses due to deaths, robberies or escapes, splitting of farming units, economic forecasting, etc. (McCallum, 2005;Soliveres et al., 2014;Pérez et al., 2015;Hofmeester et al., 2016;Føre et al., 2018). ...
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... The number and order of adjustment terms required for the analysis were automatically selected by Distance using the databased criteria with three maximum terms, of the AIC selection criterion (Franceschi et al. 2014). The encounter rate was thus obtained for each survey and its variance was estimated empirically with the default estimator (Buckland et al. 2001;Franceschi et al. 214;Pérez et al. 2015). With the Distance program, we performed all the analyses without truncating, nor grouping the data into Fig. 2 Example of a rock ptarmigan count in Andorra. ...
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The rock ptarmigan (Lagopus muta) has a wide Holarctic geographical range, within which its status changes locally from threatened to abundant. For the correct management of populations under differing scenarios, accurate and precise estimates of bird abundances and/or densities are required. We used geolocated datasets from 56 counts of singing males carried out in 2003–2017 to estimate the density of Pyrenean rock ptarmigans (Lagopus muta pyrenaica). We analysed these datasets using two methodologies: (1) a plot sampling (PS) approach with two effective detection ranges (EDR) of 250 m and 350 m and (2) a conventional distance sampling (DS) approach. Our results showed that the density estimates obtained by DS were more precise and 30–87% higher than those obtained by PS using 250 m and 350 m EDR. Monitoring with PS underestimates populations and is less precise than DS; this bias is magnified when high EDR values are used. The monitoring of the Pyrenean rock ptarmigan could be significantly improved with greater use of the DS method.
... These field data have been used totally or partially in some publications, most of these being technical documents [41][42][43][44][45][46] . ...
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... Only two adjustment terms were used to balance between bias and precision, and the lowest AIC value was used for model selection. Data were neither binned, truncated nor grouped into distance intervals for density estimation (Pérez et al., 2015). Variance was estimated empirically and the coefficient of variation (CV) of the density estimates and their associated 95% confidence interval were also obtained. ...
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... However, DS has also produced values lower than block counts, with block count value falling out of the 95% DS confidence interval, when used to estimate chamois numbers in complex and rough areas (Corlatti et al. 2015). In DS applied to mountain ungulates, such as the chamois, the use of different data analysis strategies and new approaches considering the density gradient from linear structures are recommended to improve the precision of density estimation (Marques et al. 2013;Pérez et al. 2014). As compared to BC, CMR, IPS and DS have the advantage of providing the accuracy of the estimates computed instead of a single value and to provide estimates of detection probabilities (for IPS see recent advances in N-mixture models; e.g. ...
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Summary • High-density populations of large herbivores are now widespread. Wildlife managers commonly attempt to control large herbivores through hunting to meet specific management objectives, considering population density as the minimal key source of information. Here, we review the problems of censusing populations of large herbivores and describe an alternative approach, employing indicators of ecological change. • Estimating density of large herbivores with high precision and accuracy is difficult, especially over large areas, and requires considerable investment of time, people and money. Management decisions are often made on an annual basis, informed by population changes over the previous year. However, estimating year-to-year changes in density is not a realistic goal for most large herbivores. Furthermore, population density per se provides no information on the relationship between the population and its habitat. • For successful management of large herbivores, we need to consider not only the fate of the population, but rather changes in both population and habitat features, as well as their interaction. Managers require information on trends in both the animal population and habitat quality in order to interpret changes in the interaction between these two compartments. • We propose that a set of indicators of animal performance, population abundance, habitat quality and/or herbivore habitat impact provides relevant information on the population–habitat system. Monitoring temporal changes in these indicators provides a new basis for setting hunting quotas to achieve specific management objectives. This sort of adaptive management is employed widely in France for managing roe deer Capreolus capreolus. • Synthesis and applications. The management of large herbivores would be improved by investing fewer resources in trying to estimate the absolute abundance of ungulates, and more resources in collecting additional data to inform understanding of the ecological status of the ungulate–habitat system being managed. This paper presents a set of indicators of ecological change for monitoring the interaction between a population and its habitat as a basis for adaptive management to attain explicit goals and to improve knowledge of the system. This approach could improve management for a variety of large herbivores, by harmonizing actions at wide spatial scales. Journal of Applied Ecology (2007) 44, 634–643 doi:10.1111/j.1365-2664.2007.01307.x
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Accurate assessment of the populations of mountain ungulates is difficult. Topography and behaviour of animals are important factors influencing detectability, on which direct methods are based. Sympathry with other wild and domestic ungulates increases error of dung identification. Other factors, such as the size of the area to be surveyed, or unmarked populations of the target species, suggests the choice of curvilinear transects. If the basic assumptions of Distance Sampling methodology are met, then estimates of population density and accuracy can be obtained. Current technology (GPS, laser rangefinders, and G.I.S.) can be used to achieve accurate measurements of distances and angles. A crucial problem is to estimate the effective area sampled around each travelling path. Therefore, researchers and managers of mountain ungulates need an adaptation of Distance Sampling methodology to account for a tridimensional scenario imposed by the slope of mountains. There is also a requirement to standardize protocols for collecting data. Alternatives for design surveys and collection data when working with populations of mountain ungulates are discussed. [fr] L'estimation précise de l'abondance des ongulés de montagne devient difficile. La détectabilité est conditionnée par la topographie et le comportement des animaux; c'est sur ce dernier cas que les méthodes directes s'appuient. La sympatrie entre les ongulés sauvages et domestiques augmente l'erreur d'identification des excréments. D'autres facteurs, comme par exemple les grandes surfaces à surveiller ou les populations non marquées des espèces-cibles, peuvent nous conduire à des comptages sur transect curvilignes ou sur des points. Si l'on tient compte des idées basiques concernant la méthodologie appelée «Échantillonage à distance», alors les estimations correspondantes de densité avec leurs mesures de précision peuvent être obtenues. La technologie à notre portée (GPS, laser «rangefinders» et GIS) peut aider de manière non négligeable l'obtention de valeurs précises de distances et d'angles. Il devient alors fondamental d'estimer la surface d'échantillonage autour de chacun de nos parcours. Par conséquence, tant les chercheurs que les gestionnaires des ongulés de montagne ont besoin d'une adaptation de l'échantillonage à distance de manière à construire un scénario tridimensionel imposé par les versants des montagnes ; aussi faudrait-t-il développer des protocoles standardisés pour la collecte de données. Dans ce travail, les différentes alternatives pour la mise en place des études et pour la collecte de données concernant les populations des ongulés de montagne sont discutées. [es] Valorar con exactitud la abundancia de ungulados de montaña es difícil. La detectabilidad es la base de los métodos directos, y ésta se ve influida por factores como la topografía y él comportamiento de los animales. La simpatría con otros ungulados, salvajes o domésticos, aumenta el error en la identificación de los excrementos. Otros factores, como la extensión del área a prospectar o la ausencia de poblaciones no marcadas de la especie objetivo, aconsejan el censado a partir de transectos o de puntos fijos. Si los supuestos básicos de la metodología basada en la distancia de detección se respetan, se pueden obtener estimas de densidad y evaluar su precisión. La tecnología actual (GPS, telémetros laser y SIG) permite un cálculo exacto de distancias y ángulos. Un problema crucial es estimar el área muestreada alrededor de cada transecto. Por ello, investigadores y gestores de ungulados de montaña necesitan una adaptación de la metodología basada en la distancia de detección, para reconstruir el área tridimensional impuesta por las montañas, además de estandarizar los protocolos de toma de datos. Se discuten varias alternativas para diseñar el estudio y recogida de datos en poblaciones de ungulados de montaña.
Article
Surveys were conducted from aircraft over waters off the coasts of Louisiana, Mississippi, and Alabama during the summers of 1974 and 1975 to evaluate field procedures and analytical techniques for estimating population densities of bottlenosed dolphins (Tursiops truncatus). Samples using a strip proved more reliable than those based on a quadrat. Line-transect estimates were generally not feasible because the observed distribution of distances from the flight line was different from the theoretical distribution required. Differences in counts between observer teams were significant. Based on strip censuses, the following population estimates were obtained: western Louisiana (1975), 897 ± 461; Mississippi, Chandeleur and Breton sounds, marshlands habitats (1974) 438 ± 294; and Mississippi Sound 1,342 ± 847 (1974) and 879 ± 368 (1975). The differences in the last 2 estimates reflect the large variability inherent in the population and in the estimation procedure and are not indicative of population fluctuation. Suggestions are made for future censuses of dolphins inhabiting inshore waters.
Article
An important problem in line transect sampling is that objects or point clusters of objects of different sizes have different sighting probabilities. In a recent paper Drummer and McDonald (1987, Biometrics 43, 13-21) develop a bivariate sighting function. Their function is dependent on perpendicular distance and object size. One important special case is an extension of the exponential power series sighting function first proposed by Pollock (1978, Biometrics 34, 475-478). In this note empirical evidence is given for this model based on a field test of line transect sampling theory. Beer cans were used to simulate point clusters of objects with cluster sizes 1, 2, 4, and 8. To achieve approximately equal precision of parameter estimates, equal numbers of each cluster size were taken.
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Line transect sampling is used to estimate the number of individuals in a study area. It is usually assumed that the detections of individuals constitute independent events, and that the probability of detecting an item is a function of its perpendicular distance from the transect. However, certain species of plants/animals tend to aggregate, or cluster, thus possibly violating the assumption of independence. Also, larger clusters may tend to have a higher probability of detection, thus distorting the observed probability distribution of cluster sizes. This can cause overestimation of the true population size. A similar problem occurs if the experimenter is using line transect data to estimate the mean and total amount of some attribute of the items, and this attribute influences the item's probability of detection. Bivariate detection functions that incorporate the cluster size, or another attribute, as a covariate are proposed. Estimators of total population size and of the moments of the additional variate are derived using the theory of weighted distributions. An application of the method to a shipboard survey of minke whales is provided.
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In some line transect surveys, the population of interest consists of groups or clusters of individuals rather than single items. If group size influences the probability of detecting a group, then the observed group size data are size-biased. This can lead to overestimation of the true mean group size and hence could lead to overestimation of the density of individuals. The method of line transect sampling used here incorporates group size as a covariate in line transect detection functions, and is applied to shipboard surveys of sea otter Enhydra lutris and to surveys of pellet groups from barren ground caribou Rangifer tarandus granti. Group size influence varied in the sea otter surveys. The method of estimation adequately adjusted for size bias when it was present. Estimates of pellet group density were unaffected by significant size bias. -Authors
Article
Abstract When human interventions interfere with the natural regulation of wildlife populations by favouring some species, overabundance can emerge. We evaluated different methods of estimating red deer abundance in a wide range of population densities from southern Spain. Distance sampling estimates were used as the reference method across 22 localities and were compared with two kilometric abundance indices (KAIs), four indices based on pellet group counts and two browsing indices (BWIs). The average red deer density estimated by distance sampling was 19.51±3.19 deer per 100 ha, showing a wide range across the study area (0.04–66.77). Distance sampling estimates correlated with the KAIs, pellet group-based index and the BWI. The agreement with distance sampling improved when groups were used instead of individuals in the KAIs, when the minimum pellet group size was fixed at 20 pellets in the dropping counts, and when only highly palatable species were used in the BWI. Thus, several direct and indirect methods can estimate red deer abundance in Mediterranean habitats from Southern Spain with appropriate modifications.
Article
We examined three aspects of line-transect analytical procedures: data grouping, data truncation and the use of individuals or clusters as the analytical unit. Bias and precision of density estimation in relation to various levels of these factors were assessed for 4 types of line-transect estimator (simple parametric, generalised parametric, non-parametric and quasi-strip) using line-transect survey data from macropod populations of known density. The effect of data grouping on bias and precision varied between estimators. Bias was stable across all grouping levels tested for the simple parametric estimator, and stable across aU but the coarsest grouping level for the generalised parametric and non-parametric estimators, but varied substantially across the range of levels tested for the quasi-strip estimator. Precision improved as the number of grouping levels increased for all estimators tested, but the extent of improvement varied between estimators, and for the estimator most affected, improvement was marginal beyond intermediate grouping levels. Density estimates were generally more accurate and precise when analysed in ungrouped form than in grouped form. No effects of truncation on bias or precision were detected. Varying the analytical unit did not affect bias, but precision was significantly lower for cluster analysis than individual analysis for all estimators.
Article
Aerial line transect methods have been successfully used to count animals in open country; we describe their application for assessing red deer (Cervus elaphus) numbers in Scotland. The results of a pilot study in the north of Scotland are compared to a census count carried out in the same area in the previous year. The aerial line transect method gave an estimate of 2240 red deer in May 1995. This agreed well with the census count giving 2270 in April 1994. The line transect estimate had a coefficient of variation of 25%, whereas no measure of precision is available for the census count. Separate estimates for the number of stags and the number of hinds and calves were obtained with both methods. We suggest improvements in the practical application of the aerial line transect method to increase precision of the abundance estimates. Aerial line transect surveys require fewer person-days of effort than census counts, and are appreciably more cost effective for assessing deer numbers over a large area. We present three case studies for applying aerial line transect methods in Scotland. The case studies compare the cost and effort for an aerial line transect estimate with those of a conventional ground-based census count in West Sutherland and North Ross (Red Deer Commission's counting blocks). Obtaining an estimate of red deer numbers in North Ross with a coefficient of variation of 10% would take 33% of the time of a census count, require 50% of the people and take about 60% of the resources required for a ground-based census count. A joint estimate for North Ross and West Sutherland would reduce the time demand for the line transect estimate (10% coefficient of variation) to about 18% of that required by a census and the resources to 33%.
Article
This monograph is out of print and not available. Much of the material is covered in the books on Distance Sampling. One of the early versions is available at http://www.colostate.edu/depts/coopunit/download.html or http://www.ruwpa.st-and.ac.uk/distance.book/download.html
Article
Post-release monitoring, including abundance estimation, is an important part of reintroductions, providing a basis for management intervention designed to achieve long-term persistence. The Arabian oryx Oryx leucoryx became extinct in the wild in 1972, surviving as captive populations. Since 1982 reintroductions of Arabian oryx have taken place in Oman and Saudi Arabia. Modelling of oryx population dynamics has highlighted the importance of precise estimation of population size (N). Between 1990 and 2000 three methods of estimating N have been applied in Mahazat as-Sayd protected area in Saudi Arabia: derived population estimates (DPE) based on known births and deaths, distance sampling, and mark-resighting (MR). This study assesses the feasibility and precision of these methods. Inability to assess precision, interdependence of consecutive estimates, and the assumption that all gains and losses are recorded, make DPE of limited value. At current densities, distance sampling along 455 km of driven transects yields too few detections to derive precise estimates of N. To achieve a coefficient of variation of 20% it would be necessary to drive up to c. 2,900 km of transect; this amount of survey effort could be achieved through pooling of data across repeat surveys of established transects. MR estimates, based on re-sighting of collared oryx, have the potential to yield the most precise estimates of N when the proportion of marked animals reaches 30% of the total population. The most reliable MR estimates available indicate the Mahazat as-Sayd Arabian oryx population had grown to >400 animals by 2000.
Article
1. Roe deer Capreolus capreolus were surveyed at night along tracks and roads in plantation forests in North Yorkshire, UK. Distance sampling was used to estimate their density. This method has been proposed for monitoring deer populations in state-owned forests throughout the UK. 2. Most deer were stationary on detection and the vast majority did not change their behaviour during observation. Few deer were observed on the transects, suggesting that they were avoiding tracks and roads at night as opposed to moving in response to the observer. 3. This has implications for data analysis and hence the results of surveys. Left-truncation or grouping of data close to the transect line to cope with road avoidance decreased the precision of the population estimate and may have impacted upon its accuracy. 4. Use of roads and tracks in forests is the only realistic option for transect surveys of deer at night but the influence of these features on deer distribution and hence density estimates must be taken into consideration when conducting such surveys.
Article
Summary • Accurate and precise estimates of abundance are required for the development of management regimes for deer populations. In woodland areas, indirect dung count methods, such as the clearance plot and standing crop methods, are currently the preferred procedures to estimate deer abundance. The use of line transect methodology is likely to provide a cost-effective alternative to these methods. • We outline a methodology based on line transect surveys of deer dung that can be used to obtain deer abundance estimates by geographical block and habitat type. Variance estimation procedures are also described. • As an example, we applied the method to estimate sika deer Cervus nippon abundance in south Scotland. Estimates of deer defecation and length of time to dung decay were used to convert pellet group density to deer density by geographical block and habitat type. The results obtained agreed with knowledge from cull and sightings data, and the precision of the estimates was generally high. • Relatively high sika deer densities observed in moorland areas up to 300 m from the forest edge indicated the need to encompass those areas in future surveys to avoid an underestimate of deer abundance in the region of interest. • It is unlikely that a single method for estimating deer abundance will prove to be better under all circumstances. Direct comparisons between methods are required to evaluate thoroughly the relative merits of each of them. • Line transect surveys of dung are becoming a widely used tool to aid management and conservation of a wide range of species. The survey methodology we outline is readily adaptable to other vertebrates that are amenable to dung survey methodology.
Article
Many ecotourism reserves in the Eastern Cape Province of South Africa have introduced large carnivores which prey on ungulates such as kudu. Kudu occupy thick vegetation and helicopter-based counts are not appropriate. In this study we tested line transect counts of faecal pellets in conjunction with DISTANCE analysis as a method for assessing the abundance of kudu. Transects were undertaken in three regions of two game reserves and the results compared with helicopter based game counts (for two regions) and a known kudu population in the third region (an enclosed breeding centre). Estimates of kudu abundance were two to three times greater than the helicopter counts, but within the known number of kudu in the breeding centre. The increased accuracy in the breeding centre was probably because the transects covered a greater percentage of the available habitat (0.07%) than in the reserves (approximately 0.007%). We suggest that DISTANCE software and line transects counts of pellet groups can be used for kudu and probably for other ungulates in thicket-type vegetations. Accuracy will depend on the percentage of the available habitat that is surveyed and on the accuracy of the defecation and decay rates.
Article
Effective management and conservation of wildlife populations require reliable estimates of population size, which can be difficult and costly to obtain. We evaluated how precision in estimates of herd size and abundance varies with sample size and strip width using two field surveys and bootstrap resampling of the field data. We also examined precision under distance sampling and evaluated the cost-effectiveness of both survey techniques. Precision in estimates of abundance increased with increasing sample size and varied with strip width independently of sample size. The hazard rate key function was best for five species in two surveys with contrasting visibility conditions. Precision in density was more sensitive to the number of herds sighted than to variation in herd size and effective strip width for distance sampling. Strip counts produced lower abundance estimates but higher precision than distance sampling. We estimated that distance sampling would cost about US$3.1 km−1 of transect. Strip counts deserve serious consideration for surveys of species that occur at high densities and form large, loose agglomerations but distance methods are suitable for species occurring at moderate to low densities in areas where visibility varies substantially. Distance sampling may thus need to be supplemented by strip counts to efficiently estimate densities of rare, abundant and highly clustered multi-species assemblages of African savanna mammals. In small areas, it may often prove necessary to conduct several surveys to obtain adequate sample sizes for distance models.
Article
We present a robust sampling methodology to estimate population size using line transect and capture-recapture procedures for aerial surveys. Aerial surveys usually underestimate population density due to animals being missed. A combination of capture-recapture and line transect sampling methods with multiple observers allows violation of the assumption that all animals on the centreline are sighted from the air. We illustrate our method with an example of inanimate objects which shows evidence of failure of the assumption that all objects on the centreline have probability 1 of being detected. A simulation study is implemented to evaluate the performance of three variations of the Lincoln-Petersen estimator: the overall estimator, the stratified estimator, and the general stratified estimator based on the combined likelihood proposed in this paper. The stratified Lincoln-Petersen estimator based on the combined likelihood is found to be generally superior to the other estimators.
Article
The condition of the Spanish ibex population of Sierra Magina Natural Park (southern Spain) was studied during the rut period 1991, after the appearance of the first signs of sarcoptic mange in this population. A total of 151 individuals in 53 different groups were observed during the study. The population was characterized by a sex-ratio close to 1, a reproductive index of 0.57, and a reproductive potential of 1.5. Males were mainly 2–3 (40.4%) and 4–5 (38.3%) years old. Density was estimated as 2.6 ind./km2 (SE=0.27), which represented about 406 individuals for the study area. Spanish ibex were present all over the study area, although the preferred elevations were between 1200 and 1600 m. The sarcoptic mange prevalence in the Spanish ibex population was estimated as 25%, and it was spread throughout the study area. Results are discussed in relation to conservation perspectives for this Spanish ibex population and five basic measures are recommended.
Article
The monitoring of animal populations is necessary to conserve and manage the rare or harvest species and to understand the population change over several years. We used distance sampling methods to estimate seasonal density of blue sheep in a 2,740km2 area of Helan Mountain region by walking along 32 transect lines from winter 2003 to autumn 2005. In all, 367–780 blue sheep were observed in 91–143 groups in the surveys during the seasons. Observed mean group size ranged from 3.42 to 8.35 individuals; encounter rate, the number of groups detected per kilometre, varied from 0.19 to 0.30 during the seasons. A hazard rate key function with cosine series expansion and a half-normal key function with either cosine or simple polynomial series expansion were the best fitting models based on the lowest value of Akaike’s information criterion (AIC). Density estimates varied between 3.627 sheep per square kilometre in spring 2004 and 4.635 per square kilometre in summer 2005. There were no detectable differences in estimated density among seasons (P=0.887). The estimated density of blue sheep was negatively correlated with the total number of deaths (P<0.05), number of sub-adult males’ deaths (P<0.05), number of sub-adult females’ deaths (P<0.05), and number of male lambs’ deaths (P<0.05). We concluded that distance sampling surveys should be used to monitor long-term population trends to provide the best quantitative estimates of blue sheep populations in the Helan Mountains region.
Article
When conducting line transect sampling to estimate the abundance of a clustered wildlife population, detection of a school depends not only on the perpendicular distance of the school to the transect line, but also on the size of school. Larger size schools are easier to detect than smaller schools. Thus, a bivariate detection function with distance and size as covariates should be considered. This paper considers using the kernel smoothing method to fit the bivariate line transect data in order to estimate both abundance and the mean school size. Two kernel estimators are studied: the fixed kernel estimator, which uses the same smoothing bandwidth for all data points, and the adaptive kernel estimator, which allows the bandwidth to vary across the data points.
Article
When using bivariate line transect methods to estimate the biomass density of a tightly clustered biological population, it is generally assumed that both the perpendicular distance from the trackline to the cluster and the cluster size, or biomass, are measured without error. This is unlikely to be the case in practice. In this article, assuming additive mean zero errors in distance and multiplicative errors in size, we develop an estimator of density that corrects for these errors. We use the method of moments for the case of gamma cluster size, randomly placed transect lines, and the generalized exponential detection function. We derive results that show that it may not be necessary to correct for errors in distance or size when the distance and size estimates are not biased. When the size estimates are biased, the biomass density estimate has approximately the same bias as the size estimates. The work is illustrated in the context of annual aerial surveys for juvenile southern bluefin tuna in the Great Australian Bight.
Article
Melville and Welsh (2001, Biometrics 57, 1130-1137) consider an approach to line transect sampling using a separate calibration study to estimate the detection function g. They present a simulation study contrasting their results with poor results from a traditional estimator, labeled the "Buckland" estimator and referenced to Buckland et al. (1993, Distance Sampling: Estimating Abundance of Biological populations). The poor results from the "Buckland" estimator can be explained by the following observations: (i) the estimator is designated for untruncated distance data, but was applied by Melville and Welsh to truncated distance data; (ii) distance data were not pooled across transects, contrary to standard practice; and (iii) bias of the estimator was evaluated with respect to a fixed rather than a randomized grid of transect lines. We elaborate on the points above and show that the traditional methods perform to expectation when applied correctly. We also emphasize that the estimator labeled the "Buckland" estimator by Melville and Welsh is not an estimator recommended by Buckland et al. for practical survey applications.
Article
We consider the method of distance sampling described by Buckland, Anderson, Burnham and Laake in 1993. We explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design- and model-based frameworks. In particular, we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator within each framework. These results enable us to clarify aspects of the performance of the methodology which may be of interest to users and potential users of distance sampling.
Modelo combinado captura-recaptura e transectos lineares: uma abordagem bayesiana
  • J F Monteiro
Monteiro JF. 2010. Modelo combinado captura-recaptura e transectos lineares: uma abordagem bayesiana. Ph.D. Thesis. University of Évora, Évora. [In Portuguese].
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La stima di popolazione degli ungulate mediante Distance Sampling e termocamera infrarossi
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Sizetran: Analysis of size-biased line transect data
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Analysis and management of animal populations: Modelling, estimation, and decision making
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