READER REACTION

R. M. Fewster , J. L. Laake , and S. T. Buckland 856 Melville et Welsh (2001, Biometrics 57, 1130–1137) considèrent une approche de l'échantillonnage d'un transect en ligne en employant une étude de calibration séparée pour estimer la fonction de détection g. Ils présentent une étude de simulation opposant leurs résultats à ceux bien piètres d'un estimateur traditionnel, appelé l'estimateur “Buckland” et référencé dans Buckland et al. (1993, London, Chapman and Hall). Les résultats médiocres de l'estimateur “Buckland” peuvent être expliqués par : (i) l'estimateur est prévu pour des données de distance non tronquées, mais appliqué par Melville et Welsh à des données de distance tronquées ; (ii) les données de distance n'étaient pas fusionnées le long des transects, à l'opposé des pratiques courantes ; (iii) le biais de l'estimateur était évalué par rapport à une grille fixe plutôt que randomisée des lignes de transects. Nous examinons en détail les points précédents et nous montrons que les méthodes traditionnelles marchent bien lorsqu'on les applique correctement. Nous mettons aussi l'accent sur le fait que ce que Melville et Welsh appellent estimateur “Buckland” n'est pas un estimateur recommandé par Buckland et al. pour les applications pratiques d'échantillonnage. R. V. Gueorguieva 862 Souvent dans des études longitudinales ou dans des analyses de classification on observe simultanément des variables à réponse binaires et des variables continues qui doivent être modélisées conjointement. Dans une publication récente Dunson, Chen et Harry, 2003 (DCH) proposent une approche bayésienne pour modéliser en commun les résultats binaires et les résultats continus ; ils illustrent cette approche avec un exemple sur des données de toxicité. Dans cette note nous démontrons comment un logiciel standard (PROC NLMIXED dans SAS) peut être employé pour obtenir des estimations du maximum de vraisemblance d'un modèle dont le paramétrage est une alternative à celui utilisé par DCH pour cet exemple. Nous suggérons également qu'un modèle plus général avec les effets aléatoires additionnel ajuste mieux les données. Une anomalie apparente entre les estimations obtenues par DCH et les estimations obtenues plus tôt par Catalano et Ryan en 1992 est également résolu. La question du biais concernant l'effet dose est discutée. L'approche du maximum de vraisemblance est applicable aux situations générales avec des résultats de différents types et n'exige ni spécification à priori ni programmation supplémentaire. S. Pledger 868 Dorazio et Royle (2003, Biometrics 59, 351–364) ont étudié le comportement de trois modèles de mélange pour l'analyse des données de capture‐recapture en population fermée, en présence d'une hétérogénéité de capture entre individus. Leurs simulations provenaient d'une distribution béta‐binomiale, et leurs analyses étaient faites à partir des modèles béta‐binomial, logit‐normal, ou de mélange fini (à classes latentes). Dans cette réponse, des simulations à partir de distributions nombreuses et variées permettent d'avoir une vision plus large de la valeur relative de la distribution béta‐binomiale et des modèles de mélange fini, et donnent un premier aperçu des situations dans lesquelles ces modèles sont utiles.     

Estimating the encounter rate variance in distance sampling

Summary .  The dominant source of variance in line transect sampling is usually the encounter rate variance. Systematic survey designs are often used to reduce the true variability among different realizations of the design, but estimating the variance is difficult and estimators typically approximate the variance by treating the design as a simple random sample of lines. We explore the properties of different encounter rate variance estimators under random and systematic designs. We show that a design-based variance estimator improves upon the model-based estimator of Buckland et al. (2001, Introduction to Distance Sampling. Oxford: Oxford University Press, p. 79) when transects are positioned at random. However, if populations exhibit strong spatial trends, both estimators can have substantial positive bias under systematic designs. We show that poststratification is effective in reducing this 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.     

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.     

Accurate delineation of biogeographical regions depends on the use of an appropriate distance measure

The use of analytical techniques to delineate biogeographical regions is becoming increasingly popular. One recent example, Heikinheimo et al . ( Journal of Biogeography , 2007, 34 , 1053–1064 ), applied the k -means clustering algorithm to define the biogeography of the European land mammal fauna. However, they used the Euclidean distance measure to cluster grid cells described by species-occurrence data, which is inappropriate. The Euclidian distance yields misleading results when applied to species-occurrence data because of the double-zero problem and the species-abundance paradox. We repeat their analysis using the Hellinger distance, a measure appropriate for species-occurrence data and which has been shown to outperform other such measures. Our results differ substantially from those presented by Heikinheimo et al. We argue that the rigorous application of appropriate statistical techniques is of crucial concern within conservation biogeography.     

Empirical Bayes Estimation and Prediction Using Summary-Level Information From External Big Data Sources Adjusting for Violations of Transportability

Large external data sources may be available to augment studies that collect data to address a specific research objective. In this article we consider the problem of building regression models for prediction based on individual-level data from an “internal” study while incorporating summary information from an “external” big data source. We extend the work of Chatterjee et al. (J Am Stat Assoc 111(513):107–117, 2006) by introducing an adaptive empirical Bayes shrinkage estimator that uses the external summary-level information and the internal data to trade bias with variance for protection against departures in the conditional probability distribution of the outcome given a set of covariates between the two populations. We use simulation studies and a real data application using external summary information from the Prostate Cancer Prevention Trial to assess the performance of the proposed methods in contrast to maximum likelihood estimation and the constrained maximum likelihood (CML) method developed by Chatterjee et al. (J Am Stat Assoc 111(513):107–117, 2006). Our simulation studies show that the CML method can be biased and inefficient when the assumption of a transportable covariate distribution between the external and internal populations is violated, and our empirical Bayes estimator provides protection against bias and loss of efficiency.     

On the structure of syntenic distance.

This paper examines some of the rich structure of the syntenic distance model of evolutionary distance, introduced by Ferretti et al. (1996). The syntenic distance between two genomes is the minimum number of fissions, fusions, and translocations required to transform one into the other, ignoring gene order within chromosomes. We prove that the previously unanalyzed algorithm given by Ferretti et al. (1996) is a 2-approximation and no better, and that, further, it always outperforms the algorithm presented by DasGupta et al. (1998). We also prove the same results for an improved version of the Ferretti et al. algorithm. We then prove a number of properties which give insight into the structure of optimal move sequences. We give instances in which any move sequence working solely within connected components is nearly twice optimal and prove a general lower bound based on the spread of genes from each chromosome. We then prove a monotonicity property for the syntenic distance, and bound the difficulty of the hardest instance of any size. We discuss the results of implementing these algorithms and testing them on real and simulated synteny data.     

Density estimates of two endangered nocturnal lemur species from northern Madagascar: new results and a comparison of commonly used methods

Very little information is known of the recently described Microcebus tavaratra and Lepilemur milanoii in the Daraina region, a restricted area in far northern Madagascar. Since their forest habitat is highly fragmented and expected to undergo significant changes in the future, rapid surveys are essential to determine conservation priorities. Using both distance sampling and capture-recapture methods, we estimated population densities in two forest fragments. Our results are the first known density and population size estimates for both nocturnal species. In parallel, we compare density results from four different approaches, which are widely used to estimate lemur densities and population sizes throughout Madagascar. Four approaches (King, Kelker, Muller and Buckland) are based on transect surveys and distance sampling, and they differ from each other by the way the effective strip width is estimated. The fifth method relies on a capture-mark-recapture (CMR) approach. Overall, we found that the King method produced density estimates that were significantly higher than other methods, suggesting that it generates overestimates and hence overly optimistic estimates of population sizes in endangered species. The other three distance sampling methods provided similar estimates. These estimates were similar to those obtained with the CMR approach when enough recapture data were available. Given that Microcebus species are often trapped for genetic or behavioral studies, our results suggest that existing data can be used to provide estimates of population density for that species across Madagascar.     

基于贝叶斯权重估计方法估计浙江省古田山国家级自然保护区两栖爬行动物多样性

传统的两栖爬行动物多样性调查方法在进行野外实验时,常遇到抽样限制的问题,一些稀有物种可能无法在个体样本中被发现,由于存在相对较大的物种缺失,导致不同的研究结果差距较大,较难反映真实的物种多样性.因此,基于有限的调查和监测数据尽可能准确地估计生物多样性极其重要.本文于2017—2020年的每年秋季,采用视觉遇见法调查了4...     

Consistent estimation of the expected Brier score in general survival models with right-censored event times

In survival analysis with censored data the mean squared error of prediction can be estimated by weighted averages of time-dependent residuals. Graf et al. (1999) suggested a robust weighting scheme based on the assumption that the censoring mechanism is independent of the covariates. We show consistency of the estimator. Furthermore, we show that a modified version of this estimator is consistent even when censoring and event times are only conditionally independent given the covariates. The modified estimators are derived on the basis of regression models for the censoring distribution. A simulation study and a real data example illustrate the results.     

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.     

样线法在鸟类数量调查中的运用

样线法是野生动物种群数量调查的常用方法之一。本文简要介绍其发展历史、基本原理和主要类型,并对4种常用的种群密度计算方法,即条带最大记数法、Gates截线法、Fourier截线法以及距离取样法进行比较和总结,认为在鸟类野外数量调查中应记录鸟类个体到样线的垂直距离,并使用距离取样法来计算鸟类的种群密度,以便得到更为准确的结果。     

A nonparametric estimator of species overlap

For two communities, species overlap has been defined by Smith, Solow, and Preston (1996, Biometrics 52, 1472-1477) as the probability that a randomly selected species is present in both communities given that it is present in at least one community. Species overlap can thus be used to describe the similarity of two communities. In contrast with the parametric estimator of Smith et al., we propose a nonparametric maximum likelihood estimator (NPMLE). We prove that the NPMLE is consistent and asymptotically normally distributed and show that computation of the NPMLE and its standard error is straightforward. We also compare the NPMLE and the estimator of Smith et al. for a variety of situations.     

A New Exponential Ratio-Type Estimator with Linear Combination of Two Auxiliary Variables

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al. In addition, we support these theoretical results with the aid of two numerical examples.     

Comment on: “root orientation can affect detection accuracy of ground-penetrating radar”

Introduction

In a recent paper, Tanikawa et al. Plant Soil 373:317–327, (2013) reported a considerable impact of root orientation on the accuracy of root detection and root diameter estimation by ground-penetrating radar (GPR).

Methods

In Tanikawa et al. Plant Soil 373:317–327, (2013), buried root samples in a sand box were scanned from multiple cross angles between root orientation and GPR transecting line under controlled conditions. Changes in radar waveform parameter of roots to different cross angles were investigated.

Results

Tanikawa et al. Plant Soil 373:317–327, (2013) clarified that 1) the variation in amplitude area (a signal strength related waveform parameter) to different cross angles fitted a sinusoidal waveform; and 2) the impact of root orientation on root diameter estimation by GPR could be mathematically corrected by applying a grid transect survey. However, we found that the quantitative relationship established in Tanikawa et al. Plant Soil 373:317–327, (2013) between amplitude area and cross angle was incorrect, and the application of a grid transect survey still underestimated root diameter.

Conclusion

The change in amplitude area to cross angle between transecting line and root orientation fits a sinusoidal waveform but different to that reported in Tanikawa et al. Plant Soil 373:317–327, (2013). The polarization of GPR wave may explain such sinusoidal variation in amplitude area to cross angle. The effect of root orientation on GPR-based root diameter estimation remains to be calibrated.     

Reply to: “Comment on root orientation can affect detection accuracy of ground-penetrating radar”

Introduction

We showed that root orientation affected a parameter of ground penetrating radar (GPR), amplitude area (A) (Tanikawa et al. Plant Soil 373:317–327, 2013). The aims of this reply to Wu et al. (2014) are (i) to correct the two inaccuracies in Tanikawa et al. (2013) and (ii) to improve our method of estimating A(90°) using A(x) of root angle x.

Methods

Measured A values of Tanikawa et al. (2013) were analyzed with the modified equations.

Results

The first inaccuracy was the use of incorrect units for the coefficient b (the phase shift) in the sinusoidal waveform of A(x). The units should have been radians instead of degrees. The second inaccuracy was the mis-derivation of A(x) into A(x?+?90°). In the modified method, A(90°) was estimated by A(x) from two orthogonally intersecting transect lines and a transect line at a diagonal to them.

Conclusions

The two inaccuracies did not affect the previous main conclusions that the parameter T was suitable for estimating root diameter and that grid transects are likely to identify clear hyperbolas reflecting roots in radar profiles (Tanikawa et al. 2013). By the improved method, we could accurately estimate root diameter by scanning using three transect lines intersecting at angles of x, x?+?45°, and x?+?90°.     

Estimating the Barents Sea polar bear subpopulation size

A large-scale survey was conducted in August 2004 to estimate the size of the Barents Sea polar bear subpopulation. We combined helicopter line transect distance sampling (DS) surveys in most of the survey area with total counts in small areas not suitable for DS. Due to weather constraints we failed to survey some of the areas originally planned to be covered by DS. For those, abundance was estimated using a ratio estimator, in which the auxiliary variable was the number of satellite telemetry fixes (in previous years). We estimated that the Barents Sea subpopulation had approximately 2,650 (95% CI approximately 1,900–3,600) bears. Given current intense interest in polar bear management due to the potentially disastrous effects of climate change, it is surprising that many subpopulation sizes are still unknown. We show here that line transect sampling is a promising method for addressing the need for abundance estimates.     

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

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