Incorporating covariates into standard line transect analyses

An implicit assumption of standard line transect methodology is that detection probabilities depend solely on the perpendicular distance of detected objects to the transect line. Heterogeneity in detection probabilities is commonly minimized using stratification, but this may be precluded by small sample sizes. We develop a general methodology which allows the effects of multiple covariates to be directly incorporated into the estimation procedure using a conditional likelihood approach. Small sample size properties of estimators are examined via simulations. As an example the method is applied to eastern tropical Pacific dolphin sightings data.     

A Random Field Approach to Transect Counts of Wildlife Populations

Line transect counting of a wildlife population is considered a sampling from a planar marked point process, where the marks describe the detectability of the animals. Sampling properties of transect counts and a new density estimator are derived from a counting process, which is a shot-noise field induced by the marked point process. A general formula for the sampling variance of a transect is derived and applied to compare five common types of transects. Some stereological connections of transect sampling and density estimators are shown.     

Estimation in independent observer line transect surveys for clustered populations

This paper introduces a framework for animal abundance estimation in independent observer line transect surveys of clustered populations. The framework generalizes an approach given in Chen (1999, Environmental and Ecological Statistics 6, in press) to accommodate heterogeneity in detection caused by cluster size and other covariates. Both parametric and nonparametric estimators for the local effective search widths, given the covariates, can be derived from the framework. A nonparametric estimator based on conditional kernel density estimation is proposed and studied owing to its flexibility in modeling the detection functions. A real data set on harbor porpoise in the North Sea is analyzed.     

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.     

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

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

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.     

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...     

The Effect of Animal Movement on Line Transect Estimates of Abundance

Line transect sampling is a distance sampling method for estimating the abundance of wild animal populations. One key assumption of this method is that all animals are detected at their initial location. Animal movement independent of the transect and observer can thus cause substantial bias. We present an analytic expression for this bias when detection within the transect is certain (strip transect sampling) and use simulation to quantify bias when detection falls off with distance from the line (line transect sampling). We also explore the non-linear relationship between bias, detection, and animal movement by varying detectability and movement type. We consider animals that move in randomly orientated straight lines, which provides an upper bound on bias, and animals that are constrained to a home range of random radius. We find that bias is reduced when animal movement is constrained, and bias is considerably smaller in line transect sampling than strip transect sampling provided that mean animal speed is less than observer speed. By contrast, when mean animal speed exceeds observer speed the bias in line transect sampling becomes comparable with, and may exceed, that of strip transect sampling. Bias from independent animal movement is reduced by the observer searching further perpendicular to the transect, searching a shorter distance ahead and by ignoring animals that may overtake the observer from behind. However, when animals move in response to the observer, the standard practice of searching further ahead should continue as the bias from responsive movement is often greater than that from independent movement.     

Correction for bias in visual transect censuses of coral reef fishes

Transect techniques for censusing reef fishes, and the sources of bias inherent in them are considered. A technique, derived from aeraly survey methods, is demonstrated to correct a bias in density estimates due to the width of the transect being censused. This bias is sufficient on a transect 1 m wide to underestimate density by 11.1–26.7% for five species or species groups examined. The bias is still greater on wider transects. Because this bias varies in degree among species, comparisons among species should not be made using uncorrected transect data. Comments are made on other probable sources of bias in transect data, and on ways of minimising bias when making visual transect censuses.     

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.     

How Reliable are Density Estimates for Diurnal Primates?

Primate population assessments provide the basis for comparative studies and are necessary prerequisites in determining conservation status. The most widely used assessment method is line transect sampling, which generates systematic data quickly and comparatively inexpensively. In contrast, the presumably most reliable method is long-term monitoring of known groups, which is both slow and costly. To assess the reliability of various analytical methods, we compared group and population densities for white-handed gibbons (Hylobates lar carpenteri) and Phayre’s leaf monkeys (Trachypithecus phayrei crepusculus) derived from transect walks with those from long-term group follows at Phu Khieo Wildlife Sanctuary, Thailand. Our assistants and we regularly walked a 4-km transect over 30 mo (480 km total), resulting in 155 gibbon sightings and 125 leaf monkey sightings. We then estimated densities via 1) DISTANCE and 2) the Kelker method based on perpendicular distances (PD) or animal-to-observer distances (AOD). We compared the 3 estimates to values based on known home ranges (95% kernels), accounting for home range overlap, combined with group size data. Analyses of line transect data consistently overestimated group densities for both species, while underestimating group size for leaf monkeys. Quality of results varied according to the group size and spread of each species. However, we found, in accordance with previous studies, that values derived via AOD (or its derivations) matched most closely with population estimates based on home range data.     

Adaptive line transect sampling

Adaptive line transect sampling offers the potential of improved population density estimation efficiency over conventional line transect sampling when populations are spatially clustered. In adaptive sampling, survey effort is increased when areas of high animal density are located, thereby increasing the number of observations. Its disadvantage is that the survey effort required is not known in advance. We develop an adaptive line transect methodology that, by varying the degree of adaptation, allows total effort to be fixed at the design stage. Relative to conventional line transect surveys, it also provides better survey coverage in the event of disruption in survey effort, e.g., due to poor weather. In analysis, sightings from the adaptive sections are downweighted in proportion to the increase in effort. We evaluate the methodology by simulation and report on surveys of harbor porpoise in the Gulf of Maine, in which the approach was compared with conventional line transect sampling.     

Estimating Population Size and Density Using Line Transect Sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to a class of estimators with desirable characteristics. This work was given a basic and rigorous mathematica framework by BURNHAM and ANDERSON (1976). In the present article we use this mathematical framework to develop an estimator of population size and density using weighted least squares. The approach is a two-stage Method.     

A hierarchical modeling framework for multiple observer transect surveys

Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line), these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size). We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package, hierarchicalDS, to facilitate the building and fitting of these models.     

Some comments on anderson and pospahala's correction of bias in line transect sampling

ANDERSON and POSPAHALA (1970) investigated the estimation of wildlife population size using the belt or line transect sampling method and devised a correction for bias, thus leading to an estimator with interesting characteristics. This work was given a uniform mathematical framework in BURNHAM and ANDERSON (1976). In this paper we show that the ANDERSON-POSPAHALA estimator is optimal in the sense of being the (unique) best linear unbiased estimator within the class of estimators which are linear combinations of cell frequencies, provided certain assumptions are met.     

Comparing agglomerative clustering and three weed classification frameworks to assess the invasiveness of alien species across spatial scales

To prioritize weed management at the catchment scale, information is required on the species present, their relatively frequency, abundance, and likely spread and impact. The objective of this study was to classify the invasiveness of alien species that have invaded the Upper Burdekin Catchment in Queensland, Australia, at three spatial scales. A combination of three published weed classification frameworks and multivariate techniques were employed to classify species based on their frequency and cover at a range of spatial scales. We surveyed the Upper Burdekin Catchment for alien species, and for each species determined the following distribution indices — site frequency, total cover, transect frequency per site frequency and quadrat frequency per site frequency, cover per quadrat when present, cover per transect when present, and cover per site when present. These indices capture the effect of species abundance and frequency between sites (site frequency and total cover), within sites (transect frequency per site and cover per transect when present), and within transects (quadrat frequency per site frequency and cover per site). They were used to classify the species into seven groups using a hierarchical cluster analysis. The relationship between the indices was explored to determine how effective the small scale, site‐specific indices were at predicting the broader, landscape‐scale patterns. Strong correlations were observed between transect frequency per site and frequency (r² = 0.89) and cover per transect when present and total cover (r² = 0.62). This suggests that if a weed is abundant at the site level, it has the potential to occupy large areas of the catchment. The species groupings derived from the application of the three published weed classification frameworks were compared graphically to the groupings derived from the cluster analysis. One of the frameworks classified species into three groups. The other two frameworks classified species into four groups. There was a high degree of subjectivity in applying the frameworks to the survey data. Some of the data were of no relevance to the classification frameworks and were therefore ignored. We suggest that the weed classification frameworks should be used in conjunction with existing multivariate techniques to ensure that classifications capture important natural variations in observed data that may reflect invasion processes. The combined use of the frameworks and multivariate techniques enabled us to aggregate species into categories appropriate for management.     

Comment on Cowling's "Spatial methods for line transect surveys"

We consider the problem of estimating the parameters of a two-dimensional Neyman-Scott process, from data collected through a line transect survey. Cowling (1998, Biometrics 54, 828-839) suggested an estimation method based on a one-dimensional K-function along the transect line. However, her expression for the theoretical K-function is wrong. In this article, we correct her K-function.     

Hazard models for line transect surveys with independent observers

The likelihood function for data from independent observer line transect surveys is derived, and a hazard model is proposed for the situation where animals are available for detection only at discrete time points. Under the assumption that the time points of availability follow a Poisson point process, we obtain an analytical expression for the detection function. We discuss different criteria for choosing the hazard function and consider in particular two different parametric families of hazard functions. Discrete and continuous hazard models are compared and the robustness of the discrete model is investigated. Finally, the methodology is applied to data from a survey for minke whales in the northeastern Atlantic.     

Perpendicular distance models for line transect sampling

Perpendicular distance line transect models are examined to assess whether any single model can provide a general procedure for analysing line transect data. Of the two-parameter models considered, the hazard-rate model appears promising, whereas the exponential power series and exponential quadratic models do not. Of the nonparametric models, the Fourier series is the best developed, and is favoured by many researchers as a general model. However, for a given data set, the Fourier series estimate may be highly dependent on the number of terms selected, and so the model is not a clear improvement over the hazard-rate model. A similar variable-term model, using Hermite polynomials, is considered, and is shown to be less dependent on the number of terms selected. There has been some debate about whether the derivative of the density function of perpendicular distances evaluated at 0 should be 0, so that the function has a "shoulder." The problem is examined in detail, and it is argued that reliable estimation is not possible from line transect data unless a shoulder exists. Many data sets appear to exhibit no shoulder; possible reasons are examined.