On estimating Hooded crow density from line transect data through exponential mixture models

Line transect sampling is a distance sampling method widely used for estimating wildlife population density. Since the usual approach assumes a model for the detection function, the estimate depends on the shape of such a function. In particular, the estimate is influenced by the so-called shoulder condition, which ensures that detection is nearly certain at small distances from the line transect. For instance, the half-normal model satisfies this condition, whereas the negative exponential model does not. The aim of this paper is to propose the exponential mixture model of the half-normal and the negative exponential in order to estimate the population density in the case where the shoulder condition is not guaranteed. Such a case study on Hooded crow is described in the paper.     

Factors affecting the detection distances of reef fish: implications for visual counts

Detection patterns of coral reef fish were assessed from the meta-analysis of distance sampling surveys performed by visual census in New Caledonia and French Polynesia, from 1986 to 1999. From approximately 100,000 observations relating to 593 species, the frequency distributions of fish detection distances perpendicular to the transect line were compared according to species characteristics and sampling conditions. The shape and extension of these detection profiles varied markedly with fish size, shyness, and crypticity, indicating strong differences of detectability across species. Detection of very small and cryptic fish decreased strongly 1 m away from the line. Conversely, sightings of shy and large species were excessively low in the first meters due to diver avoidance prior to detection. The larger the fish, the greater the fleeing distance. Distance data underscore how inconsistent detectability biases across species and sites can affect the accuracy of visual censuses when assessing coral reef fish populations.     

Estimating a distance dependent contagion function using point sample data

Natural events and human activities cause changes in landscape structure. Landscape metrics are used as a useful tool to study landscape trends and ecological processes related to the landscape structure. These metrics are commonly calculated on wall-to-wall raster data from remote sensing. A recent trend is to use sample data to estimate landscape metrics. In this study, point sampling was used to estimate a vector-based and distance dependent contagion metric. The metric is an extension of the established contagion. The statistical properties, for both unconditional and conditional contagions, were assessed by a point (point pairs) sampling experiment in maps from the National Inventory of landscapes in Sweden. Random and systematic sampling designs were tested for nine point distances and five sample sizes and for two classification systems. The systematic design showed slightly smaller root mean square error (RMSE) and bias than the random design. Both true and estimated values were calculated using computer programs in FORTRAN, which was specifically written for the purpose of the study. For a given sample size, RMSE and bias increased with increasing point distance. The estimator of unconditional contagion had acceptable RMSE and bias for moderate sample sizes, but in the conditional case the bias (and thus the RMSE) was unacceptably large. The main reason for this is that small classes (by area) affect both the true value of the contagion and are often missing in the sample. The method proposed can be adopted in gradient-based model of landscape structure where no distinct border is assumed between polygons. The method can also be applied in field-based inventories.     

Line transect sampling of Karner blue butterflies ( Lycaeides melissa samuelis)

Line transect sampling is an effective survey method for estimating butterfly densities because it provides unbiased estimates of site-density (provided key assumptions are met), and estimates are comparable among sites. For monitoring Karner blue butterflies in Wisconsin, USA, comparable estimates are required because each year a different selection of sites will be monitored. Annual state-wide indices of species abundance can be derived from the site-surveys and compared to previous year's indices to monitor trends. We advocate that line transect sampling is preferable to Pollard-Yates transects as a survey technique for monitoring Karner blue butter- flies. The Pollard-Yates surveys do not adjust for diferences in site detectability. As a consequence, estimates of among-site from Pollard-Yates surveys can be biased. © Rapid Science 1998     

Sample based estimation of landscape metrics; accuracy of line intersect sampling for estimating edge density and Shannon’s diversity index

A recent trend is to estimate landscape metrics using sample data and cost-efficiency is one important reason for this development. In this study, line intersect sampling (LIS) was used as an alternative to wall-to-wall mapping for estimating Shannon’s diversity index and edge length and density. Monte Carlo simulation was applied to study the statistical performance of the estimators. All combinations of two sampling designs (random and systematic distribution of transects), four sample sizes, five transect configurations (straight line, L, Y, triangle, and quadrat), two transect orientations (fixed and random), and three configuration lengths were tested, each with a large number of simulations. Reference was 50 photos of size 1 km², already manually delineated in vector format by photo interpreters using GIS environment. The performance was compared by root mean square error (RMSE) and bias. The best combination for all three metrics was found to be the systematic design and as response design the straight line configuration with random orientation of transects, with little difference between the fixed and random orientation of transects. The rate of decrease of RMSE for increasing sample size and line length was studied with a mixed linear model. It was found that the RMSE decreased to a larger degree with the systematic design than the random one, especially with increasing sample size. Due to the nonlinearity in the definition of Shannon diversity estimator its estimator has a small and negative bias, decreasing with sample size and line length. Finally, a time study was conducted, measuring the time for registration of line intersections and their lengths on non-delineated aerial photos. The time study showed that long sampling lines were more cost-efficient than short ones for photo-interpretation.     

Inference about density and temporary emigration in unmarked populations

Few species are distributed uniformly in space, and populations of mobile organisms are rarely closed with respect to movement, yet many models of density rely upon these assumptions. We present a hierarchical model allowing inference about the density of unmarked populations subject to temporary emigration and imperfect detection. The model can be fit to data collected using a variety of standard survey methods such as repeated point counts in which removal sampling, double-observer sampling, or distance sampling is used during each count. Simulation studies demonstrated that parameter estimators are unbiased when temporary emigration is either "completely random" or is determined by the size and location of home ranges relative to survey points. We also applied the model to repeated removal sampling data collected on Chestnut-sided Warblers (Dendroica pensylvancia) in the White Mountain National Forest, U.S.A. The density estimate from our model, 1.09 birds/ha, was similar to an estimate of 1.11 birds/ha produced by an intensive spot-mapping effort. Our model is also applicable when processes other than temporary emigration affect the probability of being available for detection, such as in studies using cue counts. Functions to implement the model have been added to the R package unmarked.     

The use of replicated plot,line and point sampling for estimating species abundance and ecological diversity

The paper deals with the problem of estimating diversity indexes for an ecological community. First the species abundances are unbiasedly and consistently estimated using designs based on n random and independent selections of plots, points or lines over the study area. The problem of sampling elusive populations is also considered. Finally, the diversity index estimates are obtained as functions of the abundance estimates. The resulting estimators turn out to be asymptotically (n large) unbiased, even if a considerable bias may occur for a small n. Accordingly, the method of jackknifing is made use of in order to reduce bias.     

Optimizing two- and three-stage designs for spatial inventories of natural resources by simulated annealing

This paper reviews design-based estimators for two- and three-stage sampling designs to estimate the mean of finite populations. This theory is then extended to spatial populations with continuous, infinite populations of sampling units at the latter stages. We then assume that the spatial pattern is the result of a spatial stochastic process, so the sampling variance of the estimators can be predicted from the variogram. A realistic cost function is then developed, based on several factors including laboratory analysis, time of fieldwork, and numbers of samples. Simulated annealing is used to find designs with minimum sampling variance for a fixed budget. The theory is illustrated with a real-world problem dealing with the volume of contaminated bed sediments in a network of watercourses. Primary sampling units are watercourses, secondary units are transects perpendicular to the axis of the watercourse, and tertiary units are points. Optimal designs had one point per transect, from one to three transects per watercourse, and the number of watercourses varied depending on the budget. However, if laboratory costs are reduced by grouping all samples within a watercourse into one composite sample, it appeared to be efficient to sample more transects within a watercourse.     

Line intersect sampling: Ell-shaped transects and multiple intersections

The probability of selecting a population element under line intersect sampling depends on the width of the particle in the direction perpendicular to the transect, as is well known. The consequence of this when using ell-shaped transects rather than straight-line transects are explicated, and modifications that preserve design-unbiasedness of Kaiser's (1983) conditional and unconditional estimators are presented. A case against treating multiple intersections as multiple probabilistic events is argued on the basis, also, of preserving design-unbiased estimation.     

长白山区公路对路域植物物种组成及多样性的影响

采用样线法对长白山区公路旁天然次生林和原始阔叶林的植物物种组成及多样性进行调查。分别选取具有代表性的两个试验点,在公路两侧且其垂直走向布设3条相互平行的样线,间隔5m。在样线上布设样点,调查的生态因子包括光强、温度及湿度;样方调查分为灌木和草本样方,分别记录种类、高度、盖度、株数。根据公路两侧生态因子、灌草植物组成及多样性变化情况,分析公路建设的生态影响。结果表明：（1）随着离公路距离的增加,光照、温度、湿度等环境因子呈现规律性变化,距离公路10m的位置是生态因子变化从剧烈到缓和的转折点;（2）公路建设对植物组成产生影响,随着离公路距离的增加,呈现从喜光植物到耐阴植物的变化,0～20m之间是优势种变化较剧烈的范围,而10m之内和20m之外样方之间优势种变化不大;（3）受路域环境因子改变的影响,公路建设对沿线植物的多样性影响包括正负两种,既增加了路域植物的多样性,同时也破坏了原生植被群落的稳定性;（4）从长白山区公路对草本、灌木植物组成及生物多样性影响的范围和程度来看,草本的影响范围超过20m,灌木的影响范围达到10m,影响范围：草本灌木。随着与公路距离的增加,公路对植物组成及多样性的影响程度降低。     

Effects of Detectability on Estimates of Geographic Range Size in Bignonieae

Abstract: Extinction risk has not been evaluated for 96% of all described plant species. Given that the Global Strategy for Plant Conservation proposes preliminary conservation assessments of all described plant species by 2010, herbarium specimens (i.e., primary occurrence data) are increasingly being used to infer threat components from estimates of geographic range size. Nevertheless, estimates of range size based on herbarium data may be inaccurate due to collection bias associated with interspecific variation in detectability. We used data on 377 species of Bignonieae to test the hypothesis that there is a positive relationship between detectability and estimates of geographic range size derived from herbarium specimens. This relationship is expected if the proportion of the true geographic range size of a species that is documented by herbarium specimens is given by the product of the true geographic range size and the detectability of the species, assuming no relationship between true geographic range size and detectability. We developed 4 measures of detectability that can be estimated from herbarium data and examined the relationship between detectability and 2 types of estimates of geographic range size: area of occupancy and extent of occurrence. Our results from regressing estimates of extent of occurrence and area of occupancy on detectability across genera provided no support for this hypothesis. The same was true for regressions of estimated extent of occurrence on detectability across species within genera. Nevertheless, regressions of estimated area of occupancy on detectability across species within genera provided partial support for our hypothesis. We considered 3 possible explanations for this mixed outcome: violation of the assumption of no relationship between true geographic range size and detectability; the relationships between estimated geographic range size and detectability may be an artifact of a negative relationship between estimated area of occupancy and the sampling variance of detectability; detectability may have had 2 opposite effects on estimated species range sizes: one determines the proportion of the true range of a species documented by herbarium specimens and the other determines the distribution of true range size for the species actually observed with herbarium data. Our findings should help improve understanding of the potential biases incurred with the use of herbarium data.     

Estimator bias and efficiency for adaptive cluster sampling with order statistics and a stopping rule

Practical problems facing adaptive cluster sampling with order statistics (acsord) are explored using Monte Carlo simulation for three simulated fish populations and two known waterfowl populations. First, properties of an unbiased Hansen-Hurwitz (HH) estimator and a biased alternative Horvitz-Thompson (HT) estimator are evaluated. An increase in the level of population aggregation or the initial sample size increases the efficiencies of the two acsord estimators. For less aggregated fish populations, the efficiencies decrease as the order statistic parameter r (the number of units about which adaptive sampling is carried out) increases; for the highly aggregated fish and waterfowl populations, they increase with r. Acsord is almost always more efficient than simple random sampling for the highly aggregated populations. Positive bias is observed for the HT estimator, with the maximum bias usually occurring at small values of r. Secondly, a stopping rule at the Sth iteration of adaptive sampling beyond the initial sampling unit was applied to the acsord design to limit the otherwise open-ended sampling effort. The stopping rule induces relatively high positive bias to the HH estimator if the level of the population aggregation is high, the stopping level S is small, and r is large. The bias of HT is not very sensitive to the stopping rule and its bias is often reduced by the stopping rule at smaller values of r. For more aggregated populations, the stopping rule often reduces the efficiencies of the estimators compared to the non-stopping-rule scheme, but acsord still remains more efficient than simple random sampling. Despite its bias and lack of theoretical grounding, the HT estimator is usually more efficient than the HH estimator. In the stopping rule case, the HT estimator is preferable, because its bias is less sensitive to the stopping level.     

Best linear unbiased estimators for the simple linear regression model using ranked set sampling

When sample observations are expensive or difficult to obtain, ranked set sampling is known to be an efficient method for estimating the population mean, and in particular to improve on the sample mean estimator. Using best linear unbiased estimators, this paper considers the simple linear regression model with replicated observations. Use of a form of ranked set sampling is shown to be markedly more efficient for normal data when compared with the traditional simple linear regression estimators.     

Random versus stratified location of transects or points in distance sampling: theoretical results and practical considerations

A composite approach mixing design-based and model-based inference is considered for analyzing line-transect or point-transect data. In this setting, the properties of the animal abundance estimator stem from the sampling scheme adopted to locate transects or points on the study region, as well as from the modeled detection probabilities. Moreover, the abundance estimation can be viewed as a “generalized” version of Monte Carlo integration. This approach permits to prove the superiority of the stratified placement of transects or points (based on a regular tessellation of the study region) over the uniform random placement. Even if the result was already established for the fixed-area sampling, i.e., when a perfect detection takes place, it was lacking in distance sampling. Comparisons with other widely-applied schemes pursuing an even placement of transects or points are also considered.     

Statistical inference using stratified judgment post-stratified samples from finite populations

This paper develops statistical inference for population mean and total using stratified judgment post-stratified (SJPS) samples. The SJPS design selects a judgment post-stratified sample from each stratum. Hence, in addition to stratum structure, it induces additional ranking structure within stratum samples. SJPS is constructed from a finite population using either a with or without replacement sampling design. Inference is constructed under both randomization theory and a super population model. In both approaches, the paper shows that the estimators of population mean and total are unbiased. The paper also constructs unbiased estimators for the variance (mean square prediction error) of the sample mean (predictor of population mean), and develops confidence and prediction intervals for the population mean. The empirical evidence shows that the proposed estimators perform better than their competitors in the literature.     

Site‐Occupancy Distribution Modeling to Correct Population‐Trend Estimates Derived from Opportunistic Observations

Abstract: Species’ assessments must frequently be derived from opportunistic observations made by volunteers (i.e., citizen scientists). Interpretation of the resulting data to estimate population trends is plagued with problems, including teasing apart genuine population trends from variations in observation effort. We devised a way to correct for annual variation in effort when estimating trends in occupancy (species distribution) from faunal or floral databases of opportunistic observations. First, for all surveyed sites, detection histories (i.e., strings of detection–nondetection records) are generated. Within‐season replicate surveys provide information on the detectability of an occupied site. Detectability directly represents observation effort; hence, estimating detectablity means correcting for observation effort. Second, site‐occupancy models are applied directly to the detection‐history data set (i.e., without aggregation by site and year) to estimate detectability and species distribution (occupancy, i.e., the true proportion of sites where a species occurs). Site‐occupancy models also provide unbiased estimators of components of distributional change (i.e., colonization and extinction rates). We illustrate our method with data from a large citizen‐science project in Switzerland in which field ornithologists record opportunistic observations. We analyzed data collected on four species: the widespread Kingfisher (Alcedo atthis) and Sparrowhawk (Accipiter nisus) and the scarce Rock Thrush (Monticola saxatilis) and Wallcreeper (Tichodroma muraria). Our method requires that all observed species are recorded. Detectability was <1 and varied over the years. Simulations suggested some robustness, but we advocate recording complete species lists (checklists), rather than recording individual records of single species. The representation of observation effort with its effect on detectability provides a solution to the problem of differences in effort encountered when extracting trend information from haphazard observations. We expect our method is widely applicable for global biodiversity monitoring and modeling of species distributions.     

Effects of sampling error and temporal correlations in population growth on process variance estimators

Estimates of a population’s growth rate and process variance from time-series data are often used to calculate risk metrics such as the probability of quasi-extinction, but temporal correlations in the data from sampling error, intrinsic population factors, or environmental conditions can bias process variance estimators and detrimentally affect risk predictions. It has been claimed (McNamara and Harding, Ecol Lett 7:16–20, 2004) that estimates of the long-term variance that incorporate observed temporal correlations in population growth are unaffected by sampling error; however, no estimation procedures were proposed for time-series data. We develop a suite of such long-term variance estimators, and use simulated data with temporally autocorrelated population growth and sampling error to evaluate their performance. In some cases, we get nearly unbiased long-term variance estimates despite ignoring sampling error, but the utility of these estimators is questionable because of large estimation uncertainty and difficulties in estimating correlation structure in practice. Process variance estimators that ignored temporal correlations generally gave more precise estimates of the variability in population growth and of the probability of quasi-extinction. We also found that the estimation of probability of quasi-extinction was greatly improved when quasi-extinction thresholds were set relatively close to population levels. Because of precision concerns, we recommend using simple models for risk estimates despite potential biases, and limiting inference to quantifying relative risk; e.g., changes in risk over time for a single population or comparative risk among populations.     

Factors affecting aural detections of songbirds.

Many factors affect the number of birds detected on point count surveys of breeding songbirds. The magnitude and importance of these factors are not well understood. We used a bird song simulation system to quantify the effects of detection distance, singing rate, species differences, and observer differences on detection probabilities of birds detected by ear. We simulated 40 point counts consisting of 10 birds per count for five primary species (Black-and-white Warbler Mniotilta varia, Black-throated Blue Warbler Dendroica caerulescens, Black-throated Green Warbler Dendroica virens, Hooded Warbler Wilsonia citrina, and Ovenbird Seiurus aurocapillus) over a range of 15 distances (34-143 m). Songs were played at low (two songs per count) and high (13-21 songs per count) singing rates. Detection probabilities averaged across observers ranged from 0.60 (Black-and-white Warbler) to 0.83 (Hooded Warbler) at the high singing rate and 0.41 (Black-and-white Warbler) to 0.67 (Hooded Warbler) at the low singing rate. Logistic regression analyses indicated that species, singing rate, distance, and observer were all significant factors affecting detection probabilities. Singing rate x species and singing rate X distance interactions were also significant. Simulations of expected counts, based on the best logistic model, indicated that observers detected between 19% (for the worst observer, lowest singing rate, and least detectable species) and 65% (for the best observer, highest singing rate, and most detectable species) of the true population. Detection probabilities on actual point count surveys are likely to vary even more because many sources of variability were controlled in our experiments. These findings strongly support the importance of adjusting measures of avian diversity or abundance from auditory point counts with direct estimates of detection probability.     

Estimation of small woodlot and tree row attributes in large-scale forest inventories

Forest surveys performed over a large scale (e.g. national inventories) involve several phases of sampling. The first phase is usually performed by means of a systematic search of the study region, in which the region is partitioned into regular polygons of the same size and points are randomly or systematically selected, one per polygon. In most cases, first-phase points are selected and recognized in orthophotos or very high resolution satellite images available for the whole study area. Disregarding the subsequent phases, the first phase of sampling can be effectively adopted to select small woodlots and tree rows, in the sense that a unit is selected when at least one first-phase point falls within it. On the basis of such a scheme of sampling, approximately unbiased estimators of abundance, coverage and other physical attributes readily measurable from orthophotos (e.g. tree-row length) are proposed, together with estimators of the corresponding variances. A simulation study is performed in order to check the performance of the estimators under several distributions of units over the study area (random, clustered, spatially trended).     

Cross-validation of species distribution models: removing spatial sorting bias and calibration with a null model

Species distribution models are usually evaluated with cross-validation. In this procedure evaluation statistics are computed from model predictions for sites of presence and absence that were not used to train (fit) the model. Using data for 226 species, from six regions, and two species distribution modeling algorithms (Bioclim and MaxEnt), I show that this procedure is highly sensitive to "spatial sorting bias": the difference between the geographic distance from testing-presence to training-presence sites and the geographic distance from testing-absence (or testing-background) to training-presence sites. I propose the use of pairwise distance sampling to remove this bias, and the use of a null model that only considers the geographic distance to training sites to calibrate cross-validation results for remaining bias. Model evaluation results (AUC) were strongly inflated: the null model performed better than MaxEnt for 45% and better than Bioclim for 67% of the species. Spatial sorting bias and area under the receiver-operator curve (AUC) values increased when using partitioned presence data and random-absence data instead of independently obtained presence-absence testing data from systematic surveys. Pairwise distance sampling removed spatial sorting bias, yielding null models with an AUC close to 0.5, such that AUC was the same as null model calibrated AUC (cAUC). This adjustment strongly decreased AUC values and changed the ranking among species. Cross-validation results for different species are only comparable after removal of spatial sorting bias and/or calibration with an appropriate null model.