Evaluation of aerial sampling methods for detecting waterbird colonies

ABSTRACT Estimating the number of waterbird colonies in a given area can have important conservation implications, including assessment of the regional or global importance of an area and the impacts of conservation efforts (e.g., habitat restoration) and human disturbance (e.g., oil spills). Our objective was to examine differences in estimates of the number of waterbird colonies determined using strip‐transect (ST) surveys, distance sampling, and adaptive cluster sampling (ACS), and to compare these estimates to the minimum number of known colonies (MNKC) obtained using point‐to‐point surveys. We conducted aerial surveys in May 2004 and May and June 2005 at two sites in southern Louisiana: the Atchafalaya Basin (AB), a large forested wetland, and the Barataria‐Terrebonne estuary (BTE), a large coastal marsh with isolated clumps of woody vegetation suitable for nesting. In AB, we detected nine and eight colonies using the ACS and ST/distance sampling methods, respectively. Neither ACS estimator of number of colonies (Horvitz–Thompson and Hansen–Hurwitz) was within the 95% confidence interval of the estimate determined from ST; ST estimated—two to three times more colonies than either ACS estimator. The MNKC for the AB was 33, well within the 95% confidence interval of ? by ST sampling. For the BTE, ACS estimators (?_HT= 20.49, CI = 9.3–31.7; ?_HH= 14.15, CI = 2.3–26.0) were similar to the MNKC (20), whereas the ST (?= 87.94, CI = 82.9–92.9) and distance sampling (?= 60, CI = 31–113) methods produced much larger estimates. Our results suggest that the ACS method performed better when waterbird colonies were spatially clumped (BTE) and the ST method performed better in areas where colonies were more uniformly distributed (AB). Depending on management objectives, a complete, systematic survey of a study area may be required if the potential for missing large colonies is unacceptable. If surveying an area with no previous information about colony location or dispersion, we recommend a coarse‐scale analysis of the availability and contiguity of habitat likely to contain waterbird colonies; this analysis will help determine the most appropriate survey method.     

Nondestructive, Stereological Estimation of Canopy Surface Area

Summary .  We describe a stereological procedure to estimate the total leaf surface area of a plant canopy in vivo, and address the problem of how to predict the variance of the corresponding estimator. The procedure involves three nested systematic uniform random sampling stages: (i) selection of plants from a canopy using the  smooth fractionator , (ii) sampling of leaves from the selected plants using the  fractionator , and (iii) area estimation of the sampled leaves using  point counting . We apply this procedure to estimate the total area of a chrysanthemum ( Chrysanthemum morifolium L. ) canopy and evaluate both the time required and the precision of the estimator. Furthermore, we compare the precision of point counting for three different grid intensities with that of several standard leaf area measurement techniques. Results showed that the precision of the plant leaf area estimator based on point counting is high. Using a grid intensity of 1.76 cm²/point we estimated plant and canopy surface areas with accuracies similar to or better than those obtained using image analysis and a commercial leaf area meter. For canopy surface areas of approximately 1 m² (10 plants), the fractionator leaf approach with sampling fraction equal to 1/9 followed by point counting using a 4.3 cm²/point grid produced a coefficient of error of less than 7%. The  smooth fractionator  can be used to ensure that the additional contribution to the estimator variance due to between-plant variability is small.     

Variance estimation for systematic designs in spatial surveys

Summary In spatial surveys for estimating the density of objects in a survey region, systematic designs will generally yield lower variance than random designs. However, estimating the systematic variance is well known to be a difficult problem. Existing methods tend to overestimate the variance, so although the variance is genuinely reduced, it is over‐reported, and the gain from the more efficient design is lost. The current approaches to estimating a systematic variance for spatial surveys are to approximate the systematic design by a random design, or approximate it by a stratified design. Previous work has shown that approximation by a random design can perform very poorly, while approximation by a stratified design is an improvement but can still be severely biased in some situations. We develop a new estimator based on modeling the encounter process over space. The new “striplet” estimator has negligible bias and excellent precision in a wide range of simulation scenarios, including strip‐sampling, distance‐sampling, and quadrat‐sampling surveys, and including populations that are highly trended or have strong aggregation of objects. We apply the new estimator to survey data for the spotted hyena (Crocuta crocuta) in the Serengeti National Park, Tanzania, and find that the reported coefficient of variation for estimated density is 20% using approximation by a random design, 17% using approximation by a stratified design, and 11% using the new striplet estimator. This large reduction in reported variance is verified by simulation.     

An estimator of number of species from quadrat sampling

We consider the problem of estimating the number of distinct species S in a study area from the recorded presence or absence of species in each of a sample of quadrats. A generalized jackknife estimator of S is derived, along with an estimate of its variance. It is compared with the jackknife estimator for S proposed by Heltshe and Forrester and the empirical Bayes estimator of Mingoti and Meeden. We show that the empirical Bayes estimator has the form of a generalized jackknife estimator under a specific model for species distribution. We compare the new estimators of S to the empirical Bayes estimator via simulation. We characterize circumstances under which each is superior.     

Proportionate spatial sampling and equal‐time sampling of mobile animals: A dilemma for inferring areal dependence

Abstract Patch or island area is one of the most frequently used variables for inference in conservation biology and biogeography, and is often used in ecological applications. Given that all of these disciplines deal with large spatial scales, exhaustive censusing is not often possible, especially when there are large numbers of patches (e.g. for replication and control purposes). Therefore, data for patches or islands are usually collected by sampling. We argue that if area is to be used as an inferential factor, then the objects under study (i.e. the patches) must be characterized on an areal basis. This necessarily means that fixed‐area sampling is inadequate (e.g. a single standard quadrat or transect set within patches irrespective of the patch area) and that some form of area‐proportionate sampling is needed (e.g. a fixed areal proportion of each patch is surveyed by random allocation of standard quadrats across each patch). However, use of area‐proportionate sampling is not usually dissociated from the increased temporal intensity of sampling that arises from using this approach. The dilemma we see is deciding how much of the area‐specificity of variables such as species richness, rare‐species indices or probabilities of occurrence of individual species is related to the area‐proportionate survey protocol and how much is due to the temporal intensity of surveys. We undertook a study in which we balanced temporal and spatial effects by increasing the time spent surveying smaller patches of vegetation to account for the area‐ratio difference. The estimated species richness of birds of the box–ironbark system of central Victoria, Australia, was found to depend strongly upon area when area‐proportionate sampling alone was performed. When time‐balancing was imposed upon area‐proportionate sampling, the differences between smaller (10‐ha) and larger (40‐ha) areas were much reduced or effectively disappeared. We show that species found in the additional surveys used to conduct the time‐balancing were significantly less abundant than species recorded in area‐proportionate sampling. This effect is probably most severe for mobile animals, but may emerge in other forms of sampling.     

The net result: evaluating species richness extrapolation techniques for littoral pond invertebrates

1. Total species richness for an assemblage or site is a valuable measure in conservation monitoring and assessment, but protocols for sampling and species richness determination in wetland habitats such as ponds, bogs or mires remain largely unrefined. 2. Techniques for estimation of total richness of an assemblage based upon replicated sampling offer the opportunity to derive useful estimates of total richness based upon small numbers of samples, and limit sampling‐derived disturbance which can be particularly problematic in small aquatic habitats. 3. We quantified the performance of eight of the most commonly encountered estimators of species richness for a variety of littoral zone macrofauna from ponds, comparing estimated richness to maximum richness derived from sampling. 4. Estimates using non‐parametric techniques based on species incidence provided the most accurate and precise estimates. The estimators Chao 2 and incidence‐based coverage estimator (ICE) from this category were reliable and consistent slight over‐estimators; the abundance‐based estimator Chao1 also performed well. 5. Species inventory based on relatively small numbers of samples might be significantly improved by use of non‐parametric estimators for quantification of species richness. 6. Use of non‐parametric estimators of species richness can assist biodiversity inventory by preventing erroneous rankings of habitat richness based upon observed species numbers from limited sampling.     

Five Confidence Intervals of the Closed Population Size in the Capture‐recapture Problem under Inverse Sampling with Replacement

In the capture‐recapture problem for two independent samples, the traditional estimator, calculated as the product of the two sample sizes divided by the number of sampled subjects appearing commonly in both samples, is well known to be a biased estimator of the population size and have no finite variance under direct or binomial sampling. To alleviate these theoretical limitations, the inverse sampling, in which we continue sampling subjects in the second sample until we obtain a desired number of marked subjects who appeared in the first sample, has been proposed elsewhere. In this paper, we consider five interval estimators of the population size, including the most commonly‐used interval estimator using Wald's statistic, the interval estimator using the logarithmic transformation, the interval estimator derived from a quadratic equation developed here, the interval estimator using the χ²‐approximation, and the interval estimator based on the exact negative binomial distribution. To evaluate and compare the finite sample performance of these estimators, we employ Monte Carlo simulation to calculate the coverage probability and the standardized average length of the resulting confidence intervals in a variety of situations. To study the location of these interval estimators, we calculate the non‐coverage probability in the two tails of the confidence intervals. Finally, we briefly discuss the optimal sample size determination for a given precision to minimize the expected total cost. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐Parametric Selected Ranked Set Sampling

A nonparametric selected ranked set sampling is suggested. The estimator of population mean based on the new approach is compared with that using the simple random sampling (SRS), the ranked set sampling (RSS) and the median ranked set sampling (MRSS) methods. The estimator of population mean using the new approach is found to be more efficient than its counter‐parts for almost all the cases considered.     

Robustness of an S‐Estimator in the One‐Way Random Effects Model

An S‐estimator is defined for the one‐way random effects model, analogous to an S‐estimator in the model of i.i.d. random vectors. The estimator resembles the multivariate S‐estimator with respect to existence and weak continuity. The proof of existence of the estimator yields in addition an upper bound for the breakdown point of the S‐estimator of one of the variance components which is rather low. An improvement of the estimator is proposed which overcomes this deficiency. Nevertheless this estimator is an example that new problems of robustness arise in more structured models.     

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.     

Regression on Quantile Residual Life

Summary A time‐specific log‐linear regression method on quantile residual lifetime is proposed. Under the proposed regression model, any quantile of a time‐to‐event distribution among survivors beyond a certain time point is associated with selected covariates under right censoring. Consistency and asymptotic normality of the regression estimator are established. An asymptotic test statistic is proposed to evaluate the covariate effects on the quantile residual lifetimes at a specific time point. Evaluation of the test statistic does not require estimation of the variance–covariance matrix of the regression estimators, which involves the probability density function of the survival distribution with censoring. Simulation studies are performed to assess finite sample properties of the regression parameter estimator and test statistic. The new regression method is applied to a breast cancer data set with long‐term follow‐up to estimate the patients' median residual lifetimes, adjusting for important prognostic factors.     

Small‐Sample Estimation of Species Richness Applied to Forest Communities

Summary Many well‐known methods are available for estimating the number of species in a forest community. However, most existing methods result in considerable negative bias in applications, where field surveys typically represent only a small fraction of sampled communities. This article develops a new method based on sampling with replacement to estimate species richness via the generalized jackknife procedure. The proposed estimator yields small bias and reasonably accurate interval estimation even with small samples. The performance of the proposed estimator is compared with several typical estimators via simulation study using two complete census datasets from Panama and Malaysia.     

Time‐dependent classification accuracy curve under marker‐dependent sampling

Evaluating the classification accuracy of a candidate biomarker signaling the onset of disease or disease status is essential for medical decision making. A good biomarker would accurately identify the patients who are likely to progress or die at a particular time in the future or who are in urgent need for active treatments. To assess the performance of a candidate biomarker, the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are commonly used. In many cases, the standard simple random sampling (SRS) design used for biomarker validation studies is costly and inefficient. In order to improve the efficiency and reduce the cost of biomarker validation, marker‐dependent sampling (MDS) may be used. In a MDS design, the selection of patients to assess true survival time is dependent on the result of a biomarker assay. In this article, we introduce a nonparametric estimator for time‐dependent AUC under a MDS design. The consistency and the asymptotic normality of the proposed estimator is established. Simulation shows the unbiasedness of the proposed estimator and a significant efficiency gain of the MDS design over the SRS design.     

Ranked Set Sampling and the Line Intercept Method: A More Efficient Procedure

Ranked set sampling is a method which may be used to increase the efficiency of the estimator of the mean of a population. Ranked set sampling with size biased probability of selection (i.e., the items are selected with probability proportion to its size) is combined with the line intercept method to increase the efficency of estimating cover, density and total amount of some variable of interest (e.g. biomass). A two-stage sampling plan is suggested with line intercept sampling in the first stage. Simple random sampling and ranked set sampling are compared in the second stage to show that the unbiased estimators of density, cover and total amount of some variable of interest based on ranked set sampling have smaller variances than the usual unbiased estimator based on simple random sampling. Efficiency is increased by reducing the number of items which are measured on a transect or by increasing the number of independent transects utilized in a study area. An application procedure is given for estimation of coverage, density and number of stems of mountain mahogany (Cercocarpus montanus) in a study area east of Laramie, Wyoming.     

Estimating the distribution of a renewal process from times at which events from an independent process are detected

The analysis of length-biased data has been mostly limited to the interarrival interval of a renewal process covering a specific time point. Motivated by a surveillance problem, we consider a more general situation where this time point is random and related to a specific event, for example, status change or onset of a disease. We also consider the problem when additional information is available on whether the event intervals (interarrival intervals covering the random event) end within or after a random time period (which we call a window period) following the random event. Under the assumptions that the occurrence rate of the random event is low and the renewal process is independent of the random event, we provide formulae for the estimation of the distribution of interarrival times based on the observed event intervals. Procedures for testing the required assumptions are also furnished. We apply our results to human immunodeficiency virus (HIV) test data from public test sites in Seattle, Washington, where the random event is HIV infection and the window period is from the onset of HIV infection to the time at which a less sensitive HIV test becomes positive. Results show that the estimator of the intertest interval length distribution from event intervals ending within the window period is less biased than the estimator from all event intervals; the latter estimator is affected by right truncation. Finally, we discuss possible applications to estimating HIV incidence and analyzing length-biased samples with right or left truncated data.     

Monitoring and assessing old‐growth forest stands by plot sampling

Abstract

Forest inventories are evolving towards multipurpose resource surveys, broadening their scope by including additional topics such as biodiversity issues. Surprisingly, few quantitative surveys have been devoted to old‐growth forests, even if they constitute the most acknowledged forest biodiversity icons. In this framework, the use of probabilistic sampling may provide an effective as well as rigorous support for monitoring and assessing old‐growth forests. To this purpose, the present paper proposes a two‐phase sampling scheme. In the first phase, a coarse survey of few floristic and stand structural attributes is carried out by means of small plots systematically placed on the study area. Subsequently, in the second phase, a fine assessment of a large number of ecological attributes is performed on a subset of enlarged plots selected among the first‐phase ones by means of simple random sampling without replacement. The proposed sampling scheme is implemented for monitoring and assessing the old forests of Cilento National Park (southern Italy). Results and comments are provided as an exemplicative case study.     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.     

Testing Markovianity in the three‐state progressive model via future‐past association

The three‐state progressive model is a special multi‐state model with important applications in Survival Analysis. It provides a suitable representation of the individual’s history when an intermediate event (with a possible influence on the survival prognosis) is experienced before the main event of interest. Estimation of transition probabilities in this and other multi‐state models is usually performed through the Aalen–Johansen estimator. However, Aalen–Johansen may be biased when the underlying process is not Markov. In this paper, we provide a new approach for testing Markovianity in the three‐state progressive model. The new method is based on measuring the future‐past association along time. This results in a deep inspection of the process that often reveals a non‐Markovian behaviour with different trends in the association measure. A test of significance for zero future‐past association at each time point is introduced, and a significance trace is proposed accordingly. The finite sample performance of the test is investigated through simulations. We illustrate the new method through real data analysis.     

On Double Sampling Ratio-Cum-Product-Type Estimator with Independent Samples

There are two cases in double sampling; case(i) when the second sample is a sub-sample from preliminary large sample, and case(ii) when the second sample is not a sub-sample from the preliminary large sample. Recently SISODIA and DWIVEDI (1981) proposed a ratio cum product-type estimator in double sampling in which they have studied the properties of this estimator under case (i). In this paper, we have made an attempt to study the properties of the same estimator under case (ii). It is found that the estimator is superior than double sampling linear regression estimator, usual ratio estimator, product estimator and among others. The estimator is also compared with simple mean per unit for a given cost of the survey.