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.     

二化螟种群密度的克力格估值及其模拟抽样

为设计可靠合理的二化螟幼虫种群密度抽样方案,从二化螟幼虫空间分布原始总体出发,另构建了一个随机总体和一个顺序总体,采用无放回随机抽样、间隔变程以上无放回随机抽样和基于克力格估值且初始点随机的顺序抽样对3总体进行了模拟抽样比较．结果表明,间隔变程以上随机抽样对原始总体平均数的估计优于随机抽样,且随总体聚集程度增加,间隔变程以上随机抽样愈优;正确识别种群空间格局极为重要,对聚集分布总体采用随机抽样和对随机分布总体采用间隔变程以上随机抽样均将降低抽样估计精度．针对随机抽样在应用上的局限性,提出了一种基于地统计学克力格估值、初始点随机的顺序抽样方案：它以初始点随机保证随机性,以顺序抽样保证可操作性,以二化螟种群空间分布的区域变量属性保证克力格样本较调查样本对局域样本和总体的平均数估计为优;且聚集范围一定时,总体聚集强度愈大,克力格样本局域估计和全局估计愈优于调查样本;取样间隔(以变程为标准)极为重要,样方的空间布局要平衡考虑相互独立的样方对数和变程范围内的样方对数。     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model, p=1−(1+m/k)^−k, and the empirical model, p=1−exp(−am^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

A new method of sequential sampling to obtain the population estimates with a fixed level of precision

A simple method of sequential sampling is developed which would make it automatically possible to secure, without excess sampling, a predetermined level of precision for a series of population estimates being required. It appears to have wide application to sampling field populations under various situations since it is simply based upon the relationship of variance to mean for which a comprehensive formula deduced for biological populations from the linearity in the regression of mean crowding on mean density could be adopted. Some problems that may arise in practical application of the method are also discussed.     

A sequential estimation technique for capture-recapture censuses

Summary A simple technique of sequential estimation was proposed for capture-recapture census by thePetersen method. In theory this technique makes it possible to secure automatically a required precision level for the population estimate to be obtained, irrespective of the population size. Some problems about its practical application were discussed. This study was supported by science research fund from the Ministry of Education.     

Median estimation of chemical constituents for sampling on two occasions under a log‐normal model

Sampling from a finite population on multiple occasions introduces dependencies between the successive samples when overlap is designed. Such sampling designs lead to efficient statistical estimates, while they allow estimating changes over time for the targeted outcomes. This makes them very popular in real‐world statistical practice. Sampling with partial replacement can also be very efficient in biological and environmental studies where estimation of toxicants and its trends over time is the main interest. Sampling with partial replacement is designed here on two occasions in order to estimate the median concentration of chemical constituents quantified by means of liquid chromatography coupled with tandem mass spectrometry. Such data represent relative peak areas resulting from the chromatographic analysis. They are therefore positive‐valued and skewed data, and are commonly fitted very well by the log‐normal model. A log‐normal model is assumed here for chemical constituents quantified in mainstream cigarette smoke in a real case study. Combining design‐based and model‐based approaches for statistical inference, we seek for the median estimation of chemical constituents by sampling with partial replacement on two time occasions. We also discuss the limitations of extending the proposed approach to other skewed population models. The latter is investigated by means of a Monte Carlo simulation study.     

A sequential estimation technique for capture-recapture censuses

A simple technique of sequential estimation was proposed for capture-recapture census by thePetersen method. In theory this technique makes it possible to secure automatically a required precision level for the population estimate to be obtained, irrespective of the population size. Some problems about its practical application were discussed.     

How reliable are our vegetation analyses?

Abstract. Two sets of 40 relevés, made independently by two observers on the same 5m x 5m sample plots, were compared to estimate the sampling error and to assess the effect of this sampling error on (1) estimates of species richness and diversity (2) results of multivariate analyses, and (3) estimation of species turnover in repeated sampling. The relevés were made according to the standard Braun-Blanquet method. The sampling error was estimated for (1) recording of species in sample plots and (2) visual estimation of the degree of cover (or of the general population size). Despite the fact that the sample plots were searched thoroughly for 30 - 40 min, the number of overlooked species was high with a discrepancy of 13% between corresponding relevés. Regarding multivariate analysis, the error caused by missing species was at least as important as the error in visual estimation of species cover. The estimates of degree of cover using the Braun-Blanquet scale are sufficiently reliable for use in multivariate analysis when they are subjected to ordinal transformation. When average cover values are used, the patterns detected are based solely on dominants. Species richness and species diversity could be reliably estimated from the relevés, but the estimates of equitability are very unreliable. The classical relevé method remains one of the most efficient survey methods for recognition of vegetation types on the macro-community and landscape scales.     

大中型兽类种群数量估算的研究进展

大中型兽类种群数量的估算是动物生态学中重要的基本问题, 受到研究者、管理者和公众的共同关注。国际上从20世纪中期开始研究该问题, 已出现了多种研究方法和相应案例, 且还在快速发展, 但世界各地仍有很多物种的种群数量尚未知晓。在我国, 从20世纪80年代开始调查大中型兽类种群数量, 取得了重要进展, 也还有很多物种的种群数量尚不清楚。因此, 有必要归纳国际上种群数量估算的研究进展, 同时, 总结国内研究的现状、优势和趋势, 供研究者参考。本文首先选择估算大中型兽类种群数量的原理、数据来源和模型这3个要素归纳出简明的研究框架, 将现有的多种方法置于其中予以阐述。在该框架下, 根据估算原理分为4大类方法, 为距离取样法、标志重捕法、基于遇见率法和遥感影像直接计数法。针对每一大类方法, 论述其基本原理模型和模型假设, 说明能实现该原理的相应数据来源(视觉观测、红外相机拍摄、DNA微卫星识别、卫星定位跟踪、声音监测或遥感影像)的特点及如何实现该原理, 评价其适用性及优缺点, 并选择其中具有可比性的方法予以比较评价。其次, 参照该研究框架, 总结我国的研究现状, 分析未来发展的优势和趋势: 我国的红外相机数据积累充分, 可以发展以此为数据源的距离取样法、标志重捕法和基于遇见率法; 发展以粪便样品为数据来源的距离取样法和粪便DNA标志重捕法; 相比地面调查数据, 获取高分辨率遥感影像数据更容易, 尽量以此估算符合适用条件的大中型兽类的种群数量。最后, 本文提出了适用于我国大中型兽类种群数量的估算方法的选择流程, 供研究者参考。     

Performance of sampling strategies in the presence of known spatial patterns

In crop protection and ecology accurate and precise estimates of insect populations are required for many purposes. The spatial pattern of the organism sampled, in relation to the sampling scheme adopted, affects the difference between the actual and estimated population density, the bias, and the variability of that estimate, the precision. Field monitoring schemes usually adopt time‐efficient sampling regimes involving contiguous units rather than the most efficient for estimation, the completely random sample. This paper uses spatially‐explicit ecological field data on aphids and beetles to compare common sampling regimes. The random sample was the most accurate method and often the most precise; of the contiguous schemes the line transect was superior to more compact arrangements such as a square block. Bias depended on the relationship between the size and shape of the group of units comprising the sample and the dominant cluster size underlying the spatial pattern. Existing knowledge of spatial pattern to inform the choice of sampling scheme may provide considerable improvements in accuracy. It is recommended to use line transects longer than the grain of the spatial pattern, where grain is defined as the average dimension of clusters over both patches and gaps, and with length at least twice the dominant cluster size.     

Why sampling scheme matters: the effect of sampling scheme on landscape genetic results

There has been a recent trend in genetic studies of wild populations where researchers have changed their sampling schemes from sampling pre-defined populations to sampling individuals uniformly across landscapes. This reflects the fact that many species under study are continuously distributed rather than clumped into obvious “populations”. Once individual samples are collected, many landscape genetic studies use clustering algorithms and multilocus genetic data to group samples into subpopulations. After clusters are derived, landscape features that may be acting as barriers are examined and described. In theory, if populations were evenly sampled, this course of action should reliably identify population structure. However, genetic gradients and irregularly collected samples may impact the composition and location of clusters. We built genetic models where individual genotypes were either randomly distributed across a landscape or contained gradients created by neighbor mating for multiple generations. We investigated the influence of six different sampling protocols on population clustering using program STRUCTURE, the most commonly used model-based clustering method for multilocus genotype data. For models where individuals (and their alleles) were randomly distributed across a landscape, STRUCTURE correctly predicted that only one population was being sampled. However, when gradients created by neighbor mating existed, STRUCTURE detected multiple, but different numbers of clusters, depending on sampling protocols. We recommend testing for fine scale autocorrelation patterns prior to sample clustering, as the scale of the autocorrelation appears to influence the results. Further, we recommend that researchers pay attention to the impacts that sampling may have on subsequent population and landscape genetic results. The U.S. Government's right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Efficient regression analysis with ranked-set sampling

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.     

A new method of sequential sampling to classify populations relative to a critical density

A method of sequential sampling for grading population level in relation to a critical density is proposed. The method is based on the relationship and can be used without restrictions on the distribution patterns. The formulae for simple random sampling as well as for two-stage sampling are given.     

Good–Turing frequency estimation in a finite population

Good–Turing frequency estimation (Good, 1953 ) is a simple, effective method for predicting detection probabilities of objects of both observed and unobserved classes based on observed frequencies of classes in a sample. The method has been used widely in several disciplines, such as information retrieval, computational linguistics, text recognition, and ecological diversity estimation. Nevertheless, existing studies assume sampling with replacement or sampling from an infinite population, which might be inappropriate for many practical applications. In light of this limitation, this article presents a modification of the Good–Turing estimation method to account for finite population sampling. We provide three practical extensions of the modified method, and we examine performance of the modified method and its extensions in simulation experiments.     

Confidence Intervals for Population Allele Frequencies: The General Case of Sampling from a Finite Diploid Population of Any Size

The estimation of population allele frequencies using sample data forms a central component of studies in population genetics. These estimates can be used to test hypotheses on the evolutionary processes governing changes in genetic variation among populations. However, existing studies frequently do not account for sampling uncertainty in these estimates, thus compromising their utility. Incorporation of this uncertainty has been hindered by the lack of a method for constructing confidence intervals containing the population allele frequencies, for the general case of sampling from a finite diploid population of any size. In this study, we address this important knowledge gap by presenting a rigorous mathematical method to construct such confidence intervals. For a range of scenarios, the method is used to demonstrate that for a particular allele, in order to obtain accurate estimates within 0.05 of the population allele frequency with high probability (%), a sample size of is often required. This analysis is augmented by an application of the method to empirical sample allele frequency data for two populations of the checkerspot butterfly (Melitaea cinxia L.), occupying meadows in Finland. For each population, the method is used to derive % confidence intervals for the population frequencies of three alleles. These intervals are then used to construct two joint % confidence regions, one for the set of three frequencies for each population. These regions are then used to derive a % confidence interval for Jost''s D, a measure of genetic differentiation between the two populations. Overall, the results demonstrate the practical utility of the method with respect to informing sampling design and accounting for sampling uncertainty in studies of population genetics, important for scientific hypothesis-testing and also for risk-based natural resource management.     

土壤养分循环实地采样调查方法

讨论了一种在区域尺度上研究生态系统中土壤养分循环的样区采样及调查方法.即在满足土壤养分循环研究所要求的代表性、重现性、随机性及时间性等原则的基础上,利用地形图及航空照片等资料,在区域中选定合适面积和数量的样区后,在各样区内按统一标准采集土壤和植物样品.考虑区域土壤养分循环受自然环境条件和社会经济条件等因素的制约,野外采样过程中有必要对采样单元的实地情况进行调查记载,并就样区内所有农户的基本状况、种植业结构及肥料投入等有关土壤养分循环的影响因子进行农户调查.对我国亚热带农业生态系统中土壤养分循环进行了案例研究,探讨了该采样调查方法在土壤养分循环研究中的应用.     

Reviewing population studies for forensic purposes: Dog?mitochondrial DNA

The identification of dog hair through mtDNA analysis has become increasingly important in the last 15 years, as it can provide associative evidence connecting victims and suspects. The evidential value of an mtDNA match between dog hair and its potential donor is determined by the random match probability of the haplotype. This probability is based on the haplotype’s population frequency estimate. Consequently, implementing a population study representative of the population relevant to the forensic case is vital to the correct evaluation of the evidence. This paper reviews numerous published dog mtDNA studies and shows that many of these studies vary widely in sampling strategies and data quality. Therefore, several features influencing the representativeness of a population sample are discussed. Moreover, recommendations are provided on how to set up a dog mtDNA population study and how to decide whether or not to include published data. This review emphasizes the need for improved dog mtDNA population data for forensic purposes, including targeting the entire mitochondrial genome. In particular, the creation of a publicly available database of qualitative dog mtDNA population studies would improve the genetic analysis of dog traces in forensic casework.     

Evaluation of several methods for estimating phylogenetic trees when substitution rates differ over nucleotide sites

Several maximum likelihood and distance matrix methods for estimating phylogenetic trees from homologous DNA sequences were compared when substitution rates at sites were assumed to follow a gamma distribution. Computer simulations were performed to estimate the probabilities that various tree estimation methods recover the true tree topology. The case of four species was considered, and a few combinations of parameters were examined. Attention was applied to discriminating among different sources of error in tree reconstruction, i.e., the inconsistency of the tree estimation method, the sampling error in the estimated tree due to limited sequence length, and the sampling error in the estimated probability due to the number of simulations being limited. Compared to the least squares method based on pairwise distance estimates, the joint likelihood analysis is found to be more robust when rate variation over sites is present but ignored and an assumption is thus violated. With limited data, the likelihood method has a much higher probability of recovering the true tree and is therefore more efficient than the least squares method. The concept of statistical consistency of a tree estimation method and its implications were explored, and it is suggested that, while the efficiency (or sampling error) of a tree estimation method is a very important property, statistical consistency of the method over a wide range of, if not all, parameter values is prerequisite.     

Outlier robust model‐assisted small area estimation

Small area estimation with M‐quantile models was proposed by Chambers and Tzavidis ( 2006 ). The key target of this approach to small area estimation is to obtain reliable and outlier robust estimates avoiding at the same time the need for strong parametric assumptions. This approach, however, does not allow for the use of unit level survey weights, making questionable the design consistency of the estimators unless the sampling design is self‐weighting within small areas. In this paper, we adopt a model‐assisted approach and construct design consistent small area estimators that are based on the M‐quantile small area model. Analytic and bootstrap estimators of the design‐based variance are discussed. The proposed estimators are empirically evaluated in the presence of complex sampling designs.     

Unbalanced ranked set sampling for estimating a population proportion

The application of ranked set sampling (RSS) techniques to data from a dichotomous population is currently an active research topic, and it has been shown that balanced RSS leads to improvement in precision over simple random sampling (SRS) for estimation of a population proportion. Balanced RSS, however, is not in general optimal in terms of variance reduction for this setting. The objective of this article is to investigate the application of unbalanced RSS in estimation of a population proportion under perfect ranking, where the probabilities of success for the order statistics are functions of the underlying population proportion. In particular, the Neyman allocation, which assigns sample units for each order statistic proportionally to its standard deviation, is shown to be optimal in the sense that it leads to minimum variance within the class of RSS estimators that are simple averages of the means of the order statistics. We also use a substantial data set, the National Health and Nutrition Examination Survey III (NHANES III) data, to demonstrate the feasibility and benefits of Neyman allocation in RSS for binary variables.