Quantifying the efficiency of soil sampling designs: A multivariate approach

The objective of this paper is to quantify and compare the loss functions of the standard two-stage design and its composite sample alternative in the context of multivariate soil sampling. The loss function is defined (conceptually) as the ratio of cost over information and measures design inefficiency. The efficiency of the design is the reciprocal of the loss function. The focus of this paper is twofold: (a) we define a measure of multivariate information using the Kullback–Leibler distance, and (b) we derive the variance-covariance structure for two soil sampling designs: a standard two-stage design and its composite sample counterpart. Randomness in the mass of soil samples is taken into account in both designs. A pilot study in Slovenia is used to demonstrate the calculations of the loss function and to compare the efficiency of the two designs. The results show that the composite sample design is more efficient than the two-stage design. The efficiency ratio is 1.3 for pH, 2.0 for C, 2.1 for N, and 2.5 for CEC. The multivariate efficiency ratio is 2.3. These ratios primarily reflect cost ratios; influence of the information is small.     

Editorial: Composite sampling

The high costs of laboratory analytical procedures frequently strain environmental and public health budgets. Whether soil, water or biological tissue is being analysed, the cost of testing for chemical and pathogenic contaminants can be quite prohibitive.Composite sampling can substantially reduce analytical costs because the number of required analyses is reduced by compositing several samples into one and analysing the composited sample. By appropriate selection of the composite sample size and retesting of select individual samples, composite sampling may reveal the same information as would otherwise require many more analyses.Many of the limitations of composite sampling have been overcome by recent research, thus bringing out more widespread potential for using composite sampling to reduce costs of environmental and public health assessments while maintaining and often increasing the precision of sample-based inference.     

Adjusted two-stage adaptive cluster sampling

An adjusted two-stage sampling procedure is discussed for adaptive cluster sampling where some networks are large and others are small. A two-stage sample is drawn from the large networks and a single-stage sample is drawn from the rest. The simple random sampling (SRS) procedure without replacement is used at the initial stage. An estimator for the population mean along with its properties is discussed.     

Hierarchical linear mixed models in multi-stage sampling soil studies

The issue of variances of different soil variables prevailing at different sampling scales is addressed. This topic is relevant for soil science, agronomy and landscape ecology. In multi-stage sampling there are randomness components in each stage of sampling which can be taken into account by introducing random effects in analysis through the use of hierarchical linear mixed models (HLMM). Due to the nested sampling scheme, there are several hierarchical sub-models. The selection of the best model can be carried out through likelihood ratio tests (LRTs) or Wald tests, which are asymptotically equivalent under standard conditions. However, when the comparison leads to a restricted hypothesis of variance components, standard conditions are not maintained, which leads to more elaborated versions of LRTs. These versions are not disseminated among environmental scientists. The present study shows the modeling of soil data from a sampling where sites, fields within sites, transects within fields, and sampling points within transects were selected in order to take samples from different vegetation types (open and shade). For soil data, several sub-models were compared using Wald tests, classic LRTs and adjusted LRTs where the distribution of the test statistic under the null hypothesis is the Chi-square mixture of Chi-square distributions. The inclusion of random effects via HLMM and suggested by the latest version of LRT allowed us to detect effects of vegetation type on soil properties that were not detected under a classical ANOVA.     

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.     

Two-stage estimation of ungulate abundance in Mediterranean areas using pellet group count

A design-based strategy for estimating wildlife ungulate abundance in a Mediterranean protected area (Maremma Regional Park) is considered. The estimation is based on pellet group count (clearance count technique) in a set of plots, whose size and number is established on the basis of practical considerations and available resources. The sampling scheme involves a preliminary stratification and subsequent two-stage sampling. In the first stage, large strata (defined through habitat features) are partitioned into spatial units and a sample of units is selected by means of a sampling scheme ensuring inclusion probabilities proportional to unit size, but avoiding the selection of contiguous units. Then, the abundances of the selected units are estimated in a second stage, in which plots are located using a random scheme ensuring an even coverage of the units. In small strata, only the second stage is performed. Unbiased estimators of abundance and conservative estimators of their variances are derived for each strata and for the whole study area. The proposed strategy has been applied since the Summer of 2006 and the estimation results reveal substantial improvement with respect to the previous results obtained by means of an alternative strategy.     

Detecting Rare Species with Random or Subjective Sampling: a Case Study of Red-Listed Saproxylic Beetles in Boreal Sweden

Abstract:  Efficient sampling design in field studies is important for economical and statistical reasons. We compared two ways to distribute sampling effort over an area, either randomly or subjectively. We searched for red-listed saproxylic (wood-living) beetles in 30 spruce stands in boreal Sweden by sifting wood from dead trees. We randomly selected positions within each stand with a geographic positioning system and sampled the nearest dead tree (random sample). In the same stand we also sampled dead trees that, based on literature, were likely to host such species (subjective sampling). The subjective sampling (two to five samples per stand, depending on stand size) was compared with the higher, random sampling effort (fixed level of 12 samples/stand). Subjective sampling was significantly more efficient. Red-listed species were found in 36% of the subjective samples and in 16% of the random samples. Nevertheless, the larger random effort resulted in a comparable number of red-listed species per stand and in 13 detected species in total (vs. 12 species with subjective sampling). Random sampling was less efficient, but provided an unbiased alternative more suitable for statistical purposes, as needed in, for example, monitoring programs. Moreover, new species-specific knowledge can be gained through random searches.     

A robust weighted EM algorithm for use-availability data

Wildlife sampling for habitat selection often combines a random background sample with a random sample of used sites, because the background sample could contain too few used sites to be informative for rare species. This approach is referred to as use-availability sampling. Two variants are considered where there is: (1) a random background sample including used and unused sites augmented with a sample of used sites, and (2) a sample of used sites augmented with a contaminated background sample, i.e. use is not recorded. A weighted estimator first proposed by Manski and Lerman (Econometrica 45(8):1977?C1988, 1977) forms the basis for our suggested approach. The weighted estimator has been shown to perform better than the usual unweighted approach with uncontaminated data and mis-specified logit models (Xie and Manski in Sociol Methods Res 17(3):283?C302, 1989). A weighted EM algorithm is developed for use with contaminated background data. We show that the weighted estimator continues to perform well with contaminated data and maintains its robustness to model mis-specification. The weighted estimator has not been previously used for use-availability sampling due to reliance on the assumption that only the intercept is biased, which is valid for a correct logit model. We show that adjusting the intercept may not eliminate the bias with an incorrect logit model. In this case, the weighted estimator is a relatively simple and effective alternative.     

Composite likelihood approach to the regression analysis of spatial multivariate ordinal data and spatial compositional data with exact zero values

In many environmental and ecological studies, it is of interest to model compositional data. One approach is to consider positive random vectors that are subject to a unit-sum constraint. In landscape ecological studies, it is common that compositional data are also sampled in space with some elements of the composition absent at certain sampling sites. In this paper, we first propose a practical spatial multivariate ordered probit model for multivariate ordinal data, where the response variables can be viewed as the discretized non-negative compositions without the unit-sum constraint. We then propose a novel two-stage spatial mixture Dirichlet regression model. The first stage models the spatial dependence and the presence of exact zero values, and the second stage models all the non-zero compositional data. A maximum composite likelihood approach is developed for parameter estimation and inference in both the spatial multivariate ordered probit model and the two-stage spatial mixture Dirichlet regression model. The standard errors of the parameter estimates are computed by an estimate of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods. A land cover data example in landscape ecology further illustrates that accounting for spatial dependence can improve the accuracy in the prediction of presence/absence of different land covers as well as the magnitude of land cover compositions.     

The application of generalized linear mixed models to multi-level sampling for insect population monitoring

Iwao's quadratic regression or Taylor's Power Law (TPL) are commonly used to model the variance as a function of the mean for sample counts of insect populations which exhibit spatial aggregation. The modeled variance and distribution of the mean are typically used in pest management programs to decide if the population is above the action threshold in any management unit (MU) (e.g., orchard, forest compartment). For nested or multi-level sampling the usual two-stage modeling procedure first obtains the sample variance for each MU and sampling level using ANOVA and then fits a regression of variance on the mean for each level using either Iwao or TPL variance models. Here this approach is compared to the single-stage procedure of fitting a generalized linear mixed model (GLMM) directly to the count data with both approaches demonstrated using 2-level sampling. GLMMs and additive GLMMs (AGLMMs) with conditional Poisson variance function as well as the extension to the negative binomial are described. Generalization to more than two sampling levels is outlined. Formulae for calculating optimal relative sample sizes (ORSS) and the operating characteristic curve for the control decision are given for each model. The ORSS are independent of the mean in the case of the AGLMMs. The application described is estimation of the variance of the mean number of leaves per shoot occupied by immature stages of a defoliator of eucalypts, the Tasmanian Eucalyptus leaf beetle, based on a sample of trees within plots from each forest compartment. Historical population monitoring data were fitted using the above approaches.     

Estimating parameters of neutral communities: from one single large to several small samples

The neutral theory of S. P. Hubbell postulates a two-scale hierarchical framework consisting of a metacommunity following the speciation-drift equilibrium characterized by the "biodiversity number" theta, and local communities following the migration-drift equilibrium characterized by the "migration rate" m (or the "fundamental dispersal number" I). While Etienne's sampling formula allows simultaneous estimation of theta and m from a single sample of a local community, its applicability to a network of (rather small) samples is questionable. We define here an alternative two-stage approach estimating theta from an adequate subset of the individuals sampled in the field (using Ewens' sampling formula) and m from community samples (using Etienne's sampling formula). We compare its results with the simultaneous estimation of theta and m (one-stage estimation), for simulated neutral samples and for 50 1-ha plots of evergreen forest in South India. The one-stage approach exhibits problems of bias and of poor differentiability between high-theta, low-m and low-theta, high-m solution domains. Conversely, the two-stage approach yielded reasonable estimates and is to be preferred when several small, scattered plots are available instead of a single large one.     

Variance decomposition in two-stage plot sampling: theoretical and empirical results

The statistical properties of two-stage plot sampling estimators of abundance are considered. In the first stage, some spatial units are selected over the whole study area according to a suitable sampling design, while in the second stage, the selected units are surveyed with floating plot sampling to estimate the abundance within. Some insights into the accuracy of the resulting estimators are obtained by splitting the sample variance into the first and second-stage components, while performance is empirically checked by means of a simulation study. Simulation results show that, in most situations, a relevant amount of the overall variance is due to the second stage sampling.     

Use of post-stratification in composite sampling for estimating mean

We show with the results of a study conducted in the Hamadan Province, Iran as to how the use of composite sampling for estimating mean zinc concentration in the soil can help reduce analytical costs by reducing the number of analysis required. We also introduce post-stratification methodology in the composition step to take advantage of possible spatial dispersion. We speculate that the zinc concentration value depends on the sample location, we first stratified the sample set and then composite units from different strata randomly. The results of a simulation study show that the use of this approach not only reduces the total costs but also increases the precision of the estimator.     

Occurrence,prevalence and seasonality of neoplasia in the marine mussel Mytilus edulis from three sites in Denmark

The occurrence, prevalence, seasonality and possible etiology of a neoplastic disorder in natural populations of the mussel Mytilus edulis from three sites in Denmark were studied, comprising monthly sampling of 300 mussels per sample from each site during one year (October 1983 to September 1984). Neoplasia occurred at all three sites. Statistical analysis indicated that there were significant differences in the monthly prevalences of the disorder between the three sites and within each site. At two sites the prevalences were found to be seasonally related. Cytologically, the neoplasia exhibited malignant characteristics. Electron microscopy showed that the neoplastic cells were extremely pleomorphic, with large irregular nuclei. Large (approximately 200 nm diam) virus-like particles were associated with the nuclei.     

Distribution pattern of polycyclic aromatic hydrocarbons in particle-size fractions of coking plant soils from different depth

The concentrations of 16 priority polycyclic aromatic hydrocarbons (PAHs) in four size fractions (<2, 2–20, 20–200, >200 μm) in soils at different depth from a heavily contaminated crude benzol production facility of a coking plant were determined using GC–MS. Vertically, elevated total PAHs concentrations were observed in the soils at 3.0–4.5 m (layer B) and 6.0–7.5 m (layer C), relatively lower at 1.5–3.0 m (layer A) and 10.5–12.0 m (layer D). At all sampling sites, the silt (2–20 μm) contained the highest PAHs concentration (ranged from 726 to 2,711 mg/kg). Despite the substantial change in PAHs concentrations in soils with different particle sizes and lithologies, PAHs composition was similarly dominated by 2–3 ring species (86.5–98.3 %), including acenaphthene, fluorene, and phenanthrene. For the contribution of PAHs mass in each fraction to the bulk soil, the 20–200 μm size fraction had the greatest accumulation of PAHs in loamy sand layers at 1.0–7.5 m, increasing with depth; while in deeper sand layer at 10.5–12.0 m, the >200 μm size fraction showed highest percentages and contributed 81 % of total PAHs mass. For individual PAH distribution, the 2–3 ring PAHs were highly concentrated in the small size fraction (<2 and 2–20 μm); the 4–6 ring PAHs showed the highest concentrations in the 2–20 μm size fraction, increasing with depth. The distribution of PAHs was primarily determined by the sorption on soil organic matter and the characteristics of PAHs. This research should have significant contribution to PAH migration study and remediation design for PAHs-contaminated sites.     

Contributions to composite sampling

The initial use of composite sampling involved the analysis of many negative samples with relatively high laboratory cost (Dorfman sampling). We propose a method of double compositing and compare its efficiency with Dorfman sampling. The variability of composite measurement samples has environmental interest (hot spots). The precision of these estimates depends on the kurtosis of the distribution; leptokurtic distributions (₂ > 0) have increased precision as the number of field samples is increased. The opposite effect is obtained for platykurtic distributions. In the lognormal case, coverage probabilities are reasonable for < 0.5. The Poisson distribution can be associated with temporal compositing, of particular interest where radioactive measurements are taken. Sample size considerations indicate that the total sampling effort is directly proportional to the length of time sampled. If there is background radiation then increasing levels of this radiation require larger sample sizes to detect the same difference in radiation.     

CUSUM environmental monitoring in time and space

We consider the situation where there are n sampling sites in an area, with an environmental variable measured at some or all of the sites at m sample times. We assume that there is interest in knowing whether the environmental variable displays systematic changes over time at the sites. A cumulative sum type of analysis with associated randomization tests has been proposed before for this situation, when there is negligible correlation between the observations in different times at one site, and no correlation between the results at different sites. A modification that allows for serial correlation at the individual sites but with no correlation between sites has also been proposed before. In the present paper we discuss how the method can be modified further to allow for spatial correlation between the sites, by applying it only to a reduced set of sites that are far enough apart to give effectively independent results. Simulation results indicate that this strategy is effective providing that the level of spatial correlation is not too high.     

吉林西部草地生态系统不同退化演替阶段土壤有机碳变化研究

草地盐碱化是吉林西部典型的生态环境问题。针对吉林西部具有＂羊草群落（Leymus chinense）→羊草-虎尾草群落（Carex duiuscula）→羊草-碱茅群落（Puccinellia distans）→碱蓬群落（Suaeda glauca）＂直至退化为盐碱地的逆向演替规律,本文选取大安市姜家甸草场为典型区进行野外样地调查,收集不同演替阶段植物样品30份,土壤剖面样品100份,表土样品40份,监测群落生态特征、土壤理化性质,计算土壤有机碳储量。分析结果表明：随着退化演替的进行,羊草-虎尾草群落的多样性指数、植被生物量、土壤有机质最高,土壤含水率及全N指数逐渐降低,土壤的pH值及土壤容重升高,土壤有机碳含量在0～100cm各土层呈现出先升高再降低的趋势,其中0～40cm内变化显著,50～100cm内相差不大,1m土壤有机碳密度从羊草群落的75.37t·hm-2升高到羊草-虎尾草群落的76.11t·hm-2,至盐碱地减少到52.21t·hm-2,约减少30%。研究结果对吉林省合理放牧、草地固碳量的增加和土壤碳储量的提高都有指导意义。     

鄂尔多斯不同地形下土壤养分的空间变异

通过野外调查采样与室内土壤理化分析相结合,对鄂尔多斯荒漠区不同地貌类型下的土壤养分分布特征进行了初步分析,研究表明:鄂尔多斯沙地土壤养分含量普遍较低,两断面表层有效钾的均值在６４．７３－７０．９５ｍｇ/ｋｇ之间,有机质含量在０．４９３%－０．５０８%之间,ｐＨ值在８．０左右。在地形部位较高的硬梁、丘顶处土壤养分含量最低,软梁次之,而在地势较低的滩地、丘间地土壤养分含量较高。硬梁、软梁、滩地表层土壤有机质和有效钾含量分别为０．１８%、０,５０%、１．１６%和 ３５．２９ｍｇ/ｋｇ、６０、６７ｍｇ/ｋｇ、９８．３２ ｍｇ/ｋｇ,丘顶、丘间、农田表层土壤有机质和有效钾的含量分别为０．０９%、１．０９%、０．８４%和２３．９１ ｍｇ/ｋｇ、６０．３４ｍｇ/ｋｇ、７７．４２ ｍｇ/ｋｇ。在多数土壤剖面上,土壤养分从上到下递减。通过对两地形断面上土壤有机质和有效钾的一维半方差函数均表现出明显的空间结构性,并且各种养分的独立较大,在艾碱壕断面上土壤有效钾和有机质的独立间距为７０．８９ｍ和６９．１５ｍ,在深海沟断面上土壤有效钾和有机质的独立间距为１２．４８ｍ和３５．９８ ｍ,说明在调查区域内土壤养分存在一定的相关关系。     

The use of composite sampling in contaminated sites—a case study

Simulated composite sampling was carried out using data from a contaminated site. The values obtained by composite sampling were compared with the results obtained using discrete (individual) samples. It is appropriate to use a modified investigation level (MIL) when using composite samples. The MIL is lower than the standard investigation level, (IL). Various MILs were considered in this study. Too low an MIL will indicate that some composite samples require further investigation, when none of the discrete samples comprising the composite would have exceeded the IL. Too high an MIL will result in some discrete samples that exceed the IL being missed. A suggested MIL is IL/ where n is the number of discrete samples in the composite sample. This MIL was found to give few false negatives but many fewer false positives than the IL/n rule. Although this MIL was effective on the test data it could be site specific. Some local areas of high concentration may be missed with composite samples if a lower investigation level is used. These however do not make a large contribution to the health risk because they will have a contaminant level only slightly higher than the IL, and the neighboring samples must have a low concentration of the contaminant. The increased risk due this cause may be more than offset by the higher sampling density made possible through the economies of composite sampling When composite sampling is used as the first phase of an adaptive cluster-sampling scheme, it must be augmented by additional samples to delineate the contaminated area to be cleaned up. Composite sampling can also be effectively used in a clean up unit technique, where a clean up unit is represented by one or more composite samples. Suggestions are given for when composite sampling can be used effectively.