Randomly selected order statistics in ranked set sampling: A less expensive comparable alternative to simple random sampling

Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations.     

Advantages of Volunteer-Based Biodiversity Monitoring in Europe

Abstract:  Without robust and unbiased systems for monitoring, changes in natural systems will remain enigmatic for policy makers, leaving them without a clear idea of the consequences of any environmental policies they might adopt. Generally, biodiversity-monitoring activities are not integrated or evaluated across any large geographic region. The EuMon project conducted the first large-scale evaluation of monitoring practices in Europe through an on-line questionnaire and is reporting on the results of this survey. In September 2007 the EuMon project had documented 395 monitoring schemes for species, which represents a total annual cost of about €4 million, involving more than 46,000 persons devoting over 148,000 person-days/year to biodiversity-monitoring activities. Here we focused on the analysis of variations of monitoring practices across a set of taxonomic groups (birds, amphibians and reptiles, mammals, butterflies, plants, and other insects) and across 5 European countries (France, Germany, Hungary, Lithuania, and Poland). Our results suggest that the overall sampling effort of a scheme is linked with the proportion of volunteers involved in that scheme. Because precision is a function of the number of monitored sites and the number of sites is maximized by volunteer involvement, our results do not support the common belief that volunteer-based schemes are too noisy to be informative. Just the opposite, we believe volunteer-based schemes provide relatively reliable data, with state-of-the-art survey designs or data-analysis methods, and consequently can yield unbiased results. Quality of data collected by volunteers is more likely determined by survey design, analytical methodology, and communication skills within the schemes rather than by volunteer involvement per se.     

Design-based estimators and power analyses of trend tests for the proportion of fish that exhibit gross pathological disorders

Methods for estimating the proportion of fish that exhibit gross pathological disorders and for estimating the variance of these estimates are defined. The methods are for the situation in which a probability-based sampling design is used to collect fish for examination, but geographic locations (rather than individual fish) are assigned probabilities of being selected for sampling. To illustrate the use of the methods, they are applied to data collected during the 1992 EMAP- Estuaries sampling program in the Louisianian Province (i.e., the Gulf of Mexico). Separate estimates of the proportion of fish with gross pathological disorders are computed for demersal species, commercial species, pelagic species, and all species as one group. In addition, a test for trend in the proportion of fish that exhibit gross pathological disorders is defined, and analyses of the power of the test are presented. The power analyses are based on a general underlying model of the random distribution patterns of fish and the random process of catching fish. The power analyses also take into account the features of the sampling designs used for collecting fish. Component parameter estimates were computed using data from the 1992 EMAP-Estuaries sampling program in the Louisianian Province. Results from these analyses suggest that the EMAP-Estuaries sampling designs are capable of detecting a 0.15% change per year in the proportion of fish (all species groups combined) with gross pathological disorders in estuaries of the Louisianian Province over a 12-year period with a power of at least 80%. © Rapid Science 1998     

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 neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.     

Prospective evaluation of designs for analysis of variance without knowledge of effect sizes

Estimation of design power requires knowledge of treatment effect size and error variance, which are often unavailable for ecological studies. In the absence of prior information on these parameters, investigators can compare an alternative to a reference design for the same treatment(s) in terms of its precision at equal sensitivity. This measure of relative performance calculates the fractional error variance allowed of the alternative for it to just match the power of the reference. Although first suggested as a design tool in the 1950s, it has received little analysis and no uptake by environmental scientists or ecologists. We calibrate relative performance against the better known criterion of relative efficiency, in order to reveal its unique advantage in controlling sensitivity when considering the precision of estimates. The two measures differ strongly for designs with low replication. For any given design, relative performance at least doubles with each doubling of effective sample size. We show that relative performance is robustly approximated by the ratio of reference to alternative $\alpha $ quantiles of the $F$ distribution, multiplied by the ratio of alternative to reference effective sample sizes. The proxy is easy to calculate, and consistent with exact measures. Approximate or exact measurement of relative performance serves a useful purpose in enumerating trade-offs between error variance and error degrees of freedom when considering whether to block random variation or to sample from a more or less restricted domain.     

Efficiency of composite sampling for estimating a lognormal distribution

In many environmental studies measuring the amount of a contaminant in a sampling unit is expensive. In such cases, composite sampling is often used to reduce data collection cost. However, composite sampling is known to be beneficial for estimating the mean of a population, but not necessarily for estimating the variance or other parameters. As some applications, for example, Monte Carlo risk assessment, require an estimate of the entire distribution, and as the lognormal model is commonly used in environmental risk assessment, in this paper we investigate efficiency of composite sampling for estimating a lognormal distribution. In particular, we examine the magnitude of savings in the number of measurements over simple random sampling, and the nature of its dependence on composite size and the parameters of the distribution utilizing simulation and asymptotic calculations.     

Species distribution modelling—Effect of design and sample size of pseudo-absence observations

We explored the effect of varying pseudo-absence data in species distribution modelling using empirical data for four real species and simulated data for two imaginary species. In all analyses we used a fixed study area, a fixed set of environmental predictors and a fixed set of presence observations. Next, we added pseudo-absence data generated by different sampling designs and in different numbers to assess their relative importance for the output from the species distribution model. The sampling design strongly influenced the predictive performance of the models while the number of pseudo-absences had minimal effect on the predictive performance. We attribute much of these results to the relationship between the environmental range of the pseudo-absences (i.e. the extent of the environmental space being considered) and the environmental range of the presence observations (i.e. under which environmental conditions the species occurs). The number of generated pseudo-absences had a direct effect on the predicted probability, which translated to different distribution areas. Pseudo-absence observations that fell within grid cells with presence observations were purposely included in our analyses. We discourage the practice of excluding certain pseudo-absence data because it involves arbitrary assumptions about what are (un)suitable environments for the species being modelled.     

Comparison of a two-stage sampling design and its composite sample alternative: An application to soil studies

The objective of a long-term soil survey is to determine the mean concentrations of several chemical parameters for the pre-defined soil layers and to compare them with the corresponding values in the past. A two-stage random sampling procedure is used to achieve this goal. In the first step, n subplots are selected from N subplots by simple random sampling without replacement; in the second step, m sampling sites are chosen within each of the n selected subplots. Thus n · m soil samples are collected for each soil layer. The idea of the composite sample design comes from the challenge of reducing very expensive laboratory analyses: m laboratory samples from one subplot and one soil layer are physically mixed to form a composite sample. From each of the n selected subplots, one composite sample per soil layer is analyzed in the laboratory, thus n per soil layer in total. In this paper we show that the cost is reduced by the factor m — 1 when instead of the two-stage sampling its composite sample alternative is used; however, the variance of the composite sample mean is increased. In the case of positive intraclass correlation the increase is less than 12.5%; in the case of negative intraclass correlation the increase depends on the properties of the variable as well. For the univariate case we derive the optimal number of subplots and sampling sites. A case study is discussed at the end.     

Can modeling improve estimation of desert tortoise population densities?

The federally listed desert tortoise (Gopherus agassizii) is currently monitored using distance sampling to estimate population densities. Distance sampling, as with many other techniques for estimating population density, assumes that it is possible to quantify the proportion of animals available to be counted in any census. Because desert tortoises spend much of their life in burrows, and the proportion of tortoises in burrows at any time can be extremely variable, this assumption is difficult to meet. This proportion of animals available to be counted is used as a correction factor (g0) in distance sampling and has been estimated from daily censuses of small populations of tortoises (6-12 individuals). These censuses are costly and produce imprecise estimates of go due to small sample sizes. We used data on tortoise activity from a large (N = 150) experimental population to model activity as a function of the biophysical attributes of the environment, but these models did not improve the precision of estimates from the focal populations. Thus, to evaluate how much of the variance in tortoise activity is apparently not predictable, we assessed whether activity on any particular day can predict activity on subsequent days with essentially identical environmental conditions. Tortoise activity was only weakly correlated on consecutive days, indicating that behavior was not repeatable or consistent among days with similar physical environments.     

Current Trends in Plant and Animal Population Monitoring

Abstract:  Animal and plant population monitoring programs are critical for identifying species at risk, evaluating the effects of management or harvest, and tracking invasive and pest species. Nevertheless, monitoring activities are highly decentralized, which makes it difficult for researchers or conservation planners to get a good general picture of what real-world monitoring programs actually entail. We used a Web-based survey to collect information on population monitoring programs. The survey focused on basic questions about each program, including motivations for monitoring, types of data being collected, spatiotemporal design of the program, and reasons for choosing that design. We received responses from 311 people involved in monitoring of various species and used these responses to summarize ongoing monitoring efforts. We also used responses to determine whether monitoring strategies have changed over time and whether they differed among monitoring agencies. Most commonly, monitoring entailed collection of count data at multiple sites with the primary goal of detecting trends. But we also found that goals and strategies for monitoring appeared to be diversifying, that area-occupied and presence–absence approaches appeared to be gaining in popularity, and that several other promising approaches (monitoring to reduce parameter uncertainty, risk-based monitoring, and directly linking monitoring data to management decisions) have yet to become widely established. We suggest that improved communication between researchers studying monitoring designs and those who are charged with putting these designs into practice could further improve monitoring programs and better match sampling designs to the objectives of monitoring programs.     

Network inclusion probabilities and Horvitz-Thompson estimation for adaptive simple Latin square sampling

Consider a survey of a plant or animal species in which abundance or presence/absence will be recorded. Further assume that the presence of the plant or animal is rare and tends to cluster. A sampling design will be implemented to determine which units to sample within the study region. Adaptive cluster sampling designs Thompson (1990) are sampling designs that are implemented by first selecting a sample of units according to some conventional probability sampling design. Then, whenever a specified criterion is satisfied upon measuring the variable of interest, additional units are adaptively sampled in neighborhoods of those units satisfying the criterion. The success of these adaptive designs depends on the probabilities of finding the rare clustered events, called networks. This research uses combinatorial generating functions to calculate network inclusion probabilities associated with a simple Latin square sample. It will be shown that, in general, adaptive simple Latin square sampling when compared to adaptive simple random sampling will (i) yield higher network inclusion probabilities and (ii) provide Horvitz-Thompson estimators with smaller variability.     

Precision of the mean and the design of benthos sampling programmes: caution revised

Normative variance functions can be used to accurately predict sampling exigencies, but such empirically derived formulae are continuous functions that can predict levels of sampling precision that cannot logically occur in discrete population samples. General formulae are presented that allow calculation of upper and lower boundary constraints on levels of sampling precision. These boundary constraints would only have a significant influence on sampling design where populations are so sparse that samples consist mainly of presence-absence data. A previously published empirical equation for the prediction of requisite sample number for the estimation of a freshwater benthos population correctly shows that using a small sampler can result in an up to 50-fold reduction in the amount of sediment processed, regardless of these constraints. A previously published empirical equation for the prediction of sampling variance, based on over 3000 sets of replicate samples of marine benthos populations, suggests that the use of small samplers over large ones requires the processing of between one-half and one-twentieth of the sediment for the same level of precision. It is concluded that discussions of sampling optimization should be based on knowledge of real sampling costs.     

Optimal spatial sampling schemes for environmental surveys

A practical problem in spatial statistics is that of constructing spatial sampling designs for environmental monitoring network. This paper presents a fractal-based criterion for the construction of coverage designs to optimize the location of sampling points. The algorithm does not depend on the covariance structure of the process and provides desirable results for situations in which a poor prior knowledge is available. The statistical characteristics of the method are explored by a simulation study while a design exercise concerning the Pescara area monitoring network is used to demonstrate potential designs under realistic assumptions.     

Desirable design characteristics for long-term monitoring of ecological variables

Long-term environmental monitoring places a set of demands on a sampling strategy not present in a survey designed for a single time period. The inevitability that a sample will become out of date must be a dominant consideration in planning a long-term monitoring programme. The sampling strategy must be able to accommodate periodic frame update and sample restructuring in order to address changes in the composition of the universe and changes in the perception of issues leading to new questions and concerns. The sampling strategy must be capable of adapting to such changes while maintaining its identification as a probability sample and its capacity to detect trends that span the update occasions. These issues are examined with respect to sub-population estimation, post-stratification via conditioning, and sample enlargement and reduction. Design features that involve complex sample structure create potentially serious difficulties, whereas an equal probability design permits greater adaptability and flexibility. Structure should be employed sparingly and in awareness of its undesirable effects.     

On the meta-analysis of response ratios for studies with correlated and multi-group designs

A common effect size metric used to quantify the outcome of experiments for ecological meta-analysis is the response ratio (RR): the log proportional change in the means of a treatment and control group. Estimates of the variance of RR are also important for meta-analysis because they serve as weights when effect sizes are averaged and compared. The variance of an effect size is typically a function of sampling error; however, it can also be influenced by study design. Here, I derive new variances and covariances for RR for several often-encountered experimental designs: when the treatment and control means are correlated; when multiple treatments have a common control; when means are based on repeated measures; and when the study has a correlated factorial design, or is multivariate. These developments are useful for improving the quality of data extracted from studies for meta-analysis and help address some of the common challenges meta-analysts face when quantifying a diversity of experimental designs with the response ratio.     

Estimating abundance: a non parametric mark recapture approach for open and closed systems

We present a novel, non-parametric, frequentist approach for capture-recapture data based on a ratio estimator, which offers several advantages. First, as a non-parametric model, it does not require a known underlying distribution for parameters nor the associated assumptions, eliminating the need for post-hoc corrections or additional modeling to account for heterogeneity and other violated assumptions. Second, the model explicitly deals with dependence of trials by considering trials to be dependent; therefore, cluster sampling is handled naturally and additional adjustments are not necessary. Third, it accounts for ordering, utilizing the fact that a system with a small population will have a greater frequency of recaptures “early” in the survey work compared to an identical system with a larger population. We provide mathematical proof that our estimator attains asymptotic minimum variance under open systems. We apply the model to a data set of bottlenose dolphins (Tursiops truncatus) and compare results to those from classic closed models. We show that the model has an impressive rate of convergence and demonstrate that there’s an inverse relationship between population size and the proportion of the population that need to be sampled, while achieving the same degree of accuracy for abundance estimates. The model is flexible and can apply to ecological situations as well as other situations that lend themselves to capture recapture sampling.     

Trend analyses of hierarchical pin-point cover data

The use of state-space models for analyzing longitudinal hierarchical pin-point plant cover data is demonstrated. The main advantages of using a state-space model are (1) that the observed variance is separated into sampling variance and the more interesting structural variance which are needed for quantifying prediction uncertainty, (2) that missing values or an unbalanced sampling design readily may be accounted for, and (3) that the structural equation easily may be expanded and made as complex as necessary for modeling longitudinal pin-point cover data, thus allowing the incorporation of the most important ecological processes in the state-space model without technical difficulties. Typically, there is considerable spatial variation in plant abundance, and this variation is modeled using the Pólya-Eggenberger distribution (a generalization of the beta-binomial distribution). To illustrate this method, longitudinal hierarchical pin-point data of Erica tetralix in wet Danish heathlands were analyzed, including and excluding autocorrelation and an environmental covariable in the state-space model. The pin-point plant cover data showed a significant decrease in the plant cover of E. tetralix in the period from 2004 to 2009, with an annual decrease of about 10% in the logit-transformed cover. The distribution of predicted plant cover at a given site the following year was calculated, including and excluding the information of an environmental covariable.     

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.