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.     

On Use of Transformed Auxiliary Information in Probability Proportional to Size Method of Sample Selection

A probability proportional to size (PPS) method of sample selection, based on the transformed auxiliary information as the measure of size, has been suggested. It has been observed that the PPS estimator under the suggested method is always better than the simple random sampling with replacement (SRSWR) and the usual PPSWR estimator. The efficiency of the proposed estimator with respect to the estimators under reference has also been empirically compared.     

New Ranked Set Sampling for One‐Parameter Family of Distributions

Bhoj (1997c) proposed a new ranked set sampling (NRSS) procedure for a specific two‐parameter family of distributions when the sample size is even. This NRSS procedure can be applied to one‐parameter family of distributions when the sample size is even. However, this procedure cannot be used if the sample size is odd. Therefore, in this paper, we propose a modified version of the NRSS procedure which can be used for one‐parameter distributions when the sample size is odd. Simple estimator for the parameter based on proposed NRSS is derived. The relative precisions of this estimator are higher than those of other estimators which are based on other ranked set sampling procedures and the best linear unbiased estimator using all order statistics.     

Binomial sampling to estimate rust mite (Acari: Eriophyidae) densities on orange fruit

Binomial sampling based on the proportion of samples infested was investigated for estimating mean densities of citrus rust mite, Phyllocoptruta oleivora (Ashmead), and Aculops pelekassi (Keifer) (Acari: Eriophyidae), on oranges, Citrus sinensis (L.) Osbeck. Data for the investigation were obtained by counting the number of motile mites within 600 sample units (each unit a 1-cm2 surface area per fruit) across a 4-ha block of trees (32 blocks total): five areas per 4 ha, five trees per area, 12 fruit per tree, and two samples per fruit. A significant (r2 = 0.89), linear relationship was found between ln(-ln(1 -Po)) and ln(mean), where P0 is the proportion of samples with more than zero mites. The fitted binomial parameters adequately described a validation data set from a sampling plan consisting of 192 samples. Projections indicated the fitted parameters would apply to sampling plans with as few as 48 samples, but reducing sample size resulted in an increase of bootstrap estimates falling outside expected confidence limits. Although mite count data fit the binomial model, confidence limits for mean arithmetic predictions increased dramatically as proportion of samples infested increased. Binomial sampling using a tally threshold of 0 therefore has less value when proportions of samples infested are large. Increasing the tally threshold to two mites marginally improved estimates at larger densities. Overall, binomial sampling for a general estimate of mite densities seemed to be a viable alternative to absolute counts of mites per sample for a grower using a low management threshold such as two or three mites per sample.     

Median Ranked Set Sampling with Size Biased Probability of Selection

Median ranked set sampling may be combined with size biased probability of selection. A two-phase sample is assumed. In the first phase, units are selected with probability proportional to their size. In the second phase, units are selected using median ranked set sampling to increase the efficiency of the estimators relative to simple random sampling. There is also an increase in the efficiency relative to ranked set sampling (for some probability distribution functions). There will be a loss in efficiency depending on the amount of errors in ranking the units, the median ranked set sampling can be used to reduce the errors in ranking the units selected from the population. Estimators of the population mean and the population size are considered. The median ranked set sampling with probability proportion to size and with errors in ranking is considered and compared with ranked set sampling with errors in ranking. Computer simulation results for some probability distributions are also given.     

A Note on Balanced Sampling and Robust Genetic Predictors

The concept of balanced sampling is applied to prediction in finite samples using model based inference procedures. Necessary and sufficient conditions are derived for a general linear model with arbitrary covariance structure to yield the expansion estimator as the best linear unbiased predictor for the mean. The analysis is extended to produce a robust estimator for the mean squared error under balanced sampling and the results are discussed in the context of statistical genetics where appropriate sampling produces simple efficient and robust genetic predictors free from unnecessary genetic assumptions.     

Estimating the Population Mean Using Extreme Ranked Set Sampling

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean. ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.     

Using Inverse Probability Bootstrap Sampling to Eliminate Sample Induced Bias in Model Based Analysis of Unequal Probability Samples

In ecology, as in other research fields, efficient sampling for population estimation often drives sample designs toward unequal probability sampling, such as in stratified sampling. Design based statistical analysis tools are appropriate for seamless integration of sample design into the statistical analysis. However, it is also common and necessary, after a sampling design has been implemented, to use datasets to address questions that, in many cases, were not considered during the sampling design phase. Questions may arise requiring the use of model based statistical tools such as multiple regression, quantile regression, or regression tree analysis. However, such model based tools may require, for ensuring unbiased estimation, data from simple random samples, which can be problematic when analyzing data from unequal probability designs. Despite numerous method specific tools available to properly account for sampling design, too often in the analysis of ecological data, sample design is ignored and consequences are not properly considered. We demonstrate here that violation of this assumption can lead to biased parameter estimates in ecological research. In addition, to the set of tools available for researchers to properly account for sampling design in model based analysis, we introduce inverse probability bootstrapping (IPB). Inverse probability bootstrapping is an easily implemented method for obtaining equal probability re-samples from a probability sample, from which unbiased model based estimates can be made. We demonstrate the potential for bias in model-based analyses that ignore sample inclusion probabilities, and the effectiveness of IPB sampling in eliminating this bias, using both simulated and actual ecological data. For illustration, we considered three model based analysis tools—linear regression, quantile regression, and boosted regression tree analysis. In all models, using both simulated and actual ecological data, we found inferences to be biased, sometimes severely, when sample inclusion probabilities were ignored, while IPB sampling effectively produced unbiased parameter estimates.     

Inverse Adaptive Cluster Sampling

Consider a population in which the variable of interest tends to be at or near zero for many of the population units but a subgroup exhibits values distinctly different from zero. Such a population can be described as rare in the sense that the proportion of elements having nonzero values is very small. Obtaining an estimate of a population parameter such as the mean or total that is nonzero is difficult under classical fixed sample-size designs since there is a reasonable probability that a fixed sample size will yield all zeroes. We consider inverse sampling designs that use stopping rules based on the number of rare units observed in the sample. We look at two stopping rules in detail and derive unbiased estimators of the population total. The estimators do not rely on knowing what proportion of the population exhibit the rare trait but instead use an estimated value. Hence, the estimators are similar to those developed for poststratification sampling designs. We also incorporate adaptive cluster sampling into the sampling design to allow for the case where the rare elements tend to cluster within the population in some manner. The formulas for the variances of the estimators do not allow direct analytic comparison of the efficiency of the various designs and stopping rules, so we provide the results of a small simulation study to obtain some insight into the differences among the stopping rules and sampling approaches. The results indicate that a modified stopping rule that incorporates an adaptive sampling component and utilizes an initial random sample of fixed size is the best in the sense of having the smallest variance.     

Using habitat suitability models to sample rare species in high-altitude ecosystems: a case study with Tibetan argali

Models of the distribution of rare and endangered species are important tools for their monitoring and management. Presence data used to build up distribution models can be based on simple random sampling, but this for patchy distributed species results in small number of presences and therefore low precision. Convenience sampling, either based on easily accessible units or a priori knowledge of the species habitat but with no known probability of sampling each unit, is likely to result in biased estimates. Stratified random sampling, with strata defined using habitat suitability models [estimated in the resource selection functions (RSFs) framework] is a promising approach for improving the precision of model parameters. We used this approach to sample the Tibetan argali (Ovis ammon hodgsoni) in Indian Transhimalaya in order to estimate their distribution and to test if it can lead to a significant reduction in survey effort compared to random sampling. We first used an initial sample of argali feeding sites in 2005 and 2006 based on a priori selected vantage points and survey transects. This initial sample was used to build up an initial distribution model. The spatial predictions based on estimated RSFs were then used to define three strata of the study area. The strata were randomly sampled in 2007. As expected, much more presences per hour were obtained in the high quality strata compared to the low quality strata—1.33 obs/h vs. 0.080/h. Furthermore the best models selected on the basis of the prospective sample differed from those using the first a priori sample, suggesting bias in the initial sampling effort. The method therefore has significant implications for decreasing sampling effort in terms of sampling time in the field, especially when dealing with rare species, and removing initial sampling bias.     

Assessment of methods to estimate aquatic macrophyte species richness in extrapolated sample sizes

We evaluated six methods to estimate species richness in extrapolated sample size using presence–absence data for aquatic macrophyte assemblages. Methods suitable for assemblages involving terrestrial and non-clonal (unitary) organisms may not be valid for aquatic macrophytes. The extrapolation of a species accumulation curve using a logarithmic function or using a linear model on the log of accumulated sampling units consistently overestimated species richness. The newly proposed Total-Species method gave similar results. The Negative Binomial and Logarithmic Series methods and the recently proposed Binomial Mixture Model were unbiased and accurate. We conclude that current extrapolation techniques are valid for estimation of species richness in macrophyte assemblages, and recommend the Logarithmic Series, Binomial Negative or Binomial Mixture Model methods.     

Comparative methods based on species mean values

Comparative methods that use simple linear regression based on species mean values introduce three difficulties with respect to the standard regression model. First, species values may not be independent because they form part of a hierarchically structured phylogeny. Second, variation about the regression line includes two sources of error: 'biological error' due to deviations of the true species mean values from the regression line and sampling error associated with the estimation of these mean values [B. Riska, Am. Natural. 138 (1991) 283]. Third, sampling error in the independent variable results in an attenuated estimate of the regression slope. We consider estimation and hypothesis testing using two statistical models which explicitly justify the use of the species mean values, without the need to account for phylogenetic relationships. The first (random-effects) is based on an evolutionary model whereby species evolve to fill a bivariate normal niche space, and the second (fixed-effects) is concerned with describing a relationship among the particular species included in a study, where the only source of error is in the estimation of species mean values. We use a modification of the maximum-likelihood method to obtain an unbiased estimate of the regression slope. For three real datasets we find a close correspondence between this slope and that obtained by simply regressing the species mean values on each other. In the random effects model, the P-value also approximates that based on the regression of species mean values. In the fixed effects model, the P-value is typically much lower. Simulated examples illustrate that the maximum-likelihood approach is useful when the accuracy in estimating the species mean values is low, but the traditional method based on a regression of the species mean values may often be justified provided that the evolutionary model can be justified.     

Maximizing plant species inventory efficiency by means of remotely sensed spectral distances

Aim Inventorying plant species in an area based on randomly placed quadrats can be quite inefficient. The aim of this paper is to test whether plant species richness can be inventoried more efficiently by means of a spectrally‐based ordering of sites to be sampled. Location The study area was a complex wetland ecosystem, the Lake Montepulciano Nature Reserve, central Italy. This is one of the most important wetland areas of central Italy because of the diverse plant communities and the seasonal avifauna. Methods Field sampling, based on a random stratified sampling design, was performed in June 2002. Plant species composition was recorded within sampling units of 100 m² (plots) and 1 ha (macroplots). A QuickBird multispectral image of the same date was acquired and corrected both geometrically and radiometrically. Species accumulation curves based on spectral information were obtained by ordering sites to be sampled according to a maximum spectral distance criterion (i.e. by ordering sampling units based on the maximum distances among them in a four‐dimensional spectral space derived from the remotely sensed data). Different distance measures based on mean and maximum spectral distances among sampling units were tested. The performance of the species accumulation curve derived by the spectrally‐based ordering of sampling units was tested against a rarefaction curve obtained from the mean of 10,000 accumulation curves based on randomly ordered sampling units. Results The spectrally‐derived curve based on the maximum spectral distance among sampling units showed the most rapid accumulation of species, well above the rarefaction curve, at both the plot and the macroplot scales. Other ordering criteria of sampling units captured less richness over most of the species accumulation curves at both the spatial scales. The accumulation curves based on other measurements of distance were much closer to the random curve and did not show differences with respect to the species rarefaction curve based on random ordering of sampling units. Main conclusions The present investigation demonstrated that spectral‐based ordering of sites to be sampled can lead to the maximization of the efficiency of plant species inventories, an activity usually driven by the ‘botanist's internal algorithm’ (intuition), without any formalized rule to drive field sampling. The proposed approach can reduce costs of plant species inventorying through a more efficient allotment of time and sampling.     

Evaluating Multi-Level Models to Test Occupancy State Responses of Plethodontid Salamanders

Plethodontid salamanders are diverse and widely distributed taxa and play critical roles in ecosystem processes. Due to salamander use of structurally complex habitats, and because only a portion of a population is available for sampling, evaluation of sampling designs and estimators is critical to provide strong inference about Plethodontid ecology and responses to conservation and management activities. We conducted a simulation study to evaluate the effectiveness of multi-scale and hierarchical single-scale occupancy models in the context of a Before-After Control-Impact (BACI) experimental design with multiple levels of sampling. Also, we fit the hierarchical single-scale model to empirical data collected for Oregon slender and Ensatina salamanders across two years on 66 forest stands in the Cascade Range, Oregon, USA. All models were fit within a Bayesian framework. Estimator precision in both models improved with increasing numbers of primary and secondary sampling units, underscoring the potential gains accrued when adding secondary sampling units. Both models showed evidence of estimator bias at low detection probabilities and low sample sizes; this problem was particularly acute for the multi-scale model. Our results suggested that sufficient sample sizes at both the primary and secondary sampling levels could ameliorate this issue. Empirical data indicated Oregon slender salamander occupancy was associated strongly with the amount of coarse woody debris (posterior mean = 0.74; SD = 0.24); Ensatina occupancy was not associated with amount of coarse woody debris (posterior mean = -0.01; SD = 0.29). Our simulation results indicate that either model is suitable for use in an experimental study of Plethodontid salamanders provided that sample sizes are sufficiently large. However, hierarchical single-scale and multi-scale models describe different processes and estimate different parameters. As a result, we recommend careful consideration of study questions and objectives prior to sampling data and fitting models.     

On a restricted occupancy model and its applications

With the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample of n individuals is drawn from a population consisting of m types with r individuals in each type, (i) without replacement and (ii) by returning the selected individual in the population and with it another individual of the same type. The distributions of the number Z of distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to the m equiprobable types of individuals, the existence of a control type, say, with s individuals, the joint distribution of the number U of distinct types observed in the sample and the number V of individuals of the control type present in the sample is obtained in terms of the numbers C(n, k, r) and the marginal distribution of U in terms of the Gould-Hopper numbers. Using these distributions minimum variance unbiased estimators of the number m of types are derived. Moreover small sample tests based on the zero frequency are constructed.     

Sampling strategy optimization to increase statistical power in landscape genomics: A simulation‐based approach

An increasing number of studies are using landscape genomics to investigate local adaptation in wild and domestic populations. Implementation of this approach requires the sampling phase to consider the complexity of environmental settings and the burden of logistical constraints. These important aspects are often underestimated in the literature dedicated to sampling strategies. In this study, we computed simulated genomic data sets to run against actual environmental data in order to trial landscape genomics experiments under distinct sampling strategies. These strategies differed by design approach (to enhance environmental and/or geographical representativeness at study sites), number of sampling locations and sample sizes. We then evaluated how these elements affected statistical performances (power and false discoveries) under two antithetical demographic scenarios. Our results highlight the importance of selecting an appropriate sample size, which should be modified based on the demographic characteristics of the studied population. For species with limited dispersal, sample sizes above 200 units are generally sufficient to detect most adaptive signals, while in random mating populations this threshold should be increased to 400 units. Furthermore, we describe a design approach that maximizes both environmental and geographical representativeness of sampling sites and show how it systematically outperforms random or regular sampling schemes. Finally, we show that although having more sampling locations (between 40 and 50 sites) increase statistical power and reduce false discovery rate, similar results can be achieved with a moderate number of sites (20 sites). Overall, this study provides valuable guidelines for optimizing sampling strategies for landscape genomics experiments.     

Sampling strategies for assessing the overall density of the cassava green mite (Mononychellus tanajoa)

Six different sampling methods to estimate the density of the cassava green mite, Mononychellus tanajoa, are categorized according to whether leaves or leaflets are used as secondary sampling units and whether the number of leaves on the sampled plants are enumerated, estimated from an independent plant sample, or not censused at all. In the last case, sampling can provide information only on the average number of mites per leaf and its variance, while information on stratum sizes is necessary to estimate the mean number of mites per plant as well. It is shown that leaflet-sampling is as reliable as leaf-sampling for the same number of sampling units. When stratum sizes are estimated from a separate plant sample, sampling time may also be reduced, but the estimated mean density and its variance may be biased if mite density and plant size are correlated. Sampling data show that the within-plant variance contributes relatively little to the overall variance of the population density estimates. It points at a sampling strategy in which the number of primary units (plants) is as large as possible at the expense of secondary units (leaflets) per plant. Mean-variance relationships may be applied to estimate sample variances and can be used even when only one leaflet is taken per plant per stratum. An unequal allocation of primary units among strata can increase precision, but the gain is small compared with an equal allocation. Leaf area can be predicted from the length of the longest leaflet and the number of leaflets.     

Relationship between sampling duration and concentration of culturable airborne mould and bacteria on selected culture media

AIMS: This study was designed to evaluate potential effects of sampling duration on observed concentrations of airborne culturable mould and bacteria on selected media. METHODS AND RESULTS: Airborne culturable mould and bacteria from lightly to moderately contaminated environments were collected on selected culture media using two co-located, concurrently operated, Andersen N-6 samplers for five sampling durations in the range of 1-10 min. Differences in mean concentrations, as well as linear relationships between sampling duration and both concentration and variability, were evaluated using nonparametric procedures. For the five sampling durations, there were no significant differences in mean concentrations of mould; for bacteria, there were significant differences, with a trend of decreasing concentrations as sampling duration increased. Data variability decreased with increasing sampling duration for both mould and bacteria. CONCLUSIONS: Airborne culturable mould concentrations were similar for sampling durations in the range of 1-10 min. Airborne bacteria concentrations tended to trend downwards with sampling durations exceeding 3 min. SIGNIFICANCE AND IMPACT OF THE STUDY: This study has shown that sampling durations of 1-10 min are appropriate for collection of airborne culturable mould on malt extract agar (MEA) and dichloran glycerol agar (DG-18); based on the apparent trend of decreasing bacterial sample concentrations associated with increasing sampling duration, sampling durations of 相似文献   

Limited effects of dominant ants on assemblage species richness in three Amazon forests

1. Ants are highly interactive organisms and dominant species are considered to be able to control the species richness of other ants via competitive exclusion. However, depending on the scale studied, inter‐specific competition may or may not structure biological assemblages. To date, ant dominance–richness relationships have only been studied in small sample units, where a few dominant colonies could plausibly control most of the sample unit. 2. We conducted a comprehensive survey of terrestrial ant assemblages using bait, pitfall, and litter‐sorting methods in three sites in Brazilian Amazonia. Using a spatially structured rarefaction approach, based on sampling units with linear dimensions ranging from 25 to 250 m, the mesoscale patterns of ant dominance–richness relationships (sampling units covering hundreds of meters separated by kilometers) were investigated. 3. Interference–competition models (parabolic or negative linear relationships between species richness and the abundance of dominant ants) tended to be more frequent in smaller sample units or in assemblages sampled with interactive methods, such as baits. Using more inclusive sampling methods, the relationship was generally asymptotic rather than parabolic, with no reduction in species diversity because of the presence of dominants. Random co‐occurrence patterns of species within sites support the interpretation of a limited role for present‐day competition in structuring these assemblages. 4. Competition from dominant species may reduce species richness in small areas, especially when artificial baits are used, but appears to be less important than environmental constraints in determining ant species richness across scales of hectares and greater in these Amazon forests.     

Scaling Occupancy Estimates up to Abundance for Wolves

Management of wildlife populations often requires reliable estimates of population size or distribution. Estimating abundance can be logistically difficult, and occupancy models have been used as a less expensive proxy for abundance estimation. Another alternative is to use independent estimates of home-range size and mean group size to directly scale occupancy estimates up to abundance. We used simulations to explore when scaling occupancy up to abundance is reliable, and as an example we applied an occupancy approach to estimate abundance of wolves (Canis lupus) from roadside snow-tracking surveys in northern Wisconsin, USA, in 2016 and 2018. Estimates of wolf abundance were plausible and compared favorably with independent estimates produced by territory mapping, and snow-tracking data requirements were lower than for territory mapping. Simulation results suggested that reasonable abundance estimates could be obtained under some conditions but also that severe positive bias could result under other conditions, especially when populations were small and dispersed, home range size was small, and areal sampling units were large. Positive bias in abundance estimates occurs because of closure assumption violations when tracks from a single wolf or pack are detected in >1 sample unit, and the sum of the sample unit areas where tracks were detected exceed the sum of the home range areas. Bias was minimized when sampling units were small relative to home range size or when sampling units were route segments that approximate point sample units, and when home ranges were highly aggregated. We conclude that, although caution is warranted when scaling occupancy estimates up to abundance, scaled occupancy models can provide feasible and reliable estimates of abundance, assuming home range size and mean group size are accurately known or estimated, sampling units are appropriately chosen, and covariates that aggregate home ranges can be used to accurately predict occupancy probability. © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.