On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Sampling

We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x. It is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.     

Random median sampling to enhance the precision of population estimates

We describe the characteristics of a sampling procedure called random median sampling that was proposed to enhance the precision of population estimates. In performing random median sampling, we first select a sampling item at random from the sampling area. We roughly compare the abundance of individuals in the selected item with that of the adjacent two items in order to identify the item that has median abundance, i.e., the item that has the second largest abundance among the three items. We count the number of individuals of the item having the median abundance. This procedure is repeated n times in the sampling area (i = 1, 2, ..., n). Let m _i be the ith median abundance. The estimates of the mean abundance per sampling item and the variance of estimates are given by Σm _i /n and Σ(m _i –Σm _i /n)²/n(n – 1), respectively. This method is a local application of the median ranked set sampling that was proposed by Muttlak (J Appl Stat Sci 6:245–255, 1997). Random median sampling is effective when the correlation coefficient between adjacent items is small. If the correlation coefficient is close to zero, random median sampling reduces the variance of estimates to 45 or 32% of that in simple random sampling when the distribution follows a normal distribution or a Laplace distribution, respectively. The sample size required to achieve a given precision of estimate decreases accordingly. The effectiveness of random median sampling, however, is small if the correlation coefficient is large. The condition in which random median sampling is superior to simple random sampling is also discussed.     

Time-budget data: Log-linear and analysis of variance compared

Analysis of variance (ANOVA) and log-linear analyses of time-budget data from a study of sloth bear enclosure utilization are compared. Two sampling models that plausibly underlie such data are discussed. Either could lead to an analysis of variance, but only one to a log-linear analysis. Given an appropriate sampling model and appropriate data, there is much to recommend log-linear analysis, despite its unfamiliarity to most animal behaviorists. One need not worry whether distribution assumptions are violated. Moreover, the data analyzed are the data collected, not estimates derived from those data, and thus no power is lost through a data reduction step. No matter what analysis is used, effect size should be taken into consideration. Multiple R² can be used for ANOVA, but no directly comparable statistic exists for log-linear analyses. One possible candidate for a log-linear R² analog is discussed here, and appears to give sensible and interpretable results. © 1992 Wiley-Liss Inc.     

On Asymptotically Distribution-Free Confidence Bounds for P (X1≥X2) Based on Samples not Necessarily Independent

If X₁, X₂, denote the random variables of measurement under two treatments then the probability P (X₁ ≥ X₂) is a quantity of great practical interest, especially if we consider both to be measured for the same unity. In this case the random variables cannot be assumed to be independent any longer. The following paper describes a procedure to compute approximate confidence bounds for P (X₁ ≥ X₂) where correlations between X₁, X₂ are admitted as well as between replications of the X_j. There is some relation to the FRIEDMAN-statistic with or without repeated measurements and as a special case to the sign-test. Application may be extended to ordinal data.     

Sampling bias exaggerates a textbook example of a trophic cascade

Understanding trophic cascades in terrestrial wildlife communities is a major challenge because these systems are difficult to sample properly. We show how a tradition of non-random sampling has confounded this understanding in a textbook system (Yellowstone National Park) where carnivore [Canis lupus (wolf)] recovery is associated with a trophic cascade involving changes in herbivore [Cervus canadensis (elk)] behaviour and density that promote plant regeneration. Long-term data indicate a practice of sampling only the tallest young plants overestimated regeneration of overstory aspen (Populus tremuloides) by a factor of 4–7 compared to random sampling because it favoured plants taller than the preferred browsing height of elk and overlooked non-regenerating aspen stands. Random sampling described a trophic cascade, but it was weaker than the one that non-random sampling described. Our findings highlight the critical importance of basic sampling principles (e.g. randomisation) for achieving an accurate understanding of trophic cascades in terrestrial wildlife systems.     

Accurate determination of vegetational change in meadows by successive point quadrat analysis

The point quadrat method can be used for determination of vegetational change in meadows of great species diversity. An appropriate sampling technique is described comprehending an apparatus of high rigidity and a shelter to keep off wind and rain. Sample size related to sampling time expense affects the number of species recorded and methodical error which is empirically determined by repetitive sampling. A setup of fixed points leads to higher accuracy than random sampling. When methodical error is quantitatively known, significant vegetational change can be detected by sampling at successive times.For fluctuation studies of plant populations in meadows the point quadrat technique should be preferred to visual estimates of plant cover because of its higher accuracy.Abbreviations f= frequency - s= standard deviation - Sr= variation coefficient - DWLS= distance weighted least squares     

On the Analysis of Variance for Time Sequenced Samples

The 3 way nested ANOVA model y_ijk = μ + a_i + B_ij + γ_k + (αγ)_ik + epsilon_ijk With α (treatment or group effects) and γ (time) both being fixed effects and B (the individual effects) random and nested within α, is introduced and explored. The problems associated with the usual approach are explained. The alternative model Is developed and a method of evaluation via the method of linear contrasts is recomended. The test statistic has the distribution of a convolution of F-distributions. Further, a method of investigating the assumptions of the model is offered and a further generalization using path spaces (of dim. K) is developed. Here again the appropriate test statistic has the distribution of a convolution of F-distributions. This combined with the method of linear contrasts offers an elegant solution to the BEHRENS-FISHER problem. y_ijk = f_ik + B_ij + epsilon_ijk     

Estimation of sampling variance of molecular marker data using the bootstrap procedure

Knowledge of genetic relationships among genotypes is useful in a plant breeding program because it permits the organization of germplasm and provides for more efficient sampling. The genetic distance (GD) among genotypes can be estimated using random restriction fragment length polymorphisms (RFLPs) as molecular markers. Knowledge of the sampling variance associated with RFLP markers is needed to determine how many markers are required for a given level of precision in the estimate of GD. The sampling variance for GD among all pairs of 37 maize (Z. mays L.) inbred lines was estimated from 1202 RFLPs. The 1202 polymorphisms were generated from 251 enzyme-probe combinations (EPC). The sampling variance was used to determine how large a sample of RFLPs was required to provide a given level of precision. The coefficient of variation (CV) associated with GD has a nearly linear relationship between its expected standard deviation and mean. The magnitude of the decrease in the mean CV for GD with increasing numbers of bands was dependent upon the sampling unit; e.g., individual polymorphic bands vs EPC, and the degree of relatedness among the inbreds compared. The rate of reduction in mean CV with increasing sample size was the same regardless of the restriction enzyme used, BamHI, EcoRI or HindIII, when the bootstrap sampling units were individual polymorphic bands. In constrast, although the rate of reduction (slopes) was the same, the intercepts of the mean CVs were different when EPCs were used as the bootstrap sampling unit. This difference was due to the higher number of bands per EPC in BamHI (4.94) compared with EcoRI (4.83) and HindIII (4.63).     

Evaluating sampling designs by computer simulation: a case study with the Missouri bladderpod

To effectively manage rare populations, accurate monitoring data are critical. Yet many monitoring programs are initiated without careful consideration of whether chosen sampling designs will provide accurate estimates of population parameters. Obtaining accurate estimates is especially difficult when natural variability is high, or limited budgets determine that only a small fraction of the population can be sampled. The Missouri bladderpod, Lesquerella filiformis Rollins, is a federally threatened winter annual that has an aggregated distribution pattern and exhibits dramatic interannual population fluctuations. Using the simulation program SAMPLE, we evaluated five candidate sampling designs appropriate for rare populations, based on 4 years of field data: (1) simple random sampling, (2) adaptive simple random sampling, (3) grid-based systematic sampling, (4) adaptive grid-based systematic sampling, and (5) GIS-based adaptive sampling. We compared the designs based on the precision of density estimates for fixed sample size, cost, and distance traveled. Sampling fraction and cost were the most important factors determining precision of density estimates, and relative design performance changed across the range of sampling fractions. Adaptive designs did not provide uniformly more precise estimates than conventional designs, in part because the spatial distribution of L. filiformis was relatively widespread within the study site. Adaptive designs tended to perform better as sampling fraction increased and when sampling costs, particularly distance traveled, were taken into account. The rate that units occupied by L. filiformis were encountered was higher for adaptive than for conventional designs. Overall, grid-based systematic designs were more efficient and practically implemented than the others. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Note on Systematic Sampling

In the use of systematic sampling in surveys it is known that the effect of negative correlations (=ϱ_wst) between deviations from stratum means of pairs of items in the same systematic sample is such that the resulting variance V(ȳ_st) can be zero for systematic sample means ȳ_st (e.g., Cochran, 1977, ch. 8). For such populations systematic sampling is then superior both to stratified sampling (one unit per stratum) and to simple random sampling. Cochran (loc. cit.) does not identify special types of finite populations for which ϱ_wst = −1/(n -1) and hence V(ȳ_st) =0. It is the purpose of this paper to present one type of population for which this condition is satisfied.     

Allozyme and morphological variability,outcrossing rate and core collection formation in lentil germplasm

Summary A survey of qualitative genetic variation at 3 morphological trait loci, 17 isozyme loci and a putative isozyme locus (amylase) was made for 105 lentil (Lens culinaris Medikus) germplasm accessions from Chile, Greece and Turkey. New alleles were found for Lap-1, Me-2, Pgm-c, Pgm-p and 6-Pgd-c. The average proportion of polymorphic loci per population was 0.19, with a range of 0 to 0.42 over populations. Germplasm from Chile was equally variable to that from Greece and Turkey on the basis of individual loci and in a multilocus sense, despite its post-Columbus introduction to the New World. Evidence was found from associations between allelic states at different loci of a complex multilocus structure of lentil populations. A single multilocus genotype represented 10.2% of all plants sampled. The rate of outcrossing varied from 2.2% and 2.9% in Turkish and Greek landraces to 6.6% among Chilean populations. Using the survey data, a random sampling strategy for core collection formation was compared with two stratified sampling methods. The advantage of stratified sampling over random sampling was only significant at P=0.28.     

Spatial autocorrelation and sampling design in plant ecology

Using spatial analysis methods such as spatial autocorrelation coefficients (Moran's I and Geary's c) and kriging, we compare the capacity of different sampling designs and sample sizes to detect the spatial structure of a sugar-maple (Acer saccharum L.) tree density data set gathered from a secondary growth forest of southwestern Québec. Three different types of subsampling designs (random, systematic and systematic-cluster) with small sample sizes (50 and 64 points), obtained from this larger data set (200 points), are evaluated. The sensitivity of the spatial methods in the detection and the reconstruction of spatial patterns following the application of the various subsampling designs is discussed. We find that the type of sampling design plays an important role in the capacity of autocorrelation coefficients to detect significant spatial autocorrelation, and in the ability to accurately reconstruct spatial patterns by kriging. Sampling designs that contain varying sampling steps, like random and systematic-cluster designs, seem more capable of detecting spatial structures than a systematic design.Abbreviations UPGMA = Unweighted Pair-Group Method using Arithmetic Averages     

Comparison of survey methods for an invasive plant at the subwatershed level

Invasive plant survey methods that are practical and economical are needed to describe established colonies and detect nascent invaders. We compared results from random and roadside surveys of Alliaria petiolata (Bieb.) Cavara & Grande across a 5730-ha subwatershed. The random survey included 150 1-ha plots; the roadside survey examined 0.1-mile increments (10-m deep) along paved roads (totaling 1104 0.16-ha plots). In the random survey, agriculture was the dominant land use (49% of sampled area), and most A. petiolata patches were in wooded, shaded riparian, and waste areas (34%, 34%, and 29% of patches, respectively). In the roadside survey, right-of-way land use was dominant (38% of sampled area), and most A. petiolata patches were in right-of-way, wooded, and shaded riparian areas (53%, 22%, and 19% of patches, respectively). According to generalized linear model analysis, survey methods did not differ in the overall probability of finding A. petiolata (P=0.17 and 0.11 for random and roadside surveys, respectively). Shaded riparian, wooded, and mixed-species right-of-way land uses were the dominant habitat for A. petiolata in both surveys, but only the random survey indicated waste areas as significant habitat. Alliaria petiolata occurred mostly as small patches in roadsides, but as large patches in random plots, suggesting faster spread in the roadside. Results indicated that disturbed lands along roadsides were important for invasion and spread of A. petiolata; therefore, the roadside survey was a useful, practical method for detecting nascent invasions and management planning. The random sampling lacked a land use bias, and provided data that could be generalized across the subwatershed; however, this method required at least four times more person hours to complete than the roadside survey for a similar amount of area. Although roadside sampling did not provide a completely reliable assessment of target plant populations within the landscape, it may provide an adequate approximation, depending on the specific goals of the survey. Concurrent surveys would provide the most complete information.     

Sampling strategies for the assessment of tree species diversity

Abstract. This paper aims at proposing efficient vegetation sampling strategies. It describes how the estimation of species richness and diversity of moist evergreen forest is affected by (1) sampling design (simple random sampling, random cluster sampling, systematic cluster sampling, stratified cluster sampling); (2) choice of species richness estimators (number of observed species vs. non-parametric estimators) and (3) choice of diversity index (Simpson vs. Shannon). Two sites are studied: a 28-ha area situated in the Western Ghats of India and a 25-ha area located at Pasoh in Peninsular Malaysia. The results show that: (1) whatever the sampling strategy, estimates of species richness depend on sample size in these very diverse forest ecosystems which contain many rare species; (2) Simpson's diversity index reaches a stable value at low sample sizes while Shannon's index is affected more by the addition of rare species with increasing sample size; (3) cluster sampling strategies provide a good compromise between cost and statistical efficiency; (4) 300 - 400 sample trees grouped in small clusters (10–50 individuals) are enough to obtain unbiased and precise estimates of Simpson's index; (5) the local topography of the Western Ghats has a major influence on forest composition, the steep slopes being richer and more diverse than the ridges and gentle slopes; (6) stratified cluster sampling is thus an interesting alternative to systematic cluster sampling.     

Sampling Hubbell's neutral theory of biodiversity

In the context of neutral theories of community ecology, a novel genealogy‐based framework has recently furnished an analytic extension of Ewens’ sampling multivariate abundance distribution, which also applies to a random sample from a local community. Here, instead of taking a multivariate approach, we further develop the sampling theory of Hubbell's neutral spatially implicit theory and derive simple abundance distributions for a random sample both from a local community and a metacommunity. Our result is given in terms of the average number of species with a given abundance in any randomly extracted sample. Contrary to what has been widely assumed, a random sample from a metacommunity is not fully described by the Fisher log‐series, but by a new distribution. This new sample distribution matches the log‐series expectation at high biodiversity values (θ > 1) but clearly departs from it for species‐poor metacommunities (θ < 1). Our theoretical framework should be helpful in the better assessment of diversity and testing of the neutral theory by using abundance data.     

Profile of a 24 kDa Mycobacterium tuberculosis antigen in the urine samples of tuberculosis patients under therapy regime

Secretion of a low molecular weight (24 kDa) Mycobacterium tuberculosis-specific antigen was analysed in the urine samples of tuberculosis patients under antimycobacterial therapy regime. The urine samples of sputum-positive and culture-positive tuberculosis patients under therapy regime were collected after 2, 3, 4, 5 and 6 months of antimycobacterial therapy. After concentration of the samples by ultrafiltration the proteins were resolved by SDS–PAGE. The antibodies raised in rabbits against M. tuberculosis strain H₃₇Ra were used to check specificity of the bands by Western blotting. It was found that the tuberculosis patients secreted a 24 kDa M. tuberculosis-specific antigen in their urine. This band was present in the samples taken upto 5 months of drug therapy but was absent in the samples taken after 6 months of antimycobacterial therapy. This study gives evidence in support of the continuation of chemotherapy of tuberculosis patients for at least 6 months. Also, the 24 kDa excreted/secreted antigen can be used as a marker for monitoring the drug therapy as well as for the diagnosis of tuberculosis patients. Moreover, the urine sample taken in the study is a non-invasive and safer sampling method as compared to sampling blood or sputum which is the usual procedure in these patients.     

Spatially autocorrelated sampling falsely inflates measures of accuracy for presence‐only niche models

Aim Environmental niche models that utilize presence‐only data have been increasingly employed to model species distributions and test ecological and evolutionary predictions. The ideal method for evaluating the accuracy of a niche model is to train a model with one dataset and then test model predictions against an independent dataset. However, a truly independent dataset is often not available, and instead random subsets of the total data are used for ‘training’ and ‘testing’ purposes. The goal of this study was to determine how spatially autocorrelated sampling affects measures of niche model accuracy when using subsets of a larger dataset for accuracy evaluation. Location The distribution of Centaurea maculosa (spotted knapweed; Asteraceae) was modelled in six states in the western United States: California, Oregon, Washington, Idaho, Wyoming and Montana. Methods Two types of niche modelling algorithms – the genetic algorithm for rule‐set prediction (GARP) and maximum entropy modelling (as implemented with Maxent) – were used to model the potential distribution of C. maculosa across the region. The effect of spatially autocorrelated sampling was examined by applying a spatial filter to the presence‐only data (to reduce autocorrelation) and then comparing predictions made using the spatial filter with those using a random subset of the data, equal in sample size to the filtered data. Results The accuracy of predictions from both algorithms was sensitive to the spatial autocorrelation of sampling effort in the occurrence data. Spatial filtering led to lower values of the area under the receiver operating characteristic curve plot but higher similarity statistic (I) values when compared with predictions from models built with random subsets of the total data, meaning that spatial autocorrelation of sampling effort between training and test data led to inflated measures of accuracy. Main conclusions The findings indicate that care should be taken when interpreting the results from presence‐only niche models when training and test data have been randomly partitioned but occurrence data were non‐randomly sampled (in a spatially autocorrelated manner). The higher accuracies obtained without the spatial filter are a result of spatial autocorrelation of sampling effort between training and test data inflating measures of prediction accuracy. If independently surveyed data for testing predictions are unavailable, then it may be necessary to explicitly account for the spatial autocorrelation of sampling effort between randomly partitioned training and test subsets when evaluating niche model predictions.     

Nested subset structure of larval mycophagous fly assemblages: nestedness in a non-island system

Nested subset structure has been studied in archipelagoes and fragmented habitats, and has been attributed to differential colonization and extinction rates among species and nested environmental tolerances. In this experiment, we tested for nestedness in assemblages of mycophagous fly larvae. Twenty mushrooms in each of three size classes (4.8–6.0 g, 10–15 g, 21–32 g) were placed on moist potting soil in experimental cups. The cups were placed in oak and pine forests in Greenville, S.C., USA for 5 days, where they were available to ovipositing flies. Upon collection, the mushrooms were incubated in the laboratory for 3 weeks and all emerging flies were sorted by species, counted, and weighed. A random placement analysis was conducted to determine whether the species richness pattern was a sampling artifact of the species abundance distributions. The actual species richness pattern did not conform to the random placement model; most mushrooms contained significantly fewer species than predicted by random sampling. The communities were strongly nested as measured by two different indices, and the nestedness pattern was related to mushroom size. Small mushrooms usually produced no flies or a single species, Dohrniphora sp. (Phoridae). Medium and large mushrooms typically produced more species-rich communities that usually contained the phorid and Drosophila putrida, D. tripunctata, and Leucophenga varia. This core guild was nested within a more diverse assemblage that included D. falleni, Mycodrosophila dimidiata, a muscid, and two Leptocera sp. (sphaeroceridae). These patterns are tentatively explained in the context of nested desiccation tolerances, mediated by differences in mushroom size.     

An optimized protocol for large‐scale in situ sampling and analysis of volatile organic compounds

Chemical ecology is an ever‐expanding field with a growing interest in population‐ and community‐level studies. Many such studies are hindered due to lack of an efficient and accelerated protocol for large‐scale sampling and analysis of chemical compounds. Here, we present an optimized protocol for such large‐scale study of volatiles. A large‐scale in situ study to understand role of semiochemicals in variation in mating success of lekking blackbuck was conducted. Suitable methods for sampling and statistical analysis were identified by testing and comparing the efficiencies of available techniques to reduce analysis time while retaining sensitivity and comprehensiveness. Solid‐phase extraction using polydimethylsiloxane, analysis using a semiautomated detection of retention time and base peak, and statistical analysis using random forest algorithm were identified as the most efficient methods for large‐scale in situ sampling and analysis of volatiles. The protocol for large‐scale volatile analysis can facilitate evolutionary and metaecological studies of volatiles in situ from all types of biological samples. The protocol has potential for wider application with the analysis and interpretation methods being suitable for all kinds of semiochemicals, including nonvolatile chemicals.