Adaptive cluster sampling with clusters selected without replacement and stopping rule

Adaptive cluster sampling (ACS) has received much attention in recent years since it yields more precise estimates than conventional sampling designs when applied to rare and clustered populations. These results, however, are impacted by the availability of some prior knowledge about the spatial distribution and the absolute abundance of the population under study. This prior information helps the researcher to select a suitable critical value that triggers the adaptive search, the neighborhood definition and the initial sample size. A bad setting of the ACS design would worsen the performance of the adaptive estimators. In particular, one of the greatest weaknesses in ACS is the inability to control the final sampling effort if, for example, the critical value is set too low. To overcome this drawback one can introduce ACS with clusters selected without replacement where one can fix in advance the number of distinct clusters to be selected or ACS with a stopping rule which stops the adaptive sampling when a predetermined sample size limit is reached or when a given stopping rule is verified. However, the stopping rule breaks down the theoretical basis for the unbiasedness of the ACS estimators introducing an unknown amount of bias in the estimates. The current study improves the performance of ACS when applied to patchy and clustered but not rare populations and/or less clustered populations. This is done by combining the stopping rule with ACS without replacement of clusters so as to further limit the sampling effort in form of traveling expenses by avoiding repeat observations and by reducing the final sample size. The performance of the proposed design is investigated using simulated and real data.     

Quantifying dispersal and establishment limitation in a population of an epiphytic lichen

Dispersal is a process critical for the dynamics and persistence of metapopulations, but it is difficult to quantify. It has been suggested that the old-forest lichen Lobaria pulmonaria is limited by insufficient dispersal ability. We analyzed 240 DNA extracts derived from snow samples by a L. pulmonaria-specific real-time PCR (polymerase chain reaction) assay of the ITS (internal transcribed spacer) region allowing for the discrimination among propagules originating from a single, isolated source tree or propagules originating from other locations. Samples that were detected as positives by real-time PCR were additionally genotyped for five L. pulmonaria microsatellite loci. Both molecular approaches demonstrated substantial dispersal from other than local sources. In a landscape approach, we additionally analyzed 240 snow samples with real-time PCR of ITS and detected propagules not only in forests where L. pulmonaria was present, but also in large unforested pasture areas and in forest patches where L. pulmonaria was not found. Monitoring of soredia of L. pulmonaria transplanted to maple bark after two vegetation periods showed high variance in growth among forest stands, but no significant differences among different transplantation treatments. Hence, it is probably not dispersal limitation that hinders colonization in the old-forest lichen L. pulmonaria, but ecological constraints at the stand level that can result in establishment limitation. Our study exemplifies that care has to be taken to adequately separate the effects of dispersal limitation from a limitation of establishment.     

The application of adaptive cluster sampling for rare subtidal macroalgae

Adaptive cluster sampling (ACS) is a targeting sampling method that provides unbiased abundance estimators for populations of rare species that may be inadequately sampled with simple random sampling (SRS). ACS has been used successfully to estimate abundances of rockfish and sardine larvae from shipboard surveys. In this study, we describe the application of ACS for subtidal macroalgae. Using SCUBA, we measured abundances of Codium mamillosum, C. pomoides, and Halimeda cuneata at three islands and two levels of wave exposure. The three species were relatively patchy and could be sampled with ACS at one site per dive. Their distributions differed among islands and with exposure to wave energy, with H. cuneata found at only one island. ACS is a useful tool for understanding the spatial distribution and abundance of populations of rare benthic species, but, as was the case in this study, may not be as efficient as sampling with SRS with comparable replication.     

Gravity currents with double stratification: a numerical and analytical investigation

We consider high-Reynolds-number Boussinesq gravity current and intrusion systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a rectangular lock; the height ratio of the fluids $H$ , the stratification parameter of the ambient $S$ , and the internal stratification parameter of the current, $\sigma $ , are quite general. We perform two-dimensional Navier–Stokes simulation and compare the results with those of a previously-published one-layer shallow-water model. The results provide insights into the behavior of the system and enhance the confidence in the approximate model while also revealing its limitations. The qualitative predictions of the model are confirmed, in particular: (1) there is an initial “slumping” stage of propagation with constant speed $u_N$ , after which $u_N$ decays with time; (2) for fixed $H$ and $S$ , the increase of $\sigma $ causes a slower propagation of the current; (3) for some combinations of the parameters $H,S, \sigma $ the fluid released from the lock lacks initially (or runs out quickly of) buoyancy “driving power” in the horizontal direction, and does not propagate like a gravity current. There is also a fair quantitative agreement between the predictions of the model and the simulations concerning the spread of the current.     

Application of adaptive cluster sampling to low-density populations of freshwater mussels

Freshwater mussels appear to be promising candidates for adaptive cluster sampling because they are benthic macroinvertebrates that cluster spatially and are frequently found at low densities. We applied adaptive cluster sampling to estimate density of freshwater mussels at 24 sites along the Cacapon River, WV, where a preliminary timed search indicated that mussels were present at low density. Adaptive cluster sampling increased yield of individual mussels and detection of uncommon species; however, it did not improve precision of density estimates. Because finding uncommon species, collecting individuals of those species, and estimating their densities are important conservation activities, additional research is warranted on application of adaptive cluster sampling to freshwater mussels. However, at this time we do not recommend routine application of adaptive cluster sampling to freshwater mussel populations. The ultimate, and currently unanswered, question is how to tell when adaptive cluster sampling should be used, i.e., when is a population sufficiently rare and clustered for adaptive cluster sampling to be efficient and practical? A cost-effective procedure needs to be developed to identify biological populations for which adaptive cluster sampling is appropriate.     

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.     

A diagnostic test for autocorrelation in increment-averaged data with application to soil sampling

Motivated by the problem of detecting spatial autocorrelation in increment- averaged data from soil core samples, we use the Cholesky decomposition of the inverse of an autocovariance matrix to derive a parametric linear regression model for autocovariances. In the absence of autocorrelation, the off-diagonal terms in the lower triangular matrix from the Cholesky decomposition should be identically zero, and so the regression coefficients should be identically zero. The standard F-test of this hypothesis and two bootstrapped versions of the test are evaluated as autocorrelation diagnostics via simulation. Size is assessed for a variety of heteroskedastic null hypotheses. Power is evaluated against autocorrelated alternatives, including increment-averaged Ornstein-Uhlenbeck and Matérn processes. The bootstrapped tests maintain approximately the correct size and have good power against moderately autocorrelated alternatives. The methods are applied to data from a study of carbon sequestration in agricultural soils.     

Estimator bias and efficiency for adaptive cluster sampling with order statistics and a stopping rule

Practical problems facing adaptive cluster sampling with order statistics (acsord) are explored using Monte Carlo simulation for three simulated fish populations and two known waterfowl populations. First, properties of an unbiased Hansen-Hurwitz (HH) estimator and a biased alternative Horvitz-Thompson (HT) estimator are evaluated. An increase in the level of population aggregation or the initial sample size increases the efficiencies of the two acsord estimators. For less aggregated fish populations, the efficiencies decrease as the order statistic parameter r (the number of units about which adaptive sampling is carried out) increases; for the highly aggregated fish and waterfowl populations, they increase with r. Acsord is almost always more efficient than simple random sampling for the highly aggregated populations. Positive bias is observed for the HT estimator, with the maximum bias usually occurring at small values of r. Secondly, a stopping rule at the Sth iteration of adaptive sampling beyond the initial sampling unit was applied to the acsord design to limit the otherwise open-ended sampling effort. The stopping rule induces relatively high positive bias to the HH estimator if the level of the population aggregation is high, the stopping level S is small, and r is large. The bias of HT is not very sensitive to the stopping rule and its bias is often reduced by the stopping rule at smaller values of r. For more aggregated populations, the stopping rule often reduces the efficiencies of the estimators compared to the non-stopping-rule scheme, but acsord still remains more efficient than simple random sampling. Despite its bias and lack of theoretical grounding, the HT estimator is usually more efficient than the HH estimator. In the stopping rule case, the HT estimator is preferable, because its bias is less sensitive to the stopping level.     

Analyzing spatial count data,with an application to weed counts

Count data on a lattice may arise in observational studies of ecological phenomena. In this paper a hierarchical spatial model is used to analyze weed counts. Anisotropy is introduced, and a bivariate extension of the model is presented.     

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.     

A test for space limitation with an application to recently settled lobsters

Space limitation in larval settlement can play an important role in the population dynamics of marine species. A novel statistical test for space limitation based on quadrat counts of individuals is described. The test is based on identifying a significant relationship between the relative dispersion of quadrat counts and overall mean density. An application to a time series of quadrat counts of recently settled American lobsters Homarus americanus covering the period 1993–2007 in Casco Bay, Maine, USA (43°45′N; 69°58′W), is presented. For this data set, the null hypothesis that space is not limiting could not be rejected (P = 0.10).     

Dislodgeable residues of profenofos on jasmine and risk assessment of post application exposure to flower bud pickers

A field study was conducted to measure the dislodgeable residues of profenofos applied to jasmine (Jasminum sambac) and risk assessment was done for laborers engaged in picking of flower buds. Profenofos was applied at 0.10, 0.15, and 0.20% concentration and the jasmine bud samples were analysed for residues using GC. The initial deposit of 1.6–3.8, 3.8–7.1, and 5.2–7.6 µg cm^?2 was detected on jasmine buds at 0.10, 0.15, and 0.20% concentration, respectively. At the recommended dose of 0.10%, the half-life was 1–2 days and the dislodgeable residues disappeared within 7 days. The results indicate faster disappearance of dislodgeable residues on jasmine buds. Risk assessment was done based on dislodgeable foliar residues and exposure estimates based on surrogate data and expressed as Margin of Exposure (MOE). The entry restrictions for exposure of jasmine flower pickers to profenofos, would be at least, 1 day following application, for the recommended concentration of 0.10% (MOE = 106) and 3 days, at higher concentrations of 0.15% (MOE = 156) and 0.20% (MOE = 115).     

Plant competition varies with community composition in an edaphically complex landscape

There is currently no consensus on how physical and biological factors affect competitive intensity. Tests of whether competitive intensity varies along axes of environmental change have commonly been conducted in systems with a single strong environmental gradient, such as productivity, a soil resource, or an environmental stress. Frequently, these same axes are associated with changes in species composition, yet few studies have asked whether shifts in the identity of competitors affect competitive intensity. We ask whether resources (nutrients, water), stressors (heavy metals, Ca:Mg ratio), productivity (aboveground biomass), or species identity (an ordination axis of plant community composition) were the best predictors of the intensity of competition in a heterogeneous grassland landscape that included multiple independent environmental gradients. The reproductive fitness of six annual plant species was measured in the presence and absence of competitors and used to calculate relative interaction intensity (RII). We found that RII was best predicted by community composition. Nutrient availability was also important, and a post hoc test showed that competitive intensity was best explained by the combined effects of community composition and nutrient availability. We argue that community composition may be the most effective metric for predicting competitive intensity in many ecosystems because it includes both the competitive effects of the local community and information about covarying environmental characteristics.     

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.     

Non-homogeneous Poisson models with a change-point: an application to ozone peaks in Mexico city

In this paper, we use some non-homogeneous Poisson models in order to study the behavior of ozone measurements in Mexico City. We assume that the number of ozone peaks follows a non-homogeneous Poisson process. We consider four types of rate function for the Poisson process: power law, Musa–Okumoto, Goel–Okumoto, and a generalized Goel–Okumoto rate function. We also assume that a change-point may or may not be present. The analysis of the problem is performed by using a Bayesian approach via Markov chain Monte Carlo methods. The best model is chosen using the DIC criterion as well as graphical approach.     

Distance-based eigenvector maps (DBEM) to analyse metapopulation structure with irregular sampling

Characterizing spatial patterns due to ecological processes is a major issue for analysing and predicting species distributions. Grasping the non-linear nature of population dynamics over networks of discrete suitable sites is here central, as very specific signatures are expected. In the line of promising results from Fourier analysis of metapopulation maps, we found distance-based eigenvector maps (DBEM) to help disentangle the respective signatures of habitat and metapopulation structuring, with the great advantage of being applicable to irregular sampling schemes, a common feature of ecological surveys. A smoothing procedure was required to obtain the distinguishable signatures, and this may be a critical issue for investigating non-contingent and reliable patterns in spatial ecology.     

A co-operative approach to risk management in an active lead/zinc smelter community

Trail, Canada has been the site of a large lead/zinc smelting facility since 1916. In mid 1990, the Trail Community Lead Task Force was established and given responsibility for developing a strategy to reduce children's blood lead levels. With funding from the provincial government, the smelting company and the municipal government, the Task Force has carried out blood lead screening, case management, community education, exposure pathways modelling and remediation trials. The decline in children's blood lead levels appeared to accelerate following the implementation of these programmes. The average blood lead in Trail children aged 6–72 months fell 14% from the autumn of 1991 to autumn of 1992, whereas for the previous 16 years, the average annual decline had been about 4%. In subsequent years, blood lead levels have appeared to plateau. Throughout the 5-year history of the Task Force, its members have demonstrated a strong sense of common purpose and have worked co-operatively to reach consensus on most issues.     

Zooplankton community structure across an eddy-generated upwelling band close to a tropical bay-mangrove ecosystem

Mesoscale eddies in the world’s oceans are ubiquitous and bring about episodic pulses of nutrients into the photic zone. Transient in nature, the role of eddy pumping in coastal enrichment via plankton production, and subsequent organic flux is not yet fully realised. In the context of a cyclonic cold-core eddy that propagates annually under the influence of the East India Coastal Current and enriches coastal waters in the western Bay of Bengal north of 16°N, a detailed study on zooplankton community structure along with phytoplankton composition and associated water quality was undertaken during April–May 2002 coinciding with the spring intermonsoon. Zooplankton samples were collected at 32 hydrographically different (salinity 24.5–35.6 PSU) GPS fixed locations representing bay-mangrove areas and nearshore waters (30 m) close to the River Godavari, which is one of India’s largest estuarine systems. During the study, the bay-coastal waters were typified by elevated nutrient levels (nitrate 10.73–22.04 μM), high salinity (27.98–35.52 PSU), and relatively low temperatures (30.63–31.40°C). Altogether, 95 zooplankton taxa were encountered with copepods forming the predominant population. Agglomerative Hierarchical Cluster Analysis (AHCA) and Non-metric Multidimensional Scaling (NMDS) based on Bray–Curtis similarity (PRIMER) analysis revealed appreciable alterations in zooplankton structure across bay-mangrove locations and coastal waters (Stress 0.11; ANOSIM test Global R: 0.94, P = 0.1%). Similarity Percentage (SIMPER) analysis revealed zooplankton associations through “discriminating species” for each location (Kakinada Bay, Cluster I, 27.9 ± 3.0 PSU; upwelling band, cluster II, 35.5 ± 0.2 PSU; offshore waters, cluster III, 34.2 ± 0.4 PSU; mangrove outlets, cluster IV, 32.7 ± 1.3 PSU and mangrove creeks, cluster V, 33.5 ± 0.6 PSU). The index of multivariate dispersion (IMD) illustrated high variability in zooplankton standing stock for mangrove/sea locations relative to the bay. Concurrent observations on phytoplankton revealed the importance of diatoms (r: 0.640, P ≤ 0.05). Within the eddy-generated band of upwelled water, a significant top-down control of diatoms by herbivorous zooplankton resulted in a comparative increase in abundance of dinophyceans. Based on zooplankton abundance data and species association patterns, it was possible to distinguish different zooplankton/copepod communities in accordance with mesoscale variability in physical, chemical and biological processes under tropical conditions. This was confirmed through canonical correspondence analysis (CCA) that represented coastal-offshore waters and the Bay environment in this area.     

Sine-skewed axial distributions with an application for fallen tree data

An axis is an undirected line where there is no reason to distinguish one end of the line from the other. Phenomena in nature that can be described as axial data are numerous. In this paper a method of trigonometric moments for the axial normal or axial von Mises distribution as an alternative to the method by Arnold and SenGupta (Environ Ecol Stat 13:271–285, 2006) is discussed. Sine-skewed axial Jones–Pewsey, von Mises and wrapped Cauchy distributions are introduced as special cases of a more general construction of skew axial distributions. As an example the methods are applied to a data set which consists of the orientations of logs on the floor of a primeval spruce forest.