Halton iterative partitioning: spatially balanced sampling via partitioning

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals.     

Spatially stratified sampling using auxiliary information for geostatistical mapping

This paper presents a method of spatial sampling based on stratification by Local Moran’s I _i calculated using auxiliary information. The sampling technique is compared to other design-based approaches including simple random sampling, systematic sampling on a regular grid, conditional Latin Hypercube sampling and stratified sampling based on auxiliary information, and is illustrated using two different spatial data sets. Each of the samples for the two data sets is interpolated using regression kriging to form a geostatistical map for their respective areas. The proposed technique is shown to be competitive in reproducing specific areas of interest with high accuracy.     

Spatial structure, sampling design and abundance estimates in sandy beach macroinfauna: some warnings and new perspectives

We discuss methodological aspects directed to quantify the across-shore population structure and abundance of sandy beach macroinfauna. The reliability of estimates derived from design-based (stratified random sampling) and model-based (geostatistics, kriging) approaches is discussed. Our analysis also addresses potential biases arising from environmentally driven designs that consider a priori fixed strata for sampling macroinfauna, as opposed to species-driven sampling designs, in which the entire range of across-shore distribution is covered. Model-based approaches showed, spatially, highly autocorrelated and persistent structures in two intertidal populations of the Uruguayan coast: the isopod Excirolana armata and the yellow clam Mesodesma mactroides. Both populations presented zonation patterns that ranged from the base of the dunes to upper levels of the subtidal. The Gaussian model consistently explained the spatial distribution of species and population components (clam recruits and adults), with a minor contribution (Е%) of unresolved, small-scale variability. The consistent structure of spatial dependence in annual data strongly suggests an across-shore-structured process covering close to 35 m. Kriging predictions through cross-validation corroborated the appropriateness of the models fitted through variographic analysis, and the derived abundance estimates were very similar (maximum difference=7%) to those obtained from linear interpolation. Monthly analysis of E. armata data showed marked variations in its zonation and an unstable spatial structure according to the Gaussian model. The clear spatial structure resulting from species-driven sampling was not observed when data was truncated to simulate an environmentally driven sampling design. In this case, the linear semivariogram indicated a spatial gradient, suggesting that sampling was not performed at the appropriate spatial scale. Further, the cross-validation procedure was not significant, and both density and total abundance were underestimated. We conclude that: (1) geostatistics provides useful additional information about population structure and aids in direct abundance estimation; thus we suggest it as a powerful tool for further applications in the study of sandy beach macroinfauna; and that (2) environmentally driven sampling strategies fail to provide conclusive results about population structure and abundance, and should be avoided in studies of sandy beach populations. This is especially true for microtidal beaches, where unpredictable swash strength precludes a priori stratification through environmental reference points. The need to use adaptive sampling designs and avoid snapshot sampling is also stressed. Methodological implications for the detection of macroecological patterns in sandy beach macroinfauna are also discussed.     

Geographic sampling of urban soils for contaminant mapping: how many samples and from where

Properly sampling soils and mapping soil contamination in urban environments requires that impacts of spatial autocorrelation be taken into account. As spatial autocorrelation increases in an urban landscape, the amount of duplicate information contained in georeferenced data also increases, whether an entire population or some type of random sample drawn from that population is being analyzed, resulting in conventional power and sample size calculation formulae yielding incorrect sample size numbers vis-à-vis model-based inference. Griffith (in Annals, Association of American Geographers, 95, 740–760, 2005) exploits spatial statistical model specifications to formulate equations for estimating the necessary sample size needed to obtain some predetermined level of precision for an analysis of georeferenced data when implementing a tessellation stratified random sampling design, labeling this approach model-informed, since a model of latent spatial autocorrelation is required. This paper addresses issues of efficiency associated with these model-based results. It summarizes findings from a data collection exercise (soil samples collected from across Syracuse, NY), as well as from a set of resampling and from a set of simulation experiments following experimental design principles spelled out by Overton and Stehman (in Communications in Statistics: Theory and Methods, 22, 2641–2660). Guidelines are suggested concerning appropriate sample size (i.e., how many) and sampling network (i.e., where).

Random versus stratified location of transects or points in distance sampling: theoretical results and practical considerations

A composite approach mixing design-based and model-based inference is considered for analyzing line-transect or point-transect data. In this setting, the properties of the animal abundance estimator stem from the sampling scheme adopted to locate transects or points on the study region, as well as from the modeled detection probabilities. Moreover, the abundance estimation can be viewed as a “generalized” version of Monte Carlo integration. This approach permits to prove the superiority of the stratified placement of transects or points (based on a regular tessellation of the study region) over the uniform random placement. Even if the result was already established for the fixed-area sampling, i.e., when a perfect detection takes place, it was lacking in distance sampling. Comparisons with other widely-applied schemes pursuing an even placement of transects or points are also considered.     

Design based estimation for ranked set sampling in finite populations

In this paper, we consider design-based estimation using ranked set sampling (RSS) in finite populations. We first derive the first and second-order inclusion probabilities for an RSS design and present two Horvitz–Thompson type estimators using these inclusion probabilities. We also develop an alternate Hansen–Hurwitz type estimator and investigate its properties. In particular, we show that this alternate estimator always outperforms the usual Hansen–Hurwitz type estimator in the simple random sampling with replacement design with comparable sample size. We also develop formulae for ratio estimator for all three developed estimators. The theoretical results are augmented by numerical and simulation studies as well as a case study using a well known data set. These show that RSS design can yield a substantial improvement in efficiency over the usual simple random sampling design in finite populations.     

Variance estimation in the EMAP strategy for sampling discrete ecological resources

The United States Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP) is designed to describe status, trends and spatial pattern of indicators of condition of the nation's ecological resources. The proposed sampling design for EMAP is based on a triangular systematic grid and employs both variable probability and double sampling. The Horvitz-Thompson estimator provides the foundation of the design-based estimation strategy used in EMAP. However, special features of EMAP designed to accommodate the complexity of sampling environmental resources on a national scale require modifications of standard variance estimation procedures as well as development of new techniques. An overview of variance estimation methods proposed for application to EMAP's sampling strategy for discrete resources is presented.     

Species abundance estimation using point-to-plant sampling in a design-based setting

A new species abundance estimator is proposed when point-to-plant sampling is adopted in a design-based framework. The method is based on the relationship between each species abundance and the probability density function of the relative squared point-to-plant distance. Using this result, a kernel estimator for species abundance is provided and the nearest neighbor method is suggested for bandwidth selection. The proposed estimator requires no assumptions about the species point patterns nor corrections for sampling near the edges of the study region. Moreover, the estimator shows suitable statistical properties as well as good practical performance as is shown in a simulation study.     

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.     

Multivariate bootstrap confidence regions for abundance vector using

Abundance vector estimation is a well investigated problem in statistical ecology. The use of simple random sampling with replacement or replicated sampling ensures good asymptotic properties of the abundance vector estimators. However, real surveys are based on small sample sizes, and assuming any specific distribution of the abundance vector estimator may be hazardous.In this paper we focus our attention on situations where the population is not too large and the sample size is small. We propose bootstrap multivariate confidence regions based on data depth. Data depth is a geometrical concept of ordering data from the center outwardly in higher dimensions. The Simplicial depth, the Tukey's depth and the Mahalanobis depth are presented. In order to build confidence regions in the presence of a skewed distribution of the abundance vector estimator, the use of Tukey's depth is suggested. The proposed method has been applied to the benthic community of Lake Lesina. A comparison with Mahalanobis depth and standard existing methods is reported.     

Use of Spatial Capture‐Recapture Modeling and DNA Data to Estimate Densities of Elusive Animals

Abstract: Assessment of abundance, survival, recruitment rates, and density (i.e., population assessment) is especially challenging for elusive species most in need of protection (e.g., rare carnivores). Individual identification methods, such as DNA sampling, provide ways of studying such species efficiently and noninvasively. Additionally, statistical methods that correct for undetected animals and account for locations where animals are captured are available to efficiently estimate density and other demographic parameters. We collected hair samples of European wildcat (Felis silvestris) from cheek‐rub lure sticks, extracted DNA from the samples, and identified each animals’ genotype. To estimate the density of wildcats, we used Bayesian inference in a spatial capture‐recapture model. We used WinBUGS to fit a model that accounted for differences in detection probability among individuals and seasons and between two lure arrays. We detected 21 individual wildcats (including possible hybrids) 47 times. Wildcat density was estimated at 0.29/km² (SE 0.06), and 95% of the activity of wildcats was estimated to occur within 1.83 km from their home‐range center. Lures located systematically were associated with a greater number of detections than lures placed in a cell on the basis of expert opinion. Detection probability of individual cats was greatest in late March. Our model is a generalized linear mixed model; hence, it can be easily extended, for instance, to incorporate trap‐ and individual‐level covariates. We believe that the combined use of noninvasive sampling techniques and spatial capture‐recapture models will improve population assessments, especially for rare and elusive animals.     

Bewertung heterogener Altlasten durch Probenahme, statistische und geostatistische Modellierung

A slack heap in Saxony serves as an example for the model procedure of evaluation heterogeneous waste sites via sampling as well as statistical and geostatistical data analysis. This paper demonstrates the usefulness of the known regulations for sampling and of the tried and proven geostatistical methods developed for assessing homogeneous wastes and the concornitantly contaminated soil. Emphasized here are the contents of iron and sulfur. Considered in addition are the concentrations of arsenic and the heat loss. To establish a conclusion, the variograms of the original data are used to evaluate the waste site in different directions and at determined depths. With the aid of a spot interpolation, further data can be calculated for additional sites which have not been sampled and can be used consequently for displaying the spatial variability. Finally, the statistical data analysis is applied using the standard methods of random sampling as an alternative to the geostatistical modeling. In this manner, the consequences for the sampling strategy can be demonstrated.     

An investigation of genetic population structure in blue crabs,Callinectes sapidus,using nuclear gene sequences

Spatial and temporal genetic heterogeneity in the sequences of nuclear protein-coding genes were investigated in populations of the blue crab, Callinectes sapidus. Haplotype frequencies of these novel markers were determined for adult crabs collected along 300 km in the northern Gulf of Mexico in two different years (2010 and 2011), as well as for megalopal recruits collected in 2010. Tests of genetic differentiation among all locations and between locations spanning known genetic breaks in other species were conducted. In addition, samples from distant locations within the range of C. sapidus were used to assess genetic divergence on a broader geographic scale. Significant between-year differences were found for adults at one location and near significant spatial differentiation was found across northern Gulf of Mexico locations in 2010. These results suggest that although the large population sizes and meroplanktonic life history of blue crabs promote widespread gene flow on a regional scale, genetic composition can change over just one year. Substantial divergence between the northern Gulf of Mexico and Venezuela suggests the possibility that temporal shifts in haplotype frequencies could result from variation in the rate of immigration from genetically distinct source populations. The possible effects of the Deepwater Horizon Oil Spill and attendant fisheries closures during the sampling phase of this study are also considered.     

A framework for adapting survey design through time for wildlife population assessment

Sampling strategies for monitoring the status and trends in wildlife populations are often determined before the first survey is undertaken. However, there may be little information about the distribution of the population and so the sample design may be inefficient. Through time, as data are collected, more information about the distribution of animals in the survey region is obtained but it can be difficult to incorporate this information in the survey design. This paper introduces a framework for monitoring motile wildlife populations within which the design of future surveys can be adapted using data from past surveys whilst ensuring consistency in design-based estimates of status and trends through time. In each survey, part of the sample is selected from the previous survey sample using simple random sampling. The rest is selected with inclusion probability proportional to predicted abundance. Abundance is predicted using a model constructed from previous survey data and covariates for the whole survey region. Unbiased design-based estimators of status and trends and their variances are derived from two-phase sampling theory. Simulations over the short and long-term indicate that in general more precise estimates of status and trends are obtained using this mixed strategy than a strategy in which all of the sample is retained or all selected with probability proportional to predicted abundance. Furthermore the mixed strategy is robust to poor predictions of abundance. Estimates of status are more precise than those obtained from a rotating panel design.     

An evaluation of three statistical methods used to model resource selection

The performance of statistical methods for modeling resource selection by animals is difficult to evaluate with field data because true selection patterns are unknown. Simulated data based on a known probability distribution, though, can be used to evaluate statistical methods. Models should estimate true selection patterns if they are to be useful in analyzing and interpreting field data. We used simulation techniques to evaluate the effectiveness of three statistical methods used in modeling resource selection. We generated 25 use locations per animal and included 10, 20, 40, or 80 animals in samples of use locations. To simulate species of different mobility, we generated use locations at four levels according to a known probability distribution across DeSoto National Wildlife Refuge (DNWR) in eastern Nebraska and western Iowa, USA. We either generated 5 random locations per use location or 10,000 random locations (total) within 4 predetermined areas around use locations to determine how the definition of availability and the number of random locations affected results. We analyzed simulated data using discrete choice, logistic-regression, and a maximum entropy method (Maxent). We used a simple linear regression of estimated and known probability distributions and area under receiver operating characteristic curves (AUC) to evaluate the performance of each method. Each statistical method was affected differently by number of animals and random locations used in analyses, level at which selection of resources occurred, and area considered available. Discrete-choice modeling resulted in precise and accurate estimates of the true probability distribution when the area in which use locations were generated was ≥ the area defined to be available. Logistic-regression models were unbiased and precise when the area in which use locations were generated and the area defined to be available were the same size; the fit of these models improved with increased numbers of random locations. Maxent resulted in unbiased and precise estimates of the known probability distribution when the area in which use locations were generated was small (home-range level) and the area defined to be available was large (study area). Based on AUC analyses, all models estimated the selection distribution better than random chance. Results from AUC analyses, however, often contradicted results of the linear regression method used to evaluate model performance. Discrete-choice modeling was best able to estimate the known selection distribution in our study area regardless of sample size or number of random locations used in the analyses, but we recommend further studies using simulated data over different landscapes and different resource metrics to confirm our results. Our study offers an approach and guidance for others interested in assessing the utility of techniques for modeling resource selection in their study area.     

RIVPACS models for predicting the expected macroinvertebrate fauna and assessing the ecological quality of rivers

The European Union Water Framework Directive recognises the need for and value of biological monitoring. This paper reviews the modelling approach known as River Invertebrate Prediction and Classification System (RIVPACS for assessing the ecological quality of river sites using macroinvertebrate sampling. The RIVPACS philosophy is to develop statistical relationships between the fauna and the environmental characteristics of a large set of high quality reference sites which can be used to predict the macroinvertebrate fauna to be expected at any site in the absence of pollution or other environmental stress. The observed fauna at new test sites can then be compared with their site-specific expected fauna to derive indices of ecological quality. All methodological decisions in any such model development have implications for the reliability, precision and robustness of any resulting indices for assessing the ecological quality and ecological grade (‘status’) of individual river stretches. The choice of reference sites and environmental predictor variables, the site classification and discrimination methods, the estimation of the expected fauna, and indices for comparing the agreement, or lack of it, between the observed and expected fauna, are all discussed. The indices are assessed on the reference sites and on a separate test set of 340 sites, which are subject to a wide range of types and degrees of impairment.     

Frequency of multiple paternity varies between two populations of brown smoothhound shark,Mustelus henlei

Multiple paternity was recently observed in a population of the brown smoothhound shark, Mustelus henlei, from Las Barrancas, Baja California Sur, Mexico, with litters demonstrating the greatest percentage of multiple paternity for any shark species (93 % of litters and an average number of sires = 2.3). To determine whether this frequency is consistent elsewhere in the species’ range, 4 polymorphic microsatellite loci were used to determine the frequency of multiple paternity in 18 litters of M. henlei from Santa Catalina Island, CA, sampled in 2004, 2008, and 2012. Multiple paternity varied among sampling years with 2004 demonstrating multiple sires for 40 % of sampled litters (n = 10) with an average of 1.4 sires per litter and 2008/2012 demonstrating a total lack of multiply sired litters (n = 8). Although multiple paternity was detected in this study, the range of frequencies observed is lower than that observed in the Mexican population. Based on these findings, investigators should take location into consideration when assessing the existence of multiple paternity in future studies of elasmobranch species.     

Estimation of the spatial covariance in Universal Kriging: Application to forest inventory

This paper presents a simple least squares procedure for estimating the spatial covariance and compares it with the numerically more difficult restricted maximum likelihood procedure. Thereafter, it compares design-based and kriging techniques for the estimation of spatial averages in the context of double sampling, as used in forest inventory, where terrestrial sample plots are combined with auxiliary information based on aerial photographs. A case study illustrates the theory.     

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

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