Multi-lag cluster designs for estimating the semivariogram for sediments affected by effluent discharges offshore in San Diego

Maps are useful tools for understanding, managing, and protecting the marine environment, yet few useful and statistically defensible maps of environmental quality and aquatic resources have been developed in near-coastal regions. Current environmental management efforts, such as ocean monitoring by sewage dischargers, routinely sample areas of potential impact using sparse sampling grids. Heterogeneous oceanic conditions often make extrapolation from these grids to non-sampled locations questionable. Although rarely applied in coastal monitoring, kriging offers a more rigorous statistical approach to mapping and allows confidence intervals to be calculated for predictions. Its usefulness relies on accurate models of the spatial variability through estimating the semivariogram. Many optimal designs for estimating the semivariogram have been proposed, but these designs are often difficult to implement in practice. In this paper, we present simple design strategies for augmenting existing monitoring designs with the goal of estimating the semivariogram. In particular, we investigate a multi-lag cluster design strategy, where clusters of sites, spaced at various lag distances, are placed around fixed stations on an existing sampling grid. We find that these multi-lag cluster designs provide improved accuracy in estimating the parameters of the semivariogram. Based on simulation study findings, we apply a multi-lag cluster enhancement to the monitoring grid for the City of San Diego’s Point Loma Wastewater Treatment Plant as part of a special study to map chemical contaminants in sediments around its sewage outfall.     

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions. Received: July 2005 / Revised: March 2006     

Optimal spatial sampling schemes for environmental surveys

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

Phased sampling for soil remediation

In phased sampling, data obtained in one phase is used to design the sampling network for the next phase. GivenN total observations, 1, ...,N phases are possible. Experiments were conducted with one-phase, two-phase, andN-phase design algorithms on surrogate models of sites with contaminated soils. The sampling objective was to identify through interpolation, subunits of the site that required remediation. The cost-effectiveness of alternate methods was compared by using a loss function. More phases are better, but in economic terms, the improvement is marginal. The optimal total number of samples is essentially independent of the number of phases. For two phase designs, 75% of samples in the first phase is near optimal; 20% or less is actually counterproductive.The U.S. Environmental Protection Agency (EPA) through its Office of Research and Development (ORD), partially funded and collaborated in the research described here. It has been subjected to the Agency's peer review and has been approved as an EPA publication. The U.S. Government has a non-exclusive, royalty-free licence in and to any copyright covering this article.     

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

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

Case studies of conservation plans that incorporate geodiversity

Geodiversity has been used as a surrogate for biodiversity when species locations are unknown, and this utility can be extended to situations where species locations are in flux. Recently, scientists have designed conservation networks that aim to explicitly represent the range of geophysical environments, identifying a network of physical stages that could sustain biodiversity while allowing for change in species composition in response to climate change. Because there is no standard approach to designing such networks, we compiled 8 case studies illustrating a variety of ways scientists have approached the challenge. These studies show how geodiversity has been partitioned and used to develop site portfolios and connectivity designs; how geodiversity‐based portfolios compare with those derived from species and communities; and how the selection and combination of variables influences the results. Collectively, they suggest 4 key steps when using geodiversity to augment traditional biodiversity‐based conservation planning: create land units from species‐relevant variables combined in an ecologically meaningful way; represent land units in a logical spatial configuration and integrate with species locations when possible; apply selection criteria to individual sites to ensure they are appropriate for conservation; and develop connectivity among sites to maintain movements and processes. With these considerations, conservationists can design more effective site portfolios to ensure the lasting conservation of biodiversity under a changing climate.     

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.     

Improving effectiveness of systematic conservation planning with density data

Systematic conservation planning aims to design networks of protected areas that meet conservation goals across large landscapes. The optimal design of these conservation networks is most frequently based on the modeled habitat suitability or probability of occurrence of species, despite evidence that model predictions may not be highly correlated with species density. We hypothesized that conservation networks designed using species density distributions more efficiently conserve populations of all species considered than networks designed using probability of occurrence models. To test this hypothesis, we used the Zonation conservation prioritization algorithm to evaluate conservation network designs based on probability of occurrence versus density models for 26 land bird species in the U.S. Pacific Northwest. We assessed the efficacy of each conservation network based on predicted species densities and predicted species diversity. High‐density model Zonation rankings protected more individuals per species when networks protected the highest priority 10‐40% of the landscape. Compared with density‐based models, the occurrence‐based models protected more individuals in the lowest 50% priority areas of the landscape. The 2 approaches conserved species diversity in similar ways: predicted diversity was higher in higher priority locations in both conservation networks. We conclude that both density and probability of occurrence models can be useful for setting conservation priorities but that density‐based models are best suited for identifying the highest priority areas. Developing methods to aggregate species count data from unrelated monitoring efforts and making these data widely available through ecoinformatics portals such as the Avian Knowledge Network will enable species count data to be more widely incorporated into systematic conservation planning efforts.     

Geoadditive regression modeling of stream biological condition

Indices of biotic integrity have become an established tool to quantify the condition of small non-tidal streams and their watersheds. To investigate the effects of watershed characteristics on stream biological condition, we present a new technique for regressing IBIs on watershed-specific explanatory variables. Since IBIs are typically evaluated on an ordinal scale, our method is based on the proportional odds model for ordinal outcomes. To avoid overfitting, we do not use classical maximum likelihood estimation but a component-wise functional gradient boosting approach. Because component-wise gradient boosting has an intrinsic mechanism for variable selection and model choice, determinants of biotic integrity can be identified. In addition, the method offers a relatively simple way to account for spatial correlation in ecological data. An analysis of the Maryland Biological Streams Survey shows that nonlinear effects of predictor variables on stream condition can be quantified while, in addition, accurate predictions of biological condition at unsurveyed locations are obtained.     

Neural network modelling of coastal algal blooms

An artificial neural network (ANN), a data driven modelling approach, is proposed to predict the algal bloom dynamics of the coastal waters of Hong Kong. The commonly used back-propagation learning algorithm is employed for training the ANN. The modeling is based on (a) comprehensive biweekly water quality data at Tolo Harbour (1982–2000); and (b) 4-year set of weekly phytoplankton abundance data at Lamma Island (1996–2000). Algal biomass is represented as chlorophyll-a and cell concentration of Skeletonema at the two locations, respectively. Analysis of a large number of scenarios shows that the best agreement with observations is obtained by using merely the time-lagged algal dynamics as the network input. In contrast to previous findings with more complicated neural networks of algal blooms in freshwater systems, the present work suggests the algal concentration in the eutrophic sub-tropical coastal water is mainly dependent on the antecedent algal concentrations in the previous 1–2 weeks. This finding is also supported by an interpretation of the neural networks’ weights. Through a systematic analysis of network performance, it is shown that previous reports of predictability of algal dynamics by ANN are erroneous in that ‘future data’ have been used to drive the network prediction. In addition, a novel real time forecast of coastal algal blooms based on weekly data at Lamma is presented. Our study shows that an ANN model with a small number of input variables is able to capture trends of algal dynamics, but data with a minimum sampling interval of 1 week is necessary. However, the sufficiency of the weekly sampling for real time predictions using ANN models needs to be further evaluated against longer weekly data sets as they become available.     

Modeling and Predicting Species Occurrence Using Broad-Scale Environmental Variables: an Example with Butterflies of the Great Basin

Abstract: If occurrence of individual species can be modeled as a function of easily quantified environmental variables (e.g., derived from a geographic information system [GIS]) and the predictions of these models are demonstrably successful, then the scientific foundation for management planning will be strengthened. We used Bayesian logistic regression to develop predictive models for resident butterflies in the central Great Basin of western North America. Species inventory data and values for 14 environmental variables from 49 locations (segments of canyons) in the Toquima Range ( Nevada, U.S.A.) were used to build the models. Squares of the environmental variables were also used to accommodate possibly nonmonotonic responses. We obtained statistically significant models for 36 of 56 (64%) resident species of butterflies. The models explained 8–72% of the deviance in occurrence of those species. Each of the independent variables was significant in at least one model, and squared versions of five variables contributed to models. Elevation was included in more than half of the models. Models included one to four variables; only one variable was significant in about half the models. We conducted preliminary tests of two of our models by using an existing set of data on the occurrence of butterflies in the neighboring Toiyabe Range. We compared conventional logistic classification with posterior probability distributions derived from Bayesian modeling. For the latter, we restricted our predictions to locations with a high ( 70%) probability of predicted presence or absence. We will perform further tests after conducting inventories at new locations in the Toquima Range and nearby Shoshone Mountains, for which we have computed environmental variables by using remotely acquired topographic data, digital-terrain and microclimatic models, and GIS computation.     

Mapping risk for nest predation on a barrier island

Barrier islands and coastal beach systems provide nesting habitat for marine and estuarine turtles. Densely settled coastal areas may subsidize nest predators. Our purpose was to inform conservation by providing a greater understanding of habitat-based risk factors for nest predation, for an estuarine turtle. We expected that habitat conditions at predated nests would differ from random locations at two spatial extents. We developed and validated an island-wide model for the distribution of predated Diamondback terrapin nests using locations of 198 predated nests collected during exhaustive searches at Fisherman Island National Wildlife Refuge, USA. We used aerial photographs to identify all areas of possible nesting habitat and searched each and surrounding environments for nests, collecting location and random-point microhabitat data. We built models for the probability of finding a predated nest using an equal number of random points and validated them with a reserve set (N?=?67). Five variables in 9 a priori models were used and the best selected model (AIC weight 0.98) reflected positive associations with sand patches near marshes and roadways. Model validation had an average capture rate of predated nests of 84.14 % (26.17–97.38 %, Q1 77.53 %, median 88.07 %, Q3 95.08 %). Microhabitat selection results suggest that nests placed at the edges of sand patches adjacent to upland shrub/forest and marsh systems are vulnerable to predation. Forests and marshes provide cover and alternative resources for predators and roadways provide access; a suggestion is to focus nest protection efforts on the edges of dunes, near dense vegetation and roads.     

Sensitivity of species-distribution models to error,bias, and model design: An application to resource selection functions for woodland caribou

Models that predict distribution are now widely used to understand the patterns and processes of plant and animal occurrence as well as to guide conservation and management of rare or threatened species. Application of these methods has led to corresponding studies evaluating the sensitivity of model performance to requisite data and other factors that may lead to imprecise or false inferences. We expand upon these works by providing a relative measure of the sensitivity of model parameters and prediction to common sources of error, bias, and variability. We used a one-at-a-time sample design and GPS location data for woodland caribou (Rangifer tarandus caribou) to assess one common species-distribution model: a resource selection function. Our measures of sensitivity included change in coefficient values, prediction success, and the area of mapped habitats following the systematic introduction of geographic error and bias in occurrence data, thematic misclassification of resource maps, and variation in model design. Results suggested that error, bias and model variation have a large impact on the direct interpretation of coefficients. Prediction success and definition of important habitats were less responsive to the perturbations we introduced to the baseline model. Model coefficients, prediction success, and area of ranked habitats were most sensitive to positional error in species locations followed by sampling bias, misclassification of resources, and variation in model design. We recommend that researchers report, and practitioners consider, levels of error and bias introduced to predictive species-distribution models. Formal sensitivity and uncertainty analyses are the most effective means for evaluating and focusing improvements on input data and considering the range of values possible from imperfect models.     

A comparison of periodic survey designs employing multi-stage sampling

Sampling designs considered for a national scale environmental monitoring programme are compared. Specifically, design strategies designed to monitor one aspect of this environmental programme, agro-ecosystem health, are assessed. Two types of panel survey designs are evaluated within the framework of two-stage sampling. Comparisons of these designs are discussed with regard to precision, cost, and other issues that need to be considered in planning long-term surveys. To compare precision, the underlying variance of a simple estimator of mean difference is derived for each of the two designs. A variance and cost model accounting for the different rotational sampling schemes across designs are developed. Optimum stage allocation for each design are assessed with the variance-cost models. The best choice of design varied with the conditions underlying the variance model and the degree of other sources of survey error expected in the programme.     

Optimizing two- and three-stage designs for spatial inventories of natural resources by simulated annealing

This paper reviews design-based estimators for two- and three-stage sampling designs to estimate the mean of finite populations. This theory is then extended to spatial populations with continuous, infinite populations of sampling units at the latter stages. We then assume that the spatial pattern is the result of a spatial stochastic process, so the sampling variance of the estimators can be predicted from the variogram. A realistic cost function is then developed, based on several factors including laboratory analysis, time of fieldwork, and numbers of samples. Simulated annealing is used to find designs with minimum sampling variance for a fixed budget. The theory is illustrated with a real-world problem dealing with the volume of contaminated bed sediments in a network of watercourses. Primary sampling units are watercourses, secondary units are transects perpendicular to the axis of the watercourse, and tertiary units are points. Optimal designs had one point per transect, from one to three transects per watercourse, and the number of watercourses varied depending on the budget. However, if laboratory costs are reduced by grouping all samples within a watercourse into one composite sample, it appeared to be efficient to sample more transects within a watercourse.     

Applications of artificial neural networks for patterning and predicting aquatic insect species richness in running waters

Two artificial neural networks (ANNs), unsupervised and supervised learning algorithms, were applied to suggest practical approaches for the analysis of ecological data. Four major aquatic insect orders (Ephemeroptera, Plecoptera, Trichoptera, and Coleoptera, i.e. EPTC), and four environmental variables (elevation, stream order, distance from the source, and water temperature) were used to implement the models. The data were collected and measured at 155 sampling sites on streams of the Adour–Garonne drainage basin (South-western France). The modelling procedure was carried out following two steps. First, a self-organizing map (SOM), an unsupervised ANN, was applied to classify sampling sites using EPTC richness. Second, a backpropagation algorithm (BP), a supervised ANN, was applied to predict EPTC richness using a set of four environmental variables. The trained SOM classified sampling sites according to a gradient of EPTC richness, and the groups obtained corresponded to geographic regions of the drainage basin and characteristics of their environmental variables. The SOM showed its convenience to analyze relationships among sampling sites, biological attributes, and environmental variables. After accounting for the relationships in data sets, the BP used to predict the EPTC richness with a set of four environmental variables showed a high accuracy (r=0.91 and r=0.61 for training and test data sets respectively). The prediction of EPTC richness is thus a valuable tool to assess disturbances in given areas: by knowing what the EPTC richness should be, we can determine the degree to which disturbances have altered it. The results suggested that methodologies successively using two different neural networks are helpful to understand ecological data through ordination first, and then to predict target variables.     

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

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

Spatial residual analysis of six modeling techniques

In recent years alternative modeling techniques have been used to account for spatial autocorrelations among data observations. They include linear mixed model (LMM), generalized additive model (GAM), multi-layer perceptron (MLP) neural network, radial basis function (RBF) neural network, and geographically weighted regression (GWR). Previous studies show these models are robust to the violation of model assumptions and flexible to nonlinear relationships among variables. However, many of them are non-spatial in nature. In this study, we utilize a local spatial analysis method (i.e., local Moran coefficient) to investigate spatial distribution and heterogeneity in model residuals from those modeling techniques with ordinary least-squares (OLS) as the benchmark. The regression model used in this study has tree crown area as the response variable, and tree diameter and the coordinates of tree locations as the predictor variables. The results indicate that LMM, GAM, MLP and RBF may improve model fitting to the data and provide better predictions for the response variable, but they generate spatial patterns for model residuals similar to OLS. The OLS, LMM, GAM, MLP and RBF models yield more residual clusters of similar values, indicating that trees in some sub-areas are either all underestimated or all overestimated for the response variable. In contrast, GWR estimates model coefficients at each location in the study area, and produces more accurate predictions for the response variable. Furthermore, the residuals of the GWR model have more desirable spatial distributions than the ones derived from the OLS, LMM, GAM, MLP and RBF models.     

Regression-type estimators for adaptive two-stage sequential sampling

Adaptive two-stage sequential sampling (ATSSS) design was developed to observe more rare units and gain higher efficiency, in the sense of having a smaller variance estimator, than conventional sampling designs with equal effort for rare and spatially cluster populations. For certain rare populations, incorporating auxiliary variables into a sampling design can further improve the observation of rare units and increase efficiency. In this article, we develop regression-type estimators for ATSSS so that auxiliary variables can be incorporated into the ATSSS design when warranted. Simulation studies on two populations show that the regression-type estimators can significantly increase the efficiency of ATSSS and the detection of more rare units as compared to conventional sampling counterparts. Simulation of sampling of desert shrubs in Inner Mongolia (one of the two populations studied) showed that by incorporating a GIS auxiliary variable into ATSSS with the regression estimators resulted in a gain in efficiency over ATSSS without the auxiliary variable. Further, we found that the use of the GIS auxiliary variable in a conventional two-stage design with a regression estimator did not show a gain in efficiency.