spsurvey: Spatial Sampling Design and Analysis in R.

spsurvey is an R package for design-based statistical inference, with a focus on spatial data. spsurvey provides the generalized random-tessellation stratified (GRTS) algorithm to select spatially balanced samples via the grts() function. The grts() function flexibly accommodates several sampling design features, including stratification, varying inclusion probabilities, legacy (or historical) sites, minimum distances between sites, and two options for replacement sites. spsurvey also provides a suite of data analysis options, including categorical variable analysis (cat_analysis()), continuous variable analysis cont_analysis()), relative risk analysis (relrisk_analysis()), attributable risk analysis (attrisk_analysis()), difference in risk analysis (diffrisk_analysis()), change analysis (change_analysis()), and trend analysis (trend_analysis()). In this manuscript, we first provide background for the GRTS algorithm and the analysis approaches and then show how to implement them in spsurvey. We find that the spatially balanced GRTS algorithm yields more precise parameter estimates than simple random sampling, which ignores spatial information.

Contaminants in fish from U.S. rivers: Probability-based national assessments.

Most fish consumption advisories in the United States (U.S.) are issued for mercury and polychlorinated biphenyls (PCBs), and recently per- and polyfluoroalkyl substances (PFAS) have become a contaminant group that warrants fish consumption advice. An unequal probability survey design was developed to allow a comprehensive characterization of mercury, PCB, and PFAS contamination in fish from U.S. rivers on a national scale. During 2013-14 and 2018-19, fish fillet samples were collected from 353 and 290 river sites, respectively, selected randomly from the target population of rivers (≥5th order in size) in the conterminous U.S. These comprised nationally representative samples, with results extrapolated to chemical-specific sampled populations of 48,826-79,448 river kilometers (km) in 2013-14 and 66,142 river km in 2018-19. National distribution estimates were developed for total mercury, all 209 PCB congeners, and up to 33 PFAS (including perfluorooctane sulfonate or PFOS) in river fish. All fillet tissue samples contained detectable levels of mercury and PCBs. One or more PFAS were detected in 99.7 % and 95.2 % of the fillet samples from fish collected in 2013-14 and 2018-19, respectively. Fish tissue screening levels applied to national contaminant probability distributions allowed an estimation of the percentage of the sampled population of river lengths that contained fish with fillet concentrations above a level protective of human health. Fish tissue screening level exceedances for an average level of fish consumption ranged from 23.5 % to 26.0 % for mercury, 17.3 % to 51.6 % for PCBs, and 0.7 % to 9.1 % for PFOS.

A comparison of design-based and model-based approaches for finite population spatial sampling and inference.

The design-based and model-based approaches to frequentist statistical inference rest on fundamentally different foundations. In the design-based approach, inference relies on random sampling. In the model-based approach, inference relies on distributional assumptions. We compare the approaches in a finite population spatial context.We provide relevant background for the design-based and model-based approaches and then study their performance using simulated data and real data. The real data is from the United States Environmental Protection Agency's 2012 National Lakes Assessment. A variety of sample sizes, location layouts, dependence structures, and response types are considered. The population mean is the parameter of interest, and performance is measured using statistics like bias, squared error, and interval coverage.When studying the simulated and real data, we found that regardless of the strength of spatial dependence in the data, the generalized random tessellation stratified (GRTS) algorithm, which explicitly incorporates spatial locations into sampling, tends to outperform the simple random sampling (SRS) algorithm, which does not explicitly incorporate spatial locations into sampling. We also found that model-based inference tends to outperform design-based inference, even for skewed data where the model-based distributional assumptions are violated. The performance gap between design-based inference and model-based inference is small when GRTS samples are used but large when SRS samples are used, suggesting that the sampling choice (whether to use GRTS or SRS) is most important when performing design-based inference.There are many benefits and drawbacks to the design-based and model-based approaches for finite population spatial sampling and inference that practitioners must consider when choosing between them. We provide relevant background contextualizing each approach and study their properties in a variety of scenarios, making recommendations for use based on the practitioner's goals.

Comparing spatial regression to random forests for large environmental data sets.

Environmental data may be "large" due to number of records, number of covariates, or both. Random forests has a reputation for good predictive performance when using many covariates with nonlinear relationships, whereas spatial regression, when using reduced rank methods, has a reputation for good predictive performance when using many records that are spatially autocorrelated. In this study, we compare these two techniques using a data set containing the macroinvertebrate multimetric index (MMI) at 1859 stream sites with over 200 landscape covariates. A primary application is mapping MMI predictions and prediction errors at 1.1 million perennial stream reaches across the conterminous United States. For the spatial regression model, we develop a novel transformation procedure that estimates Box-Cox transformations to linearize covariate relationships and handles possibly zero-inflated covariates. We find that the spatial regression model with transformations, and a subsequent selection of significant covariates, has cross-validation performance comparable to random forests. We also find that prediction interval coverage is close to nominal for each method, but that spatial regression prediction intervals tend to be narrower and have less variability than quantile regression forest prediction intervals. A simulation study is used to generalize results and clarify advantages of each modeling approach.

Survey design to assess condition of wetlands in the United States.

The US Environmental Protection Agency (US EPA) initiated planning in 2007 and conducted field work in 2011 for the first National Wetland Condition Assessment (NWCA) as part of the National Aquatic Resource Surveys (NARS). It complements the US Fish and Wildlife Service (USFWS) National Wetland Status and Trends (S&T) program that estimates wetland acres nationally. The NWCA used a stratified, unequal probability survey design based on wetland information from S&T plots to select 900 sites for the conterminous 48 states. Based on site evaluation information, the NWCA estimates that there are 94.9 (± 6.20) million acres of wetlands in the NWCA target wetland population (reported in acres to be consistent with S&T). Not all of the estimated target population acres could be sampled due to accessibility and field issues. Based on the sites that could be sampled, the sampled population for the NWCA is estimated to be 62.2 (± 5.28) million acres of wetland area. Landowner denial for access was the main reason (24.7% ± 3.5%) for the sampled population being smaller than the target population, and physical inaccessibility was the second reason (6.8% ± 2.1%). The NWCA 2011 survey design was successful in enabling a national survey for wetland condition to be conducted and coordinated with the USFWS S&T survey of wetland extent. The NWCA 2016 survey design has been modified to address sample frame issues resulting from the difference in S&T focusing only on national estimates and NWCA focusing on national and regional estimates.

The Lake-Catchment (LakeCat) Dataset: characterizing landscape features for lake basins within the conterminous USA.

Natural and human-related landscape features influence the ecology and water quality of lakes. Summarizing these features in a hydrologically meaningful way is critical to understanding and managing lake ecosystems. Such summaries are often done by delineating watershed boundaries of individual lakes. However, many technical challenges are associated with delineating hundreds or thousands of lake watersheds at broad spatial extents. These challenges can limit the application of analyses and models to new, unsampled locations. We present the Lake-Catchment (LakeCat) Dataset (https://www.epa.gov/national-aquatic-resource-surveys/lakecat) of watershed features for 378,088 lakes within the conterminous USA. We describe the methods we used to: 1) delineate lake catchments, 2) hydrologically connect nested lake catchments, and 3) generate several hundred watershed-level metrics that summarize both natural (e.g., soils, geology, climate, and land cover) and anthropogenic (e.g., urbanization, agriculture, and mines) features. We illustrate how this data set can be used with a random forest model to predict the probability of lake eutrophication by combining LakeCat with data from US Environmental Protection Agency's National Lakes Assessment (NLA). This model correctly predicted the trophic state of 72% of NLA lakes, and we applied the model to predict the probability of eutrophication at 297,071 unsampled lakes across the conterminous USA. The large suite of LakeCat metrics could be used to improve analyses of lakes at broad spatial extents, improve the applicability of analyses to unsampled lakes, and ultimately improve the management of these important ecosystems.

Occupancy modeling species-environment relationships with non-ignorable survey designs.

Statistical models supporting inferences about species occurrence patterns in relation to environmental gradients are fundamental to ecology and conservation biology. A common implicit assumption is that the sampling design is ignorable and does not need to be formally accounted for in analyses. The analyst assumes data are representative of the desired population and statistical modeling proceeds. However, if data sets from probability and non-probability surveys are combined or unequal selection probabilities are used, the design may be non-ignorable. We outline the use of pseudo-maximum likelihood estimation for site-occupancy models to account for such non-ignorable survey designs. This estimation method accounts for the survey design by properly weighting the pseudo-likelihood equation. In our empirical example, legacy and newer randomly selected locations were surveyed for bats to bridge a historic statewide effort with an ongoing nationwide program. We provide a worked example using bat acoustic detection/non-detection data and show how analysts can diagnose whether their design is ignorable. Using simulations we assessed whether our approach is viable for modeling data sets composed of sites contributed outside of a probability design. Pseudo-maximum likelihood estimates differed from the usual maximum likelihood occupancy estimates for some bat species. Using simulations we show the maximum likelihood estimator of species-environment relationships with non-ignorable sampling designs was biased, whereas the pseudo-likelihood estimator was design unbiased. However, in our simulation study the designs composed of a large proportion of legacy or non-probability sites resulted in estimation issues for standard errors. These issues were likely a result of highly variable weights confounded by small sample sizes (5% or 10% sampling intensity and four revisits). Aggregating data sets from multiple sources logically supports larger sample sizes and potentially increases spatial extents for statistical inferences. Our results suggest that ignoring the mechanism for how locations were selected for data collection (e.g., the sampling design) could result in erroneous model-based conclusions. Therefore, in order to ensure robust and defensible recommendations for evidence-based conservation decision-making, the survey design information in addition to the data themselves must be available for analysts. Details for constructing the weights used in estimation and code for implementation are provided.

Mapping watershed integrity for the conterminous United States.

Watershed integrity is the capacity of a watershed to support and maintain the full range of ecological processes and functions essential to sustainability. Using information from EPA's StreamCat dataset, we calculated and mapped an Index of Watershed Integrity (IWI) for 2.6 million watersheds in the conterminous US with first-order approximations of relationships between stressors and six watershed functions: hydrologic regulation, regulation of water chemistry, sediment regulation, hydrologic connectivity, temperature regulation, and habitat provision. Results show high integrity in the western US, intermediate integrity in the southern and eastern US, and the lowest integrity in the temperate plains and lower Mississippi Valley. Correlation between the six functional components was high (r = 0.85-0.98). A related Index of Catchment Integrity (ICI) was developed using local drainages of individual stream segments (i.e., excluding upstream information). We evaluated the ability of the IWI and ICI to predict six continuous site-level indicators with regression analyses - three biological indicators and principal components derived from water quality, habitat, and combined water quality and habitat variables - using data from EPA's National Rivers and Streams Assessment. Relationships were highly significant, but the IWI only accounted for 1-12% of the variation in the four biological and habitat variables. The IWI accounted for over 25% of the variation in the water quality and combined principal components nationally, and 32-39% in the Northern and Southern Appalachians. We also used multinomial logistic regression to compare the IWI with the categorical forms of the three biological indicators. Results were consistent: we found positive associations but modest results. We compared how the IWI and ICI predicted the water quality PC relative to agricultural and urban land use. The IWI or ICI are the best predictors of the water quality PC for the CONUS and six of the nine ecoregions, but they only perform marginally better than agriculture in most instances. However, results suggest that agriculture would not be appropriate in all parts of the country, and the index is meant to be responsive to all stressors. The IWI in its present form (available through the StreamCat website; https://www.epa.gov/national-aquatic-resource-surveys/streamcat) could be useful for management efforts at multiple scales, especially when combined with information on site condition. The IWI could be improved by incorporating empirical or literature-derived relationships between functional components and stressors. However, limitations concerning the absence of data for certain stressors should be considered.

Predictive mapping of the biotic condition of conterminous U.S. rivers and streams.

Understanding and mapping the spatial variation in stream biological condition could provide an important tool for conservation, assessment, and restoration of stream ecosystems. The USEPA's 2008-2009 National Rivers and Streams Assessment (NRSA) summarizes the percentage of stream lengths within the conterminous United States that are in good, fair, or poor biological condition based on a multimetric index of benthic invertebrate assemblages. However, condition is usually summarized at regional or national scales, and these assessments do not provide substantial insight into the spatial distribution of conditions at unsampled locations. We used random forests to model and predict the probable condition of several million kilometers of streams across the conterminous United States based on nearby and upstream landscape features, including human-related alterations to watersheds. To do so, we linked NRSA sample sites to the USEPA's StreamCat Dataset; a database of several hundred landscape metrics for all 1:100,000-scale streams and their associated watersheds within the conterminous United States. The StreamCat data provided geospatial indicators of nearby and upstream land use, land cover, climate, and other landscape features for modeling. Nationally, the model correctly predicted the biological condition class of 75% of NRSA sites. Although model evaluations suggested good discrimination among condition classes, we present maps as predicted probabilities of good condition, given upstream and nearby landscape settings. Inversely, the maps can be interpreted as the probability of a stream being in poor condition, given human-related watershed alterations. These predictions are available for download from the USEPA's StreamCat website. Finally, we illustrate how these predictions could be used to prioritize streams for conservation or restoration.

Assessing the accuracy and stability of variable selection methods for random forest modeling in ecology.

Random forest (RF) modeling has emerged as an important statistical learning method in ecology due to its exceptional predictive performance. However, for large and complex ecological data sets, there is limited guidance on variable selection methods for RF modeling. Typically, either a preselected set of predictor variables are used or stepwise procedures are employed which iteratively remove variables according to their importance measures. This paper investigates the application of variable selection methods to RF models for predicting probable biological stream condition. Our motivating data set consists of the good/poor condition of n = 1365 stream survey sites from the 2008/2009 National Rivers and Stream Assessment, and a large set (p = 212) of landscape features from the StreamCat data set as potential predictors. We compare two types of RF models: a full variable set model with all 212 predictors and a reduced variable set model selected using a backward elimination approach. We assess model accuracy using RF's internal out-of-bag estimate, and a cross-validation procedure with validation folds external to the variable selection process. We also assess the stability of the spatial predictions generated by the RF models to changes in the number of predictors and argue that model selection needs to consider both accuracy and stability. The results suggest that RF modeling is robust to the inclusion of many variables of moderate to low importance. We found no substantial improvement in cross-validated accuracy as a result of variable reduction. Moreover, the backward elimination procedure tended to select too few variables and exhibited numerous issues such as upwardly biased out-of-bag accuracy estimates and instabilities in the spatial predictions. We use simulations to further support and generalize results from the analysis of real data. A main purpose of this work is to elucidate issues of model selection bias and instability to ecologists interested in using RF to develop predictive models with large environmental data sets.

Statistical Survey of Persistent Organic Pollutants: Risk Estimations to Humans and Wildlife through Consumption of Fish from U.S. Rivers.

U.S. EPA conducted a national statistical survey of fish tissue contamination at 540 river sites (representing 82 954 river km) in 2008-2009, and analyzed samples for 50 persistent organic pollutants (POPs), including 21 PCB congeners, 8 PBDE congeners, and 21 organochlorine pesticides. The survey results were used to provide national estimates of contamination for these POPs. PCBs were the most abundant, being measured in 93.5% of samples. Summed concentrations of the 21 PCB congeners had a national weighted mean of 32.7 µg/kg and a maximum concentration of 857 µg/kg, and exceeded the human health cancer screening value of 12 µg/kg in 48% of the national sampled population of river km, and in 70% of the urban sampled population. PBDEs (92.0%), chlordane (88.5%) and DDT (98.7%) were also detected frequently, although at lower concentrations. Results were examined by subpopulations of rivers, including urban or nonurban and three defined ecoregions. PCBs, PBDEs, and DDT occur at significantly higher concentrations in fish from urban rivers versus nonurban; however, the distribution varied more among the ecoregions. Wildlife screening values previously published for bird and mammalian species were converted from whole fish to fillet screening values, and used to estimate risk for wildlife through fish consumption.

Evaluating the extent of pharmaceuticals in surface waters of the United States using a National-scale Rivers and Streams Assessment survey.

To assess the potential exposure of aquatic ecosystems to active pharmaceutical ingredients, the authors conducted a national-scale, probability-based statistical survey of the occurrence of these compounds in surface waters of the United States. The survey included 182 sampling sites and targeted rivers with close proximity to urban areas. The 46 analytes reported represent many classes of active pharmaceutical ingredients (APIs), including antibiotics, diuretics, antihypertensives, anticonvulsants, and antidepressants. Of the 46 analytes, 37 were detected in at least 1 sampling location. Sulfamethoxazole (an antibiotic) was the most frequently detected compound, being measured in 141 of the 182 surface waters surveyed at concentrations ranging up to 570 ng/L. Ten of the compounds were detected in 20% or more of the sampling sites. Weighted means of the analytical measurements are used with the statistical survey design and analysis to provide national estimates of the extent of contamination for these APIs in the nation's urban rivers. Published 2015 Wiley Periodicals, Inc. on behalf of SETAC. This article is a US Government work and as such, is in the public domain in the United States of America.

A national statistical survey assessment of mercury concentrations in fillets of fish collected in the U.S. EPA national rivers and streams assessment of the continental USA.

The U.S. EPA conducted a national statistical survey of fish fillet tissue with a sample size of 541 sites on boatable rivers =>5th order in 2008-2009. This is the first such study of mercury (Hg) in fish tissue from river sites focused on potential impacts to human health from fish consumption to also address wildlife impacts. Sample sites were identified as being urban or non-urban. All sample mercury concentrations were above the 3.33ugkg(-1) (ppb) quantitation limit, and an estimated 25.4% (±4.4%) of the 51663 river miles assessed exceeded the U.S. EPA 300ugkg(-1) fish-tissue based water quality criterion for mercury, representing 13144±181.8 river miles. Estimates of river miles exceeding comparable aquatic life thresholds (translated from fillet concentrations to whole fish equivalents) in avian species were similar to the number of river miles exceeding the human health threshold, whereas some mammalian species were more at risk than human from lower mercury concentrations. A comparison of means from the non-urban and urban data and among three ecoregions did not indicate a statistically significant difference in fish tissue Hg concentrations at p<0.05.

Perfluorinated compounds in fish from U.S. urban rivers and the Great Lakes.

Perfluorinated compounds (PFCs) have recently received scientific and regulatory attention due to their broad environmental distribution, persistence, bioaccumulative potential, and toxicity. Studies suggest that fish consumption may be a source of human exposure to perfluorooctane sulfonate (PFOS) or long-chain perfluorocarboxylic acids. Most PFC fish tissue literature focuses on marine fish and waters outside of the United States (U.S.). To broaden assessments in U.S. fish, a characterization of PFCs in freshwater fish was initiated on a national scale using an unequal probability design during the U.S. Environmental Protection Agency's (EPA's) 2008-2009 National Rivers and Streams Assessment (NRSA) and the Great Lakes Human Health Fish Tissue Study component of the 2010 EPA National Coastal Condition Assessment (NCCA/GL). Fish were collected from randomly selected locations--164 urban river sites and 157 nearshore Great Lake sites. The probability design allowed extrapolation to the sampled population of 17,059 km in urban rivers and a nearshore area of 11,091 km(2) in the Great Lakes. Fillets were analyzed for 13 PFCs using high-performance liquid chromatography tandem mass spectrometry. Results showed that PFOS dominated in frequency of occurrence, followed by three other longer-chain PFCs (perfluorodecanoic acid, perfluoroundecanoic acid, and perfluorododecanoic acid). Maximum PFOS concentrations were 127 and 80 ng/g in urban river samples and Great Lakes samples, respectively. The range of NRSA PFOS detections was similar to literature accounts from targeted riverine fish sampling. NCCA/GL PFOS levels were lower than those reported by other Great Lakes researchers, but generally higher than values in targeted inland lake studies. The probability design allowed development of cumulative distribution functions (CDFs) to quantify PFOS concentrations versus the sampled population, and the application of fish consumption advisory guidance to the CDFs resulted in an estimation of the proportion of urban rivers and the Great Lakes that exceed human health protection thresholds.

A national probabilistic study of polybrominated diphenyl ethers in fish from US lakes and reservoirs.

Polybrominated diphenyl ethers (PBDEs) are persistent, bioaccumulative, and toxic chemicals that are present in air, water, soil, sediment, and biota (including fish). Most previous studies of PBDEs in fish were spatially focused on targeted waterbodies. National estimates were developed for PBDEs in fish from lakes and reservoirs of the conterminous US (excluding the Laurentian Great Lakes) using an unequal probability design. Predator (fillet) and bottom-dweller (whole-body) composites were collected during 2003 from 166 lakes selected randomly from the target population of 147,343 lakes. Both composite types comprised nationally representative samples that were extrapolated to the sampled population of 76,559 and 46,190 lakes for predators and bottom dwellers, respectively. Fish were analyzed for 34 individual PBDE congeners and six co-eluting congener pairs representing a total of 46 PBDEs. All samples contained detectable levels of PBDEs, and BDE-47 predominated. The maximum aggregated sums of congeners ranged from 38.3 ng/g (predators) to 125 ng/g (bottom dwellers). Maximum concentrations in fish from this national probabilistic study exceeded those reported from recent targeted studies of US inland lakes, but were lower than those from Great Lakes studies. The probabilistic design allowed the development of cumulative distribution functions to quantify PBDE concentrations versus the cumulative number of US lakes from the sampled population.

Survey design for lakes and reservoirs in the United States to assess contaminants in fish tissue.

The National Lake Fish Tissue Study (NLFTS) was the first survey of fish contamination in lakes and reservoirs in the 48 conterminous states based on a probability survey design. This study included the largest set (268) of persistent, bioaccumulative, and toxic (PBT) chemicals ever studied in predator and bottom-dwelling fish species. The U.S. Environmental Protection Agency (USEPA) implemented the study in cooperation with states, tribal nations, and other federal agencies, with field collection occurring at 500 lakes and reservoirs over a four-year period (2000-2003). The sampled lakes and reservoirs were selected using a spatially balanced unequal probability survey design from 270,761 lake objects in USEPA's River Reach File Version 3 (RF3). The survey design selected 900 lake objects, with a reserve sample of 900, equally distributed across six lake area categories. A total of 1,001 lake objects were evaluated to identify 500 lake objects that met the study's definition of a lake and could be accessed for sampling. Based on the 1,001 evaluated lakes, it was estimated that a target population of 147,343 (+/-7% with 95% confidence) lakes and reservoirs met the NLFTS definition of a lake. Of the estimated 147,343 target lakes, 47% were estimated not to be sampleable either due to landowner access denial (35%) or due to physical barriers (12%). It was estimated that a sampled population of 78,664 (+/-12% with 95% confidence) lakes met the NLFTS lake definition, had either predator or bottom-dwelling fish present, and could be sampled.

Contaminants in fish tissue from US lakes and reservoirs: a national probabilistic study.

An unequal probability design was used to develop national estimates for 268 persistent, bioaccumulative, and toxic chemicals in fish tissue from lakes and reservoirs of the conterminous United States (excluding the Laurentian Great Lakes and Great Salt Lake). Predator (fillet) and bottom-dweller (whole body) composites were collected from 500 lakes selected randomly from the target population of 147,343 lakes in the lower 48 states. Each of these composite types comprised nationally representative samples whose results were extrapolated to the sampled population of an estimated 76,559 lakes for predators and 46,190 lakes for bottom dwellers. Mercury and PCBs were detected in all fish samples. Dioxins and furans were detected in 81% and 99% of predator and bottom-dweller samples, respectively. Cumulative frequency distributions showed that mercury concentrations exceeded the EPA 300 ppb mercury fish tissue criterion at nearly half of the lakes in the sampled population. Total PCB concentrations exceeded a 12 ppb human health risk-based consumption limit at nearly 17% of lakes, and dioxins and furans exceeded a 0.15 ppt (toxic equivalent or TEQ) risk-based threshold at nearly 8% of lakes in the sampled population. In contrast, 43 target chemicals were not detected in any samples. No detections were reported for nine organophosphate pesticides, one PCB congener, 16 polycyclic aromatic hydrocarbons, or 17 other semivolatile organic chemicals.

Using GIS to generate spatially balanced random survey designs for natural resource applications.

Sampling of a population is frequently required to understand trends and patterns in natural resource management because financial and time constraints preclude a complete census. A rigorous probability-based survey design specifies where to sample so that inferences from the sample apply to the entire population. Probability survey designs should be used in natural resource and environmental management situations because they provide the mathematical foundation for statistical inference. Development of long-term monitoring designs demand survey designs that achieve statistical rigor and are efficient but remain flexible to inevitable logistical or practical constraints during field data collection. Here we describe an approach to probability-based survey design, called the Reversed Randomized Quadrant-Recursive Raster, based on the concept of spatially balanced sampling and implemented in a geographic information system. This provides environmental managers a practical tool to generate flexible and efficient survey designs for natural resource applications. Factors commonly used to modify sampling intensity, such as categories, gradients, or accessibility, can be readily incorporated into the spatially balanced sample design.

Using relative risk to compare the effects of aquatic stressors at a regional scale.

The regional-scale importance of an aquatic stressor depends both on its regional extent (i.e., how widespread it is) and on the severity of its effects in ecosystems where it is found. Sample surveys, such as those developed by the U.S. Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP), are designed to estimate and compare the extents, throughout a large region, of elevated conditions for various aquatic stressors. In this article, we propose relative risk as a complementary measure of the severity of each stressor's effect on a response variable that characterizes aquatic ecological condition. Specifically, relative risk measures the strength of association between stressor and response variables that can be classified as either "good" (i.e., reference) or "poor" (i.e., different from reference). We present formulae for estimating relative risk and its confidence interval, adapted for the unequal sample inclusion probabilities employed in EMAP surveys. For a recent EMAP survey of streams in five Mid-Atlantic states, we estimated the relative extents of eight stressors as well as their relative risks to aquatic macroinvertebrate assemblages, with assemblage condition measured by an index of biotic integrity (IBI). For example, a measure of excess sedimentation had a relative risk of 1.60 for macroinvertebrate IBI, with the meaning that poor IBI conditions were 1.6 times more likely to be found in streams having poor conditions of sedimentation than in streams having good sedimentation conditions. We show how stressor extent and relative risk estimates, viewed together, offer a compact and comprehensive assessment of the relative importances of multiple stressors.

A more cost-effective EMAP benthic macrofaunal sampling protocol.

Benthic macrofaunal sampling protocols in the U.S. Environmental Protection Agency's Environmental Monitoring and Assessment Program (EMAP) are to collect 30 to 50 random benthic macrofauna [defined as animals retained on a 0.5 mm (East and Gulf Coasts, USA) or a 1.0 mm mesh sieve (West Coast, USA)] samples per reporting unit using a 0.044 m(2) (East and Gulf Coasts) or 0.1 m(2) (West Coast) grab. Benthic macrofaunal community conditions in the reporting unit are characterized by cumulative distribution functions (CDFs) on end points of interest, such as number of species (S), abundance (A), and Shannon-Wiener diversity (H'). An EMAP and a companion field study were conducted concurrently in Tillamook Bay (Oregon, USA) to compare the cost effectiveness of benthic macrofauna samples collected using the EMAP West Coast (0.1 m(2) x >or=7 cm deep, 1.0 mm mesh), a 0.01 m(2) x 5 cm deep, 1.0 mm mesh, and a 0.01 m(2) x 5 cm deep, 0.5 mm mesh sampling protocol. Cost was estimated in relative laboratory sample-processing time. Sampling protocols were judged equally effective for EMAP purposes if, after linear transformation to adjust for scale changes in end point distributions, their S, A, and H' CDFs were not significantly different. The 0.01 m(2) x 5 cm deep, 1.0 mm mesh sampling protocol was the most cost effective.