Spatially Balanced Sampling: Application to Environmental Surveys

Wildfire burn severity and stream chemistry influence aquatic invertebrate and riparian avian mercury exposure in forested ecosystems

Terrestrial soils in forested landscapes represent some of the largest mercury (Hg) reserves globally. Wildfire can alter the storage and distribution of terrestrial-bound Hg via reemission to the atmosphere or mobilization in watersheds where it may become available for methylation and uptake into food webs. Using data associated with the 2007 Moonlight and Antelope Fires in California, we examined the long-term direct effects of wildfire burn severity on the distribution and magnitude of Hg concentrations in riparian food webs. Additionally, we quantified the cross-ecosystem transfer of Hg from aquatic invertebrate to riparian bird communities; and assessed the influence of biogeochemical, landscape variables, and ecological factors on Hg concentrations in aquatic and terrestrial food webs. Benthic macroinvertebrate methylmercury (MeHg) and riparian bird blood total mercury (THg) concentrations varied by 710- and 760-fold, respectively, and Hg concentrations were highest in predators. We found inconsistent relationships between Hg concentrations across and within taxa and guilds in response to stream chemical parameters and burn severity. Macroinvertebrate scraper MeHg concentrations were influenced by dissolved organic carbon (DOC); however, that relationship was moderated by burn severity (as burn severity increased the effect of DOC declined). Omnivorous bird Hg concentrations declined with increasing burn severity. Overall, taxa more linked to in situ energetic pathways may be more responsive to the biogeochemical processes that influence MeHg cycling. Remarkably, 8 years post-fire, we still observed evidence of burn severity influencing Hg concentrations within riparian food webs, illustrating its overarching role in altering the storage and redistribution of Hg and influencing biogeochemical processes.

Effects of seining effort on estimates of fish diversity in a sand-bed river

Changes in species diversity can be an indicator of ecosystem disturbance, impairment, or recovery. Estimating sampling effort needed to adequately represent stream fish assemblages is necessary for informing conservation actions. Increased sampling intensity can increase species detection, affecting the accuracy and precision of biodiversity indices. Seining is commonly used in fish surveys in sand-bottomed streams of the western USA. Here, we sampled 20, 200-m long stream sites each with 40 consecutive seine hauls to determine how increased within-site effort affected measures of species diversity. An average of 10 seine hauls were required to collect 75% of species present at sites in 40 seine hauls, while 18 seine hauls were required to collect 100% of species observed at a site sampled with 40 hauls. Simpson's diversity index was highly variable when fewer than 7 seine hauls were performed at each site but stabilized when effort was > 15 seine hauls per site. Total dissimilarity and β-diversity components were variable under low sampling effort and also stabilized when effort reached 15 seine hauls per site. However, sampling with more than 18-20 seine hauls per site yielded few additional species. In shallow, sand-bed streams, we suggest sampling with < 5 seine hauls per 200 m of stream can result in unreliable estimates of α-diversity and variation in β-diversity. Increased effort of 15-20 seine hauls per 200 m of stream captured nearly all species present in 40 hauls per 200 m and stabilized species evenness and β-diversity indices.

Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations

In finite populations, pseudo-population bootstrap is the sole method preserving the spirit of the original bootstrap performed from iid observations. In spatial sampling, theoretical results about the convergence of bootstrap distributions to the actual distributions of estimators are lacking, owing to the failure of spatially balanced sampling designs to converge to the maximum entropy design. In addition, the issue of creating pseudo.populations able to mimic the characteristics of real populations is challenging in spatial frameworks where spatial trends, relationships, and similarities among neighbouring locations are invariably present. In this paper, we propose the use of the nearest-neighbour interpolation of spatial populations for constructing pseudo-populations that converge to real populations under mild conditions. The effectiveness of these proposals with respect to traditional pseudo-populations is empirically checked by a simulation study.

Remote Sensing-Guided Spatial Sampling Strategy over Heterogeneous Surface Ground for Validation of Vegetation Indices Products with Medium and High Spatial Resolution

Remote sensing (RS)-derived vegetation indices (VIs) with medium and high spatial resolution have emerged as a promising dataset for fine-scale ecosystem modeling and agricultural monitoring at local or global scales. Before they can be used as reliable inputs for other research, conducting in situ measurements for validation is very critical. However, the spatial heterogeneity due to the diversity of land cover and its spatial organization in the landscape increases the uncertainty of validation, so design of optimal sampling is an important basis for the reliability of the validation. In this paper, we propose an integrative stratified sampling strategy (INTEG-STRAT) based on normalized difference vegetation index (NDVI) data as prior knowledge. The basic idea is to realize a sampling optimization by determining the optimal combination of the spatial sampling method (e.g., simple random sampling (SRS), spatial system sampling (SYS), stratified sampling, generalized random tessellation stratified (GRTS), balanced acceptance sampling (BAS)) and spatial stratification scheme with an objective rule. The objective rule in this paper is to minimize the root mean square error (RMSE) of 10-fold cross validation between estimated values (sample are not included) and the corresponding values on prior knowledge. Relative precision, correlation coefficient, and RMSE are used to compare the effectiveness of the proposed sampling strategy with each sampling method without considering sampling optimization. After comparing, we find that the INTEG-STRAT requires fewer samples to become stable and has higher accuracy. At site 1, when the correlation coefficient between NDVI image and the simulated NDVI surface reached 80%, INTEG-STRAT needed only 70 sampling points while other methods require more sampling points. At the same time, INTEG-STRAT strategy has a smaller RMSE between the estimated values and the corresponding values on prior knowledge image. In general, INTEG-STRAT is an effective method in the selection of representative samples to support the validation of vegetation indices products with medium and high spatial resolution.

Modeling areal measures of campsite impacts on the Appalachian National Scenic Trail to enhance ecological sustainability

Campsite impacts in protected natural areas are most effectively minimized by a containment strategy that focuses use on a limited number of sustainable campsites that spatially concentrate camping activities. This research employs spatial autoregressive (SAR) modeling to evaluate the relative influence of use-related, environmental, and managerial factors on two salient measures of campsite impact. Relational analyses examined numerous field-collected and GIS-derived indicators, including several new indicators calculated using high-resolution Light Detection and Ranging (LiDAR) topographic data to evaluate the influence of terrain characteristics on the dependent variables. Chosen variables in the best SAR models explained 35% and 30% of the variation in campsite size and area of vegetation loss on campsites. Results identified three key indicators that managers can manipulate to enhance the sustainability of campsites: campsite type, and terrain characteristics relating to landform slope and topographic roughness. Results support indirect management methods that rely on the location, design, construction, and maintenance of campsites, instead of direct regulations that restrict visitation or visitor freedoms. As visitation pressures continue to increase, this knowledge can be applied to select and promote the use of more ecologically sustainable campsites.

Active regional surveillance for early detection of exotic/emerging pathogens of swine: A comparison of statistical methods for farm selection

In this study, five spatially balanced sampling methods, i.e., generalized random-tessellation stratified (GRTS), local pivotal method (LPM), spatially correlated Poisson sampling (SCPS), local cube method (LCUBE), and balanced acceptance sampling (BAS) were compared to simple random sampling (SRS) based on a livestock disease transmission model on a hypothetical region (195 km × 300 km) populated with 6000 farms in terms of the probability of detection by sample size. Given a fixed sample size, four of the five spatially balanced sampling methods provided better performance than SRS, i.e., higher probabilities of detecting at least one infected farms over a range of regional prevalence evaluated (1%-5%). That is, for any given probability of detection, spatially balanced methods required testing fewer farms than SRS. In an era of pandemics, active regional surveillance for early detection of emerging pathogens becomes urgent, yet shrinking budgets impose intractable constraints. The better performance and higher efficiency of spatially balanced sampling methods suggests a potential improvement in regional livestock disease surveillances and a partial solution to the challenge of affordable surveillance.

Spatial Spread Sampling Using Weakly Associated Vectors

Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion probabilities. The proposed method is based on the definition of a spatial structure by using a stratification matrix. Our method exactly satisfies given inclusion probabilities and provides samples that are very well spread. A set of simulations shows that our method outperforms other existing methods such as the generalized random tessellation stratified or the local pivotal method. Analysis of the variance on a real dataset shows that our method is more accurate than these two. Furthermore, a variance estimator is proposed.

Spatially balanced sampling designs for environmental surveys

Some environmental studies use non-probabilistic sampling designs to draw samples from spatially distributed populations. Unfortunately, these samples can be difficult to analyse statistically and can give biased estimates of population characteristics. Spatially balanced sampling designs are probabilistic designs that spread the sampling effort evenly over the resource. These designs are particularly useful for environmental sampling because they produce good-sample coverage over the resource, they have precise design-based estimators and they can potentially reduce the sampling cost. The most popular spatially balanced design is Generalized Random Tessellation Stratified (GRTS), which has many desirable features including a spatially balanced sample, design-based estimators and the ability to select spatially balanced oversamples. This article considers the popularity of spatially balanced sampling, reviews several spatially balanced sampling designs and shows how these designs can be implemented in the statistical programming language R. We hope to increase the visibility of spatially balanced sampling and encourage environmental scientists to use these designs.