Enhancing Quantitative Analysis of Xenobiotics in Blood Plasma through Cross-Matrix Calibration and Bayesian Hierarchical Modeling.

This study addresses the challenges of matrix effects and interspecies plasma protein binding (PPB) on measurement variability during method validation across diverse plasma types (human, rat, rabbit, and bovine). Accurate measurements of small molecules in plasma samples often require matrix-matched calibration approaches with the use of specific plasma types, which may have limited availability or affordability. To mitigate the costs associated with human plasma measurements, we explore in this work the potential of cross-matrix-matched calibration using Bayesian hierarchical modeling (BHM) to correct for matrix effects associated with PPB. We initially developed a targeted quantitative approach utilizing biocompatible solid-phase microextraction coupled with liquid chromatography-mass spectrometry for xenobiotic analysis in plasma. The method was evaluated for absolute matrix effects across human, bovine, rat, and rabbit plasma comparing pre- and postmatrix extraction standards. Absolute matrix effects from 96 to 108% for most analytes across plasma sources indicate that the biocompatibility of the extraction phase minimizes interference coextraction. However, the extent of PPB in different media can still affect the accuracy of the measurement when the extraction of small molecules is carried out via free concentration, as in the case of microextraction techniques. In fact, while matrix-matched calibration revealed high accuracy, cross-matrix calibration (e.g., using a calibration curve generated from bovine plasma) proved inadequate for precise measurements in human plasma. A BHM was used to calculate correction factors for each analyte within each plasma type, successfully mitigating the measurement bias resulting from diverse calibration curve types used to quantify human plasma samples. This work contributes to the development of cost-effective, efficient calibration strategies for biofluids. Leveraging easily accessible plasma sources, like bovine plasma, for method optimization and validation prior to analyzing costly plasma (e.g., human plasma) holds substantial advantages applicable to biomonitoring and pharmacokinetic studies.

Nutrient reduction mitigated the expansion of cyanobacterial blooms caused by climate change in Lake Taihu according to Bayesian network models.

Although nutrient reduction has been used for lake eutrophication mitigation worldwide, the use of this practice alone has been shown to be less effective in combatting cyanobacterial blooms, primarily because of climate change. In addition, quantifying the climate change contribution to cyanobacterial blooms is difficult, further complicating efforts to set nutrient reduction goals for mitigating blooms in freshwater lakes. This study employed a continuous variable Bayesian modeling framework to develop a model to predict spring cyanobacterial bloom areas and frequencies (the responses) using nutrient levels and climatic factors as predictors. Our results suggested that both spring climatic factors (e.g., increasing temperature and decreasing wind speed) and nutrients (e.g., total phosphorus) played vital roles in spring blooms in Lake Taihu, with climatic factors being the primary drivers for both bloom areas and frequencies. Climate change in spring had a 90% probability of increasing the bloom area from 35 km2 to 180 km2 during our study period, while nutrient reduction limited the bloom area to 170 km2, which helped mitigate expansion of cyanobacterial blooms. For lake management, to ensure a 90% probability of the mean spring bloom areas remaining under 154 km2 (the 75th percentile of the bloom areas in spring), the total phosphorus should be maintained below 0.073 mg·L-1 under current climatic conditions, which is a 46.3% reduction from the current level. Our modeling approach is an effective method for deriving dynamic nutrient thresholds for lake management under different climatic scenarios and management goals.

Large-scale patterns of understory biomass and its allocation across China's forests.

Plant biomass storage and its allocation reflect the ecosystem productivity and adaptation to different environments. Understory vegetation is a significant component of any forest ecosystem and plays a vital role in biodiversity maintenance and the ecosystem's carbon cycle. Although many studies have addressed the relationships of climate, stand structure and resource availability with understory biomass and its allocation at local scales, the large-scale variation of understory biomass and allocation and their underlying mechanisms remain unclear. We compiled a large database of understory biomass at the community level across China's forests to explore the large-scale patterns of understory biomass and R/S ratio, and to quantify the relative importance of drivers. Understory biomass and R/S ratio varied largely with forest types, and decreased with increasing longitude, but increased with elevation. Understory biomass increased with increasing latitude, mean annual temperature (MAT), and mean annual precipitation (MAP), while the R/S ratio decreased with latitude, MAT, and MAP. Stand structure had a strong effect on the variations in understory biomass. MAP was the most important driver in determining R/S ratio. This synthesis provides a first assessment of the large-scale patterns of understory biomass and allocation and sheds new light on the mechanisms underlying the variations in understory biomass and its allocation over a broad geographic scale. These findings will improve predictions of understory community dynamics in response to climate change and aid in further optimizing ecosystem process models.

Evaluating the impact of watershed development and climate change on stream ecosystems: A Bayesian network modeling approach.

A continuous-variable Bayesian network (cBN) model is used to link watershed development and climate change to stream ecosystem indicators. A graphical model, reflecting our understanding of the connections between climate change, weather condition, loss of natural land cover, stream flow characteristics, and stream ecosystem indicators is used as the basis for selecting flow metrics for predicting macroinvertebrate-based indicators. Selected flow metrics were then linked to variables representing watershed development and climate change. We fit the model to data from two river basins in southeast US and the resulting model was used to simulate future stream ecological conditions using projected future climate and development scenarios. The three climate models predicted varying ecological condition trajectories, but similar worst-case ecological conditions. The established modeling approach couples mechanistic understanding with field data to develop predictions of management-relevant variables across a heterogeneous landscape. We discussed the transferability of the modeling approach.

Seasonal overturn and stratification changes drive deep-water warming in one of Earth's largest lakes.

Most of Earth's fresh surface water is consolidated in just a few of its largest lakes, and because of their unique response to environmental conditions, lakes have been identified as climate change sentinels. While the response of lake surface water temperatures to climate change is well documented from satellite and summer in situ measurements, our understanding of how water temperatures in large lakes are responding at depth is limited, as few large lakes have detailed long-term subsurface observations. We present an analysis of three decades of high frequency (3-hourly and hourly) subsurface water temperature data from Lake Michigan. This unique data set reveals that deep water temperatures are rising in the winter and provides precise measurements of the timing of fall overturn, the point of minimum temperature, and the duration of the winter cooling period. Relationships from the data show a shortened winter season results in higher subsurface temperatures and earlier onset of summer stratification. Shifts in the thermal regimes of large lakes will have profound impacts on the ecosystems of the world's surface freshwater.

Effects of climate and land-use changes on fish catches across lakes at a global scale.

Globally, our knowledge on lake fisheries is still limited despite their importance to food security and livelihoods. Here we show that fish catches can respond either positively or negatively to climate and land-use changes, by analyzing time-series data (1970-2014) for 31 lakes across five continents. We find that effects of a climate or land-use driver (e.g., air temperature) on lake environment could be relatively consistent in directions, but consequential changes in a lake-environmental factor (e.g., water temperature) could result in either increases or decreases in fish catch in a given lake. A subsequent correlation analysis indicates that reductions in fish catch was less likely to occur in response to potential climate and land-use changes if a lake is located in a region with greater access to clean water. This finding suggests that adequate investments for water-quality protection and water-use efficiency can provide additional benefits to lake fisheries and food security.

All tests are imperfect: Accounting for false positives and false negatives using Bayesian statistics.

Tests with binary outcomes (e.g., positive versus negative) to indicate a binary state of nature (e.g., disease agent present versus absent) are common. These tests are rarely perfect: chances of a false positive and a false negative always exist. Imperfect results cannot be directly used to infer the true state of the nature; information about the method's uncertainty (i.e., the two error rates and our knowledge of the subject) must be properly accounted for before an imperfect result can be made informative. We discuss statistical methods for incorporating the uncertain information under two scenarios, based on the purpose of conducting a test: inference about the subject under test and inference about the population represented by test subjects. The results are applicable to almost all tests. The importance of properly interpreting results from imperfect tests is universal, although how to handle the uncertainty is inevitably case-specific. The statistical considerations not only will change the way we interpret test results, but also how we plan and carry out tests that are known to be imperfect. Using a numerical example, we illustrate the post-test steps necessary for making the imperfect test results meaningful.

Rethinking the lake trophic state index.

Lake trophic state classifications provide information about the condition of lentic ecosystems and are indicative of both ecosystem services (e.g., clean water, recreational opportunities, and aesthetics) and disservices (e.g., cyanobacteria blooms). The current classification schemes have been criticized for developing indices that are single-variable based (vs. a complex aggregate of multi-variables), discrete (vs. a continuous), and/or deterministic (vs. an inherently random). We present an updated lake trophic classification model using a Bayesian multilevel ordered categorical regression. The model consists of a proportional odds logistic regression (POLR) that models ordered, categorical, lake trophic state using Secchi disk depth, elevation, nitrogen concentration (N), and phosphorus concentration (P). The overall accuracy, when compared to existing classifications of trophic state index (TSI), for the POLR model was 0.68 and the balanced accuracy ranged between 0.72 and 0.93. This work delivers an index that is multi-variable based, continuous, and classifies lakes in probabilistic terms. While our model addresses aforementioned limitations of the current approach to lake trophic classification, the addition of uncertainty quantification is important, because the trophic state response to predictors varies among lakes. Our model successfully addresses concerns with the current approach and performs well across trophic states in a large spatial extent.

The implications of Simpson's paradox for cross-scale inference among lakes.

Using cross-sectional data for making ecological inference started as a practical means of pooling data to enable meaningful empirical model development. For example, limnologists routinely use sample averages from numerous individual lakes to examine patterns across lakes. The basic assumption behind the use of cross-lake data is often that responses within and across lakes are identical. As data from multiple study units across a wide spatiotemporal scale are increasingly accessible for researchers, an assessment of this assumption is now feasible. In this study, we demonstrate that this assumption is usually unjustified, due largely to a statistical phenomenon known as the Simpson's paradox. Through comparisons of a commonly used empirical model of the effect of nutrients on algal growth developed using several data sets, we discuss the cognitive importance of distinguishing factors affecting lake eutrophication operating at different spatial and temporal scales. Our study proposes the use of the Bayesian hierarchical modeling approach to properly structure the data analysis when data from multiple lakes are employed.

Total phosphorus-precipitation and Chlorophyll a-phosphorus relationships of lakes and reservoirs mediated by soil iron at regional scale.

Phosphorus is a critical element determining trophic status and Chlorophyll a (Chl a) level in natural lakes and reservoirs, and total phosphorus (TP) concentrations can be predicted from data on phosphorus loading, hydraulic flushing rate and sedimentation. Due to their interactions with phosphorus, iron (hydr) oxides in suspended particles, originally derived from watershed soil, can strongly influence the phosphorus sedimentation and phosphorus bioavailability in water columns. Thus, the TP-precipitation relationship and the response of Chl a to TP are likely associated with watersheds soil iron. To test this assumption, we built hierarchical linear models for summer observation of natural lakes and reservoirs across a large geographic gradient. The intercepts and slopes of TP-precipitation relationships are higher in natural lakes than those in reservoirs, and these model coefficients exhibit latitudinal variations that are explained by the natural soil iron gradient. Soil iron, operating at a regional level, significantly mediates the effect of precipitation on TP concentration in both natural lakes and reservoirs, and drives the latitudinal variation in the Chl a-TP relationships for reservoirs. Our results imply that the increase in extreme precipitation events anticipated under future climate conditions may substantially mitigate eutrophication in tropical and subtropical reservoirs, but may worsen conditions in temperate lakes.

Improving estimates of built-up area from night time light across globally distributed cities through hierarchical modeling.

Built-up area has become an important indicator for studying urban environments, but mapping built-up area at the regional/global scale remains challenging due to the complexity of impervious surface features. Nighttime light data (NTL) is one of the major remote sensing data sources for regional/global built-up or impervious surface mapping. A single regression relationship between fractional built-up/impervious area and NTL or various indices derived based on NTL and vegetation index (e.g., NDVI) data had been established in many previous studies. However, due to the varying geographical, climatic, and socio-economic characteristics of cities, the same regression relationship may vary significantly across cities. In this study, we examined the regression relationship between percentage of built-up area (pBUA) and vegetation adjusted nighttime light urban index (VANUI) for 120 randomly selected cities around the world with a hierarchical hockey-stick regression model. We found that there is a substantial variability in the slope (0.658 ±â€¯0.318), the threshold VANUI (-1.92 ±â€¯0.769, log scale) after which the linear relationship holds, and the coefficient of determination R2 (0.71 ±â€¯0.14) among globally distributed cities. A small proportion of this substantial variability can be attributed to socio-economic status (e.g., total population, GDP per capita) and landscape structures (e.g., compactness and fragmentation). Due to these variations, our hierarchical model or no-pooling model (i.e., fit each city individually) can significantly improve model prediction accuracy (17% in terms of root mean squared error) over a complete-pooling model. We, however, recommend hierarchical models as they can provide meaningful priors for future modeling under a Bayesian framework, and achieve higher prediction accuracy than no-pooling models when sample size is small.

A Meta-Analysis on the Effect of Agricultural Conservation Practices on Nutrient Loss.

Conservation practices are widely used to reduce N and P loads from agricultural fields and minimize their impact on water quality, but research using field-scale data to model the national average impact of conservation practices for different forms of N and P is needed. Thus, we quantified the effects of conservation practices (grassed waterways, terraces, contour farming, filter strips, and riparian buffers) on total, particulate, and dissolved N and P runoff from farmlands. Specifically, we conducted a meta-analysis of the Measured Annual Nutrient loads from AGricultural Environments (MANAGE) database using propensity score matching and multilevel modeling to remove the influence of confounding factors. There is no best method for addressing this influence, so we applied two alternative methods because similar results increase confidence in our findings. Propensity score matching found that conservation practices reduced total P, particulate P, and particulate N loading by an average of 67, 83, and 67%, respectively. Multilevel modeling estimated reductions of 58, 76, and 64% for the same nutrients. Although the propensity score method only yields a mean rate of reduction, multilevel modeling further estimates the reduction for different subgroups (i.e., different crops and fertilizer application methods) when such groupings are feasible. The multilevel models indicated that conservation practices affected row crops the most (e.g., corn [ L.] and soybean [ (L.) Merr.]) and fields with injected or surface-applied fertilizers. Our analysis used field-scale data to estimate the average effectiveness of conservation practices in reducing N and P runoff, providing valuable insight for regional and national decision making.

Updating the ELISA standard curve fitting process to reduce uncertainty in estimated microcystin concentrations.

This study is aimed at exploring the optimal ELISA standard curve fitting process for reducing measurement uncertainty. Using an ELISA kit for measuring cyanobacterial toxin (microcystin), we show that uncertainty associated with the estimated microcystin concentrations can be reduced by defining the standard curve as a four-parameter logistic function on the natural log concentration scale, instead of the current approach of defining the curve on the concentration scale. The model comparison method is outlined in this paper, allowing it to be transferable to test different statistical models for other ELISA test kits.

The multiple-comparison trap and the Raven's paradox-perils of using null hypothesis testing in environmental assessment.

Detecting and quantifying environmental thresholds is frequently an important step in understanding ecological responses to environmental stressors. We discuss two statistical issues often encountered in threshold detection and quantification when statistical null hypothesis testing is used as a main analytical tool. The hidden multiple-comparison trap (leading to a much higher risk of a false detection) and Raven's paradox (rendering a "detection" meaningless) are often obscured when statistical hypothesis testing is used as part of a more elaborate model, especially models based on computer-intensive methods. Using two examples, we show that the hidden multiple-comparison trap can be exposed using computer simulation to estimate the probability of making a false detection; Raven's paradox can be avoided by clearly stating the null and alternative hypotheses using scientific terms to substantiate that the rejection of the null is equivalent to proving that the alternative of interest is true. The hidden multiple-comparison trap implies that a null hypothesis testing based on a computer-intensive method should be used with caution. The implication of Raven's paradox requires that we focus on providing evidence supporting the proposed hypothesis or model, rather than seeking evidence against the frequently irrelevant null hypothesis. These two problems, and many others related to null hypothesis testing, suggest that statistical hypothesis testing should be used only as a component of the body of evidence, perhaps, as the devil's advocate.

On Abandoning Hypothesis Testing in Environmental Standard Compliance Assessment.

We use basic characteristics of statistical significance test to argue the abandonment of hypothesis testing in environmental standard (or criterion) compliance assessment. The typical sample size used for environmental assessment is small, and the natural variation of many water quality constituent concentrations is high. These conditions lead to low statistical power of the hypothesis tests used in the assessment process. As a result, using hypothesis testing is often inefficient in detecting noncompliance. When a noncompliance is detected, it is frequently due to sampling or other types of error. We illustrate the problems using two examples, through which we argue that these problems cannot be resolved under the current practice of assessing compliance one water at a time. We recommend that the hypothesis testing framework be replaced by a statistical estimation approach, which can more effectively leverage information from assessments on similar waters using a probabilistic assessment approach.

The effects of nutrients on stream invertebrates: a regional estimation by generalized propensity score.

INTRODUCTION: The effects of nutrients on stream conditions within individual streams or small areas have been studied extensively, but the same effects over a large region have rarely been examined due to the difficulty of applying large-scale manipulative experiments. In this study, we estimated the causal effects of nutrients within the Western United States on invertebrate richness, an important biological indicator of stream conditions, by using observational data. METHODS: We used the generalized propensity score method to avoid the common problem of statistical inference using observational data, i.e., correlation established based on observational data does not imply a causal relationship because the effects of confounding factors are not properly separated. RESULTS: Our analysis showed a subsidy-stress relationship between nutrients and invertebrate taxon richness in the whole Western United States and in its sub-ecoregions. The magnitude of the relationship varies among these sub-ecoregions, suggesting a varying nitrogen effect on macroinvertebrates due, in large part, to the varying natural and anthropogenic conditions from ecoregion to ecoregion. Furthermore, our analysis confirmed that causal estimation results using regression can be sensitive to the imbalance of confounding factors. CONCLUSIONS: Stratifying data into ecoregions with relatively homogeneous environmental conditions or adjusting data by generalized propensity score can improve the balance of confounding factors, thereby allowing more reliable causal inference of nutrient effects. Invertebrates respond to the same nutrient levels differently across different site conditions.

Response to CO2 enrichment of understory vegetation in the shade of forests.

Responses of forest ecosystems to increased atmospheric CO2 concentration have been studied in few free-air CO2 enrichment (FACE) experiments during last two decades. Most studies focused principally on the overstory trees with little attention given to understory vegetation. Despite its small contribution to total productivity of an ecosystem, understory vegetation plays an important role in predicting successional dynamics and future plant community composition. Thus, the response of understory vegetation in Pinus taeda plantation at the Duke Forest FACE site after 15-17 years of exposure to elevated CO2 , 6-13 of which with nitrogen (N) amendment, was examined. Aboveground biomass and density of the understory decreased across all treatments with increasing overstory leaf area index (LAI). However, the CO2 and N treatments had no effect on aboveground biomass, tree density, community composition, and the fraction of shade-tolerant species. The increases of overstory LAI (~28%) under elevated CO2 resulted in a reduction of light available to the understory (~18%) sufficient to nullify the expected growth-enhancing effect of elevated CO2 on understory vegetation.

Quantifying and Reducing Uncertainty in Estimated Microcystin Concentrations from the ELISA Method.

We discuss the uncertainty associated with a commonly used method for measuring the concentration of microcystin, a group of toxins associated with cyanobacterial blooms. Such uncertainty is rarely reported and accounted for in important drinking water management decisions. Using monitoring data from Ohio Environmental Protection Agency and from City of Toledo, we document the sources of measurement uncertainty and recommend a Bayesian hierarchical modeling approach for reducing the measurement uncertainty. Our analysis suggests that (1) much of the uncertainty is a result of the highly uncertain "standard curve" developed during each test and (2) the uncertainty can be reduced by pooling raw test data from multiple tests. Based on these results, we suggest that estimation uncertainty can be effectively reduced through the effort of either (1) regional regulatory agencies by sharing and combining raw test data from regularly scheduled microcystin monitoring program or (2) the manufacturer of the testing kit by conducting additional tests as part of an effort to improve the testing kit.

Implications of Stein's Paradox for Environmental Standard Compliance Assessment.

The implications of Stein's paradox stirred considerable debate in statistical circles when the concept was first introduced in the 1950s. The paradox arises when we are interested in estimating the means of several variables simultaneously. In this situation, the best estimator for an individual mean, the sample average, is no longer the best. Rather, a shrinkage estimator, which shrinks individual sample averages toward the overall average is shown to have improved overall accuracy. Although controversial at the time, the concept of shrinking toward overall average is now widely accepted as a good practice for improving statistical stability and reducing error, not only in simple estimation problems, but also in complicated modeling problems. However, the utility of Stein's insights are not widely recognized in the environmental management community, where mean pollutant concentrations of multiple waters are routinely estimated for management decision-making. In this essay, we introduce Stein's paradox and its modern generalization, the Bayesian hierarchical model, in the context of environmental standard compliance assessment. Using simulated data and nutrient monitoring data from wadeable streams around the Great Lakes, we show that a Bayesian hierarchical model can improve overall estimation accuracy, thereby improving our confidence in the assessment results, especially for standard compliance assessment of waters with small sample sizes.

The Frequency Component of Water Quality Criterion Compliance Assessment Should be Data Driven.

A numerical water quality criterion in the U.S. consists of three components representing magnitude, duration, and frequency. While magnitude and duration are well defined and conceptually unambiguous, the meaning of the frequency component is often debatable. We interpret the frequency component as a tool for accounting for uncertainty in estimating the mean concentration of a water quality constituent, after revisiting early works on environmental standards and criteria. Based on this interpretation, we illustrate management-related issues when using the default frequency of one exceedance in 3 years in compliance assessment. We propose a data-driven approach for estimating an appropriate frequency to ensure a consistent level of confidence in a water's compliance of a water quality criterion. The data-driven frequency is determined by water quality constituent concentration distribution characteristics and sample size. The method is illustrated using two examples.