Final Report: Ecological Thresholds and Responses of Stream Benthic Communities to Heavy Metals

EPA Grant Number: R832441
Title: Ecological Thresholds and Responses of Stream Benthic Communities to Heavy Metals
Investigators: Clements, William , Noon, Barry , Wang, Haonan
Institution: Colorado State University
EPA Project Officer: Hiscock, Michael
Project Period: July 31, 2005 through December 30, 2007 (Extended to December 30, 2008)
Project Amount: $295,760
RFA: Exploratory Research: Understanding Ecological Thresholds In Aquatic Systems Through Retrospective Analysis (2004) RFA Text |  Recipients Lists
Research Category: Aquatic Ecosystems , Ecosystems , Water

Objective:

The primary goal of our research was to identify and validate ecological thresholds for stream communities impacted by heavy metal contamination from historic mining operations. We hypothesize that the location of ecological thresholds along a well-defined gradient of metal contamination varies among state variables and is influenced by local (reach-scale) and landscape-level environmental drivers. We integrated results of 16 microcosm experiments and two spatially extensive surveys of > 150 Colorado streams to identify ecological thresholds along a gradient of heavy metal contamination. For the purposes of this project, we define an ecological threshold (Xr ) as a metal concentration that, when exceeded, results in pronounced changes in the values of one or more state variables. Using parametric and nonparametric regression techniques, we identified thresholds for state variables across several levels of biological organization. To validate and test the ecological significance of these thresholds, we examined long-term changes in response variables in a mining impacted stream where metal concentrations were recently reduced below threshold levels.

Summary/Accomplishments (Outputs/Outcomes):

Theoretical and empirical studies suggest that some ecosystems may show abrupt, nonlinear changes in one or more state variables in response to environmental drivers (e.g., May 1977, Connell and Sousa 1983, Groffman et al. 2006). Shifts to alternative stable states have been reported in a variety of ecosystems, including lakes, coral reefs, deserts, and oceans (Scheffer et al. 2001). These shifts can be triggered by natural disturbance, such as fire or flooding, or anthropogenic factors such as climate change, nutrient accumulation, exotic species, and toxic chemicals. Although communities may recover from natural disturbance through successional processes, human-induced disturbances are often unique and move ecological systems to novel, alternative states (Folke et al. 2004). In addition, if ecosystems are chronically stressed due to natural or anthropogenic disturbances, such systems may move to alternative states that remain stable even when the stressors are removed (e.g., Scheffer et al. 2001, Scheffer and Carpenter, 2003).
 
One can consider thresholds as ecological nonlinearities, where substantial changes in an ecological state variable are a consequence of small continuous changes in an independent (stressor) variable (Muradian 2001). The point or region at which rapid change initially occurs defines the threshold. Near this point, small changes in stressor intensity produce large effects on state variables. Unfortunately, there can be an inherent arbitrariness to the threshold concept because it does not consider if the change in the value of the state variable is ecologically relevant. Statistical models have been developed in other disciplines to detect breakpoints in nonlinear response functions, but it is not always clear which models are appropriate for a particular ecological data set.
 
Estimating the location of an ecological threshold along a stressor gradient is challenging, and making a wrong prediction from a management and regulatory context may have serious consequences. The “humpty-dumpty’ model of recovery (Pimm 1991) suggests that some disturbed ecosystems may never recover, or that recovery may not occur until stressor levels are reduced well below those that triggered the initial response (Scheffer et al. 2001). Furthermore, the specific trajectory of recovery following removal of a stressor is variable and often nonlinear (Lake et al. 2007), in part because other sources of disturbance or regional climatic variation may have a greater impact on community structure. Threshold models that account for these complex recovery scenarios will be necessary to insure that costly restoration efforts are focused on systems where improvements are most likely (Poole et al . 2004).
 
Application of Ecological Threshold Models to Assessing Recovery
 
The traditional applications of threshold models in ecology have focused primarily on stressor-response relationships, such as responses of primary producers to nutrients (Qian et al. 2003), threatened species to habitat destruction (Huggett 2005), or coral reefs to factors associated with global change (Bellwood et al. 2004). Because thresholds ultimately reflect the resistance and resilience of a system to stressors, these approaches can also be employed to assess restoration effectiveness and associated recovery following removal of contamination. Recent surveys conducted by the U.S. EPA estimate that approximately one third of the streams and rivers in the contiguous United States are significantly degraded or polluted (U.S. EPA 2000). Expenditures for restoration of these systems, which averaged approximately $1 billion per year from 1990 to 2003, are expected to increase, with the majority of these funds used for improving water quality (Bernhardt et al. 2005). Despite these significant investments in water quality, our ability to assess restoration effectiveness of contaminated ecosystems is seriously limited by inadequate study designs (Bernhardt et al. 2005), failure to consider ecological theory (Lake et al. 2007), and a lack of agreement regarding appropriate measures of recovery (National Research Council 2007). Developing objective criteria that define restoration effectiveness is also challenging because of significant variation among response variables. For example, apparent recovery of some indicators, such as abundance or species richness, may occur despite persistent alteration in community composition and loss of ecological resilience (Berumen et al. 2006).
 
We demonstrate the application of a a new method by Chaudhuri and Marron (1999) that makes few model assumptions and is therefore applicable to a broad range of ecological applications. Their method, Significant Zero crossings (SiZer), applies a nonparametric smoother to the stressor-response data, and then examines the derivatives of the smoothed curve to identify the existence of a threshold. To illustrate this method, we consider benthic macroinvertebrate data collected on the Arkansas River, a metal-polluted stream in Colorado. We use SiZer to examine the nature of the threshold(s) and to select between two competing threshold models. We then use SiZer in a multivariate setting by examining the first axis of the canonical discriminant analysis of the same data set.
 
Specific Hypotheses to Be Tested
 
Our research tested the following hypotheses:
1. Ecological thresholds in the abundance and diversity of benthic macroinvertebrates occur along a gradient of heavy metal contamination in Rocky Mountain streams impacted by mining.
2. The location and characteristics of ecological thresholds along a gradient of metal contamination vary among response variables.
3. Reduction in metal concentrations below threshold levels results in recovery of state variables.
5. Recovery of some state variables to pre-stressor levels may be characterized by significant time lags.
6. Measurement error associated with predictor variables significantly influences concentration-response relationships and the location of ecological thresholds.
 
Overivew of the SiZer Approach
 
Derivative Definition of Thresholds
An intuitive way of defining a threshold for a state variable that is a continuous function of an environmental driver is to consider where the function's derivatives change significantly. Nonparametric smoothers provide a method of finding a smooth response function that is data driven and requires only weak assumptions. Smoothing splines, LOESS, and its generalization, locally weighted polynomial regression (Fan and Gijbels, 1996), are well known. These techniques result in an estimated smooth response function, the estimated derivative(s), and confidence intervals (CI) for the functions and derivatives. The SiZer methodology can be implemented using any of these techniques, but we have restricted our discussion in this paper to locally weighted polynomials. Using a non-parametric smoother, every point along the independent axis can be classified into one of three states: the estimated slope is positive (i.e., the CI of the first derivative contains only positive values), possibly zero (the CI contains zero), or negative (the CI contains only negative values). Each point could be similarly classified using the estimated second (or in full generality, the pth ) derivative.
 
Details of the SiZer approach used to assess ecological thresholds in streams were published in Sonderegger et al. (2009a). An R implementation of SiZer, along with code for the piecewise linear and bent-cable models is now available through the R Project for Statistical Consulting (http://www.r-project.org/).
 
Smoothing Bandwidths
 
One complication of the derivative approach is the estimation of the smoothed function and its derivative(s). Most nonparametric smoothing algorithms, including smoothing splines and locally weighted polynomial regression, have a tuning parameter that controls the smoothness of the resulting curve. By manipulating this parameter, the resulting smoothing function can range from a simple linear regression to perfectly (over)fitting the data. There are several methods for selecting the tuning parameter, but none are uniformly superior. SiZer, as proposed and implemented by Chaudhuri and Marron (1999), uses the idea of locally weighted polynomial regression (Fan and Gijbels, 1996). When the weight function (also called a kernel function) is the normal density curve, the level of smoothing is controlled by the standard deviation of the kernel. For a given tuning parameter (h), and a given point ( x0 ), fˆ ′( x0) is obtained by weighting the data points according to a normal curve centered at x0 with a standard deviation σ = h. This means that data close to x0 (say within ±h) have a large influence over the smoothing function, data between h and 2h away are less influential, and data farther than 2h from x0 have only a slight influence. In locally weighted polynomial regression, the tuning parameter h is the width parameter of the kernel function and is commonly referred to as the bandwidth. Other common choices for the kernel function include the uniform density and triangle density functions. In this paper, the normal kernel is used.
 
The novel aspect of SiZer (Chaudhuri and Marron 2000) is that it considers all reasonable bandwidth values and exploits the notion that different values provide different information about the data. The SiZer approach explores how the derivative changes along the independent axis as well as across the range of bandwidth values and displays this information in one image. To read a SiZer map, first notice that the y-axis represents the bandwidth parameter h, displayed in units of log(h) for visual clarity. Reading from left to right at any given value of h, a significantly increasing first derivative is shown in yellow and a possible zero derivative is shown in purple. The white lines give a visual representation of the size of the bandwidth. The horizontal distance between the lines is drawn to be 2h indicating the effective width of the locally weighted polynomial.
 
Application of SiZer to Identify Ecological Thresholds in Lotic Ecosystems
 
1. Ecological Thresholds at Yellowstone National Park
We first use a relatively simple example to demonstrate the application of SiZer. Streams ofYellowstone National Park (YNP) provide a unique opportunity to identify threshold responses of benthic communities to natural stressors. Many streams in this area are strongly influenced by well-defined gradients of geothermal inputs. High water temperature and conductivity, low pH, and the input of fine sediments associated with geothermal areas are natural features of the Park’s' unique aquatic ecosystems. Elevated concentrations of several trace elements, especially arsenic, fluoride and boron, also co-occur with geothermal inputs (Goldstein et al. 2001). For this retrospective analysis, water quality, habitat, and benthic macroinvertebrate data were collected from 52 sites (25 separate streams) in YNP. Sites were located throughout the park and included streams within geothermal and non-geothermal areas of several major watersheds. Macroinvertebrate samples were collected from shallow riffle areas between August and November, 2002-2007 using a 0.09 m2 Surber sampler fitted with a 500 μm mesh net. Macroinvertebrate data were used to develop a multimetric index (the Yellowstone geothermal index) to quantify responses to geothermal influences.
 
The relationship between the Yellowstone geothermal index values and conductivity (an appropriate surrogate for geothermal discharges) across sites was highly significant and suggested a distinct threshold response to geothermal inputs (Figure 1). Index values increased slightly across low conductivity sites and then decreased abruptly at higher values. Results of piecewise linear regression (data not shown) identified a distinct threshold at approximately 81 μS/cm.
 
To illustrate the application of SiZer and demonstrate the effect of bandwidth on the smoothing function, the Yellowstone data are displayed with three different choices of bandwidth h, each highlighted by the horizontal line in the adjacent SiZer maps. The top graph represents a smoothing parameters that is too large (h = 2.0) and has over-smoothed the data and fails to detect the transition from a flat to a decreasing function. The relationship between the macroinvertebrate index and conductivity is approximately linear. However, at a smaller bandwidth (h=0.25), we see strong evidence of a threshold at relatively low levels of conductivity. Using a bandwidth of h = 0.25 (log10 h = -0.6), SiZer identified a statistically significant change in the first derivative from 0 to negative at approximately 1.75 (56 μS/cm).
 
These results provide strong support for the hypothesis that responses of macroinvertebrate communities to geothermal inputs at YNP are abrupt and show a distinct threshold at relatively low levels of conductivity.
 
 
Threshold responses to natural or anthropogenic stressors often represent a transition to an alternative stable state. These abrupt, nonlinear responses also complicate our ability to predict patterns of community composition in space and time. Our results showed significant changes in benthic community composition at relatively low levels of geothermal influences. Results of piecewise linear regression and SiZer, a new technique based on changes in the first derivative, showed distinct and statistically significant threshold responses of benthic communities. The abrupt change in benthic macroinvertebrate communities in response to geothermal influences has important implications for monitoring YNP streams. Using a conservative estimate, these data suggest that benthic communities undergo abrupt transitions at relatively low levels of geothermal influences.
 
The Yellowstone example also illustrates the importance of bandwidth in locally weighted polynomial regression. Because the SiZer map contains information at many different scales, there is seldom a "best" bandwidth to examine. Therefore, we recommend an evaluation of the derivative at different resolutions of the data. Just as viewing a tree from a distance, at large bandwidths only gross features are discernible. As the observer gets closer to the tree (i.e., the bandwidth decreases), the overall pattern cannot be seen, but smaller features come into focus. Only by examining the function across a range of bandwidths can a researcher gain a clear understanding of the data.
 
2. Ecological Thresholds in a Spatially Extensive Dataset From Colorado
Heavy metal pollution from historical mining operations is a ubiquitous stressor in Colorado and generally recognized as one of the most significant environmental problems in the west. Six of the 15 U.S. EPA ‘Superfund’ sites in Colorado are associated with mining pollution. Discharges from over 20,000 abandoned mines in Colorado have degraded or impaired macroinvertebrate communities in approximately 23 percent of the streams in the region (Clements et al. 2000). To identify potential threshold relationships between trace metals and macroinvertebrates, we conducted a spatially extensive survey of Colorado streams. The study was conducted in central Colorado from the Wyoming border to New Mexico, an area of approximately 54,000 km2, which included about 20 percent of the southern Rocky Mountain ecoregion. This area is inclusive of a geologic feature called the Colorado Mineral Belt, which has been exploited for the past 150 years for its mineral resources. The sample sites in this study are at high altitude, ranging from 2,330 to 3,550 meters above sea level. Geochemical and benthic macroinvertebrate samples were collected from n = 153 catchments during base flow conditions in the summers of 2003 (n = 20), 2004 (n = 41), 2005 (n = 38), 2006 (n = 31), and 2007 (n = 234). Geochemical and benthic macroinvertebrate samples were either collected simultaneously, or in a few cases, separated by < 10 d.
 
Because these streams are contaminated by a mixture of metals (primarily Cd, Cu, Zn) and because water-quality criteria are only available for individual metals, we used an additive measure of toxicity to express metal concentrations relative to the U.S. EPA criteria maximum concentration (CMC). The CMC is the highest concentration of a metal to which an aquatic community can be exposed briefly without resulting in an unacceptable effect. We define the cumulative criterion unit (CCU) as the ratio of the measured dissolved-metal concentration to the hardness-adjusted CMC and summed for each metal:
 
CCU = Σ mi / ci
 
where mi = the measured concentration of the ith metal and ci = the hardness-adjusted CMC for the ith metal. Criterion values were adjusted for water hardness because this parameter influences the toxicity of metals to aquatic organisms (Penttinen et al. 1998). If metal concentrations were below the analytical limits of detection, we used half of the detection limit to calculate the CCU. Assuming that responses to metals were additive, a CCU < 1.0 represents a metal concentration that should be protective of aquatic organisms. The CCU has been used previously to quantify contamination in streams receiving mixtures of metals (Clements et al. 2000).
 
Results of locally weighted polynomial regression and SiZer showed distinct and statistically significant thresholds in total macroinvertebrate abundance and species richness for these spatially extensive data (Figure 2). However, the location of these thresholds differed between metrics. SiZer showed a significant change in the first derivative from zero to negative at approximately 0.20 (= 1.78 CCU). The threshold for species richness occurred at a much lower metal concentration. SiZer analysis identified a significant threshold at approximately -0.40 (=0.40 CCU).
 
 
3. Application of SiZer to Stream Mesocosm Data
Experiments conducted in stream microcosms over the past 18 years examined the effects of single and multiple stressors (primarily heavy metals) on population, community, and ecosystem level state variables. The primary goal of these experiments was to establish concentration response relationships between metals and benthic community structure. Because metals were the only stressor in these experiments, data can be used to locate thresholds under controlled conditions and in the absence of other potential confounding variables. Benthic macroinvertebrate communities for these experiments were established on trays filled with pebble and cobble substrate. After 40 d, the colonized trays were removed and transferred to experimental streams (n = 18) in the Stream Research Laboratory at the Colorado State University (Fort Collins, CO). Previous experiments have shown that benthic communities colonizing these trays are similar to those collected from the natural substrate (Clements 1999; Courtney and Clements 2000). Our experiments examined several state variables, including mortality, size structure, macroinvertebrate drift, species richness, community composition, respiration and community metabolism. Below, we present results of SiZer analyses to identify threshold relationships between benthic community metrics (abundance and species richness) and heavy metal concentration (expressed as the CCU).
 
Experiments were conducted in different seasons and using benthic communities collected from several different streams. To allow comparisons across all experiments, we examined the percent change in total macroinvertebrate abundance and species richness relative to control (no metals) streams. Across all experiments, the percent reduction of total macroinvertebrates and species richness increased with metal concentration (Figure 3). At a bandwidth of h = 0.5, SiZer identified statistically distinct thresholds of approximately 4.0 CCU (log10 0.70) for abundance at and 2.5 (log10 0.40).
 
 
4. Recovery Thresholds for the Arkansas River, CO
In this section, we describe application of the threshold concept to characterize recovery. The Arkansas River is a metal-polluted stream located in the Southern Rocky Mountain ecoregion of Colorado. Mining operations in this watershed have had a major impact since the mid-1800s when gold was discovered near Leadville, Colorado. Concentrations of heavy metals, particularly Cd, Cu, and Zn were greatly elevated downstream from Leadville and often exceed acutely toxic levels (Clements 2004). Over the past 18 years (1989-2006), physiochemical characteristics, habitat quality, heavy metal concentrations, and the responses of macroinvertebrate communities were quantified at several stations in Upper Arkansas River Basin. During each of the 18 years, 5 replicate samples were taken. In 1993, 4 years after this research program began, state and federal agencies initiated a large-scale restoration program designed to improve water quality in the Arkansas River.
 
To illustrate the application of SiZer to identify recovery thresholds, we present two separate analyses using long-term water quality and macroinvertebrate data collected from station AR3 (Clements 2004), approximately 100 m downstream from the California Gulch Superfund Site. Concentrations of Zn, the predominant metal in this system, have declined since restoration activities were initiated in the Arkansas River (Figure 4). Superimposed on this long-term trend was considerable seasonal and annual variation associated with stream discharge, illustrated by the large peak in Zn concentrations in 1996.
 
 
Results of the first analysis show temporal changes in total abundance of several metal-sensitive taxa, including Heptageniidae, Paraleptophlebia sp., Heterlimnius corpulentus, and Pericoma sp. We defined these metal-sensitive taxa based on results of long-term monitoring in the Arkansas River and mesocosm experiments conducted with benthic communities (Clements 2004). Results of locally weighted polynomial regression analysis illustrate the influence of bandwidth on these models (Figure 5a). Note that at a relatively large bandwidth (h = 4.0), we see no evidence of a threshold and the relationship between abundance of sensitive species and year increases monotonically. In contrast, at a more narrow bandwidth (h = 2.0), we see several places where the slope of the relationship changes. The associated SiZer map for these data (Figure 5b) shows the relationship between bandwidth and year. Again, reading from left to right at a specific bandwidth, the color changes indicate significant changes in the first derivative. No threshold is indicated at a bandwidth of 4.0 (log10 h = 0.60). At a bandwidth of 2.0 (log10 h = 0.30), a threshold was observed in about 2004. At a bandwidth of 1.0 (log10 h = 0.0), the first derivative changed from significantly positive to zero in 1993, then increased significantly after 1996 until about 2003. We suggest that the changes in slope identified using the smaller bandwidths represent a recovery threshold for abundance of metal-sensitive taxa in about 2003. The changes observed from 1993 to 1996 likely reflect increases in metal contamination associated with long-term variation in stream discharge.
 
 
Multivariate analysis of macroinvertebrate data collected from the Arkansas River provided an opportunity to investigate multiple ecological thresholds in community composition over the duration of the monitoring project. A threshold response in this example represents an abrupt shift in community composition from one year to the next. Results of canonical discriminant analysis based on abundance of the 20 dominant taxa showed gradual changes in benthic communities from 1989 to 1994 (Figure 6a). Community composition was relatively stable for the following 5 years, shifted abruptly between 1999 and 2003, and then remained relatively constant for the duration of the study. Because this analysis was not limited to abundance of metal-sensitive taxa, these patterns better reflect long-term responses to metals and other environmental factors. Results of locally weighted polynomial regression analysis (h = 1.0) for the relationship between canonical variable 1 (which explained 53% of the variation) and year showed a complex function with several instances where benthic communities shifted rapidly over relatively short time periods (Figure 6b). SiZer analysis of these data clearly defined these abrupt shifts in community composition as thresholds where the first derivative changed from significantly positive to negative (Figure 6c). The first derivative shows a generally increasing function, but there is a sharp decreasing trend between 1995 and 1997. These results reflect macroinvertebrate community responses to changes in water quality from 1989 to 2006. Heavy metal concentrations declined from 1989-1994, increased abruptly in 1995 and1996, and then declined again as a result of ongoing restoration in the Arkansas River (Clements, 2004). The second threshold near 2000, which is a result of macroinvertebrate community recovery after improvements in water quality, was also statistically significant.
 
 
5. The Influence of Measurement Error on Responses to Metals in the Arkansas River
In ecological risk assessment, it is common to take a measurement of contaminant concentration and use that single observation to represent exposure that organisms experience over some duration of time. Although this is a legitimate practice if there is very little spatiotemporal variation in concentrations, this is rarely the case. Because of natural variation in stream discharge, temperature, pH, and other physicochemical characteristics, contaminant concentrations in streams often show significant temporal variation. Clements (2004) reported significant seasonal variation in heavy metal concentrations associated with stream discharge. Researchers measuring diel (24 h) cycles of heavy metals have also reported that concentrations of Zn can increase by a factor of five from afternoon to early morning (Nimick et al. 2003).
 
Measurement error is a commonly studied topic in statistics, but has received relatively little attention in the toxicological literature (Yuan 2007). The most well-known aspect of this phenomenon is that uncertainty in measuring the predictor variable leads to a substantial underestimation of the relationship between the predictor and response variables. Consequently, if measurement errors are present but unaccounted for in a statistical model, the resulting inference will be less likely to detect an association between contaminants and responses. More importantly, the magnitude of the association between contaminants and responses will typically be underestimated. We used long-term data collected from the Arkansas River to examine the influence of measurement error in metal concentrations on the relationship between heavy metals and macroinvertebrate responses. Because metal concentrations were represented by a single water sample collected on each sampling occasion and because those measurements showed considerable diel variability (Clements, unpublished data), significant measurement error may exist. We used the cumulative measure of metal effects, the cumulative criterion unit (CCU), to quantify metal contamination in this system. In this research, abundance of metal-sensitive mayflies (Ephemeroptera: Heptageniidae) was used as an indicator of stream health. Because of remediation efforts in the Arkansas River in 1993, we expected a long-term decreasing trend in CCU; however, the exact shape of this relationship was unknown. We used a nonparametric smoothing technique on the CCU values with respect to time and then regressed mayfly abundance on the smoothed CCU values. We refer to the regression of mayfly counts on the raw CCU values as the naive estimator of the slope parameter, and the regression onto the smoothed CCU values as the de-noised estimator of the slope parameter. Additional details of our approach are described in Sonderegger et al. (2009b).
 
As described above, metal concentrations (as CCU) in the Arkansas River decreased over time as a result of remediation activities (Figure 7). Standard errors and confidence intervals for the naive estimator were based on assumed asymptotic normality of the error terms. Confidence intervals for the de-noised estimator were based on n = 10000 bootstrap samples. The confidence interval lengths for the two estimators are very similar, indicating the relatively small loss of power associated with using the more complicated estimator. The most important difference is that the naive estimator has a much smaller magnitude than the de-noised estimator. The boundaries of the CI for the de-noised estimator have a substantially larger magnitude than those of the naive estimator. These results indicate that by ignoring measurement error, scientists risk underestimating the relationship between the abundance of metal-sensitive mayflies and heavy metal pollution.
 
 
To demonstrate the effect of ignoring measurement error, we examine three examples of the measurement error model where α=0, β=1, and g(t) = (1− t)2 . In the first case, δ is much smaller than σ, reflecting an instance where measurement error should not have a substantial effect. The second case shows δ =σ and the third case has δ = 2σ. We ran 2,000 simulations for each case. For the de-noised procedure, each simulation inference was based on 500 bootstrap samples. The output of this simulation is shown in Table 1.
 
Table 1. Simulation results comparing the naive estimator with the proposed de-noising procedure for a variety of parameter combinations. Bias is difference between the mean estimate and the true parameter value. Length is the average length of the resulting 95% CI. Coverage is the proportion of simulations whose 95% CI contained the true parameter value.
 
 
In the case where the measurement error standard deviation δ was small compared to the response variable standard deviation σ, the ‘de-noising’ procedure did not provide any benefit over standard linear model procedure; however, the procedure did not perform substantially worse. Neither procedure had appreciable bias, the average lengths of the 95% CIs were roughly equivalent, and coverage rates (percent of CIs that contain the true parameter value) are close to the desired 95%.
 
When measurement error was approximately the same (i.e. δ≈σ) or greater than the response error, the ‘de-noising’ procedure was clearly superior to the naive estimator. The naive estimator’s bias was quite large and the confidence interval coverage rates were far from the desired 95% rate. The ‘de-noising’ procedure handled the measurement error reasonably well in that the observed bias is quite small. The observed coverage rates are close to the desired 95% level.

Conclusions:

Fitting mathematical models to observed data is difficult in part because of the uncertainty in model selection. Traditional model selection methods tend to encourage examination of vast numbers of models. Burnham and Anderson (1998) address this issue by differentiating exploratory studies from confirmatory. When this is not possible, inference must be made carefully to avoid inflated type I error due to picking the ‘best’ model for the data. As presented here, SiZer is most naturally used in exploratory studies, but if sufficient data are available, part of the data may be used for exploratory model selection and the other part used for inference. Burnham and Anderson (1998) also strongly advocate only examining models that have sound scientific motivations. Since SiZer encourages the practitioner to create an appropriate response function from the SiZer map, the ecological justification and empirical evidence for a particular form of the response function can be combined. This should result in small numbers of models to be used in subsequent model selection steps or model averaging. SiZer also separates the question of statistical significance from ecological significance by showing the statistically significant features at each bandwidth and then allowing the researcher to decide which features are important.
 
Fitting threshold models is particularly difficult because researchers often assume that the existence and number of thresholds is known. For example, a piecewise linear analysis will always find a single threshold, regardless if the true functional relationship contains no threshold or multiple thresholds. SiZer can provide insight into the number of thresholds and general form of the relationship. Unfortunately, SiZer cannot provide estimates and confidence regions for the thresholds it detects. SiZer can only be used to select a model; a model fitting procedure such as maximum likelihood estimation must be subsequently used. Furthermore, by definition SiZer can only address thresholds in the context of changes in state of the derivative. Uniform or gradual changes that lead to irreversible state changes are not detectable by SiZer. The mathematics that SiZer employs can be readily extended to multiple dimensions by using the multidimensional gradient rather than the one dimensional derivative; however, SiZer's main strength, its graphical presentation, cannot be easily extended past two dimensions. Covariates can be accounted for in an additive fashion by using SiZer on the nonparametric portion of a generalized additive model (GAM). Finally, one direction for future research is to extend SiZer to work with local quantile regression instead of local mean regression. Pointwise estimates of the quantile function should not be difficult to obtain, but appropriate row-wise confidence intervals might be.
 
Application of SiZer to Identify Recovery Thresholds
 
The conventional application of ecological thresholds has focused primarily on assessing responses to a stressor gradient. We believe that the concept of ecological thresholds can also provide important insights into recovery processes following the removal of a stressor. Total abundance of metal-sensitive species in the Arkansas River steadily increased until about 2003, and then leveled off for the duration of the study. The gradual increase in abundance was most likely a response to the completion of major restoration activities and associated improvements in water quality (Figure 4; Clements 2004). Because abundance of metal-sensitive species at the downstream station is similar to that observed at upstream reference stations, these data suggest that recovery has occurred, at least for this particular metric. The SiZer analysis confirmed that a threshold response occurred in 2003, approximately 11 years after initiation of restoration activities in the watershed. Our results suggest that additional remediation at the site will provide progressively smaller ecological benefits because the system is approaching a stable point of recovery.
 
Assessing recovery and restoration effectiveness in stream ecosystems requires a long-term perspective, particularly in systems simultaneously experiencing effects of global change. Our results suggest that biological responses to improvements in water quality in the Arkansas River will continue to be influenced by variation in hydrologic and geochemical characteristics associated with regional climate. The abrupt shifts in community composition observed in the mid-1990s coincided with significant increases in annual stream discharge and associated heavy metals loading during one of the most severe El Nino events in the 20th century. It is unlikely that we could have identified this episodic event without a long-term perspective. Furthermore, relatively few studies have examined interactions between global change and other anthropogenic stressors. In a 25-year study of acidified streams in Wales, Durance and Ormerod (2007) speculated that climate change would exacerbate effects of acidification on macroinvertebrate communities. Similarly, Clements et al. (2008) reported that hydrological and geochemical alterations associated with global change are likely to increase toxicity and bioavailability of metals in western streams. These findings highlight the importance of assessing restoration success within the context of long-term changes in regional climate.
 
Water quality criteria and biocriteria for lotic systems are generally constructed as threshold values, and an exceedance of the threshold triggers an evaluation of both source and restoration alternatives (Davis and Simon 1995; Smith et al. 2005). However, this single threshold approach to regulation does not fit well with aquatic ecosystem responses to natural stressors (e.g., metals, temperature, sediment and nutrients), where multiple stressor-response thresholds can occur across time and space (Poole et al. 2004). Because of this and because of the inherent uncertainty in predicting threshold concentrations for many contaminants, a more conservative (protective) approach is to identify a range of stressor values where threshold responses are likely to occur (Muradian 2001). By selecting the most appropriate bandwidth, which is simply a reflection of the fit of the data, SiZer allows an investigator to consider a range of potential threshold values based on the inherent uncertainty. The SiZer map provides a more transparent graphical representation of the threshold and how it responds to variability of the data. This novel threshold approach will also be valuable in ranking the sensitivity of ecological endpoints typically utilized for regulation and restoration goals, as evidenced by the increased sensitivity of our community composition response to metals removal in the upper Arkansas River.
 
The existence of threshold responses and alternative stable states in community ecotoxicology has important consequences for ecological restoration. Identifying threshold responses along contaminant gradients will require that ecotoxicologists consider alternative statistical approaches for analyzing concentration-response relationships. For example, lakes and coral reefs are particularly sensitive to nutrient enrichment and have shown distinct threshold responses (Carpenter et al. 1999; Bellwood et al. 2004). Recovery in these communities is unlikely until stressor levels are reduced well below those that triggered the initial response (Scheffer et al. 2001). Because of the inherent uncertainty in predicting threshold concentrations for many contaminants and because of the consequences of state shifts if a threshold is exceeded, a more conservative approach is to identify a range of stressor values where threshold responses are likely to occur (Muradian 2001). By selecting the most appropriate bandwidth, SiZer allows an investigator to consider a range of potential threshold values based on the inherent uncertainty in the data.
 
Importance of Measurement Error
 
The relationship between chemical concentrations and biological responses is an integral component of ecological risk assessment. Thus, any factor that consistently affects the nature of this relationship has the potential to fundamentally alter our understanding of how contaminants impact ecosystems. Nimick et al. 2003 suggested because of temporal variation in contaminant concentrations, it may be necessary to modify traditional field sampling protocols in aquatic ecosystems. We agree with this recommendation, but feel the potential effects of unmeasured temporal variation may be considerably more insidious. Our results demonstrate that temporal variation in contaminant concentrations introduces significant error into the concentration response relationship. By ignoring this error, researchers risk introducing a strong bias in parameter estimates that will consistently underestimate the strength of the relationship between contaminants and biological response variables. Field data from the Arkansas River showed that the slope (β) of the relationship between abundance of heptageniid mayflies and metal concentration increased by approximately 25 percent when we accounted for measurement error. While this systematic bias is relatively small if measurement error is small compared to overall variability, it increases as measurement error increases. Simulation results indicated that the naive estimator consistently provided biased estimates of slope parameters. Our proposed method addresses this problem when measurement error is moderate to large, and does not result in a noticeable loss of power in the case where measurement error is absent.


Journal Articles on this Report : 32 Displayed | Download in RIS Format

Other project views: All 45 publications 38 publications in selected types All 32 journal articles
Type Citation Project Document Sources
Journal Article Bellwood DR, Hughes TP, Folke C, Nystrom M. Confronting the coral reef crisis. Nature 2004;429(6994):827-833. R832441 (Final)
  • Abstract from PubMed
  • Abstract: Nature-Abstract
    Exit
  • Journal Article Bernhardt ES, Palmer MA, Allan JD, Alexander G, Barnas K, Brooks S, Carr J, Clayton S, Dahm C, Follstad-Shah J, Galat D, Gloss S, Goodwin P, Hart D, Hassett B, Jenkinson R, Katz S, Kondolf GM, Lake PS, Lave R, Meyer JL, O'donnell TK, Pagano L, Powell B, Sudduth E. Ecology. Synthesizing U.S. river restoration efforts. Science 2005;308(5722):636-637. R832441 (Final)
    not available
    Journal Article Berumen ML, Pratchett MS. Recovery without resilience:persistent disturbance and long-term shifts in the structure of fish and coral communities at Tiahura reff, Moorea. Coral Reefs 2006;25:647-653. R832441 (Final)
  • Other: Woods Hole Oceanographic Institution-PDF
    Exit
  • Journal Article Carpenter SR, Ludwig D, Brock WA. Management of eutrophication for lakes subject to potentially irreversible change. Ecological Applications 1999;9(3):751-771. R832441 (Final)
  • Other: Integrative Biology - pdf
    Exit
  • Journal Article Chaudhuri P, Marron JS. Scale space view of curve estimation. The Annals of Statistics 2000;28(2):408-428. R832441 (Final)
  • Abstract: JSTOR-Abstract
    Exit
  • Journal Article Clements WH. Metal tolerance and predator-prey interactions in benthic macroinvertebrate stream communities. Ecological Applications 1999;9(3):1073-1084. R832441 (Final)
  • Abstract: JSTOR-Abstract
    Exit
  • Journal Article Clements WH, Carlisle DM, Lazorchak JM, Johnson PC. Heavy metals structure benthic communities in Colorado mountain streams. Ecological Applications 2000;10(2):626-638. R832441 (Final)
  • Abstract: Ecological Society of America
    Exit
  • Journal Article Clements WH. Small-scale experiments support causal relationships between metal contamination and macroinvertebrate community responses. Ecological Applications 2004;14(3):954-967. R832441 (Final)
    R829515 (2003)
    R829515 (2004)
    R829515 (Final)
  • Abstract: ESA Publications-Abstract
    Exit
  • Journal Article Clements WH, Brooks ML, Kashian DR, Zuellig RE. Changes in dissolved organic material determine exposure of stream benthic communities to UV-B radiation and heavy metals: implications for climate change. Global Change Biology 2008;14(9):2201-2214. R832441 (Final)
  • Abstract: Wiley Online-Abstract
    Exit
  • Journal Article Clements WH, Rohr JR. Community responses to contaminants: using basic ecological principles to predict ecotoxicological effects. Environmental Toxicology and Chemistry 2009;28(9):1789-1800. R832441 (Final)
    R833835 (2009)
    R833835 (2010)
    R833835 (2011)
    R833835 (Final)
  • Abstract from PubMed
  • Full-text: Wiley-Full Text HTML
    Exit
  • Abstract: Wiley-Abstract
    Exit
  • Other: Wiley-Full Text PDF
    Exit
  • Journal Article Clements WH, Kashian D, Sonderegger D, Noon B, Vieira N. The use of ecological thresholds to assess recovery in lotic ecosystems. Journal of North American Benthological Society 2010;29(3):1017-1023. R832441 (Final)
  • Abstract: BioOne - abstract
    Exit
  • Journal Article Connell JH, Sousa WP. On the evidence needed to judge ecological stability or persistence. American Naturalist 1983;121(6):789-824. R832441 (Final)
  • Abstract: JSTOR-Abstract
    Exit
  • Journal Article Courtney LA, Clements WH. Sensitivity to acidic pH in benthic invertebrate assemblages with different histories of exposure to metals. Journal of the North American Benthological Society 2000;19(1):112-127. R832441 (Final)
  • Abstract: JSTOR-Abstract
    Exit
  • Journal Article Dodds WK, Clements WH, Gido K, Hilderbrand RH. Thresholds, breakpoints, and nonlinearity in freshwaters as related to management. Journal of the North American Benthological Society 2010;29(3):988-997. R832441 (Final)
  • Abstract: North American Benthological Society
    and Society for Freshwater Science

    Exit
  • Journal Article Durance I, Ormerod SJ. Climate change effects on upland stream macroinvertebrates over a 25-year period. Global Change Biology 2007;13(5):942-957. R832441 (Final)
  • Full-text: Wiley Online - full text html
    Exit
  • Abstract: Wiley Online - abstract
    Exit
  • Other: Wiley Online - pdf
    Exit
  • Journal Article Folke C, Carpenter S, Walker B, Scheffer M, Elmqvist T, Gunderson L, Holling CS. Regime shifts, resilience, and biodiversity in ecosystem management. Annual Review of Ecology, Evolution, and Systematics 2004;35:557-581. R832441 (Final)
  • Abstract: Annual Reviews-Abstract
    Exit
  • Journal Article Goldstein JN, Hubert WA, Woodward DF, Farag AM, Meyer JS. Naturalized salmonid populations occur in the presence of elevated trace element concentrations and temperatures in the Firehole River, Yellowstone National Park, Wyoming, USA. Environmental Toxicology and Chemistry 2001;20(10):2342-2352. R832441 (Final)
    not available
    Journal Article Groffman PM, Baron JS, Blett T, Gold AJ, Goodman I, Gunderson LH, Levinson BM, Palmer MA, Paerl HW, Peterson GD, Poff NL, Rejeski DW, Reynolds JF, Turner MG, Weathers KC, Wiens J. Ecological thresholds: the key to successful environmental management or an important concept with no practical application? Ecosystems 2006;9(1):1-13. R832441 (Final)
    R828012 (Final)
    R828677C001 (Final)
    R832445 (Final)
  • Full-text: UWisc-PDF
    Exit
  • Abstract: Springer-Abstract
    Exit
  • Other: ResearchGate-Abstract & Full Text-PDF
    Exit
  • Journal Article Huggett AJ. The concept and utility of 'ecological thresholds' in biodiversity conservation. Biological Conservation 2005;124(3):301-310. R832441 (Final)
  • Full-text: ScienceDirect-Full Text HTML
    Exit
  • Journal Article Lake PS, Bond N, Reich P. Linking ecological theory with stream restoration. Freshwater Biology 2007;52(4):597-615. R832441 (Final)
  • Abstract: Wiley Online-Abstract
    Exit
  • Journal Article May RM. Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 1977;269:471-477. R832441 (Final)
  • Abstract: Nature-Abstract
    Exit
  • Journal Article Muradian R. Ecological thresholds: a survey. Ecological Economics 2001;38(1):7-24. R832441 (Final)
  • Abstract: Science Direct - abstract
    Exit
  • Journal Article Nimick DA, Gammons CH, Cleasby TE, Madison JP, Skaar D, Brick CM. Diel cycles in dissolved metal concentrations in streams:occurrence and possible causes. Water Resources Research 2003;39(9):1247-1264. R832441 (Final)
    R829400E01 (2002)
    R829400E02 (Final)
  • Abstract: Wiley Online - abstract
    Exit
  • Journal Article Penttinen S, Kostamo A, Kukkonen JVK. Combined effects of dissolved organic material and water hardness on toxicity of cadmium to Daphnia magna. Environmental Toxicology and Chemistry 1998;17(12):2498-2503. R832441 (Final)
  • Abstract: Wiley Online - abstract
    Exit
  • Journal Article Poole GC, Dunham JB, Keenan DM, Sauter ST, Mccullough DA, Mebane C, Lockwood JC, Essig DA, Hicks MP, Sturdevant DJ, Materna EJ, Spalding SA, Risley J, Deppman M. The case for regime-based water quality standards. BioScience 2004;54(2):155-161. R832441 (Final)
  • Abstract: Tree Search - abstract
    Exit
  • Journal Article Qian SS, King RS, Richardson CJ. Two statistical methods for the detection of environmental thresholds. Ecological Modelling 2003;166:87-97. R832441 (Final)
  • Abstract: CiteSeer - abstract
    Exit
  • Other: Baylor - pdf
    Exit
  • Journal Article Scheffer M, Carpenter S, Foley JA, Folke C, Walker B. Catastrophic shifts in ecosystems. Nature 2001;413:591-596. R832441 (Final)
  • Abstract: Nature - abstract
    Exit
  • Other: Gatsby - pdf
    Exit
  • Journal Article Scheffer M, Carpenter SR. Catastrophic regime shifts in ecosystems:linking theory to observation. Trends in Ecology & Evolution 2003;18(12):648-656. R832441 (Final)
  • Abstract: Cell - abstract
    Exit
  • Journal Article Smith JG ,Beauchamp JJ, Stewart AJ. Alternative approach for establishing acceptable thresholds on macroinvertebrate community metrics. Journal of the North American Benthological Society 2005;24(2):428-440. R832441 (Final)
  • Abstract: BioOne - abstract
    Exit
  • Journal Article Sonderegger DL, Wang H, Clements WH, Noon BR. Using SiZer to detect thresholds in ecological data. Frontiers in Ecology and the Environment 2009;7(4):190-195. R832441 (2008)
    R832441 (Final)
  • Abstract: Ecological Society of America
    Exit
  • Journal Article Sonderegger DL, Wang H, Huang Y, Clements WH. Effects of measurement error on the strength of concentration-response relationships in aquatic toxicology. Ecotoxicology 2009;18(7):824-828. R832441 (Final)
  • Abstract from PubMed
  • Abstract: SpringerLink - abstract
    Exit
  • Journal Article Yuan LL. Effects of measurement error on inferences of environmental conditions. Journal of the North American Benthological Society 2007;26(1):152-163. R832441 (Final)
  • Abstract: JSTOR - abstract
    Exit
  • Supplemental Keywords:

    Ecological thresholds, ecosystems, benthic communities, streams, metal contamination, heavy metals, RFA, Scientific Discipline, Ecosystem Protection/Environmental Exposure & Risk, POLLUTANTS/TOXICS, Aquatic Ecosystems & Estuarine Research, Chemicals, Aquatic Ecosystem, Environmental Monitoring, Ecological Risk Assessment, Ecology and Ecosystems, anthropogenic stress, estuarine research, ecological thresholds, anthropogenic impact, ecosystem indicators, benthic indicators, modeling ecosystem change, stream habitat, aquatic ecosystems, water quality, ecosystem stress, riverine ecosystems, trophic interactions, aquatic ecosystem restoration, heavy metals, ecosystem response

    Progress and Final Reports:

    Original Abstract
  • 2006 Progress Report
  • 2007 Progress Report
  • 2008 Progress Report