Title: Predicting the risk of toxic blooms of golden alga from cell abundance and environmental covariates
Abstract: Limnology and Oceanography: MethodsVolume 13, Issue 10 p. 568-586 New MethodsFree Access Predicting the risk of toxic blooms of golden alga from cell abundance and environmental covariates Matthew M. VanLandeghem, Corresponding Author Matthew M. VanLandeghem Department of Natural Resources Management and Texas Cooperative Fish and Wildlife Research Unit, Texas Tech University, Lubbock, TexasCorrespondence: [email protected] for more papers by this authorShawn Denny, Shawn Denny New Mexico Department of Game and Fish, Roswell, New MexicoSearch for more papers by this authorReynaldo Patiño, Reynaldo Patiño U.S. Geological Survey, Texas Cooperative Fish and Wildlife Research Unit, Texas Tech University, Lubbock, TexasSearch for more papers by this author Matthew M. VanLandeghem, Corresponding Author Matthew M. VanLandeghem Department of Natural Resources Management and Texas Cooperative Fish and Wildlife Research Unit, Texas Tech University, Lubbock, TexasCorrespondence: [email protected] for more papers by this authorShawn Denny, Shawn Denny New Mexico Department of Game and Fish, Roswell, New MexicoSearch for more papers by this authorReynaldo Patiño, Reynaldo Patiño U.S. Geological Survey, Texas Cooperative Fish and Wildlife Research Unit, Texas Tech University, Lubbock, TexasSearch for more papers by this author First published: 14 July 2015 https://doi.org/10.1002/lom3.10048Citations: 6AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Golden alga (Prymnesium parvum) is a toxic haptophyte that has caused considerable ecological damage to marine and inland aquatic ecosystems worldwide. Studies focused primarily on laboratory cultures have indicated that toxicity is poorly correlated with the abundance of golden alga cells. This relationship, however, has not been rigorously evaluated in the field where environmental conditions are much different. The ability to predict toxicity using readily measured environmental variables and golden alga abundance would allow managers rapid assessments of ichthyotoxicity potential without laboratory bioassay confirmation, which requires additional resources to accomplish. To assess the potential utility of these relationships, several a priori models relating lethal levels of golden alga ichthyotoxicity to golden alga abundance and environmental covariates were constructed. Model parameters were estimated using archived data from four river basins in Texas and New Mexico (Colorado, Brazos, Red, Pecos). Model predictive ability was quantified using cross-validation, sensitivity, and specificity, and the relative ranking of environmental covariate models was determined by Akaike Information Criterion values and Akaike weights. Overall, abundance was a generally good predictor of ichthyotoxicity as cross validation of golden alga abundance-only models ranged from ∼ 80% to ∼ 90% (leave-one-out cross-validation). Environmental covariates improved predictions, especially the ability to predict lethally toxic events (i.e., increased sensitivity), and top-ranked environmental covariate models differed among the four basins. These associations may be useful for monitoring as well as understanding the abiotic factors that influence toxicity during blooms. Harmful algal blooms (HABs) are described as the accumulation of algal or cyanobacterial cells that cause socioeconomic losses, impact human health, or negatively affect aquatic ecosystems (Anderson et al. 2012). HABs need not be large accumulations of cells—harmful impacts of toxin-producing species can occur at low abundance (Anderson et al. 2012). The increasing frequency of HABs worldwide and appearance in previously unaffected areas have raised concern, especially as a number of anthropogenic factors are suspected to be contributing to increasing HAB distribution and occurrence (Wiedner et al. 2007; Paerl and Huisman 2009; Sundareshwar et al. 2011). The toxigenic golden alga Prymnesium parvum is a HAB species responsible for substantial ecological and economic losses in estuarine and inland systems worldwide (Guo et al. 1996; Johnsen et al. 2010; Southard et al. 2010). Golden alga's invasion in North America (Lutz-Carrillo et al. 2010; Patiño et al. 2014) has occurred primarily in inland systems, where it has caused numerous fish kills and fish populations of some impacted systems have not been able to recover (Southard et al. 2010; VanLandeghem et al. 2013). Physicochemical conditions of water are known to influence golden alga's toxicity. For example, temperature, salinity, and pH have all been shown to influence the toxicity of laboratory-grown golden alga cultures (Yariv and Hestrin 1961; Ulitzur and Shilo 1964, 1966; Baker et al. 2007, 2009). Results of these laboratory studies and others have led to the conclusion that toxicity is poorly correlated with the abundance of golden alga cells in cultures (e.g., Baker et al. 2007, 2009; Brooks et al. 2010). In the field, temperature and salinity have been shown to influence toxicity (Roelke et al. 2012; Patiño et al. 2014; VanLandeghem et al. 2015a). Toxicity was also associated with pH in some (Prosser et al. 2012; Roelke et al. 2012) but not all (Patiño et al. 2014) studies of the Brazos River basin, Texas. Some studies have indicated golden alga abundance and toxicity are positively correlated (Roelke et al. 2012; VanLandeghem et al. 2015a), whereas others have reported low toxicity associated with high golden alga abundance and vice versa (Hambright et al. 2010; VanLandeghem et al. 2015b). Thus, the relationship between abundance and toxicity in the field is not simply monotonic and is likely influenced by multiple environmental factors. Understanding the interrelationships among golden alga abundance, toxicity, and environmental covariates in lakes and reservoirs may provide valuable information for golden alga monitoring and management. Although current protocols for golden alga monitoring include both abundance and toxicity determinations, management decisions rely primarily on the results of ichthyotoxicity bioassays (Barkoh et al. 2010). If a strong relationship can be established between golden alga abundance and toxicity, this would allow managers rapid assessments of the potential for ichthyotoxicity by determining abundance without bioassay confirmation, which requires additional resources to accomplish. Therefore, the objectives of this study were to (1) quantitatively evaluate the relationship between golden alga abundance and ichthyotoxicity in samples collected from lentic environments in four river basins of the southwestern United States, (2) assess the influence of environmental covariates on the abundance-toxicity relationship at the basin scale, and (3) make predictive toxicity models available to resource managers by incorporating them into readily accessible software. Methods and procedures Golden alga abundance and ichthyotoxicity Golden alga abundance and toxicity data were obtained from the New Mexico Department of Game and Fish and a database maintained by the Texas Parks and Wildlife Department (TPWD). These data were collected during standard water quality monitoring; a state-wide golden alga survey conducted in Texas; and routine monitoring of golden alga-impacted lakes and reservoirs. In addition, original abundance and toxicity data collected during previous projects (VanLandeghem et al. 2015a,b) were included in the current analysis. In all cases, golden alga abundance was determined from hemocytometer counts following the methods of Southard (2005a), and ichthyotoxicity was determined using a standard fathead minnow (Pimephales promelas) larva bioassay (Southard 2005b). Using the larva bioassay, a rank score of ichthyotoxicity is determined and enumerated as ichthyotoxic units (ITUs). Possible toxicity scores are 0, 0.5, 1, 3, 5, 15, and 25 ITUs; toxicity scores of 15 ITU and 25 ITU are indicative of lethal levels of ambient golden alga toxicity (Southard 2005b). Because resource managers are typically interested in whether conditions are likely to result in a fish kill, we reclassified toxicity data as lethal ( > 5 ITUs) or nonlethal ( ≤ 5 ITUs) and only observations that contained data for both abundance and toxicity were used. Description of sites, period of record, and data density A total of 33 lake and reservoir sites in the Colorado and Brazos river basins of Texas, the Red river basin of Texas/Oklahoma, and the Pecos River basin of Texas/New Mexico were examined. All sites in the Colorado, Brazos, and Red rivers were large reservoirs (Table 1). Sites in the Pecos included large reservoirs, a pond, small river impoundments, and natural sinkhole lakes at the Bottomless Lakes State Park in New Mexico (Table 1). The period of record (POR) and data density for golden alga abundance and bioassay data varied among sites (Table 1). Sites with recurring golden alga-related fish kills were monitored more regularly than sites without frequent golden alga problems; sites with only one or a few observations were included in order to maximize spatial coverage and data density within a basin. The POR for bioassay data did not necessarily include the earliest known golden alga-related fish kills in some reservoirs. For example, golden alga-related fish kills first occurred in Colorado City in 2001 (Southard et al. 2010; VanLandeghem et al. 2013) but the POR for the current study begins in 2002 (Table 1). Fish kills have been reported as early as 1985 in Red Bluff Reservoir (Southard et al. 2010) but the POR for this site in this study begins in 2002 (Table 1). Only two golden alga abundance-toxicity observations are available for Lake Meredith in the Canadian River basin, Texas, thus the Canadian River was excluded from all analyses. Table 1. Locations in the Colorado, Brazos, Red, and Pecos river basins used to assess the relationships among golden alga abundance, ichthyotoxicity, and environmental covariates. The POR refers to the availability of golden alga abundance and ichthyotoxicity data and does not necessarily correspond to reported fish kills. N is the number of observations at each site where both golden alga abundance and ichthyotoxicity data were available. Site Description Location Period of record (POR) Years within POR with lethal ichthyotoxicity detected N Colorado River Basin E. V. Spence Reservoir TX 2001–2011 2001–2011 126 Colorado City Reservoir TX 2002–2011 2002–2011 114 Moss Creek Reservoir TX 2002–2011 2003, 2005–2011 104 O. H. Ivie Reservoir TX 2002–2005, 2010, 2011 2002–2004 79 Twin Buttes Reservoir TX 2004, 2006, 2010, 2011 None 25 Nasworthy Reservoir TX 2010, 2011 None 19 J. B. Thomas Reservoir TX 2004 None 2 New Ballinger Reservoir TX 2005 None 1 Oak Creek Reservoir TX 2003 None 1 Mountain Creek Reservoir TX 2007 2007 1 Total 472 Brazos River Basin Possum Kingdom Reservoir TX 2004–2012 2004, 2005, 2007, 2010 106 Granbury Reservoir TX 2004, 2005, 2010, 2011 2004, 2005, 2010, 2011 40 Whitney Reservoir TX 2004, 2005, 2010 2004, 2005, 2010 32 Squaw Creek Reservoir TX 2010 None 3 Sweetwater Reservoir TX 2003, 2005 2003 3 Buffalo Springs Reservoir TX 2003 2003 3 Total 187 Red River Basin Diversion Reservoir TX 2004–2011 2004–2009, 2011 77 Texoma Reservoir TX/OK 2004 None 9 Wichita Reservoir TX 2004, 2010 None 3 Baylor Reservoir TX 2005 None 2 Childress Reservoir TX 2005 2005 2 Kemp Reservoir TX 2004 None 1 Total 94 Pecos River Basin Brantley Reservoir NM 2007–2009 2007–2009 34 Red Bluff Reservoir TX 2002, 2004, 2005, 2007, 2008 2002, 2004, 2005, 2007, 2008 14 Balmorhea Reservoir TX 2004–2008, 2010 2006 14 Inkwell Lake NM 2007–2009 2008 15 Cottonwood Lake NM 2007–2009 2009 13 Dimmitt Lake NM 2007–2009 2008, 2009 12 Spring River Pond Pond NM 2007–2009 2009 11 Bataan Impoundment NM 2005–2008 2005–2008 23 6–mile Impoundment NM 2004, 2005, 2007, 2008 2004, 2005, 2007, 2008 15 10–mile Impoundment NM 2005, 2007 2005 8 Carlsbad Impoundment NM 2007–2009 2007, 2009 7 Total 166 Water quality variables In many cases, basic water quality variables, such as temperature, pH, and specific conductance were collected along with samples processed for golden alga abundance and ichthyotoxicity. These water quality data were often included in the agency databases. For some observations in Texas, however, water quality data were located in a separate database maintained by the Texas Commission on Environmental Quality (TCEQ 2013). In these cases, water quality data were part of standard environmental monitoring collections performed by TCEQ, with samples processed for golden alga by TPWD. The TPWD database of golden alga data typically contained the TCEQ site number and date of collection; thus, golden alga abundance and toxicity data were cross-referenced with TCEQ water quality data based on the date and site number when possible. For the Red River basin, water quality was unavailable for more than 80% of observations, thus these variables were not included in analyses for this basin. The quantity of nitrogen and phosphorus and their ratios can influence the production of toxins by golden alga (e.g., Granéli et al. 2012), and toxic blooms have been associated with high levels of major ions such as sulfate and chloride (Patiño et al. 2014). In this study, however, nutrient and major ion data were generally very limited and were not used in the analysis. Reservoir percent capacity Reservoir capacity was estimated for most of the Colorado River basin and Brazos River basin sites. Capacity could not be estimated for the Red River basin or Pecos River basin due to a lack of gauges for most sites in these basins. With the exception of Lake Nasworthy (Colorado basin), elevation was determined from a single United States Geological Survey (USGS) gauge for each reservoir, which was typically located near the dam (USGS 2013). For Lake Nasworthy, elevation was determined from a gauge maintained by the United States Bureau of Reclamation (USBOR 2013). For each reservoir, the percent of reservoir capacity was estimated by comparing the reservoir elevation on the day of sample collection to an elevation-capacity curve. Elevation-capacity curves for most reservoirs are based on surveys conducted by either the USGS or the Texas Water Development Board (TWDB) and are available on TWDB's website (TWDB 2012). For Lake Nasworthy, the elevation-capacity relationship is available through the USBOR (USBOR 2013). Weather variables and wind turbulence For each site, the weather station in NOAA's National Climatic Data Center database nearest to the dam (for reservoirs) or lake center (for Bottomless Lakes and Spring River pond) containing sufficient data (3 + yr) was selected (NOAA 2012). From each station, daily averages of air temperature (°C), wind speed (m/s), and wind direction (degrees from north) were calculated. Values for these variables for up to 7 d prior to golden alga sample collection were considered for analysis. Preliminary analysis of partial correlations controlling for golden alga abundance, however, suggested the highest correlation with lethal ichthyotoxicity was either similar among the 7 d or highest for the day of sample collection. Thus, values for air temperature, wind speed, and wind direction for the day of sample collection were used. In addition to wind and air temperature variables, daily or hourly precipitation totals were used to calculate the rainfall total for 7 d prior to the sample collection date. A 7-d sum of precipitation was used because Roelke et al. (2011) assessed the effects of 7-d, 10-d, 30-d, and 365-d cumulative inflow on golden alga bloom formation in the Brazos River basin, and concluded that the 7-d inflow variable exhibited the best relationship among the four variables evaluated. Average daily wind direction and wind speed were further processed into limnologically relevant variables. Specifically, wind speed was used to estimate mean surface (0.5 m depth) current velocity using the equation from George (1981) as referenced in Kalff (2002): Average daily wind direction was used to calculate effective fetch for the specific points of sample collection when known. Effective fetch is the measurement of fetch along several directions from a given point, thus accounting for fetch shape (USACE 2002; Rohweder et al. 2012). Effective fetch was calculated in ArcGIS version 10.1 using the Shoreline Protection Method in the "Waves2012" toolbox (Rohweder et al. 2012). Once calculated, effective fetch was used to estimate the maximum wave height using the following equation modified from Wetzel (2001): Using these methods, maximum wave height takes into account the spatial context of the sample location by incorporating the wind direction and the physical features of each water body relative to the sample site. Maximum wave height was included in analyses as an estimate of vertical turbulence imparted by wind energy, whereas surface current is an estimate of horizontal turbulence. Wave height and surface current were included to assess the potential effects of wind on golden alga toxicity. Previous studies have indicated that wind can concentrate algal toxins (Carmichael 1988, 1996) as well as drive upwelling of nutrients in lakes (Wetzel 2001). Wind-driven upwelling of nutrients could be important because golden alga toxicity is generally highest during nutrient limitation (Granéli et al. 2012). Procedure Incomplete data are common phenomena in environmental studies (Hopke et al. 2001). In this study, the variables described above were not completely available for each of the golden alga sampling events (Table 2). To address the missing data issue of our dataset, we utilized a multiple imputation approach for incomplete records. Approaches for multiple imputation are described in detail elsewhere (Rubin 1987; Hopke et al. 2001; Little and Rubin 2002; Francis et al. 2009; Yuan 2011). In short, multiple imputation utilizes information contained in interrelationships among observed values to estimate plausible values for missing variables. These plausible values are used to create multiple complete-case datasets, which are then analyzed using standard, complete-case statistical methods (described below). Analyses of all datasets are then combined to form a final inference (Rubin 1987). An advantage of utilizing a multiple imputation approach is that the uncertainty of imputing missing values is incorporated in the final inference (Rubin 1987). Single value imputation approaches (e.g., imputation of the mean) essentially treat missing values as if they were known, biasing variance estimates towards zero (Yuan 2011). Table 2. Percent of missing observations by basin for environmental variables used in analysis. Missing values were replaced using a multiple imputation approach prior to analysis. Blank cells indicate data missing at an exceptionally high rate (80+%); these variables were not used in analysis for their respective basins. Basin Max. wave height Surface current Air temp. Reservoir capacity Water temp. pH Specific conductance 7-d rain sum Colorado 18.6 18.6 18.6 1.5 16.9 30.7 16.9 5.5 Brazos 7.5 7.5 7.5 1.6 52.9 52.9 53.5 0 Red 7.4 0 0 0 Pecos 0.6 0.6 0.6 31.3 31.3 15.7 0 For each basin, we utilized PROC MI to create six complete-case datasets that were used for logistic regression analysis. Prior to running PROC MI, some variables were transformed to improve compliance with the multivariate normality assumption of the Markov Chain Monte Carlo Gibbs' sampling algorithm utilized by this procedure (Hopke et al. 2001; Yuan 2011). Several logistic regression models relating golden alga ichthyotoxicity (lethal/nonlethal) to golden alga abundance and environmental variables were constructed prior to data analysis. These models were hypothesized based on known relationships between golden alga abundance or toxicity and environmental variables such as temperature (Baker et al. 2009), inflow (Roelke et al. 2011), pH (Valenti et al. 2010), and specific conductance (Roelke et al. 2011; Patiño et al. 2014); or by known relationships between algae in general and environmental conditions such as turbulence (Wetzel 2001). Each model contained golden alga toxicity as response variable, and abundance and the environmental factors as explanatory variables. A model containing only golden alga abundance (hereafter, the GAA-only model) was included in the model set for each basin. Prior to analysis, all explanatory variables were standardized to mean = 0 and standard deviation = 1. For each of the six multiply-imputed datasets, parameters of the a priori models were estimated using PROC LOGISTIC. Nonlinear (in the logit) relationships between toxicity and abundance with water quality covariates were also assessed. Piecewise regression models were constructed and estimated in PROC NLMIXED with a grid approach to identify initial parameter values (Lerman 1980; Brenden and Bence 2008). Nonlinear models were constructed only for abundance and water quality variables as these variables were hypothesized to have greater direct effects on golden alga toxicity than weather variables and reservoir capacity; piecewise GAA-only models were also included for each basin. Parameter estimates for the six multiply-imputed datasets from either PROC LOGISTIC or PROC NLMIXED were combined using PROC MIANALYZE; standard errors of these parameter estimates incorporate multiple imputation uncertainty in addition to uncertainty associated with parameter estimation (Yuan 2011). All analyses were performed with SAS version 9.3 (SAS Institute, Cary, North Carolina, USA). Assessment For each model, Akaike's Information Criterion with small sample size correction (AICC; Burnham and Anderson 2002) was calculated for each analysis of the six multiply-imputed datasets. To account for the multiple imputation procedure, the average AICC value and standard error of the mean AICC for each model are reported (Nakagawa and Freckleton 2011). Models were then ranked based on mean AICC values. Using differences in mean AICC values relative to the top-ranked model, Akaike weights were calculated (Burnham and Anderson 2002). An Akaike weight is the relative probability of a model given all models examined; the "confidence set" of models includes the top-weighted models with cumulative Akaike weights ≥ 0.95 (Burnham and Anderson 2002). We also used Akaike weights to calculate evidence ratios for the piecewise GAA-only model and environmental covariate models relative to the GAA-only model; an evidence ratio is an estimate of relative likelihood (Burnham and Anderson 2002). Because Akaike weights only provide a relative ranking of models and not an estimate of model performance, we calculated additional quantities for each model: sensitivity (true positive rate), specificity (true negative rate), and percent correct classifications from leave-one-out cross validation. In addition, "pseudo" R2 (Nagelkerke 1991) was calculated for the standard multiple logistic regression models, but not the nonlinear models as R2 has been shown to be a poor indicator of fit for these types of models (Spiess and Neumeyer 2010). Similar to AICC, sensitivity, specificity, cross-validation percent, and pseudo-R2 (standard multiple logistic regression models only) were calculated for each analysis of the six multiply-imputed datasets; mean and standard errors of the mean are reported for these quantities. In the Colorado River basin ("Colorado"), the confidence set contained four models that accounted for 99+% of the total Akaike weight, but did not contain the GAA-only model or the piecewise GAA-only model (Table 3). Models in the confidence set ranged from 5.3 × 1012 to 2.4 × 1013 times more likely than the GAA-only model, indicating very high support for toxicity modification by environmental variables (Table 3). All models in the confidence set were piecewise regression models with breakpoints estimated between ∼ 25,000 cells/mL and ∼ 27,000 cells/mL (Table 3). Parameters for GAA were larger in models below the breakpoint than in models above it, perhaps as some threshold abundance is reached where lethal levels of ichthyotoxicity will predominate (Table 3). The top model included temperature, which was negatively related to toxicity, and specific conductance, which was positively related (Table 3). Thus, as temperature decreased and specific conductance increased, the probability of lethal ichthyotoxicity at a given abundance increased (Fig. 1). The second-ranked model included pH, but the coefficient was small and had a large standard error, suggesting pH was of little importance. Although the GAA-only model was not included in the confidence set, pseudo-R2 was 0.62 and cross-validation was 87.3%, indicating reasonable prediction of toxicity based on golden alga abundance alone (Fig. 2A). Sensitivity, however, was relatively low (63.0%) for the GAA-only model, but about 15% higher for the piecewise GAA-only model (78.2%), albeit at the cost of ∼ 4% lower specificity (Table 3; Fig. 2B). Sensitivities for environmental covariate models in the confidence set were ∼ 17% to ∼ 18% higher than the GAA-only model, but had only ∼ 2% lower specificity (Table 3). Standard errors for means of AICC, pseudo-R2, cross-validation percent, sensitivity, and specificity were generally low (relative standard error < 1%) for all models, indicating the multiple imputation procedure contributed little uncertainty to the final results. Figure 1Open in figure viewerPowerPoint Predicted probabilities of lethal levels of golden alga ichthyotoxicity as a function of golden alga abundance, specific conductance, and water temperature in the Colorado River basin, Texas. The predicted probability of lethal ichthyotoxicity was calculated from estimated piecewise regression equations (Table 3) for golden alga abundances between 0 cells/mL and 100,000 cells/mL at 5 °C increments between 5 °C and 30 °C at specific conductance values of 1000 (A) and 4000 (B) μs/cm. Figure 2Open in figure viewerPowerPoint Predicted probabilities of lethal levels of golden alga ichthyotoxicity calculated from the estimated standard logistic regression equation (A; Table 3) and the estimated piecewise regression equation (B; Table 3) for golden alga abundance in the Colorado River basin, Texas. Table 3. Results from standard and piecewise multiple logistic regression assessing the influence of golden alga abundance (GAA) and environmental covariates on the probability of lethal levels of golden alga ichthyotoxicity in the Colorado River basin, Texas. The relative ranking of environmental covariate models was determined by Akaike Information Criterion values with low sample size correction (AICC), pseudo-R2 was used to assess model fit (standard models only), leave-one-out cross validation, sensitivity, and specificity were used to assess the predictive ability of models. The top-ranked models accounting for ≥ 95% of the total Akaike weight (wi; based on ΔAICC values) are shown, along with the standard and piecewise GAA-only models for comparison (weights of models in the confidence set are in bold). The relative likelihood of the piecewise GAA-only model and environmental covariate models to the GAA-only model was quantified with evidence ratios. Standard errors for mean of AICC, pseudo-R2, cross-validation, sensitivity, and specificity account for the uncertainty of the multiple imputation procedure used to address missing values in our dataset. Model Abundance range Estimated model with standardized coefficients(SE) AICc (SE) ΔAICc wi Pseudo-R2 (SE) Cross-validation % (SE) Sensitivity (SE) Specificity (SE) Likelihood relative to GAA only model GAA + water temperature + specific conductance ≤ 26,667 −1.48(0.25)+5.63(0.75)×GAA −1.20(0.26)×water temp.+0.46(0.27)×specific conductance 220.1±1.6 0 0.54 90.3 ± 0.2 80.8 ± 0.5 93.5 ± 0.2 2.4 × 1013 > 26,667 0.32+0.56(0.37)×GAA −1.20(0.26)×water temp.+0.46(0.27)×specific conductance GAA + water temperature + specific conductance + pH ≤ 26,933 −1.49(0.26)+5.60(0.73)×GAA −1.20(0.26) water temp.+0.45(0.29)×specific conductance −0.03(0.20)×pH 222.1±1.6 1.0 0.21 90.3 ± 0.2 80.5 ± 0.5 93.6 ± 0.1 9.2 × 1012 > 26,933 0.36+0.54(0.38)×GAA −1.20(0.26)×water temp.+0.45(0.29)×specific conductance −0.03(0.20)×pH GAA + water temperature ≤ 26,178 −1.34(0.26)+5.78(0.87)×GAA −0.97(0.21) ×water temperature 223.0±1.3 2.9 0.13 90.7 ± 0.3 80.8 ± 0.6 94.0 ± 0.2 5.8 × 1012 > 26,178 0.36+0.72(0.37)×GAA −0.97(0.21)×water temp. GAA + water temperature + pH ≤ 25,253 −1.20(0.49)+6.34(1.80) × GAA −0.98(0.21)×water temp. −0.13(0.19)×pH 223.2±0.9 3.1 0.12 90.6 ± 0.2 81.1 ± 0.6 93.8 ± 0.2 5.3 × 1012 > 25,253 0.48+0.75(0.39)×GAA −0.98(0.21)×water temp.−0.13(0.19)×pH GAA (piecewise) ≤ 25,413 −1.03(0.24)+6.02(0.87)×GAA 248.2±1.7 28.1 4.4 × 10−7 88.1 ± 0 78.2 ± 0 91.5 ± 0 2.0 × 107 > 25,413 0.60+0.70(0.38)×GAA GAA −1.37(0.16)+3.00(0.29)×GAA 281.8±0 61.7 2.3 × 10−14 0.62 ± 0 87.3 ± 0 63.0 ± 0 95.5 ± 0 1 In the Brazos River basin ("Brazos"), the confidence set contained 10 models that accounted for 95+% of the total