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Appendix B-1: FDEP’s Stressor-Response Analyses for Florida 

Streams 

(Chapter 6 and Appendices 6-A through 6-G from USEPA. 2009. Proposed Methods and 

Approaches for Developing Numeric Nutrient Criteria for Florida’s Inland Waters. United 

States Environmental Protection Agency, Office of Water, Office of Science and Technology, 

Health and Ecological Criteria Division, Washington, DC.) 

The following appendices from the original technical support document are included as a 

courtesy, and provide a detailed description of the stressor response analysis. 
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Appendix B-1. FDEP’s Stressor-Response Analyses for Florida Streams 

The U.S. Environmental Protection Agency (U.S. EPA) (USEPA 2000a) describes several 

general approaches, with certain options, that can be used to develop numeric nutrient criteria for 

streams. One approach is to relate nutrient concentrations to dependably measured adverse 

biological responses. EPA further suggests that the observed dose-response relationship could be 

described by a model (e.g., trophic state classification, regional predictive model, biocriteria, 

etc.), which in turn would quantitatively link nutrient concentrations to the relative risk of 

environmental harm. Florida Department of Environmental Protection (FDEP) supports this 

approach, since it establishes a correlative relationship between nutrients and valued ecological 

attributes, and is linked to the maintenance of designated uses of waterbodies. 

In attempting to define the effect of anthropogenic nutrient increases on the biological 

communities in Florida’s streams, FDEP conducted extensive statistical evaluations to 

investigate the relationship between nutrient levels and biological indices such as the Stream 

Condition Index (SCI), and the Stream Diatom Index (SDI) (currently under development) as 

well as the individual metrics that comprise these indices. FDEP also evaluated the effects of 

increased nutrient levels on other biological measures such as chl. a, taxonomic composition of 

macroinvertebrate and algal communities, and frequency of occurrence and abundance of algae 

(as measured via the Rapid Periphyton Survey (RPS)). 

To investigate the potential relationships between nutrients and biological response measures, 

FDEP utilized a variety of statistical techniques, including linear regression, multiple linear 

regression, non-linear regression, LOESS regression, change point analysis, classification and 

regression tree (CART) analysis, correlation analysis, and paired variable plots. A brief 

discussion of the results from some of the assessments performed is provided below, with more 

detailed information concerning the analyses provided in the referenced appendices. 

The results of the analyses generally indicate that many of the biological measures evaluated 

exhibit a significant adverse response to anthropogenic nutrient enrichment. However, the 

statistical relationships between the biological response variables and nutrient levels are weak, 

and FDEP could not identify specific thresholds for establishing numeric nutrient criteria from 

the analyses. The direct and indirect adverse effects of nutrient enrichment on biological 

communities have been demonstrated repeatedly under controlled conditions (Stevenson et al. 

2007). The analyses did not show strong statistical relationships between nutrients and these 

effects. This may be because the biological responses can be confounded by numerous other 

factors (including low residence time for uptake) and confounding variables under real world 

conditions found in natural streams. This is especially true for Florida streams, which can range 

from: 

 Crystal clear spring fed streams with low nutrient levels and high conductivity, to 

 Highly colored streams fed by wetlands with an abundance of organic nitrogen, to 

 Streams that exhibit naturally high phosphorus levels resulting from geologic phosphate 

deposits lying near the surface, to 

 Streams that can be any combination of the above. 
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The source water and the geologic conditions also influence other water quality variables such as 

pH and specific conductivity, which can have an overarching effect on the biological 

communities, which in-turn can alter or be more significant than the response to nutrients. In 

addition, most Florida streams are heavily canopied with the resulting light limitation also 

confounding the biological response to nutrients. 

Similar results were reported by Robertson et al. (2008) who found good relationships between 

nutrient enrichment and various adverse biological responses in open non-wadeable Wisconsin 

rivers. The relationships were much weaker in smaller wadeable streams due to the influence of 

other confounding environmental factors, with nutrients alone explaining only a small portion of 

the response (Robertson et al. 2006). Most of the biological measures exhibited a wedge-shaped 

response to increases in nutrient concentrations. At relatively low nutrient concentrations, the 

biotic indices ranged widely, but at relatively high concentrations, the indices generally were 

poor. The wedge-shaped distribution indicates that at low nutrient concentrations, factors other 

than nutrients often limit the health of biotic communities, whereas, at high nutrient 

concentrations, nutrients and factors correlated with high nutrient concentrations are the 

predominant factors. Simply stated, it is difficult to find a healthy population at a nutrient 

enriched site, but common to find a poor population at low nutrient sites due to the influence of 

other factors. 

This type of response is not surprising given the fact that the biotic community represents the 

overall ecological integrity of the stream (i.e., physicochemical habitat and biotic integrity) and 

thus provides a broad measure of the cumulative effect of all stressors (Barbour et al. 1999). The 

physicochemical habitats within the streams are in turn controlled by watershed characteristics 

such as geomorphology, geochemistry, hydrology, and land use/land cover and are therefore 

important factors affecting the biotic communities present. In Florida streams, the response to 

nutrients is confounded by broad ranges of biologically important physicochemical parameters 

such as pH, color, and specific conductance that occur naturally, sometimes at small spatial 

scales. As Robertson et al. (2006) concluded, even with these confounding factors, it is important 

to establish numeric nutrient criteria to reduce the risk of adverse effects on the biological 

communities in the water body as well as in downstream receiving waters. 

In addition to the inherent variations in the confounding physicochemical factors described 

above, Florida streams also exhibit a very wide range of nutrient levels, especially phosphorus, 

that occur regionally under natural conditions. Phosphorus concentrations can naturally range 

from less than 10 ppb (highly oligotrophic) to many hundred ppb where the water body is in 

direct contact with geologic phosphate deposits (see Chapter 2a). To account for the natural 

spatial variation in nutrient concentrations, the evaluation of the biological response to nutrients 

was conducted on a regional basis where there were sufficient data. A summary of the individual 

analyses conducted is provided below. 

Macroinvertebrate Exploratory Analysis 

The relationship between the macroinvertebrate community and nutrient levels in streams was 

examined using Florida’s Stream Condition Index (SCI), the individual measures of the 

macroinvertebrate community that comprise the index, and the abundance of other taxonomic 

groupings. Appendix B-2 has an explanation of the various biological measures. Multiple linear 
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regression techniques were used to evaluate potential relationships between nutrient 

concentrations and the measures of the macroinvertebrate community. 

The results of the analyses indicate that several macroinvertebrate variables, including SCI, % 

sensitive taxa, % clinger taxa, % clingers, % long lived taxa, % very tolerant taxa, and % 

dominant taxa, exhibited a significant adverse response to increased levels of nitrogen. In 

addition, the analyses indicated that the macroinvertebrate community also responded to other 

environmental factors such as water color, conductivity, and pH. It is likely that other 

unmeasured variables such as water velocity, water level, habitat conditions, and antecedent 

conditions also play an important role in determining the macroinvertebrate community 

composition. The adjusted R2 values for the multiple-linear regression models predicting the 

macroinvertebrate responses ranged from 0.05 to 0.55 in the models that included some form of 

nitrogen and a combination of the other environmental factors. Due to the confounding effects of 

these other factors, the macroinvertebrate response to nutrients was statistically weak and could 

be depicted by a wedge-shaped relationship as described previously. 

Figure B1-1 shows the typical relationship observed between nutrient levels and 

macroinvertebrate response variables. At low nutrient levels, the response is highly variable due 

to the controlling effects of other factors such as pH, conductivity, color, flow, water level, 

habitat conditions, etc. The analyses also demonstrate that the macroinvertebrate community 

responds negatively to increased nutrient levels, however, due to the influence of other 

environmental factors on the response, FDEP could not identify specific thresholds for 

establishing numeric nutrient criteria. The macroinvertebrate analyses and results are presented 

in greater detail below. 

Exploratory Analysis of Periphyton Response to Nutrients 

Since the algal community can be expected to respond more rapidly and directly to nutrients than 

macroinvertebrates, FDEP also evaluated the relationship between the periphyton community 

and nutrient levels in streams. The primary focus of the evaluation was the Florida’s Stream 

Diatom Index (SDI) (see Appendix B-3), which is currently under development, and the five 

individual component metrics that comprise the SDI (i.e., % pollution sensitive, % pollution 

tolerant, % taxa requiring high dissolved oxygen (DO), % oligosaprobic taxa, and average of 

Van Dam trophic taxa score), but FDEP also evaluated other taxonomic groupings (i.e., 

phosphorus and nitrogen sensitive diatoms). 

A combination of multiple-linear regression techniques and change point analyses was used to 

evaluate potential relationships between nutrient concentrations and the algal response variables. 

The analyses also evaluated the role of other environmental variables such as color, pH, and 

conductivity in determining the algal response. The analyses were conducted on both the raw 

untransformed data as well as data transformed by various techniques. To control the variability 

caused by natural regional differences in nutrient concentrations, the analyses were conducted 

for each nutrient region independently, starting with the panhandle and peninsula regions, for 

which more data exist. 

As with the macroinvertebrate community, the analyses of the periphyton data indicate that 

several algal variables exhibited a significant adverse response to increased nutrient levels. In 
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addition, the analyses indicated that periphyton also respond to other environmental factors such 

as water color, conductivity, and pH. However, other unmeasured variables such as water 

velocity, water level, and antecedent conditions likely play an important role in determining the 

composition of the periphyton community. Since the biota are responding to the combined effect 

of all of these factors along with nutrients, the natural variation in these other environmental 

factors confound the observed biological response to nutrients. 

The results of the multiple-linear regression analysis for the panhandle nutrient region are 

summarized in Table B1-1. Due to the confounding interactions between the factors included in 

the models as well as those for which data are not available, all of the adjusted R2 values for the 

regression equations were below 0.3. The results of the multiple-linear regression analyses are 

provided in more detail later in this appendix. 

Since the regression analyses showed that various forms of nutrients were significant factors in 

determining the periphyton response, change point analyses were performed to attempt to 

determine where significant thresholds in the periphyton response to nutrients occurred. Prior to 

performing the change point analyses, the data were adjusted for the other significant variables 

indicated by the regression analyses. An example of the step function and associated change 

point and confidence interval is provided in Figure B1-2, and the results of the change point 

analyses for the periphyton response variables versus total phosphorus (TP) are summarized in 

Table B1-2. 

The primary change points indicated in Table B1-2 ranged from 10 ppb to 22 ppb TP and were 

all significant at the 95% level. However, all of the primary change points occurred well below 

TP levels found at the majority of Florida’s minimally disturbed nutrient benchmark sites (see 

Chapter 2f) and appear to be highly influenced by factors other than nutrients. Most notably, 

these data were analyzed using two different laboratory method detection limits (MDL) for TP of 

4 μg/L and 20 μg/L, and this inconsistency appeared to have significantly influenced the results. 

The confidence intervals around the change points were also very wide, further limiting their 

usefulness in criteria development. 

For most periphyton variables, a second higher change point was also detected. The secondary 

change points ranged from 67 ppb to 131 ppb TP, however, they were not significant at the 95% 

confidence level. These changes were significant at the 75% to 80% level with extremely wide 

confidence intervals. The change point analyses conducted are presented in greater detail below. 

As with the analyses of the macroinvertebrate data, the results of the periphyton data analyses 

establish that increased nutrient levels have adverse impacts on the periphyton community, 

however, the response to nutrients is confounded by other environmental factors and FDEP could 

identify no clear thresholds to form the bases of numeric nutrient criteria. 

Quantile Regression Analysis of Periphyton Response to Nutrients 

As described previously, the biological response to nutrients is confounded by other measured 

environmental parameters as well as a number of unmeasured factors. Often, these confounding 

variables cause the biological measures to exhibit a wedge-shaped response to increased nutrient 

levels. At relatively low nutrient concentrations, the biological measures range widely, but at 
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relatively high concentrations, the measure is generally poor with less variation. The wedgeshaped distribution indicates that at low nutrient concentrations, factors other than nutrients often 

limit the health of biotic communities, whereas, at high nutrient concentrations, nutrients and 

factors correlated with high nutrient concentrations are the predominant limiting factors. As 

found with the analyses of the macroinvertebrate and periphyton data, linear regression and stepfunction models do not fit this type of response very well. Even though the linear regression and 

change-point analyses indicate that increased nutrient levels have negative biological effects, it is 

important to confirm this finding using statistical techniques better suited to describing complex 

relationships such as those found with nutrient effects on biological communities. Therefore, 

quantile regression was used to confirm that increased nutrient levels result in adverse biological 

responses in Florida streams. 

Quantile regression is a useful method for estimating effects associated with a measured subset 

of limiting factors while accounting for the effects of unmeasured factors in an ecologically 

realistic manner (Cade et al. 1999). This regression technique considers changes in a biological 

response variable (e.g., species biomass) as a function of limiting factors (e.g., habitat 

conditions) that are measured and as a function of other limiting factors (e.g., non-habitat factors 

such as weather and disease) that may not be measured. In this example, Cade et al. (1999) note 

that change in species biomass does not exceed limits imposed by the habitat conditions, but can 

be reduced by non-habitat factors. 

The quantile regression approach was applied to the stream periphyton data from the Florida 

panhandle nutrient region by fitting models to the 0.50 and 0.85 quantiles, with the periphyton 

metrics used in the earlier analysis as dependent variables and TP, total nitrogen (TN), total 

inorganic nitrogen (TIN), and specific conductance as independent variables. The logarithm 

(Base e) transformation was performed on the four predictor variables, and the periphyton 

metrics were transformed using the transformations chosen in the earlier analyses (Table B1-1). 

The quantile regression approach was repeated for periphyton data from the peninsula nutrient 

region, with models fitted to the 0.50 and 0.90 quantiles with the same periphyton metrics as 

dependent variables and TP, TN, TIN, and pH as independent variables. In the peninsula 

analysis, pH was substituted for conductivity as an independent variable based on the higher 

significance of pH found in the earlier analyses. 

Detailed results of the quantile regression analyses are provided below for the Panhandle and 

Peninsula, respectively. The results for the Panhandle indicated that all of the periphyton metrics 

exhibited significant responses to both TP and conductivity. In addition, the 0.50 quantile for 

some of the metrics (i.e., TP sensitive diatoms and TIN sensitive diatoms) showed significant 

responses to total nitrogen. An example of the quantile regression analysis using SDI as the 

dependent variable is provided below. 

In contrast, the results for the peninsula indicate that total nitrogen was the primary nutrient 

influencing the periphyton community in that region. This is not unexpected since the 

phosphorus-rich geology of the peninsula results in much higher natural background phosphorus 

levels when compared with the panhandle. The higher natural phosphorus levels would result in 

less phosphorus limitation in the biological community response in the peninsula. In addition to 

total nitrogen, several periphyton metrics (i.e., Van Dam’s average taxa Trophic State Index 

(TSI), average N-metabolism score, and pH optima score) showed a significant relationship to 
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total inorganic nitrogen and some metrics (i.e., % pollution tolerant taxa and % TIN sensitive 

taxa) were significantly correlated to TP. The analysis also indicated that all of the periphyton 

metrics were influenced by pH. The previous analysis showed that periphyton in the peninsula 

responded more to pH than conductivity, which was the dominant non-nutrient factor in the 

panhandle. As with phosphorus, natural conductivity levels in the peninsula are typically higher 

than those found in the panhandle, which may result in pH exerting a greater influence on the 

peninsula diatoms. However, conductivity and pH are generally highly correlated. 

Despite the confounding effects of other physicochemical variables, these results confirm that 

nutrient enrichment, primarily TP in the panhandle and nitrogen in the peninsula, has a 

significant negative effect on periphyton composition in Florida streams. Although DEP could 

not identify specific thresholds for establishing numeric nutrient criteria, the analyses provide 

further support for the need for nutrient criteria in order to protect against adverse biological 

effects. 

Analysis of Rapid Periphyton Survey Data 

Because excessive abundance of algae has been identified as a nuisance condition that should be 

avoided, the role of nutrients in determining the frequency of occurrence and abundance of algae 

in streams was also examined (in addition to the compositional metrics for the periphyton 

community described previously). The abundance of periphyton found in streams was evaluated 

using the Rapid Periphyton Survey (RPS) method, consisting of a series of 99 observations (nine 

observations across each of 11 transects along a 100 meter stream reach) of periphyton presence, 

thickness and type, per DEP-SOP-001/01 FS 7130. The RPSs were conducted in streams across 

the state in conjunction with nutrient and other physicochemical measurements. 

Correlation analysis was conducted to determine which nutrient and physicochemical variables 

exhibited the greatest influence on algal abundance in streams. Due to data limitations, the 

analysis of the algal abundance data was conducted on data collected over the entire state and not 

separated regionally. The results of the analyses are summarized in Table B1-3. The analyses 

indicated that canopy cover, color, pH, Total Kjeldahl Nitrogen (TKN), organic nitrogen, and 

nitrate-nitrite (NO3-NO2) were the factors most highly correlated to algal thickness. The strong 

correlations with color and canopy cover were expected since they can cause light limitation and 

therefore directly reduce periphyton growth. The relatively strong correlations between pH, 

TKN, and organic nitrogen and algal biomass were unexpected, but can likely be explained by 

their strong correlations with color (Spearman correlations were 0.79, 0.80, and -0.52, 

respectively). 

As shown in Figure B1-3, periphyton thickness appears to be significantly correlated with NO3-

NO2, canopy cover, and water color, but not with TP. It should be noted that color is a strong 

confounding factor in these analyses since it is correlated to some extent with canopy cover, 

NO3-NO2 concentration, and TP concentration. The initial analyses of the rapid periphyton 

assessment data are provided in greater detail in Appendix B-11. 

To account for the confounding effect of color, streams were classified based on color, and the 

relationships between algal biomass and nutrients were re-examined. The relationships between 

nutrients and periphyton thickness were much stronger in clear streams (Figure B1-4, a1–a3) 
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than in colored streams (Figure B1-4, c1-c3), indicated by the stronger spearman correlations as 

well as improved LOESS regressions in the clear streams. The main relationships observed were 

between nitrogen parameters and benthic algal thickness. The effect of phosphorus did not 

appear to be significant in these analyses. Where color is increased (increased potential for light 

limitation), nutrients do not exert as important a role in algal biomass accumulations. 

An analysis was also conducted to evaluate the relationship between nutrients and phytoplankton 

chl. a collected for the same sites. In contrast to algal biomass data, the relationships between 

phytoplankton chl. a and nutrients were much stronger in colored streams (Figure B1-5, b1-c3) 

than in clear streams (Figure B1-5, a1-a3), especially between total nitrogen and chl. a

concentrations. The Spearman correlations between chl. a and total nitrogen were 0.36 and 0.42, 

respectively, in intermediate and high color streams, but was -0.16 in clear streams. With the 

increased color and stronger light limitation to periphyton, phytoplankton appear more able to 

utilize the available nutrients than periphyton. Chl. a appeared to respond somewhat to 

phosphorus, but all of the responses were statistically weak. 

Further analysis of unshaded clear streams (i.e., color ≤ 40 and canopy cover ≤ 40%) indicate 

that TN and TIN were the variables having the strongest correlation with algal abundance 

measurements (Figure B1-6, a-c). The analysis also showed that TP concentration alone was not 

a strong predictor of the algal biomass rank. However based on the nitrogen to phosphorus (N:P) 

ratios, nitrogen and phosphorus could be co-limiting algal growth in the stream system. To test 

this hypothesis, both nitrogen and phosphorus concentrations were ranked from 1 to 10 based on 

their range, mean, and standard deviation, and the ranked nutrient variables were combined (TN+ 

TP and NOx +TP) to test if the addition of TP improved the nutrient relationships with algal 

thickness. As indicated in Figure B1-6, d-e, the combined nutrient variables have a stronger 

correlation to algal thickness than the individual nutrient concentrations, potentially indicating 

nitrogen and phosphorus co-limitation for some streams. This finding also indicates that both 

nitrogen (TN and NOx) and phosphorus are significant in controlling algal thickness in streams. 

More details concerning these analyses are provided in Appendix B-11. 

FDEP’s Conclusions 

FDEP has conducted multiple analyses using a variety of statistical techniques to investigate the 

effects of anthropogenic nutrient increases on the biological communities in Florida’s streams. 

These analyses were performed to define relationships between nutrients and biological response 

variables that could be used to develop numeric nutrient criteria. These analyses evaluated the 

influence of nutrients on biological indices such as the SCI, the SDI (currently under 

development), the individual metrics that comprise these indices, and other biological measures 

such as chl. a, taxonomic composition of macroinvertebrate and algal communities, and 

frequency of occurrence and abundance of algae (RPS). 

The results of the analyses generally indicate that many of the biological measures evaluated 

exhibit a statistically significant adverse response to nutrient enrichment, however, the 

relationships between the biological response variables and nutrient levels were confounded by 

numerous other factors such as color, pH conductivity, and canopy cover. The confounding 

effects of these other variables result in weak statistical relationships between measures of the 

biological communities and nutrient levels. While FDEP believes the effect of nutrients on the 
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biological communities is not clear enough to be used as the sole basis for establishing numeric 

nutrient criteria, the observed relationships between nutrients and the various biological 

measures demonstrate the need for nutrient criteria to prevent adverse biological effects in 

Florida streams. 

The statistical significance indicates that numeric nutrient criteria should be established and 

supports the decision to implement an alternative approach to deriving protective criteria, the 

Nutrient Benchmark Distribution Approach that is described in Chapter 2f. While the analysis in 

this Appendix did not produce numeric thresholds that could be used as water quality criteria, the 

relationships that were determined, while relatively weak, do support the values derived using 

the Nutrient Benchmark Approach. Both the analysis of the RPS (regarding probability of 

increased algal thickness) and the analysis of the second change point in the stream periphyton 

response to nutrients indicate that the biological response to nutrient enrichment will generally 

occur at levels higher than the values generated using the Benchmark Distribution Approach. 
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Table B1-1. Summary of Multiple Linear Regression Analyses Conducted for the Panhandle 

Nutrient Region 

Table B1-2. Summary of Change-point Analyses Conducted for the Panhandle Nutrient Region 

PollSens PollTol % high DO % Oligosap VD TSI TP Sens Dia TIN Sens Dia SDI N Metab pH Optima

Data Transformation None log arcsin (sqrt) arcsin (sqrt) sqrt arcsin(sqrt) None

Model SF NL SF SF SF SF SF SF SF SF

1st Change Pt. 

[confidence interval]

22 ppb 

[22,83]

10 ppb 

[8,78]

15 ppb 

[10,93]

18 ppb 

[15,131]

22 ppb 

[22,40]

22 ppb 

[10,60]

22 ppb 

[10,67]

22 ppb 

[22,40]

15 ppb 

[15,93]

22 ppb 

[10,36]

2nd Change Pt. 

[confidence interval]

 83ppb 

[10,131]

78 ppb 

[8,94]

90 ppb 

[18,149] 131 ppb [*] 131 ppb [*] NA 67 ppb [8,129]

82 ppb 

[8,131] 131 ppb [*] NA

2nd Change Pt. 

Confidence Level 75% 80% 80% 80% 80% NA 75% 80% 80% NA

SF = Step Function, NL = Non-Linear, L = Linear, NCP = No Change Point

[*] = Extreme interval outside data range

Response Variable

PollSens PollTol %Tol low DO % Oligosap VD TSI TP Sens Dia TIN Sens Dia N Metab pH Optima SDI

Data 

Transformation None SQRT arcsin(sqrt(x)) arcsin(sqrt(x)) None None None Recip Recip arcsin(sqrt(x))

1 pH pH pH pH pH CondL pH pH pH pH

2 ColorL ColorL TNL TNL CondL pH TNL

3 TNL TNL TINL TPL

4 TPL TPL TPL TINL

5 ColorL

Adjusted r2

= 0.25 0.10 0.08 0.10 0.27 0.20 0.18 0.11 0.13 0.12

Yellow shading = Pr < 0.05

Response Variable

Panhandle Nutrient Region
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Table B1-3. Correlation Matrix for Algal Abundance Measures from Rapid Periphyton 

Assessment Data vs. Nutrients and Other Physicochemical Parameters 

Sum of 

Algal 

Thickness

Mean Algal 

Thickness

Maximum 

Algal 

Thickness

Sum of 

Algal 

Thickness 

Scores

Mean 

Algal 

Thickness 

Score

Maximum 

Algal 

Thickness 

Score

Sum of 

Algal Type 

Score

Mean 

Algal Type 

Score

Maximum 

Algal Type 

Score

Sum of 

Algal 

Scores

Mean 

Algal 

Score

Maximum 

Algal 

Score

Chlorophyll a 0.14 0.22 0.18 0.12 0.22 0.16 0.08 0.16 0.16 0.1 0.16 0.14

Canopy Cover -0.29 -0.38 -0.38 -0.26 -0.36 -0.37 -0.25 -0.35 -0.36 -0.28 -0.35 -0.35

Maximum 

Canopy Cover

-0.18 -0.26 -0.25 -0.15 -0.24 -0.24 -0.15 -0.23 -0.23 -0.16 -0.22 -0.22

Minimum 

Canopy Cover

-0.32 -0.41 -0.42 -0.29 -0.39 -0.4 -0.27 -0.37 -0.4 -0.31 -0.38 -0.39

Total Nitrogen -0.11 -0.05 -0.09 -0.11 -0.06 -0.12 -0.10 -0.07 -0.08 -0.13 -0.10 -0.13

Total 

Inorganic 

Nitrogen

0.18 0.22 0.18 0.17 0.22 0.17 0.13 0.17 0.16 0.13 0.16 0.14

Organic 

Nitrogen -0.33 -0.29 -0.33 -0.32 -0.30 -0.36 -0.26 -0.25 -0.25 -0.31 -0.29 -0.32

Ammonia -0.19 -0.16 -0.21 -0.18 -0.15 -0.23 -0.20 -0.19 -0.20 -0.25 -0.23 -0.26

Total Kjeldahl 

Nitrogen -0.32 -0.28 -0.32 -0.32 -0.29 -0.35 -0.27 -0.25 -0.25 -0.32 -0.29 -0.33

Nitrate + 

Nitrite

0.23 0.29 0.26 0.22 0.29 0.36 0.19 0.15 0.25 0.20 0.25 0.23

Total 

Phosphorus -0.03 -0.04 -0.04 -0.03 -0.04 -0.03 -0.02 -0.04 -0.03 -0.03 -0.04 -0.05

Dissolved 

Oxygen

0.07 0.01 0.10 0.05 0.00 0.09 0.10 0.06 0.11 0.14 0.09 0.15

Conductivity 0.21 0.25 0.23 0.20 0.24 0.22 0.15 0.18 0.23 0.18 0.22 0.21

pH 0.22 0.24 0.24 0.21 0.24 0.24 0.18 0.20 0.24 0.21 0.24 0.24

Color -0.41 -0.42 -0.42 -0.40 -0.42 -0.42 -0.35 -0.36 -0.38 -0.38 -0.40 -0.41

Temperature 0.07 0.07 0.05 0.09 0.09 0.07 0.08 0.09 0.05 0.05 0.04 0.04

Velocity -0.01 0.00 0.04 -0.01 0.00 0.04 0.00 0.02 0.03 0.02 0.04 0.04

Note: Darker green shading indicates stronger positive relationships and darker red shading indicates stronger 

negative relationships. Values given are Spearman r values. 
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Figure B1-1. Example relationships between macroinvertebrate response variables and nutrient 

levels. TSIN is Total Soluble Inorganic Nitrogen (ammonia plus NO3-NO2). 
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Total-P (mg P/L)

Poll sensitve diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

20

40

60

80

100

120

0.022

0.083

0.022

Figure B1-2. Change-Point Model (Step Function) of percent pollution sensitive diatoms vs. TP. 

Response adjusted for ColorL and CondL. 
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Figure B1-3. Relationships between periphyton abundance and selected environmental 

predictors. The smooth curves are the locally weighted smoothing lines. The vertical lines are the 

change points (solid lines) and their confidence intervals (dashed lines). 
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Figure B1-4. Relationships between nutrient concentrations and algal thickness in clear (color ≤

40 platinum-cobalt units (PCU), Figures a1-a3), intermediate (color > 40-100 PCU, Figures b1-

b3) and highly colored (color > 100 PCU, Figures c1-c3) streams. 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B1-15 

Figure B1-5. Relationships between nutrient concentrations and chl. a concentrations in clear 

(<=40 PCU, Figures a1-a3), intermediate (40-100 PCU, Figures b1-b3) and highly colored (>100 

PCU, Figures c1-c3) streams. 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B1-16 

Figure B1-6. The relationships between periphyton thickness and TN, TP, and NOx 

concentrations as well as combined ranks of nutrients in clear streams (transect canopy ≤ 40% 

and color ≤ 40 PCU). Each dot represents a stream reach. The dashed curves are the loess 

regression lines 95% confidence limits; and the vertical lines are change points and 95% 

confidence limits. 
TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B1-17 

Appendices 6-A through 6-G 

(from USEPA. 2009. Proposed Methods and Approaches for Developing Numeric Nutrient 

Criteria for Florida’s Inland Waters. United States Environmental Protection Agency, Office of 

Water, Office of Science and Technology, Health and Ecological Criteria Division, Washington, 

DC.) 
 1 

Appendix 6-A 

Statistical Analysis of Stream Data 

Some Initial Results 

Xu-Feng Niu 

Technical Report Submitted to the 

Florida Department of Environmental Protection 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-18
 2 

Statistical Analysis of Stream Data 

Some Initial Results 

(All predictors except pH transformed by the logarithm) 

Xu-Feng Niu 

Department of Statistics 

Florida State University 

Tallahassee, FL 32306 

February 15 – March 15, 2009 

Technical Report Submitted to 

the Florida Department of Environmental Protection 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-19
 3 

I) SCI07 Scores. 

 Notes: 

a) TP, TN, TSIN, AN, Cond, KN, and Color are transformed by 

the Logarithm transformation. 

b) pH is not transformed. 

c)

 box.cox Transformations to Multinormality 

 Estimated transformation parameters 

 TP TN TSIN AN pH Color Cond 

 -0.07576708 0.2615876 0.06626942 -0.04629569 3.708665 0.121931 0.1001309 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-20
 4 

Log(Total-P) (mg P/L)

SCI_2007 Score

-4 -3 -2 -1 0 1

0

20

40

60

80

100

Log(Total Nitrogen)(mg N/L)

SCI_2007 Score

-3 -2 -1 0 1

0

20

40

60

80

100

Log(TSIN) (mg/L)

SCI_2007 Score

-5 -4 -3 -2 -1 0 1

0

20

40

60

80

100

Log(Ammonia-N) (mg N/L)

SCI_2007 Score

-5 -4 -3 -2 -1

0

20

40

60

80

100

Stream-Figure 1a. Exploratory Analysis Plots for Stream Data,

 (SCI07 versus Predictors)

Transformation Rules (Sanford Weisberg 2005, Applied Linear 

Regression, Chapter 7): 

The log rule If the values of a variable range over more than one order of 

magnitude and the variable is strictly positive, then replacing the variable by 

its logarithm is likely to be helpful. 

The range rule If the range of a variable is considerably less than one order of 

magnitude, then any transformation of that variable is unlikely to be helpful. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-21
 5 

Log(Conductivity), field (umhos/cm)

SCI_2007 Score

34567

0

20

40

60

80

100

Log(Kjeldahl Nitrogen) (mg N/L)

SCI_2007 Score

-3 -2 -1 0 1

0

20

40

60

80

100

Log(Color) (PCU)

SCI_2007 Score

123456

0

20

40

60

80

100

pH (SU)

SCI_2007 Score

45678

0

20

40

60

80

100

Stream-Figure 1b. Exploratory Analysis Plots for Stream Data,

 (SCI07 versus Predictors)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-22
 6 

-40

-20

0

20

40

Residuals Boxplot

-40 -20 0 20 40

0

5

10

15

20

Residual Histogram

QQ Plot with Normal

-2 -1 0 1 2

-40

-20

0

20

40

Residual vs Fitted Value

Fitted Value

30 40 50 60 70

-40

-20

0

20

40

Stream-Figure 1c. Exploratory Analysis Plots for Stream Data,

 (SCI07 Residual Diagnostics)

Correlation Matrix of the Chemistry-Stressor Variables 

 TP TN TSIN AN N02 KN 

 TP 1.00 0.42 0.01 0.24 -0.04 0.45 

 TN 0.42 1.00 0.40 0.56 0.30 0.87 

TSIN 0.01 0.40 1.00 0.20 0.98 -0.11 

 AN 0.24 0.56 0.20 1.00 0.01 0.57 

 N02 -0.04 0.30 0.98 0.01 1.00 -0.22 

 KN 0.45 0.87 -0.11 0.57 -0.22 1.00 

Highly correlated: 

a)Total Nitrogen(mg N/L) and Kjeldahl Nitrogen(mg N/L) 

b)TSIN(mg/L) and NO2NO3-N(mg N/L) 

c)Regression Design Matrix is singular. Kjeldahl Nitrogen(mg 

N/L) and NO2NO3-N(mg N/L) are removed. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-23
 7 

Models: 

 1) With 9 Predictors (Missing Values are removed):

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 198.3837 123.4603 1.6069 0.1129 

 Lat 1.7752 2.4479 0.7252 0.4709 

 Long 2.9092 1.7359 1.6759 0.0986 

 TP -0.3237 1.9590 -0.1652 0.8693 

 TN -15.3243 4.5418 -3.3741 0.0013 

 TSIN 8.4590 2.5816 3.2766 0.0017 

 AN -8.2434 2.3362 -3.5285 0.0008 

 pH 0.5756 2.8912 0.1991 0.8428 

 Color 10.6435 3.4438 3.0907 0.0029 

 Cond -4.9635 3.1706 -1.5655 0.1223 

Residual standard error: 15.48 on 65 degrees of freedom 

Multiple R-Squared: 0.4206 Adjusted R-squared: 0.3403 

F-statistic: 5.242 on 9 and 65 degrees of freedom, the p-value is 0.00002357 

2) Model selected stepwise by minimizing the Akaike Information 

Criterion (AIC) (Missing Values are removed): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 190.4349 119.0859 1.5991 0.1144 

 Long 2.1268 1.3300 1.5991 0.1144 

 TN -16.5237 4.1322 -3.9988 0.0002 

 TSIN 8.8790 2.4410 3.6374 0.0005 

 AN -8.3544 2.2704 -3.6797 0.0005 

 Color 10.9334 3.0517 3.5827 0.0006 

 Cond -5.2199 2.4884 -2.0977 0.0397 

Residual standard error: 15.19 on 68 degrees of freedom 

Multiple R-Squared: 0.4158 Adjusted R-squared: 0.3642 

F-statistic: 8.066 on 6 and 68 degrees of freedom, the p-value is 1.366e-006 

3) Model selected manually by backward elimination, Used for Residual 

Diagnostics. (Missing Values are removed): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -18.2656 12.9322 -1.4124 0.1615 

 TN -16.2215 3.9533 -4.1033 0.0001 

 TSIN 8.4474 2.2150 3.8137 0.0003 

 AN -7.5832 2.1076 -3.5980 0.0005 

 Color 12.9831 2.5098 5.1729 0.0000 

Residual standard error: 16.25 on 84 degrees of freedom 

Multiple R-Squared: 0.2998 Adjusted R-squared: 0.2665 

F-statistic: 8.992 on 4 and 84 degrees of freedom, the p-value is 4.288e-006 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-24
 8 

II) Clinger Taxa 

 Notes: 

d) TP, TN, TSIN, AN, Cond, KN, and Color are transformed by 

the Logarithm transformation. 

e) pH is not transformed. 

Log(Total-P) (mg P/L)

ClingerTaxa 

-4 -3 -2 -1 0 1

0

5

10

15

Log(Total Nitrogen) (mg N/L)

ClingerTaxa 

-3 -2 -1 0 1

0

5

10

15

Log(TSIN) (mg/L)

ClingerTaxa 

-5 -4 -3 -2 -1 0 1

0

5

10

15

Log(Ammonia-N) (mg N/L)

ClingerTaxa 

-5 -4 -3 -2 -1

0

5

10

15

Stream-Figure 2a. Exploratory Analysis Plots for Stream Data,

 (ClingerTaxa versus Predictors)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-25
 9 

Log(Conductivity), field (umhos/cm)

ClingerTaxa 

34567

0

5

10

15

Log(Kjeldahl Nitrogen) (mg N/L)

ClingerTaxa 

-3 -2 -1 0 1

0

5

10

15

Log(Color) (PCU)

ClingerTaxa 

123456

0

5

10

15

pH (SU)

ClingerTaxa 

45678

0

5

10

15

Stream-Figure 2b. Exploratory Analysis Plots for Stream Data,

 (ClingerTaxa versus Predictors)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-26
 10 

-4

-2

0

2

4

Residuals Boxplot

-4 -2 0 2 4

0

5

10

15

Residual Histogram

QQ Plot with Normal

-2 -1 0 1 2

-4

-2

0

2

4

Residual vs Fitted Value

Fitted Value

2468

-4

-2

0

2

4

Stream-Figure 2c. Exploratory Analysis Plots for Stream Data,

 (ClingerTaxa Residual Diagnostics)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-27
 11 

Models: 

1) With 9 Predictors (Missing Values are removed): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -11.1684 15.9500 -0.7002 0.4863 

 Lat 0.1033 0.3163 0.3266 0.7450 

 Long -0.0656 0.2243 -0.2926 0.7707 

 TP -0.2639 0.2531 -1.0428 0.3009 

 TN -1.5908 0.5868 -2.7111 0.0086 

 TSIN 0.9788 0.3335 2.9348 0.0046 

 AN -0.9541 0.3018 -3.1613 0.0024 

 pH 0.3468 0.3735 0.9285 0.3566 

 Color 1.4397 0.4449 3.2360 0.0019 

 Cond -0.7589 0.4096 -1.8527 0.0685 

Residual standard error: 1.999 on 65 degrees of freedom 

Multiple R-Squared: 0.4856 Adjusted R-squared: 0.4144 

F-statistic: 6.818 on 9 and 65 degrees of freedom, the p-value is 7.852e-007 

2) Model selected stepwise and manually by minimizing the Akaike 

Information Criterion (AIC). With two predictors significant at 

alpha=0.05 (Missing Values are removed): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.5520 3.0039 0.8496 0.3984 

 TN -1.6927 0.5374 -3.1500 0.0024 

 TSIN 0.9236 0.3104 2.9753 0.0040 

 AN -0.8434 0.2878 -2.9302 0.0045 

 Color 1.0575 0.3943 2.6823 0.0091 

 Cond -0.8083 0.2687 -3.0083 0.0036 

Residual standard error: 2.018 on 72 degrees of freedom 

Multiple R-Squared: 0.4227 Adjusted R-squared: 0.3826 

F-statistic: 10.54 on 5 and 72 degrees of freedom, the p-value is 1.277e-007 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-28
 12 

IV) Sensitive Taxa. 

Log(Total-P) (mg P/L)

SensitiveTaxa 

-4 -3 -2 -1 0 1

0

5

10

15

Log(Total Nitrogen) (mg N/L)

SensitiveTaxa 

-3 -2 -1 0 1

0

5

10

15

Log(TSIN) (mg/L)

SensitiveTaxa 

-5 -4 -3 -2 -1 0 1

0

5

10

15

Log(Ammonia-N) (mg N/L)

SensitiveTaxa 

-5 -4 -3 -2 -1

0

5

10

15

Stream-Figure 4a. Exploratory Analysis Plots for Stream Data,

 (SensitiveTaxa versus Predictors)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-29
 13 

Log(Conductivity), field (umhos/cm)

SensitiveTaxa 

34567

0

5

10

15

Log(Kjeldahl Nitrogen) (mg N/L)

SensitiveTaxa 

-3 -2 -1 0 1

0

5

10

15

Log(Color) (PCU)

SensitiveTaxa 

123456

0

5

10

15

pH (SU)

SensitiveTax 

45678

0

5

10

15

Stream-Figure 4b. Exploratory Analysis Plots for Stream Data,

 (SensitiveTaxa versus Predictors)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-30
 14 

-4

-2

0

2

4

Residuals Boxplot

-4 -2 0 2 4

0

5

10

15

Residual Histogram

QQ Plot with Normal

-2 -1 0 1 2

-4

-2

0

2

4

Residual vs Fitted Value

Fitted Value

-2 0 2 4 6 8 10 12

-4

-2

0

2

4

Stream-Figure 4c. Exploratory Analysis Plots for Stream Data,

 (SensitiveTaxa Residual Diagnostics, from Stepwise)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-31
 15 

Models: 

1) With 9 Predictors (Missing Values are removed): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -13.8548 19.0101 -0.7288 0.4687 

 Lat 0.2431 0.3769 0.6449 0.5213 

 Long -0.1413 0.2673 -0.5287 0.5988 

 TP 0.3491 0.3016 1.1575 0.2513 

 TN -2.4418 0.6993 -3.4916 0.0009 

 TSIN 1.2307 0.3975 3.0959 0.0029 

 AN -1.7558 0.3597 -4.8809 0.0000 

 pH -0.3907 0.4452 -0.8776 0.3834 

 Color 1.4420 0.5303 2.7194 0.0084 

 Cond -1.3758 0.4882 -2.8180 0.0064 

Residual standard error: 2.383 on 65 degrees of freedom 

Multiple R-Squared: 0.6991 Adjusted R-squared: 0.6574 

F-statistic: 16.78 on 9 and 65 degrees of freedom, the p-value is 7.117e-014 

2) Model selected manually and stepwise by minimizing the Akaike 

Information Criterion (AIC). With three predictors (Missing Values 

are removed): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -14.0808 9.4278 -1.4935 0.1397 

 Lat 0.5550 0.2697 2.0578 0.0433 

 TN -2.1205 0.6664 -3.1819 0.0022 

 TSIN 1.1533 0.3810 3.0270 0.0034 

 AN -1.5661 0.3358 -4.6642 0.0000 

 Color 1.4806 0.4666 3.1733 0.0022 

 Cond -1.4319 0.3765 -3.8036 0.0003 

Residual standard error: 2.352 on 71 degrees of freedom 

Multiple R-Squared: 0.6828 Adjusted R-squared: 0.656 

F-statistic: 25.47 on 6 and 71 degrees of freedom, the p-value is 6.661e-016 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-32
 1 

Appendix 6-B 

Statistical Analysis of Stream Data-Periphyton Metrics 

(Weaver Region Panhandle) 

Xu-Feng Niu 

March 15 – April 25, 2009 

Technical Report Submitted to the 

Florida Department of Environmental Protection 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-33
 2 

Statistical Analysis of Stream Data-Periphyton Metrics 

(Weaver Region Panhandle) 

 Xu-Feng Niu 

Department of Statistics 

Florida State University 

Tallahassee, FL 32306 

1.1 March 15 – April 25, 2009 

Technical Report Submitted to 

the Florida Department of Environmental Protection 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-34
 3 

I) Pollution Sensitive Diatoms 

Notes: 

a) Correlation Matrix: 

 TP TN TIN TKN Nox Cond pH Color 

 TP 1.00 0.01 -0.13 0.22 -0.16 -0.05 0.20 0.02 

 TN 0.01 1.00 0.80 0.50 0.74 0.06 -0.07 0.26 

 TIN -0.13 0.80 1.00 -0.10 0.98 0.13 0.16 -0.23 

 TKN 0.22 0.50 -0.10 1.00 -0.21 -0.04 -0.30 0.71 

 Nox -0.16 0.74 0.98 -0.21 1.00 0.10 0.15 -0.26 

 Cond -0.05 0.06 0.13 -0.04 0.10 1.00 0.62 -0.22 

 pH 0.20 -0.07 0.16 -0.30 0.15 0.62 1.00 -0.49 

Color 0.02 0.26 -0.23 0.71 -0.26 -0.22 -0.49 1.00 

 

b) TP, TN, TIN, Cond, and Color are transformed by the 

Logarithm transformation. 

c) pH is not transformed. 

d)box.cox Transformations to Multinormality 

 TP TN TIN Cond Color 

 0.0453 0.0927 0.254 -0.274 0.0877

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-35
 4 

Total-P (mg P/L)

Poll sensitive diatoms 

0.0 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Poll sensitve diatoms 

01234

0

20

40

60

80

100

TIN(mg/L)

Poll sensitve diatoms 

01234

0

20

40

60

80

100

pH

Poll sensitve diatoms 

45678

0

20

40

60

80

100

Conductance, field (umhos/cm)

Poll sensitve diatoms 

0 100 200 300 400 500

0

20

40

60

80

100

Color

Poll sensitve diatoms 

0 100 200 300 400 500

0

20

40

60

80

100

Stream-Figure 1a. Exploratory Analysis Plots for Stream Data,

 (Poll Sensitve Diatoms versus Predictors; Red: pH<6.5)

Notes: 

1) Outliers TP=0.580 and TP=0.565 are removed. 

2) Outliers Cond=1344 and Cond=1557 are removed. 

3) Outliers TN=5.88 and TN=5.51 are removed. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-36
 5 

Models: 

1) Response PollSens not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 25.8313 34.5008 0.7487 0.4563 

 TPL -10.5795 2.8289 -3.7399 0.0004 

 TNL -4.1199 6.2190 -0.6625 0.5097 

 TINL 3.5605 2.9994 1.1871 0.2389 

 CondL -13.3088 5.0446 -2.6382 0.0101 

 pH 0.0198 3.8845 0.0051 0.9960 

 ColorL 9.1516 4.2382 2.1593 0.0340 

Residual standard error: 26.96 on 76 degrees of freedom 

Multiple R-Squared: 0.4052 Adjusted R-squared: 0.3583 

F-statistic: 8.631 on 6 and 76 degrees of freedom, the p-value is 3.673e-007 

 

2) Response PollSens transformed by Square-Root (Chosen in the Box-Cox 

Power Transformation Family) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.1003 3.1897 1.2855 0.2025 

 TPL -0.8964 0.2615 -3.4273 0.0010 

 TNL -0.2898 0.5750 -0.5041 0.6157 

 TINL 0.3725 0.2773 1.3435 0.1831 

 CondL -1.1642 0.4664 -2.4962 0.0147 

 pH 0.0384 0.3591 0.1070 0.9151 

 ColorL 0.8736 0.3918 2.2297 0.0287 

Residual standard error: 2.492 on 76 degrees of freedom 

Multiple R-Squared: 0.3708 Adjusted R-squared: 0.3212 

F-statistic: 7.466 on 6 and 76 degrees of freedom, the p-value is 2.639e-006 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-37
 6 

3) Response PollSens transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.5254 0.4168 1.2607 0.2113 

 TPL -0.1262 0.0341 -3.7009 0.0004 

 TNL -0.0342 0.0750 -0.4562 0.6496 

 TINL 0.0418 0.0362 1.1527 0.2527 

 CondL -0.1798 0.0612 -2.9361 0.0044 

 pH 0.0137 0.0471 0.2912 0.7717 

 ColorL 0.1001 0.0519 1.9299 0.0574 

Residual standard error: 0.3248 on 75 degrees of freedom 

Multiple R-Squared: 0.4026 Adjusted R-squared: 0.3548 

F-statistic: 8.424 on 6 and 75 degrees of freedom, the p-value is 5.426e-007 

4) Selected Model; Response PollSens not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 32.5436 25.8431 1.2593 0.2113 

 TPL -11.0050 2.4738 -4.4486 0.0000 

 CondL -14.6813 3.3183 -4.4244 0.0000 

 ColorL 6.9044 2.9799 2.3170 0.0229 

Residual standard error: 25.97 on 87 degrees of freedom 

Multiple R-Squared: 0.4146 Adjusted R-squared: 0.3945 

F-statistic: 20.54 on 3 and 87 degrees of freedom, the p-value is 3.747e-010 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-38
 7 

II) Pollution tolerant diatoms 

 

Total-P (mg P/L)

Poll Tol diatoms 

0.0 0.05 0.10 0.15 0.20

0

10

20

30

40

50

60

Total Nitrogen (mg N/L)

Poll Tol diatoms 

01234

0

10

20

30

40

50

60

TIN(mg/L)

Poll Tol diatoms 

01234

0

10

20

30

40

50

60

pH

Poll Tol diatoms 

45678

0

10

20

30

40

50

60

Conductance, field (umhos/cm)

Poll Tol diatoms 

0 100 200 300 400 500

0

10

20

30

40

50

60

Color

Poll Tol diatoms 

0 100 200 300 400 500

0

10

20

30

40

50

60

Stream-Figure 2a. Exploratory Analysis Plots for Stream Data,

 (Poll Tol Diatoms versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-39
 8 

Models: 

1) Response PollTol not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 12.3286 11.9458 1.0320 0.3053 

 TPL 3.7790 0.9795 3.8581 0.0002 

 TNL -1.7822 2.1533 -0.8276 0.4105 

 TINL -0.5608 1.0385 -0.5400 0.5908 

 CondL 2.8074 1.7467 1.6073 0.1121 

 pH 1.1702 1.3450 0.8700 0.3870 

 ColorL -2.8289 1.4675 -1.9278 0.0576 

Residual standard error: 9.334 on 76 degrees of freedom 

Multiple R-Squared: 0.3912 Adjusted R-squared: 0.3432 

F-statistic: 8.141 on 6 and 76 degrees of freedom, the p-value is 8.323e-007 

2) Response PollTol transformed by Logarithm (Chosen in the Box-Cox 

Power Transformation Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -2.4121 2.0476 -1.1780 0.2425 

 TPL 0.8415 0.1679 5.0119 0.0000 

 TNL -0.7261 0.3691 -1.9673 0.0528 

 TINL 0.2397 0.1780 1.3466 0.1821 

 CondL 0.6685 0.2994 2.2329 0.0285 

 pH 0.5589 0.2305 2.4242 0.0177 

 ColorL 0.0533 0.2515 0.2120 0.8326 

Residual standard error: 1.6 on 76 degrees of freedom 

Multiple R-Squared: 0.5576 Adjusted R-squared: 0.5227 

F-statistic: 15.96 on 6 and 76 degrees of freedom, the p-value is 8.788e-012 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-40
 9 

3) Response PollTol transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.1538 0.1789 0.8597 0.3927 

 TPL 0.0678 0.0147 4.6242 0.0000 

 TNL -0.0479 0.0322 -1.4856 0.1415 

 TINL 0.0037 0.0156 0.2366 0.8136 

 CondL 0.0606 0.0262 2.3163 0.0232 

 pH 0.0287 0.0201 1.4231 0.1588 

 ColorL -0.0288 0.0220 -1.3087 0.1946 

Residual standard error: 0.1398 on 76 degrees of freedom 

Multiple R-Squared: 0.5043 Adjusted R-squared: 0.4652 

F-statistic: 12.89 on 6 and 76 degrees of freedom, the p-value is 5.454e-010 

4) Selected Model; Response PollTol transformed by the logarithm: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -2.8286 1.1733 -2.4109 0.0178 

 TPL 0.5847 0.1424 4.1067 0.0001 

 pH 0.9337 0.1495 6.2440 0.0000 

Residual standard error: 1.655 on 96 degrees of freedom 

Multiple R-Squared: 0.4458 Adjusted R-squared: 0.4343 

F-statistic: 38.62 on 2 and 96 degrees of freedom, the p-value is 4.95e-013 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-41
 10 

III) Percentage cells tolerant of low O2 

 

Total-P (mg P/L)

% cells tol of low O2

0.0 0.05 0.10 0.15 0.20

20

40

60

80

100

Total Nitrogen (mg N/L)

% cells tol of low O2

01234

20

40

60

80

100

TIN(mg/L)

% cells tol of low O2

01234

20

40

60

80

100

pH

% cells tol of low O2

45678

20

40

60

80

100

Conductance, field (umhos/cm)

% cells tol of low O2

0 100 200 300 400 500

20

40

60

80

100

Color

% cells tol of low O2

0 100 200 300 400 500

20

40

60

80

100

Stream-Figure 3a. Exploratory Analysis Plots for Stream Data,

 (% cells tol of low O2 versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-42
 11 

Models: 

1) Response OxyTol not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 73.2474 18.9134 3.8728 0.0002 

 TPL -5.9120 1.5508 -3.8122 0.0003 

 TNL 1.2899 3.4093 0.3784 0.7062 

 TINL 1.6932 1.6443 1.0298 0.3064 

 CondL -4.8371 2.7654 -1.7491 0.0843 

 pH -2.2012 2.1295 -1.0337 0.3046 

 ColorL 6.2281 2.3234 2.6806 0.0090 

Residual standard error: 14.78 on 76 degrees of freedom 

Multiple R-Squared: 0.4414 Adjusted R-squared: 0.3973 

F-statistic: 10.01 on 6 and 76 degrees of freedom, the p-value is 3.98e-008 

2) Response OxyTol transformed by Square (Chosen transformation in the 

Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 6548.3635 2458.5276 2.6635 0.0094 

 TPL -843.7919 201.5843 -4.1858 0.0001 

 TNL 118.3553 443.1694 0.2671 0.7901 

 TINL 237.6286 213.7381 1.1118 0.2697 

 CondL -745.7362 359.4753 -2.0745 0.0414 

 pH -346.6107 276.8091 -1.2522 0.2143 

 ColorL 800.9695 302.0127 2.6521 0.0097 

Residual standard error: 1921 on 76 degrees of freedom 

Multiple R-Squared: 0.4937 Adjusted R-squared: 0.4538 

F-statistic: 12.35 on 6 and 76 degrees of freedom, the p-value is 1.17e-009 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-43
 12 

3) Response OxyTol transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1457 0.2348 4.8799 0.0000 

 TPL -0.0857 0.0193 -4.4537 0.0000 

 TNL 0.0134 0.0423 0.3170 0.7521 

 TINL 0.0216 0.0204 1.0588 0.2930 

 CondL -0.0724 0.0343 -2.1096 0.0382 

 pH -0.0352 0.0264 -1.3315 0.1870 

 ColorL 0.0721 0.0288 2.4993 0.0146 

Residual standard error: 0.1834 on 76 degrees of freedom 

Multiple R-Squared: 0.5073 Adjusted R-squared: 0.4684 

F-statistic: 13.04 on 6 and 76 degrees of freedom, the p-value is 4.386e-010 

4) Selected Model; Response OxyTol transformed by arcsin(sqrt(x)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0990 0.2294 4.7902 0.0000 

 TPL -0.0869 0.0189 -4.5903 0.0000 

 ColorL 0.0520 0.0235 2.2098 0.0297 

 pH -0.0727 0.0201 -3.6088 0.0005 

Residual standard error: 0.1909 on 90 degrees of freedom 

Multiple R-Squared: 0.4307 Adjusted R-squared: 0.4117 

F-statistic: 22.7 on 3 and 90 degrees of freedom, the p-value is 4.966e-011 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-44
 13 

IV) Percentage cells preferring oligosaprobic condition 

 

Total-P (mg P/L)

Saprobic % Cells

0.0 0.05 0.10 0.15 0.20

40

60

80

100

Total Nitrogen (mg N/L)

Saprobic % Cells

01234

40

60

80

100

TIN(mg/L)

Saprobic % Cells

01234

40

60

80

100

pH

Saprobic % Cells

45678

40

60

80

100

Conductance, field (umhos/cm)

Saprobic % Cells

0 100 200 300 400 500

40

60

80

100

Color

Saprobic % Cells

0 100 200 300 400 500

40

60

80

100

Stream-Figure 4a. Exploratory Analysis Plots for Stream Data,

 (Saprobic % Cells versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-45
 14 

Models: 

1) Response Sapr not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 80.9551 13.5833 5.9599 0.0000 

 TPL -4.7722 1.1137 -4.2848 0.0001 

 TNL -0.2864 2.4485 -0.1170 0.9072 

 TINL 1.7069 1.1809 1.4454 0.1525 

 CondL -1.8219 1.9861 -0.9173 0.3619 

 pH -2.9761 1.5294 -1.9460 0.0554 

 ColorL 4.2649 1.6686 2.5559 0.0126 

Residual standard error: 10.61 on 76 degrees of freedom 

Multiple R-Squared: 0.4736 Adjusted R-squared: 0.432 

F-statistic: 11.4 on 6 and 76 degrees of freedom, the p-value is 4.762e-009 

2) Response Sapr transformed by Square (Chosen transformation in the 

Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 7466.3770 2029.9720 3.6781 0.0004 

 TPL -734.8560 166.4454 -4.4150 0.0000 

 TNL 20.1396 365.9188 0.0550 0.9563 

 TINL 221.1997 176.4806 1.2534 0.2139 

 CondL -349.3512 296.8138 -1.1770 0.2429 

 pH -481.4851 228.5574 -2.1066 0.0385 

 ColorL 585.3839 249.3677 2.3475 0.0215 

Residual standard error: 1586 on 76 degrees of freedom 

Multiple R-Squared: 0.5004 Adjusted R-squared: 0.4609 

F-statistic: 12.68 on 6 and 76 degrees of freedom, the p-value is 7.279e-010 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-46
 15 

3) Response Sapr transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.2921 0.1887 6.8457 0.0000 

 TPL -0.0714 0.0155 -4.6147 0.0000 

 TNL 0.0016 0.0340 0.0481 0.9617 

 TINL 0.0177 0.0164 1.0812 0.2830 

 CondL -0.0398 0.0276 -1.4438 0.1529 

 pH -0.0501 0.0213 -2.3554 0.0211 

 ColorL 0.0477 0.0232 2.0586 0.0430 

Residual standard error: 0.1475 on 76 degrees of freedom 

Multiple R-Squared: 0.5331 Adjusted R-squared: 0.4963 

F-statistic: 14.46 on 6 and 76 degrees of freedom, the p-value is 6.237e-011 

 

 

4) Selected Model; Response Sapr transformed by arcsin(sqrt(x)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1991 0.1847 6.4918 0.0000 

 TPL -0.0754 0.0152 -4.9456 0.0000 

 ColorL 0.0405 0.0189 2.1400 0.0351 

 pH -0.0663 0.0162 -4.0892 0.0001 

Residual standard error: 0.1537 on 90 degrees of freedom 

Multiple R-Squared: 0.4734 Adjusted R-squared: 0.4558 

F-statistic: 26.97 on 3 and 90 degrees of freedom, the p-value is 1.558e-012 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-47
 16 

V) Van Dam Trophic State Index 

 

Total-P (mg P/L)

Van Dam TSI

0.0 0.05 0.10 0.15 0.20

1

2

3

4

5

Total Nitrogen (mg N/L)

Van Dam TSI

01234

1

2

3

4

5

TIN(mg/L)

Van Dam TSI

01234

1

2

3

4

5

pH

Van Dam TSI

45678

1

2

3

4

5

Conductance, field (umhos/cm)

Van Dam TSI

0 100 200 300 400 500

1

2

3

4

5

Color

Van Dam TSI

0 100 200 300 400 500

1

2

3

4

5

Stream-Figure 5a. Exploratory Analysis Plots for Stream Data,

 (Van Dam TSI versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-48
 17 

Models: 

1) Response TSI not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.8923 1.0245 3.7992 0.0003 

 TPL 0.4065 0.0840 4.8397 0.0000 

 TNL 0.1478 0.1847 0.8001 0.4261 

 TINL -0.1333 0.0891 -1.4969 0.1386 

 CondL 0.3149 0.1498 2.1019 0.0389 

 pH 0.0221 0.1154 0.1920 0.8483 

 ColorL -0.2848 0.1259 -2.2632 0.0265 

Residual standard error: 0.8005 on 76 degrees of freedom 

Multiple R-Squared: 0.4433 Adjusted R-squared: 0.3993 

F-statistic: 10.09 on 6 and 76 degrees of freedom, the p-value is 3.527e-008 

 

2) Response TSI transformed by the Square-Root transformation (Chosen in 

the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.9443 0.3028 6.4204 0.0000 

 TPL 0.1252 0.0248 5.0406 0.0000 

 TNL 0.0456 0.0546 0.8354 0.4061 

 TINL -0.0395 0.0263 -1.4988 0.1381 

 CondL 0.1025 0.0443 2.3149 0.0233 

 pH 0.0057 0.0341 0.1669 0.8679 

 ColorL -0.0819 0.0372 -2.2021 0.0307 

Residual standard error: 0.2366 on 76 degrees of freedom 

Multiple R-Squared: 0.4661 Adjusted R-squared: 0.424 

F-statistic: 11.06 on 6 and 76 degrees of freedom, the p-value is 7.901e-009 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-49
 18 

3) Selected Model; Response TSI transformed by the Square-Root 

transformation: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.8881 0.2259 8.3583 0.0000 

 TPL 0.1358 0.0216 6.2822 0.0000 

 CondL 0.1148 0.0290 3.9586 0.0002 

 ColorL -0.0468 0.0260 -1.7980 0.0756 

Residual standard error: 0.227 on 87 degrees of freedom 

Multiple R-Squared: 0.4679 Adjusted R-squared: 0.4496 

F-statistic: 25.5 on 3 and 87 degrees of freedom, the p-value is 6.252e-012 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-50
 19 

VI) TP Sensitive Diatoms 

 

Total-P (mg P/L)

TP sensitive diatoms

0.0 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TP sensitive diatoms

01234

0

20

40

60

80

100

TIN(mg/L)

TP sensitive diatoms

01234

0

20

40

60

80

100

pH

TP sensitive diatoms

45678

0

20

40

60

80

100

Conductance, field (umhos/cm)

TP sensitive diatoms

0 100 200 300 400 500

0

20

40

60

80

100

Color

TP sensitive diatoms

0 100 200 300 400 500

0

20

40

60

80

100

Stream-Figure 6a. Exploratory Analysis Plots for Stream Data,

 (TP sensitive diatoms versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-51
 20 

Models: 

1) Response TP sensitive diatoms not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -7.4726 35.9549 -0.2078 0.8359 

 TPL -11.5752 2.9481 -3.9264 0.0002 

 TNL -12.0043 6.4812 -1.8522 0.0679 

 TINL 2.4909 3.1258 0.7969 0.4280 

 CondL -5.8388 5.2572 -1.1106 0.2702 

 pH 1.9768 4.0482 0.4883 0.6267 

 ColorL 6.8129 4.4168 1.5425 0.1271 

Residual standard error: 28.09 on 76 degrees of freedom 

Multiple R-Squared: 0.3002 Adjusted R-squared: 0.245 

F-statistic: 5.434 on 6 and 76 degrees of freedom, the p-value is 0.0001017 

2) Response TP sensitive diatoms transformed by the logarithm 

transformation (Actually, the identical transformation was Chosen in 

the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.9179 1.4381 1.3337 0.1863 

 TPL -0.2730 0.1179 -2.3154 0.0233 

 TNL -0.5052 0.2592 -1.9490 0.0550 

 TINL 0.0374 0.1250 0.2991 0.7657 

 CondL -0.1048 0.2103 -0.4984 0.6197 

 pH 0.0459 0.1619 0.2836 0.7775 

 ColorL 0.1357 0.1767 0.7681 0.4448 

Residual standard error: 1.124 on 76 degrees of freedom 

Multiple R-Squared: 0.1802 Adjusted R-squared: 0.1155 

F-statistic: 2.784 on 6 and 76 degrees of freedom, the p-value is 0.01679 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-52
 21 

3) Response TP sensitive diatoms transformed by arcsin(sqrt(x)) 

(Theoretical Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.1267 0.4280 0.2961 0.7680 

 TPL -0.1317 0.0351 -3.7536 0.0003 

 TNL -0.1466 0.0772 -1.9001 0.0612 

 TINL 0.0270 0.0372 0.7253 0.4705 

 CondL -0.0685 0.0626 -1.0949 0.2770 

 pH 0.0218 0.0482 0.4525 0.6522 

 ColorL 0.0777 0.0526 1.4769 0.1438 

Residual standard error: 0.3345 on 76 degrees of freedom 

Multiple R-Squared: 0.292 Adjusted R-squared: 0.2361 

F-statistic: 5.223 on 6 and 76 degrees of freedom, the p-value is 0.0001508 

4) Selected Model; Response TP sensitive diatoms transformed by 

arcsin(sqrt(x)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.0529 0.2081 -0.2543 0.7999 

 TPL -0.1335 0.0315 -4.2425 0.0001 

 TNL -0.1257 0.0528 -2.3817 0.0195 

 ColorL 0.0681 0.0369 1.8454 0.0685 

Residual standard error: 0.3391 on 84 degrees of freedom 

Multiple R-Squared: 0.2521 Adjusted R-squared: 0.2254 

F-statistic: 9.438 on 3 and 84 degrees of freedom, the p-value is 0.00001925 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-53
 22 

VII) TIN Sensitive Diatoms 

Total-P (mg P/L)

TIN sensitive diatoms

0.0 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TIN sensitive diatoms

01234

0

20

40

60

80

100

TIN(mg/L)

TIN sensitive diatoms

01234

0

20

40

60

80

100

pH

TIN sensitive diatoms

45678

0

20

40

60

80

100

Conductance, field (umhos/cm)

TIN sensitive diatoms

0 100 200 300 400 500

0

20

40

60

80

100

Color

TIN sensitive diatoms

0 100 200 300 400 500

0

20

40

60

80

100

Stream-Figure 7a. Exploratory Analysis Plots for Stream Data,

 (TIN sensitive diatoms versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-54
 23 

Models: 

1) Response TIN sensitive diatoms not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -6.0366 34.6617 -0.1742 0.8622 

 TPL -11.0117 2.8420 -3.8746 0.0002 

 TNL -10.0678 6.2480 -1.6113 0.1112 

 TINL 4.5030 3.0134 1.4943 0.1392 

 CondL -7.4767 5.0681 -1.4753 0.1443 

 pH 1.7451 3.9026 0.4472 0.6560 

 ColorL 7.4455 4.2579 1.7486 0.0844 

Residual standard error: 27.08 on 76 degrees of freedom 

Multiple R-Squared: 0.3117 Adjusted R-squared: 0.2574 

F-statistic: 5.736 on 6 and 76 degrees of freedom, the p-value is 0.0000581 

2) Response TIN sensitive diatoms transformed by the SQRT 

transformation (Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.5496 3.7224 0.1476 0.8830 

 TPL -0.9710 0.3052 -3.1813 0.0021 

 TNL -1.1687 0.6710 -1.7417 0.0856 

 TINL 0.4719 0.3236 1.4583 0.1489 

 CondL -0.5275 0.5443 -0.9691 0.3356 

 pH 0.2631 0.4191 0.6277 0.5321 

 ColorL 0.5706 0.4573 1.2477 0.2160 

Residual standard error: 2.909 on 76 degrees of freedom 

Multiple R-Squared: 0.2297 Adjusted R-squared: 0.1688 

F-statistic: 3.776 on 6 and 76 degrees of freedom, the p-value is 0.002412 

\ 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-55
 24 

3) Response TIN sensitive diatoms transformed by arcsin(sqrt(x)) 

(Theoretical Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.0069 0.4647 0.0148 0.9883 

 TPL -0.1324 0.0381 -3.4752 0.0008 

 TNL -0.1399 0.0838 -1.6707 0.0989 

 TINL 0.0591 0.0404 1.4618 0.1479 

 CondL -0.0837 0.0679 -1.2316 0.2219 

 pH 0.0308 0.0523 0.5879 0.5583 

 ColorL 0.0872 0.0571 1.5282 0.1306 

Residual standard error: 0.3631 on 76 degrees of freedom 

Multiple R-Squared: 0.2627 Adjusted R-squared: 0.2045 

F-statistic: 4.514 on 6 and 76 degrees of freedom, the p-value is 0.0005795 

 

4) Selected Model; Response TIN sensitive diatoms Not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 38.9760 18.0349 2.1611 0.0333 

 TPL -9.6582 2.5085 -3.8502 0.0002 

 CondL -9.2965 3.3079 -2.8104 0.0060 

Residual standard error: 28.07 on 92 degrees of freedom 

Multiple R-Squared: 0.2328 Adjusted R-squared: 0.2162 

F-statistic: 13.96 on 2 and 92 degrees of freedom, the p-value is 5.071e-006 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-56
 25 

VIII) N Metab (Count Avg) 

Total-P (mg P/L)

N Metab (Count Avg)

0.0 0.05 0.10 0.15 0.20

1.0

1.5

2.0

2.5

3.0

Total Nitrogen (mg N/L)

N Metab (Count Avg)

01234

1.0

1.5

2.0

2.5

3.0

TIN(mg/L)

N Metab (Count Avg)

01234

1.0

1.5

2.0

2.5

3.0

pH

N Metab (Count Avg)

45678

1.0

1.5

2.0

2.5

3.0

Conductance, field (umhos/cm)

N Metab (Count Avg)

0 100 200 300 400 500

1.0

1.5

2.0

2.5

3.0

Color

N Metab (Count Avg)

0 100 200 300 400 500

1.0

1.5

2.0

2.5

3.0

Stream-Figure 8a. Exploratory Analysis Plots for Stream Data,

 (N Metab (Count Avg) versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-57
 26 

Models: 

1) Response N Metab not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.3258 0.2908 4.5586 0.0000 

 TPL 0.1105 0.0238 4.6336 0.0000 

 TNL -0.0609 0.0524 -1.1622 0.2488 

 TINL -0.0047 0.0253 -0.1861 0.8529 

 CondL 0.0889 0.0425 2.0906 0.0399 

 pH 0.0705 0.0327 2.1515 0.0346 

 ColorL -0.0633 0.0357 -1.7707 0.0806 

Residual standard error: 0.2273 on 76 degrees of freedom 

Multiple R-Squared: 0.5544 Adjusted R-squared: 0.5192 

F-statistic: 15.76 on 6 and 76 degrees of freedom, the p-value is 1.14e-011 

 

2) Response N Metab transformed by the logarithm transformation: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.2296 0.1733 1.3248 0.1892 

 TPL 0.0708 0.0142 4.9826 0.0000 

 TNL -0.0389 0.0312 -1.2466 0.2164 

 TINL -0.0017 0.0151 -0.1114 0.9116 

 CondL 0.0575 0.0253 2.2694 0.0261 

 pH 0.0477 0.0195 2.4429 0.0169 

 ColorL -0.0333 0.0213 -1.5620 0.1224 

Residual standard error: 0.1354 on 76 degrees of freedom 

Multiple R-Squared: 0.5903 Adjusted R-squared: 0.5579 

F-statistic: 18.25 on 6 and 76 degrees of freedom, the p-value is 5.309e-013 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-58
 27 

3) Response N Metab transformed by the Reciprocal transformation 

(Chosen in the Box-Cox Power Family): 

 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.8224 0.1087 7.5630 0.0000 

 TPL -0.0469 0.0089 -5.2648 0.0000 

 TNL 0.0255 0.0196 1.3032 0.1964 

 TINL 0.0003 0.0095 0.0302 0.9760 

 CondL -0.0383 0.0159 -2.4116 0.0183 

 pH -0.0330 0.0122 -2.6918 0.0087 

 ColorL 0.0174 0.0134 1.2995 0.1977 

Residual standard error: 0.08496 on 76 degrees of freedom 

Multiple R-Squared: 0.6158 Adjusted R-squared: 0.5855 

F-statistic: 20.31 on 6 and 76 degrees of freedom, the p-value is 4.974e-014 

4) Selected Model; Response N Metab transformed by Reciprocal: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.9197 0.0664 13.8481 0.0000 

 TPL -0.0352 0.0081 -4.3673 0.0000 

 pH -0.0591 0.0085 -6.9865 0.0000 

Residual standard error: 0.09371 on 96 degrees of freedom 

Multiple R-Squared: 0.4933 Adjusted R-squared: 0.4827 

F-statistic: 46.73 on 2 and 96 degrees of freedom, the p-value is 6.772e-015 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-59
 28 

IX) pH Optima (Count Avg) 

Total-P (mg P/L)

pH Optima

0.0 0.05 0.10 0.15 0.20

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Total Nitrogen (mg N/L)

pH Optima

01234

2.0

2.5

3.0

3.5

4.0

4.5

5.0

TIN(mg/L)

pH Optima

01234

2.0

2.5

3.0

3.5

4.0

4.5

5.0

pH

pH Optima

45678

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Conductance, field (umhos/cm)

pH Optima

0 100 200 300 400 500

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Color

pH Optima

0 100 200 300 400 500

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Stream-Figure 9a. Exploratory Analysis Plots for Stream Data,

 (pH Optima versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-60
 29 

Models: 

1) Response pH Optima not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.8643 0.8438 3.3944 0.0011 

 TPL 0.1542 0.0692 2.2288 0.0288 

 TNL 0.1406 0.1521 0.9245 0.3582 

 TINL -0.0852 0.0734 -1.1614 0.2491 

 CondL 0.3172 0.1234 2.5707 0.0121 

 pH -0.0300 0.0950 -0.3157 0.7531 

 ColorL -0.0903 0.1037 -0.8712 0.3864 

Residual standard error: 0.6594 on 76 degrees of freedom 

Multiple R-Squared: 0.2722 Adjusted R-squared: 0.2147 

F-statistic: 4.737 on 6 and 76 degrees of freedom, the p-value is 0.0003785 

2) Response pH Optima transformed by the logarithm transformation: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0421 0.2619 3.9785 0.0002 

 TPL 0.0603 0.0215 2.8061 0.0064 

 TNL 0.0449 0.0472 0.9509 0.3447 

 TINL -0.0275 0.0228 -1.2061 0.2315 

 CondL 0.1039 0.0383 2.7125 0.0083 

 pH -0.0049 0.0295 -0.1648 0.8695 

 ColorL -0.0323 0.0322 -1.0042 0.3185 

Residual standard error: 0.2047 on 76 degrees of freedom 

Multiple R-Squared: 0.33 Adjusted R-squared: 0.2772 

F-statistic: 6.24 on 6 and 76 degrees of freedom, the p-value is 0.00002313

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-61
 30 

3) Response pH Optima transformed by the Reciprocal transformation 

(Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.3606 0.0852 4.2334 0.0001 

 TPL -0.0232 0.0070 -3.3274 0.0014 

 TNL -0.0148 0.0154 -0.9613 0.3395 

 TINL 0.0092 0.0074 1.2468 0.2163 

 CondL -0.0354 0.0125 -2.8448 0.0057 

 pH 0.0001 0.0096 0.0096 0.9924 

 ColorL 0.0114 0.0105 1.0905 0.2790 

Residual standard error: 0.06657 on 76 degrees of freedom 

Multiple R-Squared: 0.3827 Adjusted R-squared: 0.334 

F-statistic: 7.854 on 6 and 76 degrees of freedom, the p-value is 1.353e-006 

4) Selected Model; Response pH Optima transformed by the Reciprocal 

transformation (Chosen in the Box-Cox Power Family):

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.4000 0.0435 9.1919 0.0000 

 TPL -0.0209 0.0061 -3.4516 0.0008 

 CondL -0.0361 0.0080 -4.5171 0.0000 

Residual standard error: 0.06772 on 92 degrees of freedom 

Multiple R-Squared: 0.3019 Adjusted R-squared: 0.2868 

F-statistic: 19.9 on 2 and 92 degrees of freedom, the p-value is 6.597e-008

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-62
 31 

X) Stream Diatom Index 

Total-P (mg P/L)

Stream Diatom Index

0.0 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Stream Diatom Index

01234

0

20

40

60

80

100

TIN(mg/L)

Stream Diatom Index

01234

0

20

40

60

80

100

pH

Stream Diatom Index

45678

0

20

40

60

80

100

Conductance, field (umhos/cm)

Stream Diatom Index

0 100 200 300 400 500

0

20

40

60

80

100

Color

Stream Diatom Index

0 100 200 300 400 500

0

20

40

60

80

100

Stream-Figure 10a. Exploratory Analysis Plots for Stream Data,

 (Stream Diatom Index versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-63
 32 

Models: 

1) Response Stream Diatom Index not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 64.8417 19.6893 3.2932 0.0015 

 TPL -8.8330 1.6144 -5.4714 0.0000 

 TNL 0.9227 3.5492 0.2600 0.7956 

 TINL 2.1027 1.7117 1.2284 0.2231 

 CondL -8.8859 2.8789 -3.0866 0.0028 

 pH -2.8275 2.2169 -1.2754 0.2060 

 ColorL 5.7664 2.4187 2.3841 0.0196 

Residual standard error: 15.38 on 76 degrees of freedom 

Multiple R-Squared: 0.5959 Adjusted R-squared: 0.564 

F-statistic: 18.68 on 6 and 76 degrees of freedom, the p-value is 3.202e-013 

2) Response Stream Diatom Index transformed by the Square-Root 

transformation (Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 7.5253 1.3535 5.5597 0.0000 

 TPL -0.5950 0.1110 -5.3610 0.0000 

 TNL 0.0608 0.2440 0.2491 0.8039 

 TINL 0.1610 0.1177 1.3681 0.1753 

 CondL -0.5576 0.1979 -2.8174 0.0062 

 pH -0.1915 0.1524 -1.2568 0.2127 

 ColorL 0.4553 0.1663 2.7384 0.0077 

Residual standard error: 1.058 on 76 degrees of freedom 

Multiple R-Squared: 0.5855 Adjusted R-squared: 0.5527 

F-statistic: 17.89 on 6 and 76 degrees of freedom, the p-value is 8.127e-013 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-64
 33 

3) Response Stream Diatom Index transformed by arcsin(sqrt(x)) (Not a 

percentage, try this anyway) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.9839 0.2389 4.1174 0.0001 

 TPL -0.1095 0.0196 -5.5874 0.0000 

 TNL 0.0123 0.0431 0.2849 0.7765 

 TINL 0.0259 0.0208 1.2452 0.2169 

 CondL -0.1053 0.0349 -3.0127 0.0035 

 pH -0.0359 0.0269 -1.3327 0.1866 

 ColorL 0.0641 0.0294 2.1838 0.0321 

Residual standard error: 0.1867 on 76 degrees of freedom 

Multiple R-Squared: 0.5951 Adjusted R-squared: 0.5632 

F-statistic: 18.62 on 6 and 76 degrees of freedom, the p-value is 3.422e-013 

4) Selected Model; Response Stream Diatom Index not transformed:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 46.4025 15.4090 3.0114 0.0035 

 TPL -9.6199 1.4873 -6.4681 0.0000 

 TINL 2.9075 1.2094 2.4040 0.0185 

 CondL -10.5584 1.9702 -5.3589 0.0000 

 ColorL 7.5285 1.9743 3.8133 0.0003 

Residual standard error: 15.21 on 81 degrees of freedom 

Multiple R-Squared: 0.5895 Adjusted R-squared: 0.5692 

F-statistic: 29.08 on 4 and 81 degrees of freedom, the p-value is 5.44e-015 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-65
 

Appendix 6-C

 

Statistical Analysis of Stream Data-Periphyton Metrics 

(Weaver Region Peninsula, Some Initial Results) 

 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-66
 1 

Statistical Analysis of Stream Data-Periphyton Metrics 

(Weaver Region Peninsula, Some Initial Results) 

 

 Xu-Feng Niu 

Department of Statistics 

Florida State University 

Tallahassee, FL 32306 

March 15 – May 12, 2009 

Technical Report Submitted to 

the Florida Department of Environmental Protection 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-67
 2 

I) Pollution Sensitive Diatoms 

Notes: 

a) Correlation Matrix: 

 TP TN TIN TKN Nox Cond pH Color 

 TP 1.00 0.41 0.11 0.37 0.06 0.21 -0.03 0.05 

 TN 0.41 1.00 0.32 0.84 0.25 -0.10 -0.31 0.42 

 TIN 0.11 0.32 1.00 -0.23 0.99 0.07 0.18 -0.24 

 TKN 0.37 0.84 -0.23 1.00 -0.31 -0.13 -0.42 0.56 

 Nox 0.06 0.25 0.99 -0.31 1.00 0.06 0.22 -0.29 

 Cond 0.21 -0.10 0.07 -0.13 0.06 1.00 0.47 -0.41 

 pH -0.03 -0.31 0.18 -0.42 0.22 0.47 1.00 -0.66 

Color 0.05 0.42 -0.24 0.56 -0.29 -0.41 -0.66 1.00 

 

b) TP, TN, TIN, Cond, and Color are transformed by the 

Logarithm transformation. 

c) pH is not transformed. 

d)box.cox Transformations to Multinormality 

 Estimated transformation parameters 

 TP TN TIN Cond Color 

 -0.014 0.49 0.13 0.16 0.22 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-68
 3 

Total-P (mg P/L)

Poll sensitive diatoms 

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Poll sensitve diatoms 

0123

0

20

40

60

80

100

TIN(mg/L)

Poll sensitve diatoms 

0.0 0.5 1.0 1.5

0

20

40

60

80

100

pH

Poll sensitve diatoms 

5678

0

20

40

60

80

100

Conductance, field (umhos/cm)

Poll sensitve diatoms 

0 500 1000 1500

0

20

40

60

80

100

Color

Poll sensitve diatoms 

0 200 400 600 800

0

20

40

60

80

100

Stream-Figure 1a. Exploratory Analysis Plots for Stream Data,

 (Poll Sensitve Diatoms versus Predictors; Red: pH<6.5)

Notes: 

1) Outliers TP=2.3 and TP=2.39 are removed. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-69
 4 

Models: 

1) Response PollSens not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 134.8908 18.9148 7.1315 0.0000 

 TPL -0.1265 1.5427 -0.0820 0.9347 

 TNL 2.0823 2.4055 0.8656 0.3876 

 TINL -1.1322 1.2382 -0.9143 0.3616 

 CondL -3.2891 1.9396 -1.6958 0.0914 

 pH -13.4605 2.3858 -5.6419 0.0000 

 ColorL -1.3871 1.5285 -0.9075 0.3652 

Residual standard error: 16.95 on 217 degrees of freedom 

Multiple R-Squared: 0.336 Adjusted R-squared: 0.3176 

F-statistic: 18.3 on 6 and 217 degrees of freedom, the p-value is 0 

 

2) Response PollSens transformed by Square-Root (Chosen in the 

Box-Cox Power Transformation Family) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 13.9918 2.0773 6.7356 0.0000 

 TPL 0.0123 0.1694 0.0727 0.9421 

 TNL 0.3017 0.2642 1.1421 0.2547 

 TINL -0.1768 0.1360 -1.3005 0.1948 

 CondL -0.4461 0.2130 -2.0942 0.0374 

 pH -1.1374 0.2620 -4.3410 0.0000 

 ColorL -0.0259 0.1679 -0.1544 0.8774 

Residual standard error: 1.861 on 217 degrees of freedom 

Multiple R-Squared: 0.3092 Adjusted R-squared: 0.2901 

F-statistic: 16.18 on 6 and 217 degrees of freedom, the p-value is 2.22e-015 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-70
 5 

3) Response PollSens transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.7432 0.2456 7.0973 0.0000 

 TPL 0.0006 0.0200 0.0302 0.9759 

 TNL 0.0312 0.0312 0.9979 0.3194 

 TINL -0.0191 0.0161 -1.1865 0.2367 

 CondL -0.0506 0.0252 -2.0079 0.0459 

 pH -0.1521 0.0310 -4.9101 0.0000 

 ColorL -0.0072 0.0198 -0.3640 0.7162 

Residual standard error: 0.2201 on 217 degrees of freedom 

Multiple R-Squared: 0.3294 Adjusted R-squared: 0.3108 

F-statistic: 17.76 on 6 and 217 degrees of freedom, the p-value is 1.11e-016 

4) Selected Model; Response PollSens not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 111.6550 9.6280 11.5969 0.0000 

 pH -13.2084 1.3675 -9.6589 0.0000 

Residual standard error: 16.83 on 279 degrees of freedom 

Multiple R-Squared: 0.2506 Adjusted R-squared: 0.2479 

F-statistic: 93.29 on 1 and 279 degrees of freedom, the p-value is 0 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-71
 6 

II) Pollution tolerant diatoms 

 

Total-P (mg P/L)

Poll Tol diatoms 

0.0 0.1 0.2 0.3 0.4 0.5

0

10

20

30

40

50

60

Total Nitrogen (mg N/L)

Poll Tol diatoms 

0123

0

10

20

30

40

50

60

TIN(mg/L)

Poll Tol diatoms 

0.0 0.5 1.0 1.5

0

10

20

30

40

50

60

pH

Poll Tol diatoms 

5678

0

10

20

30

40

50

60

Conductance, field (umhos/cm)

Poll Tol diatoms 

0 500 1000 1500

0

10

20

30

40

50

60

Color

Poll Tol diatoms 

0 200 400 600 800

0

10

20

30

40

50

60

Stream-Figure 2a. Exploratory Analysis Plots for Stream Data,

 (Poll Tol Diatoms versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-72
 7 

Models: 

1) Response PollTol not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -31.1282 20.2500 -1.5372 0.1257 

 TPL 4.3075 1.6516 2.6081 0.0097 

 TNL -5.1871 2.5753 -2.0142 0.0452 

 TINL 0.1772 1.3256 0.1337 0.8938 

 CondL -0.1900 2.0765 -0.0915 0.9272 

 pH 7.1399 2.5542 2.7953 0.0056 

 ColorL 3.0451 1.6364 1.8608 0.0641 

Residual standard error: 18.15 on 217 degrees of freedom 

Multiple R-Squared: 0.1025 Adjusted R-squared: 0.07773 

F-statistic: 4.132 on 6 and 217 degrees of freedom, the p-value is 0.0005951 

 

 

2) Response PollTol transformed by Square-Root (Chosen in the BoxCox Power Transformation Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -3.9953 2.3898 -1.6718 0.0960 

 TPL 0.4305 0.1949 2.2085 0.0283 

 TNL -0.7680 0.3039 -2.5270 0.0122 

 TINL 0.0876 0.1564 0.5596 0.5763 

 CondL -0.1161 0.2451 -0.4738 0.6361 

 pH 1.0592 0.3014 3.5138 0.0005 

 ColorL 0.5338 0.1931 2.7641 0.0062 

Residual standard error: 2.142 on 217 degrees of freedom 

Multiple R-Squared: 0.1203 Adjusted R-squared: 0.09602 

F-statistic: 4.948 on 6 and 217 degrees of freedom, the p-value is 0.00009087 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-73
 8 

3) Response PollTol transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.4169 0.2763 -1.5092 0.1327 

 TPL 0.0529 0.0225 2.3461 0.0199 

 TNL -0.0853 0.0351 -2.4285 0.0160 

 TINL 0.0079 0.0181 0.4395 0.6607 

 CondL -0.0121 0.0283 -0.4279 0.6691 

 pH 0.1150 0.0348 3.2995 0.0011 

 ColorL 0.0548 0.0223 2.4546 0.0149 

Residual standard error: 0.2476 on 217 degrees of freedom 

Multiple R-Squared: 0.1139 Adjusted R-squared: 0.08937 

F-statistic: 4.648 on 6 and 217 degrees of freedom, the p-value is 0.0001818 

4) Selected Model; Response PollTol transformed by the Square-Root: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -4.0714 2.3524 -1.7308 0.0849 

 TPL 0.4223 0.1840 2.2948 0.0227 

 TNL -0.6744 0.2567 -2.6269 0.0092 

 pH 0.9763 0.2451 3.9826 0.0001 

 ColorL 0.4878 0.1709 2.8549 0.0047 

Residual standard error: 2.134 on 219 degrees of freedom 

Multiple R-Squared: 0.1183 Adjusted R-squared: 0.1022 

F-statistic: 7.347 on 4 and 219 degrees of freedom, the p-value is 0.00001433

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-74
 9 

III) Percentage cells tolerant of low O2 

 

Total-P (mg P/L)

% cells tol of low O2

0.0 0.1 0.2 0.3 0.4 0.5

20

40

60

80

100

Total Nitrogen (mg N/L)

% cells tol of low O2

0123

20

40

60

80

100

TIN(mg/L)

% cells tol of low O2

0.0 0.5 1.0 1.5

20

40

60

80

100

pH

% cells tol of low O2

5678

20

40

60

80

100

Conductance, field (umhos/cm)

% cells tol of low O2

0 500 1000 1500

20

40

60

80

100

Color

% cells tol of low O2

0 200 400 600 800

20

40

60

80

100

Stream-Figure 3a. Exploratory Analysis Plots for Stream Data,

 (% cells tol of low O2 versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-75
 10 

Models: 

1) Response OxyTol not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 140.6197 22.7078 6.1926 0.0000 

 TPL -1.5336 1.8521 -0.8281 0.4085 

 TNL 8.5831 2.8879 2.9721 0.0033 

 TINL -0.8903 1.4865 -0.5989 0.5499 

 CondL 0.2619 2.3286 0.1125 0.9105 

 pH -9.3330 2.8643 -3.2584 0.0013 

 ColorL -3.0498 1.8351 -1.6620 0.0980 

Residual standard error: 20.35 on 217 degrees of freedom 

Multiple R-Squared: 0.1366 Adjusted R-squared: 0.1127 

F-statistic: 5.722 on 6 and 217 degrees of freedom, the p-value is 0.0000152 

2) Response OxyTol transformed by the Power 1.5 (Chosen in the 

Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1522.3646 265.6376 5.7310 0.0000 

 TPL -16.8162 21.6657 -0.7762 0.4385 

 TNL 103.2271 33.7826 3.0556 0.0025 

 TINL -12.1177 17.3897 -0.6968 0.4867 

 CondL 7.3693 27.2396 0.2705 0.7870 

 pH -122.0659 33.5062 -3.6431 0.0003 

 ColorL -41.1808 21.4668 -1.9184 0.0564 

Residual standard error: 238 on 217 degrees of freedom 

Multiple R-Squared: 0.1491 Adjusted R-squared: 0.1256 

F-statistic: 6.339 on 6 and 217 degrees of freedom, the p-value is 3.667e-006

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-76
 11 

3) Response OxyTol transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.9202 0.2695 7.1241 0.0000 

 TPL -0.0160 0.0220 -0.7282 0.4673 

 TNL 0.1016 0.0343 2.9635 0.0034 

 TINL -0.0140 0.0176 -0.7920 0.4292 

 CondL 0.0100 0.0276 0.3618 0.7179 

 pH -0.1231 0.0340 -3.6216 0.0004 

 ColorL -0.0403 0.0218 -1.8504 0.0656 

Residual standard error: 0.2415 on 217 degrees of freedom 

Multiple R-Squared: 0.143 Adjusted R-squared: 0.1193 

F-statistic: 6.033 on 6 and 217 degrees of freedom, the p-value is 7.412e-006 

4) Selected Model; Response OxyTol transformed by arcsin(sqrt(x)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.4388 0.1534 9.3773 0.0000 

 TNL 0.0825 0.0258 3.2008 0.0015 

 pH -0.0590 0.0219 -2.6959 0.0075 

Residual standard error: 0.2477 on 252 degrees of freedom 

Multiple R-Squared: 0.08788 Adjusted R-squared: 0.08064 

F-statistic: 12.14 on 2 and 252 degrees of freedom, the p-value is 9.263e-006 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-77
 12 

IV) Percentage cells preferring oligosaprobic condition 

 

Total-P (mg P/L)

Saprobic % Cells

0.0 0.1 0.2 0.3 0.4 0.5

40

60

80

100

Total Nitrogen (mg N/L)

Saprobic % Cells

0123

40

60

80

100

TIN(mg/L)

Saprobic % Cells

0.0 0.5 1.0 1.5

40

60

80

100

pH

Saprobic % Cells

5678

40

60

80

100

Conductance, field (umhos/cm)

Saprobic % Cells

0 500 1000 1500

40

60

80

100

Color

Saprobic % Cells

0 200 400 600 800

40

60

80

100

Stream-Figure 4a. Exploratory Analysis Plots for Stream Data,

 (Saprobic % Cells versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-78
 13 

Models: 

1) Response Sapr not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 123.6331 20.2185 6.1148 0.0000 

 TPL -3.1141 1.6490 -1.8884 0.0603 

 TNL 5.2947 2.5713 2.0592 0.0407 

 TINL 0.4133 1.3236 0.3123 0.7551 

 CondL 0.1018 2.0733 0.0491 0.9609 

 pH -7.0538 2.5503 -2.7659 0.0062 

 ColorL -1.4413 1.6339 -0.8821 0.3787 

Residual standard error: 18.12 on 217 degrees of freedom 

Multiple R-Squared: 0.1085 Adjusted R-squared: 0.0839 

F-statistic: 4.404 on 6 and 217 degrees of freedom, the p-value is 0.0003188 

2) Response Sapr transformed by the Power 1.5 (Chosen in the BoxCox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1330.3452 245.9825 5.4083 0.0000 

 TPL -36.7703 20.0626 -1.8328 0.0682 

 TNL 65.7367 31.2829 2.1014 0.0368 

 TINL 3.5451 16.1030 0.2201 0.8260 

 CondL 2.5803 25.2241 0.1023 0.9186 

 pH -94.4991 31.0270 -3.0457 0.0026 

 ColorL -21.9771 19.8784 -1.1056 0.2701 

Residual standard error: 220.4 on 217 degrees of freedom 

Multiple R-Squared: 0.1163 Adjusted R-squared: 0.0919 

F-statistic: 4.761 on 6 and 217 degrees of freedom, the p-value is 0.0001399 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-79
 14 

3) Response Sapr transformed by arcsin(sqrt(x)) (Theoretical 

Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.7838 0.2552 6.9897 0.0000 

 TPL -0.0383 0.0208 -1.8418 0.0669 

 TNL 0.0705 0.0325 2.1735 0.0308 

 TINL 0.0003 0.0167 0.0196 0.9844 

 CondL 0.0089 0.0262 0.3398 0.7343 

 pH -0.1052 0.0322 -3.2691 0.0013 

 ColorL -0.0245 0.0206 -1.1859 0.2369 

Residual standard error: 0.2287 on 217 degrees of freedom 

Multiple R-Squared: 0.1196 Adjusted R-squared: 0.09521 

F-statistic: 4.911 on 6 and 217 degrees of freedom, the p-value is 0.00009892 

 

 

4) Selected Model; Response Sapr transformed by arcsin(sqrt(x)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.5089 0.1439 10.4853 0.0000 

 TNL 0.0575 0.0242 2.3770 0.0182 

 pH -0.0584 0.0205 -2.8486 0.0048 

Residual standard error: 0.2323 on 252 degrees of freedom 

Multiple R-Squared: 0.07037 Adjusted R-squared: 0.06299 

F-statistic: 9.538 on 2 and 252 degrees of freedom, the p-value is 0.0001016 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-80
 15 

V) Van Dam Trophic State Index 

 

Total-P (mg P/L)

Van Dam TSI

0.0 0.1 0.2 0.3 0.4 0.5

1

2

3

4

5

Total Nitrogen (mg N/L)

Van Dam TSI

0123

1

2

3

4

5

TIN(mg/L)

Van Dam TSI

0.0 0.5 1.0 1.5

1

2

3

4

5

pH

Van Dam TSI

5678

1

2

3

4

5

Conductance, field (umhos/cm)

Van Dam TSI

0 500 1000 1500

1

2

3

4

5

Color

Van Dam TSI

0 200 400 600 800

1

2

3

4

5

Stream-Figure 5a. Exploratory Analysis Plots for Stream Data,

 (Van Dam TSI versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-81
 16 

Models: 

1) Response TSI not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.4379 0.6308 -0.6942 0.4883 

 TPL -0.1022 0.0514 -1.9858 0.0483 

 TNL -0.0449 0.0802 -0.5595 0.5764 

 TINL 0.0887 0.0413 2.1487 0.0328 

 CondL 0.1568 0.0647 2.4246 0.0161 

 pH 0.3726 0.0796 4.6824 0.0000 

 ColorL 0.0990 0.0510 1.9426 0.0534 

Residual standard error: 0.5653 on 217 degrees of freedom 

Multiple R-Squared: 0.2912 Adjusted R-squared: 0.2716 

F-statistic: 14.86 on 6 and 217 degrees of freedom, the p-value is 3.264e-014 

2) Response TSI transformed by the Power 1.5 (Chosen in the BoxCox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -3.8750 1.7424 -2.2239 0.0272 

 TPL -0.2985 0.1421 -2.1005 0.0368 

 TNL -0.1463 0.2216 -0.6604 0.5097 

 TINL 0.2479 0.1141 2.1736 0.0308 

 CondL 0.4479 0.1787 2.5068 0.0129 

 pH 0.9647 0.2198 4.3893 0.0000 

 ColorL 0.2659 0.1408 1.8881 0.0603 

Residual standard error: 1.561 on 217 degrees of freedom 

Multiple R-Squared: 0.2809 Adjusted R-squared: 0.261 

F-statistic: 14.13 on 6 and 217 degrees of freedom, the p-value is 1.45e-013 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-82
 17 

3) Selected Model; Response TSI not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.4890 0.6242 -0.7835 0.4342 

 TPL -0.1100 0.0498 -2.2102 0.0281 

 TINL 0.0782 0.0345 2.2623 0.0246 

 CondL 0.1553 0.0636 2.4430 0.0153 

 ColorL 0.0930 0.0465 2.0015 0.0466 

 pH 0.3787 0.0786 4.8160 0.0000 

Residual standard error: 0.5618 on 221 degrees of freedom 

Multiple R-Squared: 0.288 Adjusted R-squared: 0.2719 

F-statistic: 17.88 on 5 and 221 degrees of freedom, the p-value is 7.105e-015 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-83
 18 

VI) TP Sensitive Diatoms 

 

Total-P (mg P/L)

TP sensitive diatoms

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TP sensitive diatoms

0123

0

20

40

60

80

100

TIN(mg/L)

TP sensitive diatoms

0.0 0.5 1.0 1.5

0

20

40

60

80

100

pH

TP sensitive diatoms

5678

0

20

40

60

80

100

Conductance, field (umhos/cm)

TP sensitive diatoms

0 500 1000 1500

0

20

40

60

80

100

Color

TP sensitive diatoms

0 200 400 600 800

0

20

40

60

80

100

Stream-Figure 6a. Exploratory Analysis Plots for Stream Data,

 (TP sensitive diatoms versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-84
 19 

Models: 

1) Response TP sensitive diatoms not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 108.8607 24.9735 4.3590 0.0000 

 TPL -4.6016 2.0369 -2.2592 0.0249 

 TNL -1.0872 3.1760 -0.3423 0.7324 

 TINL 2.8051 1.6349 1.7158 0.0876 

 CondL -6.9191 2.5609 -2.7018 0.0074 

 pH -7.4074 3.1500 -2.3515 0.0196 

 ColorL 0.7870 2.0182 0.3899 0.6970 

Residual standard error: 22.38 on 217 degrees of freedom 

Multiple R-Squared: 0.2018 Adjusted R-squared: 0.1797 

F-statistic: 9.142 on 6 and 217 degrees of freedom, the p-value is 6.366e-009 

2) Response TP sensitive diatoms transformed by the Square-Root 

transformation (Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 10.6185 2.5965 4.0895 0.0001 

 TPL -0.3959 0.2118 -1.8692 0.0629 

 TNL -0.1402 0.3302 -0.4246 0.6715 

 TINL 0.2902 0.1700 1.7071 0.0892 

 CondL -0.6833 0.2663 -2.5664 0.0109 

 pH -0.5077 0.3275 -1.5502 0.1226 

 ColorL 0.2221 0.2098 1.0586 0.2910 

Residual standard error: 2.327 on 217 degrees of freedom 

Multiple R-Squared: 0.1632 Adjusted R-squared: 0.14 

F-statistic: 7.051 on 6 and 217 degrees of freedom, the p-value is 7.157e-007 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-85
 20 

3) Response TP sensitive diatoms transformed by arcsin(sqrt(x)) 

(Theoretical Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.3909 0.3136 4.4359 0.0000 

 TPL -0.0511 0.0256 -1.9999 0.0468 

 TNL -0.0162 0.0399 -0.4050 0.6859 

 TINL 0.0342 0.0205 1.6677 0.0968 

 CondL -0.0822 0.0322 -2.5572 0.0112 

 pH -0.0804 0.0396 -2.0323 0.0433 

 ColorL 0.0183 0.0253 0.7203 0.4721 

Residual standard error: 0.281 on 217 degrees of freedom 

Multiple R-Squared: 0.1808 Adjusted R-squared: 0.1581 

F-statistic: 7.98 on 6 and 217 degrees of freedom, the p-value is 8.642e-008 

 

4) Selected Model; Response TP sensitive diatoms not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 119.1198 14.2085 8.3837 0.0000 

 TPL -3.7968 1.7530 -2.1659 0.0313 

 TINL 2.3749 1.1842 2.0055 0.0460 

 CondL -8.0270 2.3192 -3.4611 0.0006 

 pH -7.5417 2.5663 -2.9388 0.0036 

Residual standard error: 21.73 on 247 degrees of freedom 

Multiple R-Squared: 0.2172 Adjusted R-squared: 0.2046 

F-statistic: 17.14 on 4 and 247 degrees of freedom, the p-value is 2.032e-012 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-86
 21 

VII) TIN Sensitive Diatoms 

Total-P (mg P/L)

TIN sensitive diatoms

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TIN sensitive diatoms

0123

0

20

40

60

80

100

TIN(mg/L)

TIN sensitive diatoms

0.0 0.5 1.0 1.5

0

20

40

60

80

100

pH

TIN sensitive diatoms

5678

0

20

40

60

80

100

Conductance, field (umhos/cm)

TIN sensitive diatoms

0 500 1000 1500

0

20

40

60

80

100

Color

TIN sensitive diatoms

0 200 400 600 800

0

20

40

60

80

100

Stream-Figure 7a. Exploratory Analysis Plots for Stream Data,

 (TIN sensitive diatoms versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-87
 22 

Models: 

1) Response TIN sensitive diatoms not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 81.4594 18.4760 4.4089 0.0000 

 TPL -1.7296 1.5069 -1.1477 0.2523 

 TNL -3.3848 2.3497 -1.4405 0.1512 

 TINL 1.4517 1.2095 1.2002 0.2314 

 CondL -2.1360 1.8946 -1.1274 0.2608 

 pH -8.5897 2.3305 -3.6858 0.0003 

 ColorL 1.7533 1.4931 1.1743 0.2416 

Residual standard error: 16.56 on 217 degrees of freedom 

Multiple R-Squared: 0.2079 Adjusted R-squared: 0.1859 

F-statistic: 9.49 on 6 and 217 degrees of freedom, the p-value is 2.937e-009 

2) Response TIN sensitive diatoms transformed by the SQRT 

transformation ( Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 8.2210 2.1772 3.7759 0.0002 

 TPL -0.1434 0.1776 -0.8074 0.4203 

 TNL -0.5037 0.2769 -1.8191 0.0703 

 TINL 0.2613 0.1425 1.8336 0.0681 

 CondL -0.3352 0.2233 -1.5012 0.1348 

 pH -0.5440 0.2746 -1.9809 0.0489 

 ColorL 0.3260 0.1759 1.8530 0.0652 

Residual standard error: 1.951 on 217 degrees of freedom 

Multiple R-Squared: 0.1387 Adjusted R-squared: 0.1149 

F-statistic: 5.826 on 6 and 217 degrees of freedom, the p-value is 0.00001196 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-88
 23 

3) Response TIN sensitive diatoms transformed by arcsin(sqrt(x)) 

(Theoretical Transformation to stabilize the variance) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0399 0.2507 4.1480 0.0000 

 TPL -0.0180 0.0204 -0.8812 0.3792 

 TNL -0.0551 0.0319 -1.7291 0.0852 

 TINL 0.0269 0.0164 1.6374 0.1030 

 CondL -0.0360 0.0257 -1.4003 0.1628 

 pH -0.0812 0.0316 -2.5684 0.0109 

 ColorL 0.0323 0.0203 1.5953 0.1121 

Residual standard error: 0.2247 on 217 degrees of freedom 

Multiple R-Squared: 0.16 Adjusted R-squared: 0.1368 

F-statistic: 6.89 on 6 and 217 degrees of freedom, the p-value is 1.035e-006 

 

4) Selected Model; Response TIN sensitive diatoms Not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 89.8510 9.2278 9.7370 0.0000 

 pH -10.3954 1.3106 -7.9315 0.0000 

Residual standard error: 16.13 on 279 degrees of freedom 

Multiple R-Squared: 0.184 Adjusted R-squared: 0.1811 

F-statistic: 62.91 on 1 and 279 degrees of freedom, the p-value is 5.262e-014 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-89
 24 

VIII) N Metab (Count Avg) 

Total-P (mg P/L)

N Metab (Count Avg)

0.0 0.1 0.2 0.3 0.4 0.5

1.0

1.5

2.0

2.5

3.0

Total Nitrogen (mg N/L)

N Metab (Count Avg)

0123

1.0

1.5

2.0

2.5

3.0

TIN(mg/L)

N Metab (Count Avg)

0.0 0.5 1.0 1.5

1.0

1.5

2.0

2.5

3.0

pH

N Metab (Count Avg)

5678

1.0

1.5

2.0

2.5

3.0

Conductance, field (umhos/cm)

N Metab (Count Avg)

0 500 1000 1500

1.0

1.5

2.0

2.5

3.0

Color

N Metab (Count Avg)

0 200 400 600 800

1.0

1.5

2.0

2.5

3.0

Stream-Figure 8a. Exploratory Analysis Plots for Stream Data,

 (N Metab (Count Avg) versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-90
 25 

Models: 

1) Response N Metab not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.6845 0.3380 2.0254 0.0441 

 TPL 0.0230 0.0276 0.8342 0.4051 

 TNL -0.1168 0.0430 -2.7164 0.0071 

 TINL 0.0254 0.0221 1.1500 0.2514 

 CondL -0.0118 0.0347 -0.3415 0.7331 

 pH 0.1577 0.0426 3.6997 0.0003 

 ColorL 0.0447 0.0273 1.6381 0.1029 

Residual standard error: 0.3029 on 217 degrees of freedom 

Multiple R-Squared: 0.1441 Adjusted R-squared: 0.1205 

F-statistic: 6.091 on 6 and 217 degrees of freedom, the p-value is 6.493e-006 

 

2) Response N Metab transformed by the logarithm transformation 

 (Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.1572 0.1876 -0.8375 0.4032 

 TPL 0.0074 0.0153 0.4855 0.6278 

 TNL -0.0627 0.0239 -2.6269 0.0092 

 TINL 0.0163 0.0123 1.3262 0.1862 

 CondL -0.0067 0.0192 -0.3465 0.7293 

 pH 0.0989 0.0237 4.1784 0.0000 

 ColorL 0.0298 0.0152 1.9675 0.0504 

Residual standard error: 0.1681 on 217 degrees of freedom 

Multiple R-Squared: 0.1613 Adjusted R-squared: 0.1382 

F-statistic: 6.958 on 6 and 217 degrees of freedom, the p-value is 8.856e-007 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-91
 26 

3) Response N Metab transformed by the Reciprocal transformation: 

 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0528 0.1082 9.7320 0.0000 

 TPL -0.0012 0.0088 -0.1389 0.8896 

 TNL 0.0347 0.0138 2.5237 0.0123 

 TINL -0.0106 0.0071 -1.4998 0.1351 

 CondL 0.0039 0.0111 0.3548 0.7231 

 pH -0.0631 0.0136 -4.6228 0.0000 

 ColorL -0.0198 0.0087 -2.2697 0.0242 

Residual standard error: 0.09694 on 217 degrees of freedom 

Multiple R-Squared: 0.1787 Adjusted R-squared: 0.156 

F-statistic: 7.872 on 6 and 217 degrees of freedom, the p-value is 1.105e-007 

4) Selected Model; Response N Metab transformed by Reciprocal: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.8511 0.0623 13.6531 0.0000 

 TNL 0.0231 0.0105 2.2055 0.0283 

 pH -0.0389 0.0089 -4.3775 0.0000 

Residual standard error: 0.1006 on 252 degrees of freedom 

Multiple R-Squared: 0.1126 Adjusted R-squared: 0.1056 

F-statistic: 15.99 on 2 and 252 degrees of freedom, the p-value is 2.902e-007 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-92
 27 

IX) pH Optima (Count Avg) 

Total-P (mg P/L)

pH Optima

0.0 0.1 0.2 0.3 0.4 0.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Total Nitrogen (mg N/L)

pH Optima

0123

2.0

2.5

3.0

3.5

4.0

4.5

5.0

TIN(mg/L)

pH Optima

0.0 0.5 1.0 1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

pH

pH Optima

5678

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Conductance, field (umhos/cm)

pH Optima

0 500 1000 1500

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Color

pH Optima

0 200 400 600 800

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Stream-Figure 9a. Exploratory Analysis Plots for Stream Data,

 (pH Optima versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-93
 28 

Models: 

1) Response pH Optima not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.2625 0.5436 4.1619 0.0000 

 TPL 0.0315 0.0443 0.7110 0.4778 

 TNL -0.0566 0.0691 -0.8188 0.4138 

 TINL 0.0107 0.0356 0.3011 0.7636 

 CondL 0.0497 0.0557 0.8916 0.3736 

 pH 0.1799 0.0686 2.6234 0.0093 

 ColorL -0.0221 0.0439 -0.5026 0.6158 

Residual standard error: 0.4871 on 217 degrees of freedom 

Multiple R-Squared: 0.1449 Adjusted R-squared: 0.1213 

F-statistic: 6.129 on 6 and 217 degrees of freedom, the p-value is 5.945e-006 

2) Response pH Optima transformed by the logarithm 

transformation (No transformation chosen in the Box-Cox family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.7773 0.1542 5.0421 0.0000 

 TPL 0.0069 0.0126 0.5490 0.5835 

 TNL -0.0148 0.0196 -0.7544 0.4514 

 TINL 0.0047 0.0101 0.4635 0.6435 

 CondL 0.0152 0.0158 0.9634 0.3364 

 pH 0.0635 0.0194 3.2634 0.0013 

 ColorL -0.0020 0.0125 -0.1633 0.8704 

Residual standard error: 0.1381 on 217 degrees of freedom 

Multiple R-Squared: 0.1751 Adjusted R-squared: 0.1523 

F-statistic: 7.676 on 6 and 217 degrees of freedom, the p-value is 1.722e-007 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-94
 29 

3) Response pH Optima transformed by the Reciprocal 

transformation: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.4618 0.0459 10.0710 0.0000 

 TPL -0.0015 0.0037 -0.4113 0.6813 

 TNL 0.0039 0.0058 0.6650 0.5067 

 TINL -0.0018 0.0030 -0.6016 0.5481 

 CondL -0.0046 0.0047 -0.9888 0.3239 

 pH -0.0225 0.0058 -3.8820 0.0001 

 ColorL -0.0006 0.0037 -0.1525 0.8789 

Residual standard error: 0.04109 on 217 degrees of freedom 

Multiple R-Squared: 0.2043 Adjusted R-squared: 0.1823 

F-statistic: 9.286 on 6 and 217 degrees of freedom, the p-value is 4.613e-009 

4) Selected Model; Response pH Optima transformed by the 

Reciprocal transformation:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.4371 0.0232 18.8251 0.0000 

 pH -0.0216 0.0033 -6.5434 0.0000 

Residual standard error: 0.04059 on 279 degrees of freedom 

Multiple R-Squared: 0.133 Adjusted R-squared: 0.1299 

F-statistic: 42.82 on 1 and 279 degrees of freedom, the p-value is 2.868e-010 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-95
 30 

X) Stream Diatom Index 

Total-P (mg P/L)

Stream Diatom Index

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Stream Diatom Index

0123

0

20

40

60

80

100

TIN(mg/L)

Stream Diatom Index

0.0 0.5 1.0 1.5

0

20

40

60

80

100

pH

Stream Diatom Index

5678

0

20

40

60

80

100

Conductance, field (umhos/cm)

Stream Diatom Index

0 500 1000 1500

0

20

40

60

80

100

Color

Stream Diatom Index

0 200 400 600 800

0

20

40

60

80

100

Stream-Figure 10a. Exploratory Analysis Plots for Stream Data,

 (Stream Diatom Index versus Predictors; Red: pH<6.5)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-96
 31 

Models: 

1) Response Stream Diatom Index not transformed: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 167.8576 25.5516 6.5694 0.0000 

 TPL -1.5593 2.0840 -0.7482 0.4551 

 TNL 6.8927 3.2495 2.1211 0.0350 

 TINL -1.2963 1.6727 -0.7750 0.4392 

 CondL -2.5703 2.6202 -0.9810 0.3277 

 pH -11.6625 3.2230 -3.6186 0.0004 

 ColorL -2.9433 2.0649 -1.4254 0.1555 

Residual standard error: 22.9 on 217 degrees of freedom 

Multiple R-Squared: 0.178 Adjusted R-squared: 0.1553 

F-statistic: 7.832 on 6 and 217 degrees of freedom, the p-value is 1.209e-007 

2) Response Stream Diatom Index transformed by the Power 1.5 

transformation (Chosen in the Box-Cox Power Family): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1832.5424 294.1563 6.2298 0.0000 

 TPL -15.9677 23.9917 -0.6655 0.5064 

 TNL 86.2913 37.4094 2.3067 0.0220 

 TINL -17.3772 19.2566 -0.9024 0.3678 

 CondL -24.2028 30.1640 -0.8024 0.4232 

 pH -149.3720 37.1034 -4.0258 0.0001 

 ColorL -38.1747 23.7714 -1.6059 0.1097 

Residual standard error: 263.6 on 217 degrees of freedom 

Multiple R-Squared: 0.196 Adjusted R-squared: 0.1738 

F-statistic: 8.819 on 6 and 217 degrees of freedom, the p-value is 1.309e-008 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-97
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3) Response Stream Diatom Index transformed by arcsin(sqrt(x)) (Not 

a percentage, try this anyway) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.4409 0.3080 7.9247 0.0000 

 TPL -0.0181 0.0251 -0.7191 0.4728 

 TNL 0.0778 0.0392 1.9870 0.0482 

 TINL -0.0167 0.0202 -0.8267 0.4093 

 CondL -0.0265 0.0316 -0.8397 0.4020 

 pH -0.1728 0.0389 -4.4470 0.0000 

 ColorL -0.0420 0.0249 -1.6879 0.0929 

Residual standard error: 0.276 on 217 degrees of freedom 

Multiple R-Squared: 0.2133 Adjusted R-squared: 0.1916 

F-statistic: 9.807 on 6 and 217 degrees of freedom, the p-value is 1.457e-009 

4) Selected Model; Response Stream Diatom Index transformed by 

arcsin(sqrt(x)):

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.9927 0.1613 12.3580 0.0000 

 pH -0.1413 0.0229 -6.1707 0.0000 

Residual standard error: 0.2819 on 279 degrees of freedom 

Multiple R-Squared: 0.1201 Adjusted R-squared: 0.1169 

F-statistic: 38.08 on 1 and 279 degrees of freedom, the p-value is 2.385e-009 

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Appendix 6-D 

Change Point Analysis of Stream Data-Periphyton Metrics vs TP 

(Weaver Region Panhandle, Responses Adjusted) 

Xu-Feng Niu 

April 20 – May 8, 2009 

Technical Report Submitted to the 

Florida Department of Environmental Protection 

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Change Point Analysis of Stream Data-Periphyton Metrics vs TP 

(Weaver Region Panhandle, Responses Adjusted) 

Xu-Feng Niu 

Department of Statistics 

Florida State University 

Tallahassee, FL 32306 

April 20 – May 8, 2009 

Technical Report Submitted to 

the Florida Department of Environmental Protection 

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I. The Detection Procedure 

Niu et al. (2000) introduced an iterative procedure for detecting and modeling level-shift change 

points. The procedure is similar to that suggested by Chang (1982) and further developed by 

Chang et al. (1988) for detecting outliers and level shifts in time series analysis. Statistical 

details of this procedure can also be found in Pankratz (1991, Chapter 8). 

For simplicity, let us consider a response variable Y, after an appropriate transformation. Suppose 

that observations {( , ) Xi i Y , i n  1, 2, ,  } are available where n is the sample size and X is an 

independent variable. Moreover, we assume that the observations are arranged in the following 

manner: 

 The values { , Xi i n  1, 2, ,  } are distinct. If several ' Y s i are corresponding to a 

single X value, the median of the ' Y s i is taken to be the response value for the X value. 

 {( , ) Xi i Y , i n  1, 2, ,  } are sorted according to the values of X from least to greatest. 

For each integer l 1, define the step variable ( ) 0 i S l  for i l  and ( ) 1 i S l  for i l  . 

Step 1. Fit the linear regression model: 

0 1 () () () () Y l lSl l i i      i , i n  1, 2, ,  , (1) 

where for a fixed l, the ( )' i  l s are assumed to be independent and identically distributed normal 

random variables with mean zero and variance 2  ( )l . 

Step 2. Calculate the values { 1 1 L l l se l ( ) ( ) / ( ( ))   

  , l n  2, 3, , ( 1)   } where 1 se l ( ( ))  is the 

estimated standard error of 1  ( )l  . 

Step 3. Let 1 Ll L L Ln ( ) max{ (2), (3), , ( 1)}    and compare 1 L l( ) with the critical value C=3.0 

(or C=3.5). The critical value C=3.0 (or C=3.5) corresponds roughly to   0.10 (or  0.05), 

or the 10% (or the 5%) significance level, based on the simulation results of Chang et al. (1988). 

If 1 L l( ) is significant, we conclude that the response Y has a change point at 1 Xl with a levelshift 1  ( )l  . 

Step 4. Let *

11 1 () () Y Y lSl ii i    . Repeat Steps 1-3 on the new response variable * Yi for 

detecting a possible second change point. Continue the process until no further change point can 

be identified. 

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Step 5. Suppose that k change points are detected in the response variable Y and the 

corresponding X values are 1 2 {, ,, }k Xll l X X  . Fit the model 

0 11 2 2 () () () Y Sl Sl Sl i ii k           i k i , i n  1, 2, ,  . (2) 

Then the estimated coefficients 1 2 {, , , }   k

    will be the k estimated level-shift values. 

II. Model Comparison 

Model (2) fits a step function 0 11 2 2 () () () ii k i k       Sl Sl Sl  to estimate the mean (or 

median) value of the response variable Y and the predictor variable X. In practice, many other 

models may be considered to describe the relationship between Y and X. In particular, if the 

scatter plot of observations { ( , ) Xi i Y , i n  1, 2, ,  } shows a straight line or a smooth curve 

pattern, a linear regression model or a nonlinear smooth-curve model should be fitted to the data 

instead of the step-function change point model in (2). 

For the response variable Y and the predictor variable X, the linear regression model has the 

form: 

 Y X i ii   0 1   , i n  1, 2, ,  . (3) 

If the relationship between Y and X is nonlinear, many smooth-curve models may be considered. 

One of the choices is transforming the predictor variable X and fitting a regression model. For 

example, we may use the natural logarithm transformation log(X) instead of X as the predictor 

variable and fit the regression model: 

 0 1 log( ) Y X i i      i , i n  1, 2, ,  . (4) 

When different models are fitted to the observations { ( , ) Xi i Y , i n  1, 2, ,  }, model selection 

techniques need to be used to decide which model fits the data better. Statistical inferences such 

as estimation and prediction will then be based on the best model selected. The Bayesian 

Information Criterion (SBC) suggested by Schwartz (1978) is one of the popular criteria for 

model comparison. For a fitted model (linear or nonlinear) with p parameters, the SBC is defined 

as 

SBC(p) =  2 log(maximum likelihood function) + p  log(n), 

where the likelihood function is based on the distribution assumption of the model such as 

normal or log-normal or other distribution families, and n is the sample size. When the random 

errors i  ’s have a normal distribution, the SBC(p) has the simplified form: 

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SBC(p) =   2

1

ˆ log ( ) /( 1) n

i i i n YY np      + p  log(n), (5) 

where ˆY i is the fitted value based on one of the candidate models and 2

1

ˆ ( ) n

i i i

Y Y    is the 

Residual Sum of Squares (RSS) based on the fitted candidate model. 

 Intuitively, there are two parts in (5), the first part is 

  2

1

ˆ log ( ) /( 1) n

i i i n YY np      = 

2

n logˆ , 

which is a measure of the goodness-of-fit of the candidate model. In general, increasing the 

number of parameters in a model will improve the goodness-of-fit of the model to the data 

regardless how many parameters are in the true model that generated the data. When a model 

with too many predicators (significant or not significant ones) is fitted to a data set, we may get a 

perfect fit but the model will be useless for inference such as prediction. In statistics, fitting a 

model with too many unnecessary parameters is called over-fitting. The second part in SBC, p 

log(n), puts a penalty term on the complexity of a candidate model, which will increase when the 

number of parameters in a candidate model increases. Thus the criterion SBC requires a 

candidate model fitting the data well and penalizing the complexity of the model. For a group of 

candidate models, the SBC value can be calculated for each of the models and the preferred 

model is the one with the lowest SBC value. 

III. Change Point Analysis of Stream Data-Periphyton Metrics vs TP 

 In this report, we present results of Total Phosphorus (TP) change point analysis of stream 

periphyton metrics after adjusted for effects of other variables on the responses. Specifically, 

with each periphyton metric as the response variable and TP, TN, TIN, Conductivity, Color, pH 

as predictors, we select the best linear regression model with the best transformations (in terms 

of R-squares). Then variables other than TP are removed from the fitted model. Change point 

analysis is performed on the residuals verses TP. 

 After removing missing values and rounding TP to three digits after the decimal, there are 59 

distinct TP values ranging from 0.002 to 0.200 in the Weaver Panhandle region. For a given 

response variable, if several values correspond to the same TP value, median is taken as the 

value corresponding to this TP point. For example, if there are three replicates of a response 

variable y, say 30, 40, 50, corresponding to TP=0.010, we will take y=40 as the response value 

for TP=0.010. 

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1) Pollution Sensitive Diatoms VS TP 

Regression Model used for adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 32.5436 25.8431 1.2593 0.2113 

 TPL -11.0050 2.4738 -4.4486 0.0000 

 ColorL 6.9044 2.9799 2.3170 0.0229 

 CondL -14.6813 3.3183 -4.4244 0.0000 

Residual standard error: 25.97 on 87 degrees of freedom 

Multiple R-Squared: 0.4146 Adjusted R-squared: 0.3945 

F-statistic: 20.54 on 3 and 87 degrees of freedom, the p-value 

is 3.747e-010 

Figure 1a. Change-Point Model (Step Function) 

Response adjusted for ColorL and CondL

Total-P (mg P/L)

Poll sensitve diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

20

40

60

80

100

120

0.022

0.083

0.022

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Change Points: TP=0.022 (the point after change occurs) with the test statistic of 5.09 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.022, 0.083] based on 

500 bootstrapping samples with median=0.022. 

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Figure 1a+. Change-Point Model (Step Function) 

Response adjusted for ColorL and CondL

Total-P (mg P/L)

Poll sensitve diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

20

40

60

80

100

120

0.010

0.131

0.076

Change Point: TP=0.022 (the point after change occurs) with the test 

statistic of 5.09 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.083 with the test 

statistic of 1.72 and confidence level about 75%; Bootstrapping 95% 

Confidence Interval [0.010, 0.131] based on 500 bootstrapping samples with 

median=0.076. 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 96.9502 5.9139 16.3937 0.0000 

 TP022 -29.8791 7.3864 -4.0451 0.0002 

 TP083 -12.5678 6.7346 -1.8661 0.0674 

Residual standard error: 22.13 on 55 degrees of freedom 

Multiple R-Squared: 0.3569 Adjusted R-squared: 0.3335 

F-statistic: 15.26 on 2 and 55 degrees of freedom, the p-value 

is 5.345e-006 

SBC=373.9

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Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 1b presents the two 

fitted models. 

Figure 1b. Linear Model (Solid Black) and Non-Linear Model 

(Poll Sensitive Diatoms on log(TP)) 

Response adjusted for ColorL and CondL 

Total-P (mg P/L)

Poll sensitve diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

20

40

60

80

100

120

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The three fitted regression models are presented in Table 1. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are 369.9, 378.9, and 

371.1, respectively. Thus, the change-point model was the best model among the three models. 

Based on the fitted change-point model, the change point at TP=0.022 is extremely significant 

(with p-values =0.0000). The Poll Sensitive Diatoms at the change point decreased about 35%. 

Table 1. Fitted Regression Models 

(Response adjusted for ColorL and CondL) 

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 96.9502 6.0435 16.0420 0.0000 

 TP022 -35.3061 6.9387 -5.0883 0.0000 

Residual standard error: 22.61 on 56 degrees of freedom 

Multiple R-Squared: 0.3162 Adjusted R-squared: 0.304 

F-statistic: 25.89 on 1 and 56 degrees of freedom, the p-value 

is 4.362e-006 

 

SBC Value: 369.9 

Model 2. Linear Regression Model (Poll Sensitive Diatoms vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 85.4509 5.1794 16.4981 0.0000 

 TP -239.2086 63.6339 -3.7591 0.0004 

Residual standard error: 24.44 on 56 degrees of freedom 

Multiple R-Squared: 0.2015 Adjusted R-squared: 0.1872 

F-statistic: 14.13 on 1 and 56 degrees of freedom, the p-value 

is 0.0004089 

SBC Value: 378.9 

Model 3. Non-Linear Regression Model (Poll Sensitive Diatoms vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 25.2971 9.5949 2.6365 0.0108 

 TPL -14.1579 2.8758 -4.9231 0.0000 

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Residual standard error: 22.84 on 56 degrees of freedom 

Multiple R-Squared: 0.3021 Adjusted R-squared: 0.2896 

F-statistic: 24.24 on 1 and 56 degrees of freedom, the p-value 

is 7.883e-006 

SBC Value: 371.1 

2) Log(Pollution tolerant diatoms) vs TP 

Regression Model used for adjustment: 

 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -2.8286 1.1733 -2.4109 0.0178 

 TPL 0.5847 0.1424 4.1067 0.0001 

 pH 0.9337 0.1495 6.2440 0.0000 

Residual standard error: 1.655 on 96 degrees of freedom 

Multiple R-Squared: 0.4458 Adjusted R-squared: 0.4343 

F-statistic: 38.62 on 2 and 96 degrees of freedom, the p-value 

is 4.95e-013 

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Figure 2a. Change-Point Model (Step Function) 

Response adjusted for pH

Total-P (mg P/L)

log(Poll Tol diatoms) (Adjusted)

0.0 0.05 0.10 0.15 0.20

-8

-6

-4

-2

0.008 0.078

0.010

Change Points: TP=0.010 (the point after change occurs) with the test 

statistic of 4.3 and confidence level over 95%; Bootstrapping 95% Confidence 

Interval [0.008, 0.078] based on 500 bootstrapping samples with median 

=0.010. 

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Figure 2a+. Change-Point Model (Step Function) 

Response adjusted for pH

Total-P (mg P/L)

log(Poll Tol diatoms) (Adjusted)

0.0 0.05 0.10 0.15 0.20

-8

-6

-4

-2

0.008 0.094

0.067

Change Point: TP=0.010 (the point after change occurs) with the test 

statistic of 4.3 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.078 with the test 

statistic of 2.3 and confidence level about 80%; Bootstrapping 95% 

Confidence Interval [0.008, 0.094] based on 500 bootstrapping samples with 

median =0.067. 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -6.7417 0.5259 -12.8191 0.0000 

 TP010 2.1382 0.5746 3.7214 0.0005 

 TP078 0.8450 0.3641 2.3210 0.0240 

Residual standard error: 1.288 on 55 degrees of freedom 

Multiple R-Squared: 0.3152 Adjusted R-squared: 0.2903 

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F-statistic: 12.66 on 2 and 55 degrees of freedom, the p-value 

is 0.00003007 

SBC=45.9

Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 2b presents the two 

fitted models. 

Figure 2b. Linear Model (Solid Black) and Non-Linear Model 

 (log(Poll Tolerant Diatoms) on log(TP)) 

Response adjusted for pH 

Total-P (mg P/L)

log(Poll Tol diatoms) (Adjusted)

0.0 0.05 0.10 0.15 0.20

-8

-6

-4

-2

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The three fitted regression models are presented in Table 2. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are 41.9, 51.6, and 

44.3, respectively. Thus, the non-linear model was the best model among the three models. 

Based on the fitted change-point model, the change point at TP=0.010 is extremely significant 

(with p-values =0.0001). The log(Poll Tolerant Diatoms) at the change point increased about 

2.48 

Table 2. Fitted Regression Models (Response adjusted for pH) 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -6.7417 0.5461 -12.3447 0.0000 

 TP010 2.4794 0.5768 4.2988 0.0001 

Residual standard error: 1.338 on 56 degrees of freedom 

Multiple R-Squared: 0.2481 Adjusted R-squared: 0.2347 

F-statistic: 18.48 on 1 and 56 degrees of freedom, the p-value 

is 0.00006924 

SBC Value: 41.9 

Model 2. Linear Regression Model (log(Poll Tolerant Diatoms) vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -5.1561 0.3085 -16.7141 0.0000 

 TP 9.9742 3.7900 2.6317 0.0110 

Residual standard error: 1.455 on 56 degrees of freedom 

Multiple R-Squared: 0.1101 Adjusted R-squared: 0.09417 

F-statistic: 6.926 on 1 and 56 degrees of freedom, the p-value 

is 0.01096 

SBC Value: 51.6 

Model 3. Non-Linear Regression Model (log(Poll Tolerant Diatoms) vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -2.3773 0.5737 -4.1440 0.0001 

 TPL 0.6757 0.1719 3.9300 0.0002 

Residual standard error: 1.366 on 56 degrees of freedom 

Multiple R-Squared: 0.2162 Adjusted R-squared: 0.2022 

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F-statistic: 15.44 on 1 and 56 degrees of freedom, the p-value 

is 0.0002358 

SBC Value: 44.3 

3) arcsin(sqrt(Percentage cells tolerant of low O2)) vs TP 

Regression Model for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0990 0.2294 4.7902 0.0000 

 TPL -0.0869 0.0189 -4.5903 0.0000 

 pH -0.0727 0.0201 -3.6088 0.0005 

 ColorL 0.0520 0.0235 2.2098 0.0297 

Residual standard error: 0.1909 on 90 degrees of freedom 

Multiple R-Squared: 0.4307 Adjusted R-squared: 0.4117 

F-statistic: 22.7 on 3 and 90 degrees of freedom, the p-value is 

4.966e-011 

Figure 3a. Change-Point Model (Step Function) 

Response adjusted for pH and ColorL

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Total-P (mg P/L)

arcsin(sqrt(% cells tol of low O2))(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.5

1.0

1.5

2.0

0.010 0.093

0.015

Change Points: TP=0.015 (the point after change occurs) with the test 

statistic of 4.32 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.010, 0.093] based on 500 bootstrapping samples with 

median =0.015. 

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Figure 3a+. Change-Point Model (Step Function) 

Response adjusted for pH and ColorL

Total-P (mg P/L)

arcsin(sqrt(% cells tol of low O2))(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.5

1.0

1.5

2.0

0.018 0.093 0.149

Change Point: TP=0.015 (the point after change occurs) with the test 

statistic of 4.32 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.090 with the test 

statistic of 2.06 and confidence level about 80%; Bootstrapping 95% 

Confidence Interval [0.018, 0.149] based on 500 bootstrapping samples with 

median =0.093. 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.6019 0.0557 28.7520 0.0000 

 TP015 -0.2343 0.0638 -3.6713 0.0005 

 TP090 -0.1153 0.0539 -2.1376 0.0370 

Residual standard error: 0.1762 on 55 degrees of freedom 

Multiple R-Squared: 0.3074 Adjusted R-squared: 0.2822 

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F-statistic: 12.2 on 2 and 55 degrees of freedom, the p-value is 

0.0000411 

SBC=-185.6

Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 3b presents the two 

fitted models. 

Figure 3b. Linear Model (Solid Black) and Non-Linear Model 

(arcsin(sqrt(OxyTol)) on log(TP)) 

 Response adjusted for pH and ColorL

Total-P (mg P/L)

arcsin(sqrt(% cells tol of low O2))(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.5

1.0

1.5

2.0

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The three fitted regression models are presented in Table 3. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are -189.7, -181.2, and 

-187.1, respectively. Thus, the change-point model was the best model among the three models. 

Based on the fitted change-point model, the change point at TP=0.015 is highly significant 

(with p-values =0.0001). The arcsin(sqrt( OxyTol)) at the change point decreased about 0.27. 

. 

Table 3. Fitted Regression Models (Response adjusted for pH and ColorL)

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.6019 0.0575 27.8773 0.0000 

 TP015 -0.2728 0.0632 -4.3184 0.0001 

Residual standard error: 0.1817 on 56 degrees of freedom 

Multiple R-Squared: 0.2498 Adjusted R-squared: 0.2364 

F-statistic: 18.65 on 1 and 56 degrees of freedom, the p-value is 0.00006479 

 

 

SBC Value: -189.7 

Model 2. Linear Regression Model (arcsin(sqrt(OxyTol)) vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.4710 0.0414 35.4981 0.0000 

 TP -1.4839 0.5091 -2.9147 0.0051 

Residual standard error: 0.1955 on 56 degrees of freedom 

Multiple R-Squared: 0.1317 Adjusted R-squared: 0.1162 

F-statistic: 8.496 on 1 and 56 degrees of freedom, the p-value is 0.005109 

 

SBC Value: -181.2 

Model 3. Non-Linear Regression Model (arcsin(sqrt(OxyTol)) vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0856 0.0781 13.9068 0.0000 

 TPL -0.0917 0.0234 -3.9186 0.0002 

Residual standard error: 0.1859 on 56 degrees of freedom 

Multiple R-Squared: 0.2152 Adjusted R-squared: 0.2012 

F-statistic: 15.36 on 1 and 56 degrees of freedom, the p-value is 0.0002448 

 

SBC Value: -187.1 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-118
 21 

4) arcsin(sqrt(Percentage cells preferring oligosaprobic condition)) 

Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1991 0.1847 6.4918 0.0000 

 TPL -0.0754 0.0152 -4.9456 0.0000 

 pH -0.0663 0.0162 -4.0892 0.0001 

 ColorL 0.0405 0.0189 2.1400 0.0351 

Residual standard error: 0.1537 on 90 degrees of freedom 

Multiple R-Squared: 0.4734 Adjusted R-squared: 0.4558 

F-statistic: 26.97 on 3 and 90 degrees of freedom, the p-value 

is 1.558e-012 Figure 4a. Change-Point Model (Step Function) 

Response adjusted for pH and ColorL

Total-P (mg P/L)

arcsin(sqrt(Saprobic % Cells)) (Adjusted)

0.0 0.05 0.10 0.15 0.20

1.0

1.2

1.4

1.6

1.8

0.015 0.131

0.018

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-119
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Change Points: TP=0.018 (the point after change occurs) with the test 

statistic of 4.28 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.015, 0.131] based on 500 bootstrapping samples with 

median =0.018. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-120
 23 

Figure 4a+. Change-Point Model (Step Function) 

Response adjusted for pH and ColorL

Total-P (mg P/L)

arcsin(sqrt(Saprobic % Cells)) (Adjusted)

0.0 0.05 0.10 0.15 0.20

1.0

1.2

1.4

1.6

1.8

Change Point: TP=0.018 (the point after change occurs) with the test 

statistic of 4.283 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.131 with the test 

statistic of 1.98 and confidence level about 80%; 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.6088 0.0429 37.5318 0.0000 

 TP018 -0.1944 0.0489 -3.9777 0.0002 

 TP131 -0.1299 0.0650 -1.9986 0.0506 

Residual standard error: 0.1485 on 55 degrees of freedom 

Multiple R-Squared: 0.2974 Adjusted R-squared: 0.2718 

F-statistic: 11.64 on 2 and 55 degrees of freedom, the p-value 

is 0.00006099 

SBC=-206.0

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Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 4b presents the two 

fitted models. 

Figure 4b. Linear Model (Solid Black) and Non-Linear Model 

(arcsin(sqrt(Saprobic % Cells)) on log(TP)) 

Response adjusted for pH and ColorL

Total-P (mg P/L)

arcsin(sqrt(Saprobic % Cells)) (Adjusted)

0.0 0.05 0.10 0.15 0.20

1.0

1.2

1.4

1.6

1.8

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-122
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The three fitted regression models are presented in Table 4. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are -210.1, -201.8, and 

 -208.2.1, respectively. Thus, the change-point model was the best model among the three 

models. Based on the fitted change-point model, the change point at TP=0.018 is extremely 

significant (with p-values =0.0001). The arcsin(sqrt(Saprobic % Cells)) at the change point 

decreased about 0.21. 

Table 4. Fitted Regression Models (Response adjusted for pH and ColorL) 

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.6088 0.0440 36.5670 0.0000 

 TP018 -0.2114 0.0494 -4.2781 0.0001 

Residual standard error: 0.1524 on 56 degrees of freedom 

Multiple R-Squared: 0.2463 Adjusted R-squared: 0.2329 

F-statistic: 18.3 on 1 and 56 degrees of freedom, the p-value is 

0.00007426 

 

SBC Value: -210.1 

Model 2. Linear Regression Model (arcsin(sqrt(Saprobic % Cells)) vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.5199 0.0347 43.7822 0.0000 

 TP -1.2321 0.4265 -2.8887 0.0055 

Residual standard error: 0.1638 on 56 degrees of freedom 

Multiple R-Squared: 0.1297 Adjusted R-squared: 0.1141 

F-statistic: 8.345 on 1 and 56 degrees of freedom, the p-value 

is 0.005491 

SBC Value:-201.8 

Model 3. Non-Linear Regression Model (arcsin(sqrt(Saprobic % Cells)) vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1946 0.0651 18.3606 0.0000 

 TPL -0.0778 0.0195 -3.9912 0.0002 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-123
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Residual standard error: 0.1549 on 56 degrees of freedom 

Multiple R-Squared: 0.2215 Adjusted R-squared: 0.2076 

F-statistic: 15.93 on 1 and 56 degrees of freedom, the p-value 

is 0.0001931 

 

SBC Value: -208.2 

5) sqrt(Van Dam Trophic State Index) vs TP 

Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.8881 0.2259 8.3583 0.0000 

 TPL 0.1358 0.0216 6.2822 0.0000 

 ColorL -0.0468 0.0260 -1.7980 0.0756 

 CondL 0.1148 0.0290 3.9586 0.0002 

Residual standard error: 0.227 on 87 degrees of freedom 

Multiple R-Squared: 0.4679 Adjusted R-squared: 0.4496 

F-statistic: 25.5 on 3 and 87 degrees of freedom, the p-value is 

6.252e-012 

 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-124
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Figure 5a. Change-Point Model (Step Function) 

Response adjusted for ColorL and CondL

Total-P (mg P/L)

sqrt(Van Dam TSI) (Adjusted)

0.0 0.05 0.10 0.15 0.20

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.022 0.040

0.022

Change Points: TP=0.022 (the point after change occurs) with the test 

statistic of 6.02 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.022, 0.040] based on 500 bootstrapping samples with 

median=0.022. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-125
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Figure 5a+. Change-Point Model (Step Function) 

Response adjusted for ColorL and CondL 

Total-P (mg P/L)

sqrt(Van Dam TSI) (Adjusted)

0.0 0.05 0.10 0.15 0.20

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Change Point: TP=0.022 (the point after change occurs) with the test 

statistic of 6.02 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.131 with the test 

statistic of 2.27 and confidence level about 80%; 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1466 0.0535 21.4432 0.0000 

 TP022 0.3559 0.0626 5.6897 0.0000 

 TP131 0.2014 0.0879 2.2919 0.0258 

Residual standard error: 0.2001 on 55 degrees of freedom 

Multiple R-Squared: 0.4458 Adjusted R-squared: 0.4257 

F-statistic: 22.12 on 2 and 55 degrees of freedom, the p-value 

is 8.916e-008 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-126
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SBC=-170.2 

Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 5b presents the two 

fitted models. 

Figure 5b. Linear Model (Solid Black) and Non-Linear Model 

(sqrt(Van Dam Trophic State Index) on log(TP)) 

Response adjusted for ColorL and CondL

Total-P (mg P/L)

sqrt(Van Dam TSI) (Adjusted)

0.0 0.05 0.10 0.15 0.20

0.8

1.0

1.2

1.4

1.6

1.8

2.0

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The three fitted regression models are presented in Table 5. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are -174.28, -163.4, and 

 -174.33, respectively. Thus, the change-point model and the non-linear regression model were 

better than the linear regression model. Based on the fitted change-point model, the change point 

at TP=0.022 is extremely significant (with p-values =0.0000). The sqrt(Van Dam Trophic State 

Index) at the change point increased about 0.38. 

.Table 5. Fitted Regression Models 

(Response adjusted for ColorL and CondL) 

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1466 0.0555 20.6726 0.0000 

 TP022 0.3834 0.0637 6.0202 0.0000 

Residual standard error: 0.2075 on 56 degrees of freedom 

Multiple R-Squared: 0.3929 Adjusted R-squared: 0.3821 

F-statistic: 36.24 on 1 and 56 degrees of freedom, the p-value 

is 1.41e-007 

 

 

SBC Value: -174.28 

Model 2. Linear Regression Model (sqrt(Van Dam Trophic State Index) vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.2658 0.0483 26.2033 0.0000 

 TP 2.6870 0.5935 4.5274 0.0000 

Residual standard error: 0.2279 on 56 degrees of freedom 

Multiple R-Squared: 0.2679 Adjusted R-squared: 0.2549 

F-statistic: 20.5 on 1 and 56 degrees of freedom, the p-value is 

0.00003166 

 

SBC Value: -163.4 

Model 3. Non-Linear Regression Model (sqrt(Van Dam Trophic State Index) vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.9362 0.0871 22.2210 0.0000 

 TPL 0.1574 0.0261 6.0259 0.0000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-128
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Residual standard error: 0.2075 on 56 degrees of freedom 

Multiple R-Squared: 0.3934 Adjusted R-squared: 0.3825 

F-statistic: 36.31 on 1 and 56 degrees of freedom, the p-value 

is 1.38e-007 

SBC Value: -174.33 

6) arcsin(sqrt(TP Sensitive Diatoms)) vs TP 

Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.0529 0.2081 -0.2543 0.7999 

 TPL -0.1335 0.0315 -4.2425 0.0001 

 ColorL 0.0681 0.0369 1.8454 0.0685 

 TNL -0.1257 0.0528 -2.3817 0.0195 

Residual standard error: 0.3391 on 84 degrees of freedom 

Multiple R-Squared: 0.2521 Adjusted R-squared: 0.2254 

F-statistic: 9.438 on 3 and 84 degrees of freedom, the p-value 

is 0.00001925 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-129
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Figure 6a. Change-Point Model (Step Function) 

Response adjusted for ColorL and TNL

Total-P (mg P/L)

arcsin(sqrt(TP Sensitive Diatoms)) (Adjusted)

0.0 0.05 0.10 0.15 0.20

0.0

0.5

1.0

1.5

0.010 0.027 0.060

Change Points: TP=0.022 (the point after change occurs) with the test 

statistic of 4.74 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.010, 0.060] based on 500 bootstrapping samples with 

median=0.027. 

Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 6b presents the two 

fitted models. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-130
 33 

Figure 6b. Linear Model (Solid Black) and Non-Linear Model 

(arcsin(sqrt(TP Sensitive Diatoms)) on log(TP)) 

Response adjusted for ColorL and TNL

Total-P (mg P/L)

arcsin(sqrt(TP Sensitive Diatoms))(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.0

0.5

1.0

1.5

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The three fitted regression models are presented in Table 6. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are -129.6, -118..9, and 

-127.1, respectively. Thus, the change-point model was the best model among the three models. 

Based on the fitted change-point model, the change point at TP=0.022 is extremely significant 

(with p-values =0.0000). The arcsin(sqrt(TP Sensitive Diatoms)) at the change point decreased 

about 0.44. 

Table 6. Fitted Regression Models (Response adjusted for ColorL and TNL)

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0775 0.0815 13.2215 0.0000 

 TP022 -0.4437 0.0936 -4.7421 0.0000 

Residual standard error: 0.3049 on 56 degrees of freedom 

Multiple R-Squared: 0.2865 Adjusted R-squared: 0.2738 

F-statistic: 22.49 on 1 and 56 degrees of freedom, the p-value 

is 0.00001497 

 

SBC Value: -129.6 

Model 2. Linear Regression Model (arcsin(sqrt(TP Sensitive Diatoms)) vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.9102 0.0709 12.8405 0.0000 

 TP -2.6497 0.8709 -3.0425 0.0036 

Residual standard error: 0.3344 on 56 degrees of freedom 

Multiple R-Squared: 0.1419 Adjusted R-squared: 0.1265 

F-statistic: 9.257 on 1 and 56 degrees of freedom, the p-value 

is 0.003568 

 

SBC Value: -118.9 

Model 3. Non-Linear Regression Model (arcsin(sqrt(TP Sensitive Diatoms)) vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.1970 0.1309 1.5052 0.1379 

 TPL -0.1716 0.0392 -4.3739 0.0001 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-132
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Residual standard error: 0.3117 on 56 degrees of freedom 

Multiple R-Squared: 0.2546 Adjusted R-squared: 0.2413 

F-statistic: 19.13 on 1 and 56 degrees of freedom, the p-value 

is 0.00005364 

SBC Value: -127.1 

7) TIN Sensitive Diatoms vs TP 

 Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 38.9760 18.0349 2.1611 0.0333 

 TPL -9.6582 2.5085 -3.8502 0.0002 

 CondL -9.2965 3.3079 -2.8104 0.0060 

Residual standard error: 28.07 on 92 degrees of freedom 

Multiple R-Squared: 0.2328 Adjusted R-squared: 0.2162 

F-statistic: 13.96 on 2 and 92 degrees of freedom, the p-value 

is 5.071e-006 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-133
 36 

Figure 7a. Change-Point Model (Step Function) 

Response adjusted for CondL

Total-P (mg P/L)

TIN sensitive diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

40

60

80

100

120

140

0.010 0.067

0.022

Change Points: TP=0.022 (the point after change occurs) with the test 

statistic of 4.24 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.010, 0.067] based on 500 bootstrapping samples with 

median=0.022. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-134
 37 

Figure 7a+. Change-Point Model (Step Function) 

Response adjusted for CondL

Total-P (mg P/L)

TIN sensitive diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

40

60

80

100

120

140

0.008 0.129

0.041

Change Point: TP=0.022 (the point after change occurs) with the test 

statistic of 4.24 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.067 with the test 

statistic of 1.78 and confidence level about 75%; Bootstrapping 95% 

Confidence Interval [0.008, 0.129] based on 500 bootstrapping samples with 

median=0.041. 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 99.8041 6.7940 14.6900 0.0000 

 TP022 -27.5216 8.9538 -3.0737 0.0033 

 TP067 -10.1840 7.7369 -1.3163 0.1935 

Residual standard error: 25.42 on 55 degrees of freedom 

Multiple R-Squared: 0.2663 Adjusted R-squared: 0.2397 

F-statistic: 9.983 on 2 and 55 degrees of freedom, the p-value 

is 0.0002001 

SBC=388.3

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-135
 38 

Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 7b presents the two 

fitted models. 

Figure 7b. Linear Model (Solid Black) and Non-Linear Model 

(TIN Sensitive Diatoms on log(TP)) 

Response adjusted for CondL 

Total-P (mg P/L)

TIN sensitive diatoms (Adjusted)

0.0 0.05 0.10 0.15 0.20

40

60

80

100

120

140

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-136
 39 

The three fitted regression models are presented in Table 7. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are 384.2, 393.95, and 

 387.8, respectively. Thus, the change-point model was the best model among the three models. 

Based on the fitted change-point model, the change point at TP=0.022 is extremely significant 

(with p-values =0.0001). The TIN Sensitive Diatoms at the change point decreased about 33%. 

Table 7. Fitted Regression Models (Response adjusted for CondL) 

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 99.8041 6.8383 14.5949 0.0000 

 TP022 -33.3079 7.8512 -4.2424 0.0001 

Residual standard error: 25.59 on 56 degrees of freedom 

Multiple R-Squared: 0.2432 Adjusted R-squared: 0.2297 

F-statistic: 18 on 1 and 56 degrees of freedom, the p-value is 

0.00008378 

SBC Value: 384.2 

Model 2. Linear Regression Model (TIN Sensitive Diatoms vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 86.3863 5.8991 14.6441 0.0000 

 TP -185.4610 72.4748 -2.5590 0.0132 

Residual standard error: 27.83 on 56 degrees of freedom 

Multiple R-Squared: 0.1047 Adjusted R-squared: 0.0887 

F-statistic: 6.548 on 1 and 56 degrees of freedom, the p-value 

is 0.01323 

SBC Value: 393.95 

Model 3. Non-Linear Regression Model (TIN Sensitive Diatoms vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 35.8035 11.0867 3.2294 0.0021 

 TPL -12.2215 3.3229 -3.6780 0.0005 

Residual standard error: 26.4 on 56 degrees of freedom 

Multiple R-Squared: 0.1946 Adjusted R-squared: 0.1802 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-137
 40 

F-statistic: 13.53 on 1 and 56 degrees of freedom, the p-value 

is 0.0005289 

SBC Value: 387.8 

8) Stream Diatom Index vs TP 

Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 46.4025 15.4090 3.0114 0.0035 

 TPL -9.6199 1.4873 -6.4681 0.0000 

 ColorL 7.5285 1.9743 3.8133 0.0003 

 CondL -10.5584 1.9702 -5.3589 0.0000 

 TINL 2.9075 1.2094 2.4040 0.0185 

Residual standard error: 15.21 on 81 degrees of freedom 

Multiple R-Squared: 0.5895 Adjusted R-squared: 0.5692 

F-statistic: 29.08 on 4 and 81 degrees of freedom, the p-value 

is 5.44e-015 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-138
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Figure 8a. Change-Point Model (Step Function) 

Response adjusted for ColorL, CondL, and TINL

Total-P (mg P/L)

Stream Diatom Index (Adjusted)

0.0 0.05 0.10 0.15 0.20

40

60

80

100

120

0.022

0.040

0.022

Change Points: TP=0.022 (the point after change occurs) with the test 

statistic of 6.45 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.022, 0.040] based on 500 bootstrapping samples with 

median=0.022. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-139
 42 

Figure 8a+. Change-Point Model (Step Function) 

Response adjusted for ColorL, CondL, and TINL

Total-P (mg P/L)

Stream Diatom Index (Adjusted)

0.0 0.05 0.10 0.15 0.20

40

60

80

100

120

0.008

0.131

0.083

Change Point: TP=0.022 (the point after change occurs) with the test 

statistic of 6.45 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.082 with the test 

statistic of 2.25 and confidence level about 80%; Bootstrapping 95% 

Confidence Interval [0.008, 0.131] based on 500 bootstrapping samples with 

median=0.083. 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 98.8309 3.5619 27.7470 0.0000 

 TP022 -23.5610 4.4819 -5.2569 0.0000 

 TP082 -10.3317 4.2248 -2.4455 0.0179 

Residual standard error: 13.33 on 52 degrees of freedom 

Multiple R-Squared: 0.4978 Adjusted R-squared: 0.4785 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-140
 43 

F-statistic: 25.77 on 2 and 52 degrees of freedom, the p-value 

is 1.673e-008 

SBC=301.8

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-141
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Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 8b presents the two 

fitted models. 

Figure 8b. Linear Model (Solid Black) and Non-Linear Model 

(Stream Diatom Index on log(TP)) 

Response adjusted for ColorL, CondL, and TINL

Total-P (mg P/L)

Stream Diatom Index (Adjusted)

0.0 0.05 0.10 0.15 0.20

40

60

80

100

120

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-142
 45 

The three fitted regression models are presented in Table 8. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are 297.8, 314.3, and 

301.3, respectively. Thus, the change-point model and the nonlinear model were better than the 

linear model. Based on the fitted change-point model, the change point at TP=0.022 is extremely 

significant (with p-values =0.0000). The Stream Diatom Index at the change point decreased 

about 28. 

Table 8. Fitted Regression Models 

Response adjusted for ColorL, CondL, and TINL

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 98.8309 3.7255 26.5285 0.0000 

 TP022 -27.8449 4.3149 -6.4532 0.0000 

Residual standard error: 13.94 on 53 degrees of freedom 

Multiple R-Squared: 0.44 Adjusted R-squared: 0.4294 

F-statistic: 41.64 on 1 and 53 degrees of freedom, the p-value 

is 3.414e-008 

 

 

SBC Value: 297.8 

Model 2. Linear Regression Model (Stream Diatom Index vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 89.1591 3.4556 25.8012 0.0000 

 TP -179.5329 43.3772 -4.1389 0.0001 

Residual standard error: 16.19 on 53 degrees of freedom 

Multiple R-Squared: 0.2443 Adjusted R-squared: 0.23 

F-statistic: 17.13 on 1 and 53 degrees of freedom, the p-value 

is 0.0001256 

SBC Value: 314.3 

Model 3. Non-Linear Regression Model (Stream Diatom Index vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 42.4807 6.2558 6.7906 0.0000 

 TPL -11.0683 1.8494 -5.9847 0.0000 

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Residual standard error: 14.39 on 53 degrees of freedom 

Multiple R-Squared: 0.4033 Adjusted R-squared: 0.392 

F-statistic: 35.82 on 1 and 53 degrees of freedom, the p-value 

is 1.915e-007 

SBC Value: 301.3 

9) (N Metab)-1 (Count Avg) vs TP 

Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.9197 0.0664 13.8481 0.0000 

 TPL -0.0352 0.0081 -4.3673 0.0000 

 pH -0.0591 0.0085 -6.9865 0.0000 

Residual standard error: 0.09371 on 96 degrees of freedom 

Multiple R-Squared: 0.4933 Adjusted R-squared: 0.4827 

F-statistic: 46.73 on 2 and 96 degrees of freedom, the p-value 

is 6.772e-015 

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Figure 9a. Change-Point Model (Step Function) 

Response adjusted for pH

Total-P (mg P/L)

 Reciprocal of N Metab (Adjusted)

0.0 0.05 0.10 0.15 0.20

0.8

0.9

1.0

1.1

1.2

0.015 0.093

0.015

Change Points: TP=0.015 (the point after change occurs) with the test 

statistic of 4.39 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.015, 0.093] based on 500 bootstrapping samples with 

median=0.015. 

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Figure 9a+. Change-Point Model (Step Function) 

Response adjusted for pH

Total-P (mg P/L)

Reciprocal of N Metab(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.8

0.9

1.0

1.1

1.2

Change Point: TP=0.015 (the point after change occurs) with the test 

statistic of 4.39 and confidence level over 95%; 

Potential Change Point (just for your information): TP=0.131 with the test 

statistic of 2.28 and confidence level about 80%; 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1386 0.0267 42.7134 0.0000 

 TP015 -0.1229 0.0297 -4.1430 0.0001 

 TP131 -0.0842 0.0368 -2.2891 0.0259 

Residual standard error: 0.0843 on 55 degrees of freedom 

Multiple R-Squared: 0.3207 Adjusted R-squared: 0.296 

F-statistic: 12.98 on 2 and 55 degrees of freedom, the p-value 

is 0.00002405 

SBC=-270.5

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Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 9b presents the two 

fitted models. 

Figure 9b. Linear Model (Solid Black) and Non-Linear Model 

((N Metab)-1 on log(TP)) 

Response adjusted for pH

Total-P (mg P/L)

Reciprocal of N Metab(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.8

0.9

1.0

1.1

1.2

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The three fitted regression models are presented in Table 9. The SBC values for the change-point 

model, the linear regression model, and the non-linear regression model are -274.6, -265.3, and 

 -270.2, respectively. Thus, the change-point model and the nonlinear model were better than the 

linear model. Based on the fitted change-point model, the change point at TP=0.015 is extremely 

significant (with p-values =0.0001). The (N Metab)-1 at the change point decreased about 

0.13. 

Table 9. Fitted Regression Models 

Response adjusted for pH

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.1386 0.0276 41.1828 0.0000 

 TP015 -0.1334 0.0304 -4.3898 0.0001 

Residual standard error: 0.08743 on 56 degrees of freedom 

Multiple R-Squared: 0.256 Adjusted R-squared: 0.2427 

F-statistic: 19.27 on 1 and 56 degrees of freedom, the p-value 

is 0.00005081 

SBC Value: -274.6 

Model 2. Linear Regression Model ((N Metab)-1 vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.0731 0.0201 53.4470 0.0000 

 TP -0.7031 0.2467 -2.8504 0.0061 

Residual standard error: 0.09472 on 56 degrees of freedom 

Multiple R-Squared: 0.1267 Adjusted R-squared: 0.1111 

F-statistic: 8.125 on 1 and 56 degrees of freedom, the p-value 

is 0.006102 

 

SBC Value: -265.3 

Model 3. Non-Linear Regression Model ((N Metab)-1 vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.8938 0.0381 23.4322 0.0000 

 TPL -0.0424 0.0114 -3.7093 0.0005 

Residual standard error: 0.09082 on 56 degrees of freedom 

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Multiple R-Squared: 0.1972 Adjusted R-squared: 0.1829 

F-statistic: 13.76 on 1 and 56 degrees of freedom, the p-value 

is 0.000479 

SBC Value: -270.2 

10) (pH Optima)-1 (Count Avg) vs TP 

Regression Model used for Adjustment: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.4000 0.0435 9.1919 0.0000 

 TPL -0.0209 0.0061 -3.4516 0.0008 

 CondL -0.0361 0.0080 -4.5171 0.0000 

Residual standard error: 0.06772 on 92 degrees of freedom 

Multiple R-Squared: 0.3019 Adjusted R-squared: 0.2868 

F-statistic: 19.9 on 2 and 92 degrees of freedom, the p-value is 

6.597e-008 

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Figure 10a. Change-Point Model (Step Function) 

Response adjusted for CondL

Total-P (mg P/L)

 Reciprocal of pHOp (Adjusted)

0.0 0.05 0.10 0.15 0.20

0.3

0.4

0.5

0.6

0.7

0.010 0.036

0.022

Change Points: TP=0.022 (the point after change occurs) with the test 

statistic of 4.44 and confidence level over 95%; Bootstrapping 95% 

Confidence Interval [0.010, 0.036] based on 500 bootstrapping samples with 

median=0.022. 

Model Comparison 

For the purpose of model comparison, two other models, the linear regression model in (3) and 

the non-linear regression model in (4), were also fitted to the data. Figure 10b presents the two 

fitted models. 

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Figure 10b. Linear Model (Solid Black) and Non-Linear Model 

((pH Optima)-1 on log(TP)) 

Response adjusted for CondL

Total-P (mg P/L)

Reciprocal of pHOp(Adjusted)

0.0 0.05 0.10 0.15 0.20

0.3

0.4

0.5

0.6

0.7

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The three fitted regression models are presented in Table 10. The SBC values for the changepoint model, the linear regression model, and the non-linear regression model are -326.8, -317.3, 

and -324.6, respectively. Thus, the change-point model and the nonlinear model were better 

than the linear model. Based on the fitted change-point model, the change point at TP=0.022 is 

extremely significant (with p-values =0.0000). The (pH Optima)-1 at the change point 

decreased about 0.08. 

Table 10. Fitted Regression Models 

Response adjusted for CondL

 

Model 1. Step-Function Regression (Change Point Model) : 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.5354 0.0149 35.9293 0.0000 

 TP022 -0.0760 0.0171 -4.4435 0.0000 

Residual standard error: 0.05575 on 56 degrees of freedom 

Multiple R-Squared: 0.2607 Adjusted R-squared: 0.2475 

F-statistic: 19.74 on 1 and 56 degrees of freedom, the p-value 

is 0.00004228 

SBC Value: -326.8 

Model 2. Linear Regression Model ((pH Optima)-1 vs TP): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.5067 0.0128 39.5049 0.0000 

 TP -0.4540 0.1576 -2.8809 0.0056 

Residual standard error: 0.06051 on 56 degrees of freedom 

Multiple R-Squared: 0.1291 Adjusted R-squared: 0.1135 

F-statistic: 8.3 on 1 and 56 degrees of freedom, the p-value is 

0.00561 

SBC Value: -317.3 

Model 3. Non-Linear Regression Model ((pH Optima)-1 vs log(TP)): 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.3843 0.0239 16.1101 0.0000 

 TPL -0.0295 0.0071 -4.1209 0.0001 

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Residual standard error: 0.0568 on 56 degrees of freedom 

Multiple R-Squared: 0.2327 Adjusted R-squared: 0.219 

F-statistic: 16.98 on 1 and 56 degrees of freedom, the p-value 

is 0.0001258 

SBC Value: -324.6 

IV) Summary: 

1) Pollution Sensitive Diatoms VS TP 

Change Points: TP=0.022 (the point after change occurs) with the test statistic of 5.09 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.022, 0.083] based on 

500 bootstrapping samples with median=0.022. 

2) Log(Pollution tolerant diatoms) vs TP 

Change Points: TP=0.010 (the point after change occurs) with the test statistic of 4.3 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.008, 0.078] based 

on 500 bootstrapping samples with median =0.010. 

3) arcsin(sqrt(Percentage cells tolerant of low O2)) vs TP 

Change Points: TP=0.015 (the point after change occurs) with the test statistic of 4.32 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.010, 0.093] based on 

500 bootstrapping samples with median =0.015. 

4) arcsin(sqrt(Percentage cells preferring oligosaprobic condition)) 

vs TP 

Change Points: TP=0.018 (the point after change occurs) with the test statistic of 4.28 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.015, 0.131] based 

on 500 bootstrapping samples with median =0.018. 

 5) sqrt(Van Dam Trophic State Index) vs TP 

Change Points: TP=0.022 (the point after change occurs) with the test statistic of 6.02 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.022, 0.040] based on 

500 bootstrapping samples with median=0.022. 

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6) arcsin(sqrt(TP Sensitive Diatoms)) vs TP 

Change Points: TP=0.022 (the point after change occurs) with the test statistic of 4.74 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.010, 0.060] based 

on 500 bootstrapping samples with median=0.027. 

7) TIN Sensitive Diatoms vs TP 

Change Points: TP=0.022 (the point after change occurs) with the test statistic of 4.24 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.010, 0.067] based on 

500 bootstrapping samples with median=0.022. 

8) Stream Diatom Index vs TP 

Change Points: TP=0.022 (the point after change occurs) with the test statistic of 6.45 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.022, 0.040] based on 

500 bootstrapping samples with median=0.022. 

9) (N Metab)-1 (Count Avg) vs TP 

Change Points: TP=0.015 (the point after change occurs) with the test statistic of 4.39 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.015, 0.093] based on 

500 bootstrapping samples with median=0.015. 

10) (pH Optima)-1 (Count Avg) vs TP 

Change Points: TP=0.022 (the point after change occurs) with the test statistic of 4.44 and 

confidence level over 95%; Bootstrapping 95% Confidence Interval [0.010, 0.036] based on 

500 bootstrapping samples with median=0.022. 

References: 

Chang, I. 1982. “Outliers in Time Series," Unpublished Ph.D. Dissertation, Department of 

Statistics, University of Wisconsin, Madison. 

Chang, I., G.C. Tiao, and C. Chen. 1988. “Estimation of Time Series Parameters in the Presence 

of Outliers," Technometrics, 30: 193-204. 

Niu, X., P. Lin, and D. Meeter. 2000. “Detecting Change Points in the Species Composition and 

Water Quality Data of WCA2A”. Department of Statistics, Florida State University, 

Tallahassee. Technical Report Submitted to the Florida Department of Environmental 

Protection. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-154
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Pankratz, A. 1991. Forecasting with Dynamic Regression Models. John Wiley & Sons Inc. 

 New York. 

Schwartz, G. 1978. Estimating the Dimension of A Model. The Annals of Statistics, 6: 461-464. 

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Appendix 6-E 

Quantile Regression Models for Stream Data-Periphyton Metrics 

(Weaver Region Panhandle) 

Xu-Feng Niu 

May10 – May 18, 2009 

Technical Report Submitted to the 

Florida Department of Environmental Protection 

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Quantile Regression Models for Stream Data-Periphyton Metrics 

(Weaver Region Panhandle) 

Xu-Feng Niu 

Department of Statistics 

Florida State University 

Tallahassee, FL 32306 

May10 – May 18, 2009 

Technical Report Submitted to 

the Florida Department of Environmental Protection 

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1. Quantile Regression 

 Quantile regression is a generalized approach of linear regression and usually provides a 

more complete analysis of a data set than linear regression. Mosteller and Tukey (1977) pointed 

out that “What the regression curve does is give a grand summary for the average of the 

distributions corresponding to the set of x ’s. We could go further and compute several 

different regression curves corresponding to the various percentage points of the 

distributions and thus get a more complete picture of the set. Ordinarily this is not done, 

and so regression often gives a rather incomplete picture. Just as the mean gives an 

incomplete picture of a single distribution, so the regression curve gives a corresponding 

incomplete picture for a set of distributions.” 

 The statistical theory of quantile regression has been developed by econometricians in the 

last 20 years (Koenker and Bassett, 1978, 1982; Bassett and Koenker, 1982a, b, 1986; Koenker 

et al. 1994). Ecological applications of quantile regression have also been documented in recent 

years (e.g., Terrell et al. 1996; Cade et al. 1999; McClain and Rex, 2001). Cade et al. (1999) 

pointed out that quantile regression is a very useful method for estimating effects associated with 

a measured subset of limiting factors while accounting for the effects of unmeasured factors in 

an ecologically realistic manner. Specifically, they considered changes in a biological response 

variable (species biomass) as a function of limiting factors (habitat conditions) that are measured 

and as a function of other limiting factors (non-habitat factors such as weather and disease) that 

may not be measured. “Change in species biomass does not exceed limits imposed by the 

habitat conditions, but can be reduced by non-habitat factors. One simple representation of 

this relationship is a linear function in which species biomass is a positive linear function of 

habitat factors and a negative function of the interaction of habitat and non-habitat factors, i.e., 

an interference interaction model.” Cade et al. (1999) further argued that in a full regression 

model “Change in biomass, due to change in habitat conditions, as the active limiting factor is 

easily estimated because we can account for the non-habitat factors with an estimate of the 

interaction effect; variation about the estimated change in means is small and homogeneous. If, 

however, we do not measure the non-habitat factors, we cannot estimate the interaction. 

The resultant distribution of biomass has greater variation that increases with the level of 

habitat that would support more biomass if habitat were the active constraint. Unmeasured 

non-habitat factors can reduce biomass more where habitat would limit biomass to higher 

levels. The linear relation between species biomass and the measured habitat factors most 

consistent with the relation expected if habitat is the active limiting factor is near the upper 

‘edge,’ rather that through the center of the data distribution.” 

 In this report, we briefly discuss the quantile regression using the notation in Koenker and 

Bassett (1982). Let Y be a random variable with right continuous distribution function F(y) = 

P(Y y). For any  [,] 0 1 , the quantile function of Y is defined as 

 Q F yFy Y ( ) ( ) inf{ | ( ) }.       1 (1) 

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Suppose that { , , , } Y1 2 Y  Yn is a random sample from the distribution F(y). The empirical 

distribution function based on this sample is Fy Y y n ( ) #{ }/  i and the empirical quantile 

function is defined as 

 ( )  ( ) inf{ |  Q F yFy( ) }. Y     1 (2) 

Equivalently, the empirical quantile function may also be defined in terms of solutions to a 

simple optimization problem with the form: 



Q y Yy ( ) inf{ | ( ) min!} Y i i

n

       1 (3) 

where  ( ) is the “check function” with    () || z z   for z  0 and    () ( )|| z z  1 for z  0 

Consider the random variable Y having conditional distribution function F y(| ) x where x is a row 

vector of exogenous variables. The first component of x is an intercept so that xi1  1 for all i. 

For example, in our study the response variable Y is one of the Florida Steam periphyton metrics 

and the exogenous variable is the logarithm of specific conductance (here labeled conductivity 

for brevity). If log(Conductivity) and Y follow a linear model 

Y Conductivity i i      i  0 1 log( ) , (4) 

where the random errors  i’s are independent and identically distributed with N(, ) 0 2  . Then 

the conditional distribution of Y given log(Conductivity) is 

F y Conductivity N ( |log( )) ( log(   0 1   Conductivity), ) 2 . (5) 

 The conditional quantile function of Y given x is defined as 

Q x F x yFyx Y ( | ) ( | ) inf{ | ( | ) }.      1 (6) 

Suppose that Q x Y (| )  is linear function of x, that is 

Q xF x x x Y k k

p

k (| ) (| ) () ()        

 

1

1 , (7) 

where ( )  is a vector of unknown coefficients depending upon  . These coefficients can be 

estimated by minimizing the “sum of residuals”    i

n

Y x i i   1 ( ( )). Denote the estimated 

coefficient by  ( ). Then the empirical conditional quantile function of Y is 

 (| )  ( )  Qx x x ( ) Y k k

p

k        1 . (8) 

Quantile regression models with quantiles (0.50, 0.85) were fitted to the Florida stream data with 

periphyton metrics as dependent variables and TP, TN, TIN, and specific conductance as 

independent variables. The logarithm (Base e) transformation is performed on the four predictor 

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variables. The periphyton metrics are transformed using the transformations chosen in Niu 

(2009). Only simple linear regression models with one predictor are considered in this study. 

Consider a periphyton metric denoted by y and a predictor, say Conductivity. For a given 

quantile , the empirical conditional quantile function has the form: 



Q Conductivity Conductivity ( |log( )) ( ) ( ) log( ) Y i i        0 1 , (9) 

where   0 ( ) is the intercept and   1( ) is the slope. In the more familiar notation of OLS 

regression and using the 90th quantile regression as an example, 

Y90 =a90 + b90X, (10) 

where a90 is the intercept of the 90th quantile regression of Y on X and b90 is the slope. 

 The quantreg Package in the R computer language was used for computations (http://cran.at.rproject.org/src/contrib/PACKAGES.html#quantreg ). The coefficients   0 ( ) and   1( ) were 

estimated using the “rq” function from quantreg. The default estimation method in the “rq” 

function was chosen, which is the modified version of the Barrodale and Robert algorithm for 

L1-regression, described in Koenker and d’Orey (1987, 1994). This algorithm is quite efficient 

for problems up to several thousand observations. 

 A quantile version of the coefficient of determination (R1) defined in Koenker and Machado 

(1999) is calculated, which is a natural analog of R2 for classical least square regressions. R1 is 

interpreted as the proportionate reduction in variation between the quantile estimate of the 

dependent variable and the estimate calculated with respect to the independent variable (McClain 

and Rex 2001). As in OLS regression, R1 value for a given quantile is a measure of the scatter 

around the quantile regression line. 

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2. Quantile Regression Models for Florida Stream Periphyton Metrics 

I) Pollution Sensitive Diatoms 

0.00 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total-P (mg P/L)

Poll sensitive diatoms 

R1=0.13**

R1=0.07**

01234

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Poll sensitve diatoms 

R1=0.01

R1=0.005

01234

0

20

40

60

80

100

TIN(mg/L)

Poll sensitve diatoms 

R1=0.0005

R1=0.0009

0 100 200 300 400 500

0

20

40

60

80

100

Conductance, field (umhos/cm)

Poll sensitve diatoms 

R1=0.15**

R1=0.17**

Stream-Figure 1. Quantile Regressions for Poll Sensitive Diatoms,

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

 Notes: 

1) Outliers TP=0.580 and TP=0.565 are removed. 

2) Outliers Cond=1344 and Cond=1557 are removed. 

3) Outliers TN=5.88 and TN=5.51 are removed. 

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Quantile Regression Models: 

1) PollSens on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -24.53253 16.62969 -1.47523 0.14385 

TPL -17.28037 4.33182 -3.98917 0.00014 

b) The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 40.51796 10.17727 3.98122 0.00014 

TPL -9.12668 2.65105 -3.44267 0.00090 

2) PollSens on log(TN): 

a. The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 21.24755 5.54216 3.83380 0.00024 

TNL -6.80250 6.15434 -1.10532 0.27214 

b. The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 80.12102 5.75788 13.91503 0.00000 

TNL -3.26447 6.39388 -0.51056 0.61098

3) PollSens on log(TIN): 

c) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 24.06520 8.40283 2.86394 0.00527 

TINL -0.44134 3.15113 -0.14006 0.88895 

d) The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 81.08065 8.98027 9.02876 0.00000 

TINL -1.10719 3.36767 -0.32877 0.74314 

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4) PollSens on log(Cond): 

a. The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 137.22391 24.54876 5.58985 0.00000 

CondL -23.92165 5.85856 -4.08319 0.00010 

b. The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 162.86957 13.19682 12.34158 0.00000 

CondL -22.90022 3.14942 -7.27124 0.00000

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II) Log(Pollution tolerant diatoms) 

0.00 0.05 0.10 0.15 0.20

-4

-2

0

2

4

Total-P (mg P/L)

log(Poll Tol diatoms) 

R^2=0.07**

R^2=0.13**

01234

-4

-2

0

2

4

Total Nitrogen (mg N/L)

log(Poll Tol diatoms) 

R^2=0.002

R^2=0.003

01234

-4

-2

0

2

4

TIN(mg/L)

log(Poll Tol diatoms) 

R^2=0.008

R^2=0.0007

0 100 200 300 400 500

-4

-2

0

2

4

Conductance, field (umhos/cm)

log(Poll Tol diatoms) 

R^2=0.13**

R^2=0.12**

Stream-Figure 2. Quantile Regressions for log(Poll ToL Diatoms),

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-164
 10 

Quantile Regression Models: 

1) Log(PollTol) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.38553 0.64678 6.78054 0.00000 

TPL 0.83243 0.16848 4.94089 0.00000 

b) The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.93351 0.36217 13.62190 0.00000 

TPL 0.61378 0.09434 6.50589 0.00000

2) Log(PollTol) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.98684 0.35725 2.76230 0.00703 

TNL -0.25590 0.39671 -0.64506 0.52063 

b) The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.70032 0.33541 8.05089 0.00000 

TNL -0.25813 0.37245 -0.69305 0.49017

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-165
 11 

3) Log(PollTol) on log(TIN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.74865 0.41223 4.24196 0.00006 

TINL 0.21173 0.15459 1.36963 0.17441 

b) The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.89321 0.36429 7.94199 0.00000 

TINL -0.01669 0.13661 -0.12219 0.90304 

4) Log(PollTol) on log(Cond): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -3.30512 0.96392 -3.42883 0.00094 

CondL 1.09947 0.23004 4.77946 0.00001 

b) The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.10884 1.05948 -1.04659 0.29826 

CondL 0.87084 0.25285 3.44416 0.00089 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-166
 12 

III) arcsin(sqrt(Percentage Requiring high D.O)) 

0.00 0.05 0.10 0.15 0.20

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Total-P (mg P/L)

arcsin(sqrt(%Requiring high D.O))

R1=0.13**

R1=0.10**

01234

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Total Nitrogen (mg N/L)

arcsin(sqrt(%Requiring high D.O))

R1=0.003

R1=0.007

01234

0.4

0.6

0.8

1.0

1.2

1.4

1.6

TIN(mg/L)

arcsin(sqrt(%Requiring high D.O))

R1=0.004

R1=0.0003

0 100 200 300 400 500

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Conductance, field (umhos/cm)

arcsin(sqrt(%Requiring high D.O))

R1=0.16**

R1=0.15**

Stream-Figure 3. Quantile Regressions for arcsin(sqrt(% Requiring high D.O))

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-167
 13 

Quantile Regression Models: 

1) Arcsin(sqrt(%Requiring high D.O)) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.86212 0.07994 10.78426 0.00000 

TPL -0.09350 0.02082 -4.49020 0.00002 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.16537 0.09225 12.63233 0.00000 

TPL -0.05764 0.02403 -2.39840 0.01865

2) Arcsin(sqrt(%Requiring high D.O)) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.18109 0.04195 28.15701 0.00000 

TNL -0.02456 0.04658 -0.52728 0.59937 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.41955 0.02920 48.61593 0.00000 

TNL -0.01575 0.03242 -0.48574 0.62840

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-168
 14 

 3) Arcsin(sqrt(%Requiring high D.O)) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.23107 0.05951 20.68532 0.00000 

TINL 0.01522 0.02232 0.68189 0.49716 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.41427 0.04061 34.82278 0.00000 

TINL -0.00892 0.01523 -0.58571 0.55962

4) Arcsin(sqrt(%Requiring high D.O)) on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.90212 0.11573 16.43598 0.00000 

CondL -0.17213 0.02762 -6.23231 0.00000 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.86462 0.09661 19.29960 0.00000 

CondL -0.12424 0.02306 -5.38846 0.00000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-169
 15 

IV) Arcsin(sqrt(Percentage cells preferring oligosaprobic 

condition)) 

0.00 0.05 0.10 0.15 0.20

0.6

0.8

1.0

1.2

1.4

1.6

Total-P (mg P/L)

arcsin(sqrt(Saprobic % Cells))

R1=0.15**

R1=0.05

01234

0.6

0.8

1.0

1.2

1.4

1.6

Total Nitrogen (mg N/L)

arcsin(sqrt(Saprobic % Cells))

R1=0.00006

R1=0.001

01234

0.6

0.8

1.0

1.2

1.4

1.6

TIN(mg/L)

arcsin(sqrt(Saprobic % Cells))

R1=0.002

R1=0.008

0 100 200 300 400 500

0.6

0.8

1.0

1.2

1.4

1.6

Conductance, field (umhos/cm)

arcsin(sqrt(Saprobic % Cells))

R1=0.17**

R1=0.13**

Stream-Figure 4. Quantile Regressions for arcsin(sqrt(Saprobic % Cells))

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-170
 16 

Quantile Regression Models: 

 1)Arcsin(sqrt(Saprobic % Cells)) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.88438 0.05838 15.14800 0.00000 

TPL -0.09880 0.01521 -6.49660 0.00000 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.29171 0.08211 15.73093 0.00000 

TPL -0.03731 0.02139 -1.74415 0.08475 

 

 2)Arcsin(sqrt(Saprobic % Cells)) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.23174 0.03765 32.71903 0.00000 

TNL -0.00097 0.04180 -0.02313 0.98160 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.44120 0.01851 77.85225 0.00000 

TNL -0.01361 0.02056 -0.66206 0.50972

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-171
 17 

 3) Arcsin(sqrt(Saprobic % Cells)) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.22095 0.04665 26.17234 0.00000 

TINL -0.00608 0.01749 -0.34750 0.72908 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.43176 0.02069 69.19187 0.00000 

TINL -0.01111 0.00776 -1.43234 0.15571

4) Arcsin(sqrt(Saprobic % Cells)) on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.80534 0.08481 21.28690 0.00000 

CondL -0.12875 0.02024 -6.36123 0.00000 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.72692 0.09788 17.64350 0.00000 

CondL -0.07510 0.02336 -3.21493 0.00185 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-172
 18 

V) Van Dam Trophic State Index 

0.00 0.05 0.10 0.15 0.20

1.0

1.5

2.0

2.5

Total-P (mg P/L)

sqrt(Van Dam TSI)

R1=0.18**

R1=0.04**

01234

1.0

1.5

2.0

2.5

Total Nitrogen (mg N/L)

sqrt(Van Dam TSI)

R1=0.02

R1=0.01

01234

1.0

1.5

2.0

2.5

TIN(mg/L)

sqrt(Van Dam TSI)

R1=0.01

R1=0.001

0 100 200 300 400 500

1.0

1.5

2.0

2.5

Conductance, field (umhos/cm)

sqrt(Van Dam TSI)

R1=0.10**

R1=0.02

Stream-Figure 5. Quantile Regressions for sqrt(Van Dam TSI)

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-173
 19 

Quantile Regression Models: 

 1) sqrt(Van Dam TSI) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.30545 0.12699 18.15471 0.00000 

TPL 0.17239 0.03308 5.21153 0.00000 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.25804 0.06975 32.37155 0.00000 

TPL 0.05968 0.01817 3.28478 0.00148 

 2) sqrt(Van Dam TSI) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.79076 0.07024 25.49390 0.00000 

TNL 0.06551 0.07800 0.83990 0.40332 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.99197 0.02911 68.43242 0.00000 

TNL -0.08471 0.03232 -2.62058 0.01040

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-174
 20 

 3) sqrt(Van Dam TSI) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.83057 0.07679 23.83979 0.00000 

TINL 0.02578 0.02880 0.89532 0.37314 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.00119 0.04751 42.11970 0.00000 

TINL -0.01934 0.01782 -1.08549 0.28077

4) sqrt(Van Dam TSI) on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.81185 0.28485 2.85005 0.00548 

CondL 0.21431 0.06798 3.15248 0.00224 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.88321 0.08396 22.42857 0.00000 

CondL 0.03328 0.02004 1.66062 0.10047 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-175
 21 

VI) arcsin(sqrt(TP Sensitive Diatoms)) 

0.00 0.05 0.10 0.15 0.20

0.0

0.5

1.0

1.5

Total-P (mg P/L)

arcsin(sqrt(TP Sensitive Diatoms))

R1=0.16**

R1=0.10**

01234

0.0

0.5

1.0

1.5

Total Nitrogen (mg N/L)

arcsin(sqrt(TP Sensitive Diatoms))

R1=0.06**

R1=0.01

01234

0.0

0.5

1.0

1.5

TIN(mg/L)

arcsin(sqrt(TP Sensitive Diatoms))

R1=0.005

R1=0.004

0 100 200 300 400 500

0.0

0.5

1.0

1.5

Conductance, field (umhos/cm)

arcsin(sqrt(TP Sensitive Diatoms))

R1=0.08**

R1=0.09**

Stream-Figure 6. Quantile Regressions for arcsin(sqrt(TP Sensitive Diatoms))

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-176
 22 

Quantile Regression Models: 

 1) arcsin(sqrt(TP Sensitive Diatoms)) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.25754 0.15028 1.71369 0.09023 

TPL -0.15744 0.03915 -4.02171 0.00012 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.71357 0.11271 6.33126 0.00000 

TPL -0.11484 0.02936 -3.91172 0.00018 

 2) arcsin(sqrt(TP Sensitive Diatoms)) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.63177 0.09999 6.31842 0.00000 

TNL -0.26048 0.11103 -2.34595 0.02131 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.12236 0.06370 17.61918 0.00000 

TNL -0.08873 0.07074 -1.25433 0.21316

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-177
 23 

 3) arcsin(sqrt(TP Sensitive Diatoms)) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.71476 0.17822 4.01048 0.00013 

TINL -0.03991 0.06683 -0.59711 0.55202 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.19609 0.08241 14.51390 0.00000 

TINL -0.00590 0.03090 -0.19089 0.84907

4) arcsin(sqrt(TP Sensitive Diatoms)) on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.78065 0.27395 6.49982 0.00000 

CondL -0.22488 0.06538 -3.43964 0.00090 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.59651 0.09952 16.04282 0.00000 

CondL -0.11349 0.02375 -4.77882 0.00001 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-178
 24 

VII) TIN Sensitive Diatoms 

0.00 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total-P (mg P/L)

Poll sensitive diatoms 

R1=0.14**

R1=0.11**

01234

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TIN sensitve diatoms 

R1=0.04**

R1=0.01

01234

0

20

40

60

80

100

TIN(mg/L)

TIN sensitve diatoms 

R1=0.008

R1=0.001

0 100 200 300 400 500

0

20

40

60

80

100

Conductance, field (umhos/cm)

TIN sensitve diatoms 

R1=0.04**

R1=0.18**

Stream-Figure 7. Quantile Regressions for TIN Sensitive Diatoms,

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-179
 25 

Quantile Regression Models: 

 1) TIN Sensitive Diatoms on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -17.32723 16.04785 -1.07972 0.28332 

TPL -15.34935 4.18026 -3.67187 0.00042 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 41.50912 11.27219 3.68244 0.00041 

TPL -7.95394 2.93626 -2.70887 0.00816

 2) TIN Sensitive Diatoms on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 25.16663 6.83497 3.68204 0.00041 

TNL -17.17930 7.58995 -2.26343 0.02616 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 71.41102 7.40514 9.64343 0.00000 

TNL -5.90897 8.22310 -0.71858 0.47437

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-180
 26 

 3) TIN Sensitive Diatoms on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 44.41215 11.37735 3.90356 0.00019 

TINL 3.83167 4.26659 0.89806 0.37169 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 78.04102 11.18393 6.97796 0.00000 

TINL 0.91480 4.19406 0.21812 0.82786

4) TIN Sensitive Diatoms on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 120.04918 33.09214 3.62772 0.00049 

CondL -19.40106 7.89744 -2.45662 0.01606 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 138.27044 9.43794 14.65048 0.00000 

CondL -16.48616 2.25237 -7.31948 0.00000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-181
 27 

VIII) (N Metab)-1 (Count Avg) 

0.00 0.05 0.10 0.15 0.20

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Total-P (mg P/L)

Reciprocal of N-Metab

R1=0.18**

R1=0.12**

01234

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Total Nitrogen (mg N/L)

Reciprocal of N-Metab

R1=0.006

R1=0.007

01234

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

TIN(mg/L)

Reciprocal of N-Metab

R1=0.001

R1=0.0002

0 100 200 300 400 500

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Conductance, field (umhos/cm)

Reciprocal of N-Metab

R1=0.24**

R1=0.15**

Stream-Figure 8. Quantile Regressions for Reciprocal of N-Metab

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-182
 28 

Quantile Regression Models: 

 1) (N Metab)-1 on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.43721 0.04627 9.44944 0.00000 

TPL -0.06921 0.01205 -5.74211 0.00000 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.68391 0.04139 16.52176 0.00000 

TPL -0.03505 0.01078 -3.25019 0.00165 

 2) (N Metab)-1 on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.71411 0.02691 26.54037 0.00000 

TNL 0.02022 0.02988 0.67661 0.50049 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.83776 0.01201 69.75611 0.00000 

TNL -0.00461 0.01334 -0.34560 0.73050

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-183
 29 

 3) (N Metab)-1 on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.71383 0.03187 22.39504 0.00000 

TINL 0.00263 0.01195 0.22018 0.82626 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.83613 0.01614 51.79198 0.00000 

TINL -0.00128 0.00605 -0.21070 0.83363 

4) (N Metab)-1 on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.16979 0.05588 20.93590 0.00000 

CondL -0.11392 0.01333 -8.54323 0.00000 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.04170 0.06132 16.98887 0.00000 

CondL -0.05674 0.01463 -3.87753 0.00021 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-184
 30 

IX) (pH Optima)-1 (Count Avg) 

0.00 0.05 0.10 0.15 0.20

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Total-P (mg P/L)

Reciprocal of pH Optima

R1=0.12**

R1=0.16**

01234

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Total Nitrogen (mg N/L)

Reciprocal of pH Optima

R1=0.02

R1=0.01

01234

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

TIN(mg/L)

Reciprocal of pH Optima

R1=0.003

R1=0.01

0 100 200 300 400 500

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Conductance, field (umhos/cm)

Reciprocal of pH Optima

R1=0.12**

R1=0.26**

Stream-Figure 9. Quantile Regressions for Reciprocal of pH Optima

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

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Quantile Regression Models: 

 1) (pH Optima)-1 on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.18341 0.03645 5.03171 0.00000 

TPL -0.04070 0.00950 -4.28668 0.00005 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.25240 0.04185 6.03066 0.00000 

TPL -0.04119 0.01090 -3.77850 0.00029 

 2) (pH Optima)-1 on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.28984 0.01435 20.19411 0.00000 

TNL -0.02765 0.01594 -1.73482 0.08640 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.43254 0.02294 18.85683 0.00000 

TNL -0.01364 0.02547 -0.53565 0.59360

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 3) (pH Optima)-1 on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.29441 0.02377 12.38499 0.00000 

TINL -0.00538 0.00891 -0.60316 0.54801 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.45651 0.03046 14.98597 0.00000 

TINL 0.00935 0.01142 0.81858 0.41532 

4) (pH Optima)-1 on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.54631 0.05099 10.71397 0.00000 

CondL -0.05275 0.01217 -4.33460 0.00004 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.64550 0.02080 31.03358 0.00000 

CondL -0.05886 0.00496 -11.85704 0.00000 

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X) Stream Diatom Index 

0.00 0.05 0.10 0.15 0.20

0

20

40

60

80

100

Total-P (mg P/L)

Stream Diatom Index

R1=0.12**

R1=0.13**

01234

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Stream Diatom Index

R1=0.0

R1=0.003

01234

0

20

40

60

80

100

TIN(mg/L)

Stream Diatom Index

R1=0.0

R1=0.004

0 100 200 300 400 500

0

20

40

60

80

100

Conductance, field (umhos/cm)

Stream Diatom Index

R1=0.17**

R1=0.21**

Stream-Figure 10. Quantile Regressions for Stream Diatom Index,

 (Blue Line: 85% Quantile; Green Line: 50% Quantile)

 (Red: pH<6.5; **: Significant Regression)

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Quantile Regression Models: 

 1) Stream Diatom Index on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 16.59615 11.37235 1.45934 0.14816 

TPL -12.45515 2.96235 -4.20448 0.00006 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 54.74576 6.78646 8.06691 0.00000 

TPL -7.28191 1.76779 -4.11923 0.00009 

 2) Stream Diatom Index on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 58.00000 4.06656 14.26268 0.00000 

TNL 0.00000 4.51574 0.00000 1.00000 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 87.32069 2.56595 34.03061 0.00000 

TNL -1.34295 2.84938 -0.47131 0.63862

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 3) Stream Diatom Index on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 58.00000 5.65876 10.24960 0.00000 

TINL 0.00000 2.12208 0.00000 1.00000 

b)The 85th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 95.38136 4.57770 20.83607 0.00000 

TINL 2.14115 1.71667 1.24726 0.21573 

4) Stream Diatom Index on log(Cond): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 138.61102 13.22551 10.48058 0.00000 

CondL -18.42359 3.15627 -5.83714 0.00000 

b)The 85th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 143.13107 15.62534 9.16019 0.00000 

CondL -15.81087 3.72899 -4.23999 0.00006 

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References: 

Bassett, G. and Koenker, R. W. 1982a. Tests of Linear Hypotheses and L1 Estimation. 

Econometrica, 50:1577-1583. 

Bassett, G. and Koenker, R. W. 1982b. An Empirical Quantile Function for Linear Models with 

iid Errors. Journal of American Statistical Association 77:407-415. 

Bassett, G. and Koenker, R. W. 1986. Strong Consistency of Regression Quantiles and Related 

Empirical Processes. Econometric Theory 2:191-201. 

Cade, B. S. and Noon, B. R. 2003. A Gentle Introduction to Quantile Regression for Ecologists. 

Frontiers in Ecology and the Environment 1: 412-420. 

Cade, B. S., Terrell, J. W., and Schroeder, R. L. 1999. Estimating Effects of Limiting Factors 

with Regression Quantiles. Ecology 80:311-323. 

Koenker, R. W. 1994. Confidence Intervals for Regression Quantiles. In P. Mandl and M. 

Huskova (eds.) Asymptotic Statistics, 349-359, Proceedings of the Fifth Prague Symposium, 

Physica-Verlag, Heidelberg, Germany. 

Koenker, R. W. and Bassett, G. 1978. Regression Quantiles. Econometrica 46:33-50. 

Koenker, R. W. and Bassett, G. 1982. Robust Tests for Heteroscedasticity Based on Regression 

Quantiles. Econometrica 50:43-61. 

Koenker, R. W. and d’Orey, V. 1987. Computing Regression Quantiles, Applied Statistics, 

36:383-393, 

Koenker, R. W. and d’Orey, V. 1994 A Remark on Algorithm AS229: Computing Dual 

Regression Quantiles and Regression Rank Scores. Applied Statistics 43:410-414 

Koenker, R. W. and Machado, J.A.F. 1999. Goodness of Fit and Related Inference Processes for 

Quantile Regression. Journal of the American Statistical Association, 94:1296 -1310

 Koenker, R., Ng, P., and Portnoy, S. 1994. Quantile Smoothing Splines. Biometrika 81:673-

680. 

Kolbe, R. W. 1927. Zur Őkologie, Morphologie, und Systematik der Brackenwasser-Diatomeen 

(The ecology, morphology and systematics of the brackish-water diatoms) Pflanzenforschung 

(Jena) 7: 1-146. 

McClain, C. R. and Rex, M. A. 2001. The Relationship Between Dissolved Oxygen 

Concentration and Maximum Size in Deep-Sea Turrid Gastropods: An Application of 

Quantile Regression. Marine Biology 139:681-685. 

Mosteller, F. and Tukey, J. W. 1977. Data Analysis and Regression. Reading, Massachusetts: 

Addison-Wesley. 

Niu, X.F. 2009. Statistical Analysis of Stream Data-Periphyton Metrics (Weaver Region 

Panhandle). Technical Report Submitted to the Florida Department of Environmental 

Protection. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-191
 37 

Terrell, J.W., Cade, B. S., Carpenter, J., and Thomson, J. M. 1996. Modeling Stream Fish 

Habitat Limitations from Wedged-Shaped Patterns of Variation in Standing Stock. 

Transactions of the American Fisheries Society 125:104-117. 

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Appendix 6-F 

Quantile Regression Models for Stream Data-Periphyton Metrics 

(Weaver Region Peninsula) 

Xu-Feng Niu 

May10 – May 22, 2009 

Technical Report Submitted to the 

Florida Department of Environmental Protection 

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Quantile Regression Models for Stream Data-Periphyton Metrics 

(Weaver Region Peninsula) 

Xu-Feng Niu 

Department of Statistics 

Florida State University 

Tallahassee, FL 32306 

1.1 May10 – May 22, 2009 

Technical Report Submitted to 

the Florida Department of Environmental Protection 

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1. Quantile Regression 

Quantile regression is a generalized approach of linear regression and usually provides a 

more complete analysis of a data set than linear regression. Mosteller and Tukey (1977) pointed 

out that “What the regression curve does is give a grand summary for the average of the 

distributions corresponding to the set of x ’s. We could go further and compute several 

different regression curves corresponding to the various percentage points of the 

distributions and thus get a more complete picture of the set. Ordinarily this is not done, 

and so regression often gives a rather incomplete picture. Just as the mean gives an 

incomplete picture of a single distribution, so the regression curve gives a corresponding 

incomplete picture for a set of distributions.” 

 The statistical theory of quantile regression has been developed by econometricians in the 

last 20 years (Koenker and Bassett, 1978, 1982; Bassett and Koenker, 1982a, b, 1986; Koenker 

et al. 1994). Ecological applications of quantile regression have also been documented in recent 

years (e.g., Terrell et al. 1996; Cade et al. 1999; McClain and Rex, 2001). Cade et al. (1999) 

pointed out that quantile regression is a very useful method for estimating effects associated with 

a measured subset of limiting factors while accounting for the effects of unmeasured factors in 

an ecologically realistic manner. Specifically, they considered changes in a biological response 

variable (species biomass) as a function of limiting factors (habitat conditions) that are measured 

and as a function of other limiting factors (non-habitat factors such as weather and disease) that 

may not be measured. “Change in species biomass does not exceed limits imposed by the 

habitat conditions, but can be reduced by non-habitat factors. One simple representation of 

this relationship is a linear function in which species biomass is a positive linear function of 

habitat factors and a negative function of the interaction of habitat and non-habitat factors, i.e., 

an interference interaction model.” Cade et al. (1999) further argued that in a full regression 

model “Change in biomass, due to change in habitat conditions, as the active limiting factor is 

easily estimated because we can account for the non-habitat factors with an estimate of the 

interaction effect; variation about the estimated change in means is small and homogeneous. If, 

however, we do not measure the non-habitat factors, we cannot estimate the interaction. 

The resultant distribution of biomass has greater variation that increases with the level of 

habitat that would support more biomass if habitat were the active constraint. Unmeasured 

non-habitat factors can reduce biomass more where habitat would limit biomass to higher 

levels. The linear relation between species biomass and the measured habitat factors most 

consistent with the relation expected if habitat is the active limiting factor is near the upper 

‘edge,’ rather that through the center of the data distribution.” 

 In this report, we briefly discuss the quantile regression using the notation in Koenker and 

Bassett (1982). Let Y be a random variable with right continuous distribution function F(y) = 

P(Y y). For any  [,] 0 1 , the quantile function of Y is defined as 

 Q F yFy Y ( ) ( ) inf{ | ( ) }.       1 (1) 

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Suppose that { , , , } Y1 2 Y  Yn is a random sample from the distribution F(y). The empirical 

distribution function based on this sample is Fy Y y n ( ) #{ }/  i and the empirical quantile 

function is defined as 

 ( )  ( ) inf{ |  Q F yFy( ) }. Y     1 (2) 

Equivalently, the empirical quantile function may also be defined in terms of solutions to a 

simple optimization problem with the form: 



Q y Yy ( ) inf{ | ( ) min!} Y i i

n

       1 (3) 

where  ( ) is the “check function” with    () || z z   for z  0 and    () ( )|| z z  1 for z  0 

Consider the random variable Y having conditional distribution function F y(| ) x where x is a row 

vector of exogenous variables. The first component of x is an intercept so that xi1  1 for all i. 

For example, in our study the response variable Y is one of the Florida Steam periphyton metrics 

and the exogenous variable is the logarithm of Total Phosphorus (TP). If log(TP) and Y follow a 

linear model 

0 1 log( ) Y T i i      P i , (4) 

where the random errors  i’s are independent and identically distributed with N(, ) 0 2  . Then 

the conditional distribution of Y given log(TP) is 

2

0 1 F y TP N TP ( | log( )) ( log( ), )      . (5) 

 The conditional quantile function of Y given x is defined as 

Q x F x yFyx Y ( | ) ( | ) inf{ | ( | ) }.      1 (6) 

Suppose that Q x Y (| )  is linear function of x, that is 

Q xF x x x Y k k

p

k (| ) (| ) () ()        

 

1

1 , (7) 

where ( )  is a vector of unknown coefficients depending upon  . These coefficients can be 

estimated by minimizing the “sum of residuals”    i

n

Y x i i   1 ( ( )). Denote the estimated 

coefficient by  ( ). Then the empirical conditional quantile function of Y is 

 (| )  ( )  Qx x x ( ) Y k k

p

k        1 . (8) 

 Quantile regression models with quantiles (0.50, 0.90) were fitted to the Florida stream data 

(Weaver Peninsula Region) with periphyton metrics as dependent variables and TP, TN, TIN, 

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and pH as independent variables. The logarithm (Base e) transformation is performed on TP, 

TN, and TIN, while pH is not transformed. The periphyton metrics are transformed using the 

transformations chosen in Niu (2009). Only simple linear regression models with one predictor 

are considered in this study. 

Consider a periphyton metric denoted by y and a predictor, say TP. For a given quantile , the 

empirical conditional quantile function has the form: 

0 1 ˆ ( | log( )) ( ) ( ) log( ) Y i i Q TP      TP , (9) 

where   0 ( ) is the intercept and   1( ) is the slope. In the more familiar notation of OLS 

regression and using the 90th quantile regression as an example, 

Y90 =a90 + b90X, (10) 

where a90 is the intercept of the 90th quantile regression of Y on X and b90 is the slope. 

 The quantreg Package in the R computer language was used for computations (http://cran.at.rproject.org/src/contrib/PACKAGES.html#quantreg ). The coefficients   0 ( ) and   1( ) were 

estimated using the “rq” function from quantreg. The default estimation method in the “rq” 

function was chosen, which is the modified version of the Barrodale and Robert algorithm for 

L1-regression, described in Koenker and d’Orey (1987, 1994). This algorithm is quite efficient 

for problems up to several thousand observations. 

 A quantile version of the coefficient of determination (R1) defined in Koenker and Machado 

(1999) is calculated, which is a natural analog of R2 for classical least square regressions. R1 is 

interpreted as the proportionate reduction in variation between the quantile estimate of the 

dependent variable and the estimate calculated with respect to the independent variable (McClain 

and Rex 2001). As in OLS regression, R1 value for a given quantile is a measure of the scatter 

around the quantile regression line. 

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2. Quantile Regression Models for Florida Stream Periphyton Metrics 

I) Pollution Sensitive Diatoms 

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total-P (mg P/L)

Poll sensitive diatoms 

R1=0.001

R1=0.01

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

Poll sensitve diatoms 

R1=0.024*

R1=0.021

0.0 0.5 1.0 1.5

0

20

40

60

80

100

TIN(mg/L)

Poll sensitve diatoms 

R1=0.006

R1=0.01

5678

0

20

40

60

80

100

pH

Poll sensitve diatoms 

R1=0.11**

R1=0.28**

Stream-Figure 1. Quantile Regressions for Poll Sensitive Diatoms,

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

 Notes: 

a) Outliers TP=2.3 and TP=2.39 are removed. 

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Quantile Regression Models: 

1) PollSens on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 14.76458 4.51338 3.27129 0.00122 

TPL 0.58773 1.65919 0.35422 0.72347 

b) The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 35.63810 18.49827 1.92656 0.05519 

TPL -4.89112 6.80026 -0.71925 0.47267 

2) PollSens on log(TN): 

a. The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 13.35291 1.02820 12.98664 0.00000 

TNL 4.11598 1.63806 2.51272 0.01262 

b. The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 46.54954 6.05750 7.68461 0.00000 

TNL 10.44593 9.65036 1.08244 0.28012

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3) PollSens on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 9.27865 2.51006 3.69658 0.00027 

TINL -1.47089 1.00189 -1.46812 0.14335 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 37.20741 11.33092 3.28370 0.00117 

TINL -4.66761 4.52271 -1.03204 0.30307 

4) PollSens on pH: 

a. The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 108.41455 8.90724 12.17151 0.00000 

pH -13.40909 1.26785 -10.57626 0.00000 

b. The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 188.22883 25.70293 7.32325 0.00000 

pH -21.34529 3.65853 -5.83439 0.00000

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II) SQRT(Pollution tolerant diatoms) 

0.0 0.1 0.2 0.3 0.4 0.5

0

2

4

6

8

10

Total-P (mg P/L)

Sqrt(Poll Tol diatoms) 

R1=0.003

R1=0.034**

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

2

4

6

8

10

Total Nitrogen (mg N/L)

Sqrt(Poll Tol diatoms) 

R1=0.025*

R1=0.000009

0.0 0.5 1.0 1.5

0

2

4

6

8

10

TIN(mg/L)

Sqrt(Poll Tol diatoms) 

R1=0.0002

R1=0.0003

5678

0

2

4

6

8

10

pH

Sqrt(Poll Tol diatoms) 

R1=0.036*

R1=0.017**

Stream-Figure 2. Quantile Regressions for Sqrt(Poll Tol Diatoms),

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

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Quantile Regression Models: 

1) Sqrt(PollTol) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.67321 0.88861 5.25902 0.00000 

TPL 0.37668 0.32667 1.15310 0.24999 

b) The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 7.98486 0.46152 17.30103 0.00000 

TPL 0.45080 0.16966 2.65702 0.00840

2) Sqrt(PollTol) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.32537 0.23291 14.27741 0.00000 

TNL -0.82184 0.37106 -2.21486 0.02769 

b) The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 6.79726 0.22281 30.50647 0.00000 

TNL -0.07768 0.35497 -0.21883 0.82697

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3) Sqrt(PollTol) on log(TIN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.35691 0.64141 5.23367 0.00000 

TINL -0.07125 0.25602 -0.27829 0.78102 

b) The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 6.65135 0.42532 15.63833 0.00000 

TINL -0.05086 0.16977 -0.29961 0.76473

4) Sqrt(PollTol) on pH: 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -2.10970 2.69038 -0.78416 0.43370 

pH 0.81761 0.38295 2.13506 0.03374 

 

b) The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.29294 1.12614 1.14812 0.25204 

pH 0.75199 0.16029 4.69133 0.00000 

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III) arcsin(sqrt(Percentage Requiring high D.O))

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.5

1.0

1.5

Total-P (mg P/L)

Arcsin(sqrt(% Requiring high D.O))

R1=0.0003

R1=0.002

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0

0.5

1.0

1.5

Total Nitrogen (mg N/L)

Arcsin(sqrt(% Requiring high D.O))

R1=0.046**

R1=0.003

0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

TIN(mg/L)

Arcsin(sqrt(% Requiring high D.O))

R1=0.0004

R1=0.002

5678

0.0

0.5

1.0

1.5

pH

Arcsin(sqrt(% Requiring high D.O))

R1=0.054**

R1=0.007

Stream-Figure 3. Quantile Regressions for Arcsin(sqrt(%Requiring high D.O))

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-204
 13 

Quantile Regression Models: 

1) Arcsin(sqrt(%Requiring high D.O)) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.07554 0.07951 13.52699 0.00000 

TPL 0.01448 0.02923 0.49550 0.62069 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.38141 0.07138 19.35222 0.00000 

TPL 0.01510 0.02624 0.57548 0.56550 

 

2) Arcsin(sqrt(%Requiring high D.O)) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.05135 0.01918 54.82834 0.00000 

TNL 0.10441 0.03055 3.41795 0.00074 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.34223 0.02073 64.75180 0.00000 

TNL 0.02441 0.03302 0.73908 0.46056

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-205
 14 

 3) Arcsin(sqrt(%Requiring high D.O)) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.04248 0.05012 20.79770 0.00000 

TINL 0.00478 0.02001 0.23916 0.81118 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.33300 0.03755 35.49602 0.00000 

TINL -0.00431 0.01499 -0.28722 0.77418

4) Arcsin(sqrt(%Requiring high D.O)) on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.81475 0.17757 10.21967 0.00000 

pH -0.11040 0.02528 -4.36768 0.00002 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.50404 0.10470 14.36577 0.00000 

 pH -0.02575 0.01490 -1.72770 0.08530 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-206
 15 

IV) Arcsin(sqrt(Percentage cells preferring oligosaprobic 

condition)) 

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.5

1.0

1.5

Total-P (mg P/L)

Arcsin(sqrt(Saprobic % Cells))

R1=0.0000004

R1=0.002

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.0

0.5

1.0

1.5

Total Nitrogen (mg N/L)

Arcsin(sqrt(Saprobic % Cells))

R1=0.023**

R1=0.007

0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

TIN(mg/L)

Arcsin(sqrt(Saprobic % Cells))

R1=0.0001

R1=0.003

5678

0.0

0.5

1.0

1.5

pH

Arcsin(sqrt(Saprobic % Cells))

R1=0.054**

R1=0.017*

Stream-Figure 4. Quantile Regressions for Arcsin(sqrt(Saprobic % Cells))

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-207
 16 

Quantile Regression Models: 

 1)Arcsin(sqrt(Saprobic % Cells)) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.09753 0.07682 14.28714 0.00000 

TPL -0.00015 0.02824 -0.00520 0.99586 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.38826 0.04914 28.24934 0.00000 

TPL -0.00582 0.01807 -0.32231 0.74749 

 2)Arcsin(sqrt(Saprobic % Cells)) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.11954 0.02047 54.69826 0.00000 

TNL 0.10570 0.03261 3.24151 0.00135 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.39545 0.01883 74.11897 0.00000 

TNL 0.02976 0.02999 0.99231 0.32202

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-208
 17 

 3) Arcsin(sqrt(Saprobic % Cells)) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.08216 0.04181 25.88341 0.00000 

TINL -0.00790 0.01669 -0.47323 0.63647 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.38099 0.03807 36.27409 0.00000 

TINL -0.00912 0.01520 -0.60038 0.54881

4) Arcsin(sqrt(Saprobic % Cells)) on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.79499 0.15710 11.42557 0.00000 

 pH -0.09986 0.02236 -4.46564 0.00001 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.59344 0.09578 16.63697 0.00000 

pH -0.03068 0.01363 -2.25019 0.02532 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-209
 18 

V) Van Dam Trophic State Index 

0.0 0.1 0.2 0.3 0.4 0.5

1

2

3

4

5

Total-P (mg P/L)

Van Dam TSI

R1=0.014

R1=0.011

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1

2

3

4

5

Total Nitrogen (mg N/L)

Van Dam TSI

R1=0.012**

R1=0.015

0.0 0.5 1.0 1.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

TIN(mg/L)

Van Dam TSI

R1=0.014*

R1=0.008

5678

1

2

3

4

5

pH

Van Dam TSI

R1=0.076**

R1=0.092*

Stream-Figure 5. Quantile Regressions for Van Dam TSI

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-210
 19 

Quantile Regression Models: 

 1) Van Dam TSI on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.35067 0.13093 25.59172 0.00000 

TPL -0.09084 0.04813 -1.88734 0.06029 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.21616 0.17778 23.71625 0.00000 

TPL -0.05599 0.06535 -0.85671 0.39244 

 

 2) Van Dam TSI on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.57693 0.04393 81.42419 0.00000 

 TNL -0.18513 0.06999 -2.64533 0.00869 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.33579 0.05590 77.57013 0.00000 

 TNL -0.07653 0.08905 -0.85939 0.39096

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-211
 20 

 3) Van Dam TSI on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.77902 0.10107 37.39089 0.00000 

TINL 0.08315 0.04034 2.06129 0.04033 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.47033 0.11156 40.07030 0.00000 

TINL 0.04168 0.04453 0.93595 0.35022

4) Van Dam TSI on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.24053 0.53491 2.31913 0.02121 

 pH 0.33591 0.07614 4.41180 0.00002 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.67427 0.48426 3.45741 0.00064 

 pH 0.36792 0.06893 5.33769 0.00000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-212
 21 

VI) TP Sensitive Diatoms 

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total-P (mg P/L)

TP Sensitive Diatoms 

R1=0.009

R1=0.023

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TP Sensitve Diatoms 

R1=0.0008

R1=0.009*

0.0 0.5 1.0 1.5

0

20

40

60

80

100

TIN(mg/L)

TP Sensitive Diatoms

R1=0.0001

R1=0.003

5678

0

20

40

60

80

100

pH

TP Sensitive Diatoms

R1=0.082**

R1=0.116*

Stream-Figure 6. Quantile Regressions for TP Sensitive Diatoms

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-213
 22 

Quantile Regression Models: 

 1) TP Sensitive Diatoms on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 10.31008 8.03581 1.28302 0.20069 

TPL -3.21291 2.95409 -1.08761 0.27783 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 44.68382 11.39708 3.92064 0.00011 

 TPL -7.28294 4.18975 -1.73827 0.08341 

 2) TP Sensitive Diatoms on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 18.39949 2.82283 6.51811 0.00000 

 TNL 1.51562 4.49712 0.33702 0.73639 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 62.55324 3.18994 19.60956 0.00000 

 TNL 11.96770 5.08197 2.35493 0.01931

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-214
 23 

 3) TP Sensitive Diatoms on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 16.23814 5.57288 2.91378 0.00390 

 TINL -0.75816 2.22440 -0.34084 0.73352 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 65.91723 3.95181 16.68027 0.00000 

TINL 1.59683 1.57735 1.01235 0.31237

4) TP Sensitive Diatoms on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 139.24166 20.30397 6.85785 0.00000 

 pH -16.90535 2.89005 -5.84950 0.00000 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 150.91418 35.98612 4.19368 0.00004 

 pH -13.26241 5.12223 -2.58918 0.01019 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-215
 24 

VII) TIN Sensitive Diatoms 

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

Total-P (mg P/L)

TIN Sensitive Diatoms 

R1=0.004

R1=0.026**

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0

20

40

60

80

100

Total Nitrogen (mg N/L)

TIN Sensitve Diatoms 

R1=0.0007

R1=0.007

0.0 0.5 1.0 1.5

0

20

40

60

80

100

TIN(mg/L)

TIN Sensitive Diatoms

R1=0.0007

R1=0.026

5678

0

20

40

60

80

100

pH

TIN Sensitive Diatoms

R1=0.047**

R1=0.279**

Stream-Figure 7. Quantile Regressions for TIN Sensitive Diatoms

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-216
 25 

Quantile Regression Models: 

 1) TIN Sensitive Diatoms on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 8.63304 3.01665 2.86180 0.00458 

TPL -1.65693 1.10897 -1.49412 0.13643 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 20.84992 7.16511 2.90992 0.00395 

TPL -7.73829 2.63401 -2.93784 0.00362 

 2) TIN Sensitive Diatoms on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 12.18387 1.25947 9.67377 0.00000 

TNL -1.00006 2.00650 -0.49841 0.61864 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 43.10522 3.88443 11.09693 0.00000 

TNL 5.15335 6.18838 0.83275 0.40579

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-217
 26 

 3) TIN Sensitive Diatoms on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 10.67062 2.34688 4.54673 0.00001 

TINL -0.78918 0.93675 -0.84246 0.40035 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 32.90901 5.61556 5.86032 0.00000 

TINL -4.09035 2.24144 -1.82488 0.06923

4) TIN Sensitive Diatoms on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 92.45060 12.46371 7.41758 0.00000 

pH -11.00885 1.77407 -6.20540 0.000006 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 177.84783 16.08171 11.05901 0.00000 

 pH -19.68296 2.28906 -8.59872 0.00000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-218
 27 

VIII) (N Metab)-1 (Count Avg) 

0.0 0.1 0.2 0.3 0.4 0.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Total-P (mg P/L)

Reciprocal of N-Metab

R1=0.0004

R1=0.005

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Total Nitrogen (mg N/L)

Reciprocal of N-Metab

R1=0.024*

R1=0.022**

0.0 0.5 1.0 1.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

TIN(mg/L)

Reciprocal of N-Metab

R1=0.0004

R1=0.026**

5678

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

pH

Reciprocal of N-Metab

R1=0.050**

R1=0.097**

Stream-Figure 8. Quantile Regressions for Reciprocal of N-Metab

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-219
 28 

Quantile Regression Models: 

 1) (N Metab)-1 on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.57736 0.03476 16.60932 0.00000 

 TPL 0.00711 0.01278 0.55674 0.57821 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.75201 0.02642 28.46242 0.00000 

 TPL 0.01517 0.00971 1.56234 0.11949 

 2) (N Metab)-1 on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.56554 0.01120 50.50247 0.00000 

TNL 0.04044 0.01784 2.26685 0.02427 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.71437 0.00861 82.97004 0.00000 

 TNL 0.04258 0.01372 3.10450 0.00213

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-220
 29 

 3) (N Metab)-1 on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.55677 0.01954 28.49890 0.00000 

 TINL -0.00263 0.00780 -0.33721 0.73624 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.68362 0.01606 42.57156 0.00000 

TINL -0.01869 0.00641 -2.91525 0.00388 

4) (N Metab)-1 on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.97874 0.11364 8.61234 0.00000 

 pH -0.05914 0.01618 -3.65580 0.00031 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.02054 0.09258 11.02361 0.00000 

 pH -0.04321 0.01318 -3.27884 0.00119 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-221
 30 

IX) (pH Optima)-1 (Count Avg) 

0.0 0.1 0.2 0.3 0.4 0.5

0.1

0.2

0.3

0.4

0.5

Total-P (mg P/L)

Reciprocal of pH Optima

R1=0.0003

R1=0.000007

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.1

0.2

0.3

0.4

0.5

Total Nitrogen (mg N/L)

Reciprocal of pH Optima

R1=0.008

R1=0.01

0.0 0.5 1.0 1.5

0.1

0.2

0.3

0.4

0.5

TIN(mg/L)

Reciprocal of pH Optima

R1=0.0036

R1=0.030*

5678

0.1

0.2

0.3

0.4

0.5

pH

Reciprocal of pH Optima

R1=0.058**

R1=0.228**

Stream-Figure 9. Quantile Regressions for Reciprocal of pH Optima

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-222
 31 

Quantile Regression Models: 

 1) (pH Optima)-1 on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.27877 0.00992 28.09764 0.00000 

TPL 0.00098 0.00365 0.26778 0.78909 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.33076 0.01259 26.27345 0.00000 

 TPL 0.00017 0.00463 0.03669 0.97076 

 2) (pH Optima)-1 on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.27753 0.00304 91.16602 0.00000 

 TNL 0.00542 0.00485 1.11761 0.26482 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.33971 0.01179 28.80961 0.00000 

 TNL 0.01784 0.01879 0.94988 0.34310

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-223
 32 

 3) (pH Optima)-1 on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.27049 0.00575 47.07336 0.00000 

 TINL -0.00207 0.00229 -0.90100 0.36847 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.31274 0.01360 23.00122 0.00000 

 TINL -0.01334 0.00543 -2.45870 0.01463 

4) (pH Optima)-1 on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.43235 0.02257 19.15566 0.00000 

 pH -0.02210 0.00321 -6.88021 0.00000 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.60303 0.03572 16.88330 0.00000 

 pH -0.03837 0.00508 -7.54794 0.00000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-224
 33 

X) Arcsin(Sqrt( Stream Diatom Index)) 

0.0 0.1 0.2 0.3 0.4 0.5

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Total-P (mg P/L)

Arcsin(sqrt(Stream Diatom Index))

R1=0.0

R1=0.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Total Nitrogen (mg N/L)

Arcsin(sqrt(Stream Diatom Index))

R1=0.037**

R1=0.013

0.0 0.5 1.0 1.5

0.4

0.6

0.8

1.0

1.2

1.4

1.6

TIN(mg/L)

Arcsin(sqrt(Stream Diatom Index))

R1=0.002

R1=0.0

5678

0.4

0.6

0.8

1.0

1.2

1.4

1.6

pH

Arcsin(sqrt(Stream Diatom Index))

R1=0.096**

R1=0.120*

Stream-Figure 10. Quantile Regressions for Arcsin(sqrt(Stream Diatom Index))

 (Blue Line: 90% Quantile; Green Line: 50% Quantile)

 [Red: pH<6.5; (*: 0.05) or (**: 0.01) Significant]

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-225
 34 

Quantile Regression Models: 

 1) Arcsin(Sqrt(Stream Diatom Index)) on log(TP): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.99116 0.11702 8.47023 0.00000 

 TPL 0.00000 0.04302 0.00000 1.00000 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.36944 0.18371 7.45419 0.00000 

 TPL 0.00000 0.06754 0.00000 1.00000 

 2) Arcsin(Sqrt(Stream Diatom Index)) on log(TN): 

a) The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.05223 0.01845 57.04067 0.00000 

 TNL 0.10694 0.02939 3.63879 0.00033 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.36306 0.03371 40.43819 0.00000 

 TNL 0.09057 0.05370 1.68665 0.09294

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-226
 35 

 3) Arcsin(Sqrt(Stream Diatom Index)) on log(TIN): 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.96747 0.06225 15.54248 0.00000 

 TINL -0.01376 0.02485 -0.55369 0.58030 

b)The 90th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.36944 0.11734 11.67095 0.00000 

 TINL 0.00000 0.04683 0.00000 1.00000 

4) Arcsin(Sqrt(Stream Diatom Index)) on pH: 

a)The 50th Quantile Regression Model: 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.42251 0.22487 10.77290 0.00000 

 pH -0.20345 0.03201 -6.35618 0.00000 

b)The 90th Quantile Regression Model:

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.13968 0.15477 13.82515 0.00000 

 pH -0.11563 0.02203 -5.24877 0.00000 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-227
 36 

References: 

Bassett, G. and Koenker, R. W. 1982a. Tests of Linear Hypotheses and L1 Estimation. 

Econometrica, 50:1577-1583. 

Bassett, G. and Koenker, R. W. 1982b. An Empirical Quantile Function for Linear Models with 

iid Errors. Journal of American Statistical Association 77:407-415. 

Bassett, G. and Koenker, R. W. 1986. Strong Consistency of Regression Quantiles and Related 

Empirical Processes. Econometric Theory 2:191-201. 

Cade, B. S. and Noon, B. R. 2003. A Gentle Introduction to Quantile Regression for Ecologists. 

Frontiers in Ecology and the Environment 1: 412-420. 

Cade, B. S., Terrell, J. W., and Schroeder, R. L. 1999. Estimating Effects of Limiting Factors 

with Regression Quantiles. Ecology 80:311-323. 

Koenker, R. W. 1994. Confidence Intervals for Regression Quantiles. In P. Mandl and M. 

Huskova (eds.) Asymptotic Statistics, 349-359, Proceedings of the Fifth Prague Symposium, 

Physica-Verlag, Heidelberg, Germany. 

Koenker, R. W. and Bassett, G. 1978. Regression Quantiles. Econometrica 46:33-50. 

Koenker, R. W. and Bassett, G. 1982. Robust Tests for Heteroscedasticity Based on Regression 

Quantiles. Econometrica 50:43-61. 

Koenker, R. W. and d’Orey, V. 1987. Computing Regression Quantiles, Applied Statistics, 

36:383-393, 

Koenker, R. W. and d’Orey, V. 1994 A Remark on Algorithm AS229: Computing Dual 

Regression Quantiles and Regression Rank Scores. Applied Statistics 43:410-414 

Koenker, R. W. and Machado, J.A.F. 1999. Goodness of Fit and Related Inference Processes for 

Quantile Regression. Journal of the American Statistical Association, 94:1296 -1310

 Koenker, R., Ng, P., and Portnoy, S. 1994. Quantile Smoothing Splines. Biometrika 81:673-

680. 

Kolbe, R. W. 1927. Zur Őkologie, Morphologie, und Systematik der Brackenwasser-Diatomeen 

(The ecology, morphology and systematics of the brackish-water diatoms) Pflanzenforschung 

(Jena) 7: 1-146. 

McClain, C. R. and Rex, M. A. 2001. The Relationship Between Dissolved Oxygen 

Concentration and Maximum Size in Deep-Sea Turrid Gastropods: An Application of 

Quantile Regression. Marine Biology 139:681-685. 

Mosteller, F. and Tukey, J. W. 1977. Data Analysis and Regression. Reading, Massachusetts: 

Addison-Wesley. 

Niu, X.F. 2009. Statistical Analysis of Stream Data-Periphyton Metrics (Weaver Region 

Peninsula). Technical Report Submitted to the Florida Department of Environmental 

Protection. 

Terrell, J.W., Cade, B. S., Carpenter, J., and Thomson, J. M. 1996. Modeling Stream Fish 

Habitat Limitations from Wedged-Shaped Patterns of Variation in Standing Stock. 

Transactions of the American Fisheries Society 125:104-117. 

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-228
 

Appendix 6-G

 

 

 

Florida’s Nutrient Criteria Based on Rapid Periphyton Survey Data

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Florida’s Nutrient Criteria Based on Rapid Periphyton Survey Data 

June 2, 2009

Lei Zheng  

Tetra Tech, Inc.  

I. INTRODUCTION

RAPID PERIPHYTON SURVEY (RPS)

Florida Department of Environmental Protection (FDEP) conducted rapid periphyton surveys (RPS) as a

measure of periphyton abundance in stream reaches.  Since the RPS included direct measures of

nuisance algae (% algal cover, depth of algal slime), it was thought to be a potentially useful indicator of

use impairment.  The objectives of this analysis were to determine associations between nutrient

enrichment and algal response as measured with the RPS, and to develop potential nutrient endpoints.

RPSs used a 100 meter stream reach consistent with the FDEP bioassessment protocols. The 100m

segment of stream was evenly divided into 11 transects and each transect was flagged/marked.  Nine

sampling points were selected approximately equidistant along each transect. Periphyton

abundance/thickness was visually estimated at each sampling point and was assigned a rank from 0 to 5,

where 0 meant no algae and 5 meant high algal abundance (>20 mm).  In the middle of each transect,

canopy cover was measured using a spherical densitometer and percent canopy cover

calculated for each transect.

CONCEPTUAL MODEL

We developed a simple conceptual model of factors that may potentially contribute to algal

thickness in FL streams (Figure 1)

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Figure 1. Conceptual model of excessive algal accumulation in a stream ecosystem.  

Six principal factors may affect algal production in FL streams, i.e., temperature, flow (velocity), turbidity

(color), canopy cover, grazing, and nutrients.  The effects of accumulation time and physical

habitat/substrate on algal biomass are hard to measure in observational studies, so we did not include

them in our model.  We expect: 1) higher temperatures and nutrient concentrations to stimulate the

growth of periphyton and consequently lead to high algal biomass, 2) higher turbidity and canopy cover

to lead to light limitation and reduce the abundance of benthic algal biomass, and 3) higher grazing also

to reduce algal biomass.  Stream velocity was more complicated to predict since flow could increase

nutrient uptake rates for periphyton at intermediate level but reduce algal biomass at during scouring

floods.  We used a surrogate measure of flow velocity from FDEP’s habitat measurement and examined

the effect of temperature on stream algal abundance. We found that this surrogate measure of flow

either did not reflect scouring floods or did not have a strong effect on algal biomass. The correlation

between temperature and algal biomass was weak (Spearman r=0.08).  Therefore, we dropped both

flow and temperature from further analysis.  Information on grazers was available as scraper density

from the benthic macroinvertebrate sampling and showed a slightly positive correlation with algal

thickness (Table 1). We expect it was due to inaccurate measure of true grazer density so we dropped

this parameter as well. The most critical predictors remaining were measures of light penetration

(canopy cover and water color) and nutrients (total N and P).   

A theoretical model of algal biomass response to light and nutrient concentration was represented with

the following equation (Yi is algal biomass):

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Yi = a[0] + a[1] * nitrogen + a[2]* phosphorus + a[3] * canopy + a[4] * color  

II. DATA EXPLORATION ‐ CORRELATIONS

Part of the rapid periphyton survey was measuring algal mat thickness in 6 ordinal categories from 0 to 5

according to the following rules:

“1” for algae less than 0.5 mm OR no algae visible but surface is slimy (including muck),

“2” for 0.5 mm to 1 mm,  

“3” indicates an algal cover of greater than 1 mm but less than 6 mm,  

“4” for 6‐20 mm,  

“5” for algae over 20 mm.

In order to compare periphyton thickness among stream reaches or among transects and to relate

nutrient concentrations to algal thickness in a reach, raw categorical thickness data were transformed

by FDEP into a thickness score.  The algal thickness score was a ranking based on the following:

Thickness Raw Thickness Category Thickness Score

0 0 0

<6 mm <3 1

<6‐20mm <5 2

>20 >=5 3

The Type score was based on the following:

Algal Type Type Score

None 0

Diatoms 1

Filamentous 2

Also the final algal score was the product of the thickness score and the type score (i.e., thickness score

* type score).  All scores were assigned to each of the potential 99 monitoring points comprising a

sampling event.   The sum and average scores were calculated to summarize the data for each sampling

transect and stream reach.  

Objectives:  

1. To examine potential causal relationships between nutrients, other covariates, and algal mat

thickness in FL streams;  

2. To detect any change points or non‐linear responses from Loess regression and change point analyses.

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Table 1. Spearman correlations between algal thickness parameters and environmental variables.   

Mean

Thick

Max

Thick

Mean

ThickSc

Max

ThickSc

Mean

TypeSc

Max

TypeSc

Mean

AlgSc

Max

AlgSc

Chl a 0.22 0.18 0.22 0.16 0.16 0.16 0.16 0.14

CanopyCov ‐0.38  ‐0.38  ‐0.36  ‐0.37  ‐0.35  ‐0.36  ‐0.35  ‐0.35

MinCanopy ‐0.41  ‐0.42  ‐0.39  ‐0.40  ‐0.37  ‐0.40  ‐0.38  ‐0.39

TN ‐0.05  ‐0.09  ‐0.06  ‐0.12  ‐0.07  ‐0.08  ‐0.10  ‐0.13

TIN 0.22 0.18 0.22 0.17 0.17 0.16 0.16 0.14

OrgN ‐0.29  ‐0.33  ‐0.30  ‐0.36  ‐0.25  ‐0.25  ‐0.29  ‐0.32

NH4 ‐0.16  ‐0.21  ‐0.15  ‐0.23  ‐0.19  ‐0.20  ‐0.23  ‐0.26

TKN ‐0.28  ‐0.32  ‐0.29  ‐0.35  ‐0.25  ‐0.25  ‐0.29  ‐0.33

Nox 0.29 0.26 0.29 0.36 0.15 0.25 0.25 0.23

TP ‐0.04  ‐0.04  ‐0.04  ‐0.03  ‐0.04  ‐0.03  ‐0.04  ‐0.05

DO 0.01 0.10 0.00 0.09 0.06 0.11 0.09 0.15

COND 0.25 0.23 0.24 0.22 0.18 0.23 0.22 0.21

pH 0.24 0.24 0.24 0.24 0.20 0.24 0.24 0.24

Color ‐0.42  ‐0.42  ‐0.42  ‐0.42  ‐0.36  ‐0.38  ‐0.40  ‐0.41

TEMP 0.07 0.05 0.09 0.07 0.09 0.05 0.04 0.04

Velocity 0.00 0.04 0.00 0.04 0.02 0.03 0.04 0.04

Scrap_Dns 0.22 0.29 0.21 0.28 0.19 0.24 0.25 0.29

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Figure 2. Factors contributing to algal biomass. The smooth curves are the locally weighted smoothing

lines. The vertical lines are the change points (solid lines) and their confidence intervals (dashed lines).

The bivariate plots showing relationships between algal biomass and various environmental variables

are presented (Figure 2).  Spearman correlations between different parameters of algal biomass and

environmental variables, Lowess lines along the environmental gradients, and change point analysis

results are also presented in these graphs.  Several environmental variables were unexpectedly

correlated with algal biomass, including pH, TKN, and organic nitrogen (Table 1). TKN, organic nitrogen,

and pH, as expected, were strongly correlated with color (Spearman correlations were 0.79, 0.80, and ‐

0.52, respectively). These strong correlations may explain the unexpected correlations between pH,

organic nitrogen, and periphyton thickness since water color can cause light limitation and therefore

directly reduce periphyton thickness.  Other noticeable correlations were observed among conductivity,

TP (r = 0.39), and Chl a (r=0.45), which are common correlations in streams. High conductivity, TP, and

water column Chl a are often associated with watershed urbanization.

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Periphyton thickness was correlated with nitrate + nitrite, canopy cover, and water color, but not with

TP (Table 1, Figure 1). According to these analyses, periphyton abundance increased when the NO2+3

concentration was above 140 μg/L and reached a peak when NO2+3 concentrations reached 1100 μg/L.

We also observed a decline of algal abundance when color increased from approximately 20 platinum‐

cobalt units (PCU) to 150 PCU, and average canopy cover increased from 45% to 80%. Color was a strong

confounding factor in all of these analyses since it was correlated to some extent with canopy cover,

NO2+3 concentration, and TP concentration.  

Summary: Scatter plots with change point analysis, Lowess regression, and Spearman correlation

coefficients were created for each pair of relationships.  Noticeable relationships were:

a. Algal thickness was strongly light limited in most FL streams, and was limited by both forest

canopy cover and water color;

b. Algal thickness was strongly correlated with color, a factor that potentially led to light limitation

but also released algae from nutrient limitation since higher color was associated with higher

nutrient concentrations;

c. The only nutrient variable that was significantly correlated with algal thickness was NO 2+3

concentration.  However, this correlation was confounded by the correlation between color and

algal thickness; in other words, colored streams had both lower NO2+3 concentrations and

reduced algal thickness compared to clear streams.

III. NUTRIENT LIMITATION (N:P RATIOS)

Data sources: 1) FL nutrient gradient study with rapid periphyton survey; 2) Vetted Benchmark Sites

revised.xls (dated 20090331).

Objectives: To examine whether Florida streams were primarily limited by N or P, or whether they may

be co‐limited.

Table 2. Molar N:P ratios in benchmark sites and gradient stream sites.

Percentile 0 0.1 0.25 0.5 0.75 0.9 1

Percentile distribution for benchmark sites

NO2+3: TP 0.0 0.1 0.1 0.8 3.9 10.8 36.5

DIN:TP 0.1 0.4 0.8 2.5 6.0 12.2 37.6

TN:TP 2.3 6.8 14.2 22.7 45.5 79.1 108.6

Percentile distribution for gradient stream sites

NO2+3: TP 0.0 0.0 0.2 0.7 2.7 12.5 770.0

DIN:TP 0.0 0.3 0.6 1.6 4.0 15.5 776.0

TN:TP 0.1 3.2 6.3 12.0 25.3 47.1 4110.9

Summary: Based on N:P ratios, nitrate + nitrite was likely the principal limiting nutrient for algal growth

in most FL streams, but a minortity of streams appear to be co‐limited. We examined the DIN: TP and

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-235
NO2+3 : TP ratios in benchmark sites and found that few samples had a molar N:P ratio of more than 17.

We also examined the NO2+3 : TP ratio in the gradient study sites and found that more than 90% of the

samples had both DIN:TP and NO2+3: TP ratios less than 17. It is possible that these streams are either

nitrate limited or co‐limited by N and P. Therefore, our follow‐up analyses must consider both N and P.   

IV. PERIPHYTON AND PHYTOPLANKTON

In examining the RPS data, we found an inverse relationship between algal mat thickness, and

phytoplankton (as chlorophyll).  This relationship was only found in streams with low canopy

cover, that is, in streams where sufficient light reached the water surface.  We explored the

relationship between periphyton and phytoplankton further below.

Data sources: FL nutrient gradient study with rapid periphyton survey  

Objectives:

1).To further explore relationships between nutrients and algal thickness in classified FL streams (clear,

medium, and colored streams);  

2). To examine the possible interactions between light and nutrient limitations and possible interactions

between different nutrient variables.   

1. Stream classification

The shift in periphyton abundance response to color mostly occurred when water color exceeded  75

PCU (Figure 2). For better confidence, we classified streams into three color categories: color <= 40 PCU

as clear streams, 40‐100 PCU as intermediate streams, and >100 PCU as colored streams. We also

selected transects with less than 40% canopy cover and averaged algal thickness in the remaining

transects as the mean algal thickness in each stream reach (Figure 5). Since the shaded stream segments

were most likely light limited, excluding these light limited stream segments was designed to  strengthen

the signal of the algal abundance response along an increasing nutrient concentration gradient.

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Figure 3. Periphyton and phytoplankton algal biomass in different colored streams. Different letters

on top of each box indicate significant differences (P<0.05).  

The observed patterns of algal biomass in different colored streams (Figure 3) indicated that clear

streams had higher algal thickness than colored streams. At the same time, intermediate colored

streams had lower periphyton biomass than clear streams, but higher planktonic chlorophyll a (measure

of algal biomass). Highly colored streams had significantly lower periphyton biomass than both clear and

intermediate colored streams, but had comparable phytoplankton biomass to clear streams.

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Figure 4. Relationships between nutrient concentrations and algal thickness in clear (<=40, a1‐a3),

intermediate (40~100, b1‐b3) and colored (>100, c1‐c3) streams.

The relationships between nutrients and periphyton thickness were stronger in clear streams (Figure 4

a1‐3) than in colored streams (Figure 4 c1‐c3), indicated by the Lowess regressions and higher Spearman

correlations in clear streams. Greater correlative relationships were observed between nitrogen

(especially total nitrogen) and benthic algal thickness. The effect of phosphorus seemed to be negligible,

except in clear streams.  Nutrients were not related to benthic algal biomass accumulation in colored

streams, probably due to potentially stronger light limitation.

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Figure 5. Relationships between nutrient concentrations and Chl a concentrations in clear (<=40, a1‐

a3), intermediate (40~100, b1‐b3) and colored (>=100, c1‐c3) streams.

In contrast to attached algae, relationships between nutrients and phytoplankton Chl a were stronger in

colored streams (Figure 5 b1‐c3) than in clear streams (Figure 5 a1‐a3), especially with TN.  The

spearman correlations between Chl a and TN were 0.32 and 0.42 respectively in intermediate and high

color streams but was ‐0.16 in clear streams.  With increased color and potentially stronger light

limitation for periphyton, phytoplankton appear more responsive to nutrient concentrations than

periphyton in more colored streams. There may be signal of Chl a response to phosphorus in colored

streams, but it was weaker than that for TN.

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The observed relationships between algal thickness and nutrient concentrations were weak due to light

limitation in most of these streams. Light limitation to periphyton is driven by three factors: canopy

cover, color, and particulate turbidity (including phytoplankton). In relatively clear streams, periphyton

biomass is mainly regulated by nutrient limitation so it is easier to find a relationship between

periphyton thickness and nutrient concentrations. In heavily shaded / colored streams, light limitation

becomes the dominant limiting factor to periphyton growth so nutrient limitation is less of a driving

force for periphyton growth.  

If light penetration into the water column was limited by water color rather than tree shading, then

phytoplankon algae, which are floating cells, would take advantage of the available light because they

can float at or near the surface, and are not attached to substrates on the stream bottom. In this

situation (colored streams with limited or no tree canopy), we may expect phytoplankton chlorophyll to

respond to nutrient enrichment.

Due to co‐linearity among nutrients and a number of factors, e.g., color and canopy cover, alternative

approaches could be used to infer the causal effect of nutrients on algal abundance. Classification based

on stream color may be able to solve most of the problems and would be simple and easy to interpret.  

2. Clear stream (color<=40)

a. Bivariate analysis

The mean periphyton thickness scores in clear (<=40 color unit) and unshaded streams(<=40% canopy

cover) responded weakly to nutrient concentrations (Figure 6a‐c).  Among all variables, TN and TIN were

most strongly associated with algal abundance measurements (Figure 6 b, c).  TP concentration was not

a strong predictor of algal biomass rank alone (Figure 6a). However, N and P could be co‐limiting algal

growth in the stream system. To verify that, we standardized/scaled  nutrient concentrations according

to their range, mean, and standard deviation, and ranked both scaled N and P from 1 to 10 according to

their percentile range. We then summarized the nutrient rank at a single site as the sum of N and P

ranks.  The combined rank of nutrient variables (TN+ TP and NOx +TP) showed stronger effects on algal

thickness (Figure 6d, e), indicating possible N and P co‐limitation.  Change points based on this analysis

were observed at a TN+TP rank of approximately (10, 13, 14) and a NOx+TP rank of (8, 11, 14). If both N

and P were controlled equally, the corresponding concentrations are shown in Table 3.

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0.01 0.02 0.05 0.10 0.20

01234

TP.raw

Algal thickness

Spearman r= 0.19

a

0.2 0.5 1.0 2.0 5.0

01234

TN.raw

Algal thickness

Spearman r= 0.43

b

0.002 0.020 0.200 2.000

01234

NOx.raw

Algal thickness

Spearman r= 0.5

c

4 6 8 10 12 14 16

012345

TNP

Algal thickness

Spearman r= 0.56

d

4 6 8 10 12 14 16

012345

NOxP

Algal thickness

Spearman r= 0.58

e

Figure 6. The relationships between periphyton thickness and TN, TP, and NOx concentrations as well

as combined ranks of nutrients in clear streams (transect canopy <=40% and color <=40). To calculate

the TNP and NOxP rank in 8d and 8e, nutrient concentrations were first scaled/standardized according

to their mean and standard deviation; and were then were ranked 1 to 10 according to their

percentile range. Nutrient rank(TNP and NOxP) at a single site as the sum of N and P ranks.  Each dot

represents a stream reach. The dashed curves are the Loess regression lines 95% confidence limits;

and the vertical lines are change points and 95% confidence limits.

Table 3. Change point analysis from Figure 8d,e and their corresponding nutrient concentrations.  

Model    TNP     NOxP   

ChangePoint    Lower CL Mean Upper CL Lower CL Mean Upper CL

Rank 10 13 14 8 11 14

TN/NOx 1.02 1.39 1.55 0.240 0.85   

TP    0.036 0.04 0.045 0.026 0.036 0.045

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b. Logistic regression and contour plots

Since the response variable algal thickness rank is a categorical variable, logistic regression analysis may

be more appropriate for examining the causal effect of nutrients and other environmental factors. To

expand sample size and examine the effect of canopy and nutrient interactions, we treated each

transect as an independent sample.  When 50% or more of a transect exceeded an algal thickness rank

of 5 (>20 mm thickness), it was considered impacted. A number of logistic regression models were

constructed to examine the relationship between the probability of impact and TN, TP, canopy cover

and their interaction terms.  

Table 4. Logistic regression models of probability of algal thickness impairment as a function of

nutrient and shading variables.

Akaike's information criterion (AIC) is a measure of the goodness of fit of an estimated statistical model  

and describes the tradeoff between bias and variance in model construction.  It is often used for model

selection.  The best regression model for TN, TP, and canopy cover according to AIC criterion was: TN  +

TP + canopy .   The best regression model for NOx, TP, and canopy cover according to AIC criterion was:  

NOx * TP  + NOx * Canopy + TP * canopy (Table 4).   

A C‐index (the probability of concordance) was used to measure the predicted probability of response

and actual response.  A value of 0.5 indicates random predictions and a value of 1 indicates perfect

prediction. Both models performed reasonably well, though the C‐index for both models was less than

0.8. The Nitrate model (model 2) was more complicated due to significant interactions among predictor

variables, and was relatively less precise than the TN model (model 1).   

Estimate Std. Error z value Pr(>|z|) Significant

Model 1: Prob= TN  + TP + canopy   

(Intercept)         ‐1.5542 0.2119  ‐7.336 2.20e‐13 ***

TN 0.8849 0.2083 4.248 2.15e‐05 ***

TP     0.6050 0.1878 3.221 0.00128 **

Canopy 0.6348 0.1897 3.346 0.00082 ***

AIC: 184.2, C‐index=0.779

Model 2: Prob= NOx * TP  + NOx * Canopy + TP * canopy

Intercept  ‐1.7133 0.2522  ‐6.79 0 ***

NOx 0.9733 0.2518 3.87 0.0001 ***

TP 0.6513 0.2149 3.03 0.0024 **

Canopy 1.0472 0.2256 4.64 0 ***

NOx*TP  ‐0.7474 0.2815  ‐2.66 0.0079 **

NOx*Canopy  ‐0.1664 0.1924  ‐0.86 0.3872   

TP*Canopy  ‐0.504 0.2184  ‐2.31 0.021 *

AIC=211.59, C‐index=0.765

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Figure 7. Contour plots of logistic regression results where canopy is assumed to be at its mean value.

The contour lines are probability of impact. The red lines are 25% probability and the triangles are the

N and P concentrations where both N and P are equally controlled at 25% impairment probability.

The model results were plotted as contour plots where impact probabilities are shown as contour lines

and the two nutrient predictors compose the two axes (Figure 7). Mean values of canopy cover were

used in the model prediction. Each blue dot represents a site and red lines are the 25% probability of

impairment, a threshold that was considered as the unacceptable level based on consistency with the

USEPA nutrient criteria guidance (25% of all sites). The purple triangles are the maximum allowable N

and P concentrations that have less then or equal to 25% impact probability. According to this analysis,

the TN and TP criteria would be 1.54 and 0.11 mg/L, respectively (Table 5).

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-243
Table 5. Model derived nutrient criteria based on 25% impairment probability

Model 1 Mean Upper confidence Lower confidence

TN 1.54 1.08 4.07

TP 0.11 0.08 0.06

Model 2    

NOx 0.55 0.32 3.61

TP 0.15 0.09 0.06

3. Intermediate colored (40~100) and colored streams (color>100)

The negative relationships between SCI scores and chl a concentrations in colored streams

(Figure 8) indicate declining water quality with increased phytoplankton biomass. At the same

time, dissolved oxygen also declines with elevated chl a levels in the water column. The

declines in DO concentrations may be affected by elevated microbial respiration at the bottom

of these light limited streams.  

Figure 8. Correlations between water column chl a and DO, SCI, and periphyton in intermediate (a1‐3)

and high color(b1‐3) streams.  

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-244
Summary:   Stream classification.  

a. Clear streams:

i. Algal thickness in clear streams (30 streams, 220 observations) was correlated with TN

concentrations only; not with other nutrient variables; multiple variable interactions were

possible;

ii. Multiple logistic regression analyses indicated potential interactions among predictors. Both

TN and TP, and NOx and TP models were significant;

iii. Contour plots may be able to help guide nutrient criteria selection; however, the

impairment thresholds and the allowable impairment probabilities would have to be

determined by management.    

b. Colored streams:

i. Periphyton thickness became increasingly limited by light and correlations with nutrients

were very weak; however, water column Chl a concentrations became increasingly more

highly correlated with nutrients;

ii. Planktonic algal biomass (Chl a)  was correlated with TN and TKN concentrations;

iii. Dissolved oxygen in the water column was negatively correlated with water column Chl a

concentrations;

iv. SCI was also negatively correlated with Chl a in the water.

TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters B1-245