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



## 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, Offi ce of Water, Office of Science and Technology, Health and Ecological Criteri a Division, Washington, DC.)

The following appendices from the original technical support documen t are included as a courtesy, and provide a detailed descri ption of the stressor response analysis.TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-1 

## Appendix B-1. FDEP’s Stressor-Respon se Analyses for Florida Streams

The U.S. Environmental Protection Agency (U.S. EPA) (USEPA 2000a) describes several general approaches, with certain op tions, that can be used to devel op 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-re sponse relationship could be described by a model (e.g., trophic state classifica tion, regional predictive model, biocriteria, etc.), which in turn would quantitatively link nut rient concentrations to the relative risk of environmental harm. Florida Department of En vironmental Protection (FDEP) supports this approach, since it establishes a correlative relati onship between nutrients and valued ecological attributes, and is linked to the maintena nce of designated uses of waterbodies.

In attempting to define the effect of anthropogenic nutrient increas es on the biological

communities in Florida’s stream s, 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 In dex (SDI) (currently under development) as well as the individual metrics that comprise thes e 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 fr equency of occurrence and abundance of algae (as measured via the Rapid Periphyton Survey (RPS)).

To investigate the potential re lationships between nutrients a nd biological response measures, FDEP utilized a variety of statistical techniqu es, including linear regression, multiple linear regression, non-linear re gression, LOESS regression, change poi nt analysis, classification and regression tree (CART) analysis, correlation an alysis, and paired vari able plots. A brief

discussion of the results from some of the asse ssments performed is provided below, with more detailed information concerning the analyses provided in the referenced appendices.

The results of the analyses gene rally indicate that many of the biological measures evaluated exhibit a significant adverse response to anth ropogenic 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 statisti cal 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 uptak e) 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 fr om geologic phosphate deposits lying near the surface, to

 Streams that can be any combination of the above.TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-2 The source water and the geologic c onditions also influence other wa ter quality variables such as pH and specific conductivity, which can have an overarching eff ect 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 canopi ed 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 biologi cal responses in open non-wadeable Wisconsin rivers. The relationships were mu ch 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 meas ures exhibited a wedge-shaped response to increases in nutrien t concentrations. At relatively low nutrient concentrations, the biotic indices ranged widely, but at relatively high concentrati ons, the indices generally were poor. The wedge-shaped distribution indicates that at low nutrient concentrations, factors other

than nutrients often limit the health of bi otic communities, whereas, at high nutrient concentrations, nutrients and f actors correlated with high nutr ient concentrations are the predominant factors. Simply stated, it is di fficult to find a healthy population at a nutrient enriched site, but common to find a poor population at low nutrient sites du e to the influence of

other factors.

This type of response is not surp rising given the fact that the biotic community represents the overall ecological integrity of th e stream (i.e., physicochemical ha bitat and biotic integrity) and thus provides a broad measure of the cumulative e ffect 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 bi otic communities present. In Florida streams, the response to nutrients is confounded by broad ranges of biologically importa nt physicochemical parameters such as pH, color, and specific conductance th at occur naturally, sometimes at small spatial scales. As Robertson et al. (2006) concluded, even with these confounding fact ors, it is important

to establish numeric nutrient cr iteria to reduce the risk of ad verse 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 physicochemi cal factors described above, Florida streams also exhibit a very wide range of nutrient levels, especially phosphorus, that occur regionally under natu ral conditions. Phosphorus concen trations can naturally range from less than 10 ppb (highly ol igotrophic) 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 con centrations, 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 Inde x (SCI), the individu al measures of the macroinvertebrate community that comprise the index, and the abundance of other taxonomic groupings. Appendix B-2 has an explanation of th e various biological measures. Multiple linearTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-3 regression techniques were us ed to evaluate potential re lationships between nutrient

concentrations and the measures of the macroinvertebrate community.

The results of the analyses indi cate that several macroinvertebra te variables, including SCI, % sensitive taxa, % clinger taxa, % clingers, % long lived taxa, % very tolerant taxa, and % dominant taxa, exhibited a significant adverse response to increased leve ls of nitrogen. In addition, the analyses indicated that the macroinvertebrate comm unity also responded to other

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

unmeasured variables such as water velocity, water level, ha bitat conditions, and antecedent conditions also play an impor tant 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 in cluded some form of nitrogen and a combination of the other environm ental 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 rela tionship as described previously.

Figure B1-1 shows the typical relationsh ip observed between nutrient levels and macroinvertebrate response variables. At low nutri ent levels, the response is highly variable due to the controlling effects of ot her factors such as pH, conductiv ity, color, flow, water level, habitat conditions, etc. The anal yses also demonstrate that th e macroinvertebrate community responds negatively to increased nutrient levels, however, due to the influence of other

environmental factors on the response, FDEP could not iden tify specific thresholds for establishing numeric nutrient criteria. The macroi nvertebrate analyses and results are presented in greater detail below.



### Exploratory Analysis of Periph yton Response to Nutrients

Since the algal community can be expected to res pond more rapidly and directly to nutrients than macroinvertebrates, FDEP also evaluated th e relationship between the periphyton community and nutrient levels in streams. The primary fo cus 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 hi gh dissolved oxygen (DO), % oligos aprobic 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 techni ques and change point analyses was used to evaluate potential relations hips 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 nutrien t concentrations, the analyses were conducted for each nutrient region independently, starting w ith the panhandle and peninsula regions, for

which more data exist.

As with the macroinvertebrate community, the an alyses of the periphyton data indicate that several algal variables exhibited a significant ad verse response to increased nutrient levels. InTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-4 addition, the analyses indicated th at periphyton also respond to ot her environmental factors such as water color, conductivity, and pH. However, other unmeasured variables such as water velocity, water level, and antecedent conditions like ly play an important role in determining the composition of the periphyton comm unity. Since the biota are res ponding to the combined effect of all of these factors along w ith nutrients, the natural variatio n in these other environmental

factors confound the observed biol ogical response to nutrients.

The results of the multiple-linear regression an alysis for the panhandle nutrient region are summarized in Table B1-1. Due to the confounding interactions between th e 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 show ed that various forms of nutrie nts were significant factors in determining the periphyton response, change point analyses were performed to attempt to determine where signific ant thresholds in the periphyton resp onse to nutrients occurred. Prior to performing the change point analyses, the data we re adjusted for the other significant variables indicated by the regression analyses. An exampl e of the step function and associated change point and confidence interval is provided in Fi gure B1-2, and the results of the change point analyses for the periphyton response variables ve rsus 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 mi nimally disturbed nutrient benchmark sites (see Chapter 2f) and appear to be hi ghly influenced by factors other than nutrients. Most notably, these data were analyzed using two different la boratory method detection limits (MDL) for TP of 4 μg/L and 20 μg/L, and this inconsistency appeared to have significantly in fluenced 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 ch ange point was also detected. The secondary change points ranged from 67 ppb to 131 ppb TP, how ever, they were not significant at the 95% confidence level. These changes were significant at the 75% to 80% leve l with extremely wide confidence intervals. The change point analyses conducted are presented in greater detail below.

As with the analyses of the macroinvertebrate da ta, the results of the pe riphyton data analyses

establish that increased nutrient levels ha ve adverse impacts on the periphyton community, however, the response to nutrients is confounded by other environm ental factors and FDEP could identify no clear thresholds to form the bases of numeri c nutrient criteria.



### Quantile Regression Analysis of Pe riphyton Response to Nutrients

As described previously, the biological respons e to nutrients is conf ounded by other measured environmental parameters as well as a number of unmeasured factors. Often, these confounding variables cause the biological measures to exhi bit a wedge-shaped response to increased nutrient levels. At relatively low nutrient concentrations , the biological measures range widely, but atTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-5 relatively high concentrations, the measure is generally poor with less variation. The wedgeshaped distribution indicates that at low nutrient concentrations, f actors other than nutrients often limit the health of biotic communities, whereas, at high nutrient concentrations, nutrients and factors correlated with high nutri ent concentrations are the predominant limiting factors. As found with the analyses of the m acroinvertebrate 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 nutrien t levels have negative bi ological effects, it is important to confirm this finding using statistica l techniques better suited to describing complex relationships such as those found with nutrient effects on biolog ical communities. Therefore, quantile regression was used to confirm that increa sed nutrient levels resultin adverse biological responses in Florida streams.

Quantile regression is a useful method for estimati ng effects associated with a measured subset of limiting factors while accounting for the effect s of unmeasured factor s in an ecologically realistic manner (Cade et al. 1999). This regres sion 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 me asured. 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 anal ysis as dependent variables a nd TP, total nitrogen (TN), total inorganic nitrogen (TIN), and specific conductanc e as independent variables. The logarithm (Base e) transformation was pe rformed 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 qua ntiles 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 variab le based on the higher significance of pH found in the earlier analyses.

Detailed results of the quantile regression an alyses are provided below for the Panhandle and Peninsula, respectively. The results for the Panha ndle 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 regres sion analysis using SDI as the dependent variable is provided below.

In contrast, the results for the peninsula indi cate that total nitrogen was the primary nutrient influencing the periphyton community in thatregion. This is not unexpected since the phosphorus-rich geology of the peninsula result s in much higher natural background phosphorus levels when compared with the panhandle. The higher natural phosphorus le vels 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 optim a score) showed a significant relationship toTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-6 total inorganic nitrogen and some metrics (i.e ., % pollution tolerant taxa and % TIN sensitive taxa) were significantly correlated to TP. The anal ysis also indicated th at 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 re sult 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 panha ndle and nitrogen in the peninsula, has a significant negative effect on periphyton compos ition 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 pr otect against adverse biological

effects.



### Analysis of Rapid Periphyton Survey Data

Because excessive abundance of algae has been id entified as a nuisance condition that should be avoided, the role of nutrients in determining the frequency of occurren ce and abundance of algae in streams was also examined (in addition to the compositional metrics for the periphyton community described previously). The abundanc e of periphyton found in streams was evaluated using the Rapid Periphyton Survey (RPS) method, c onsisting of a series of 99 observations (nine

observations across each of 11 tr ansects along a 100 meter stream reach) of periphyton presence, thickness and type, per DEP-SO P-001/01 FS 7130. The RPSs were conducted in streams across the state in conjunction w ith nutrient and other physicochemical measurements.

Correlation analysis was conducted to determin e which nutrient and physicochemical variables exhibited the greatest influence on algal abundance in stream s. Due to data limitations, the analysis of the algal abundance data was conducte d 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, colo r, pH, Total Kjeldahl Nitrogen (TKN), organic nitrogen, and nitrate-nitrite (NO 3 

### -NO 2 

### ) were the factors most highly corre lated to algal thickness. The strong correlations with color and canopy cover were expected since they can cause light limitation and therefore directly reduce peri phyton 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 w ith color (Spearman correlations were 0.79, 0.80, and -0.52, respectively).

As shown in Figure B1-3, peri phyton thickness appears to be significantly correlated with NO 3 

### - NO 2 

### , 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,

NO 3 

### -NO 2 

### concentration, and TP concentration. The in itial analyses of the rapid periphyton assessment data are provided in greater detail in Appendix B-11.

To account for the confounding effect of color, st reams 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 st ronger in clear streams (Figure B1-4, a1–a3)TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-7 than in colored streams (Figure B1-4, c1-c3), i ndicated by the stronger spearman correlations as well as improved LOESS regression s in the clear streams. The main relationships observed were between nitrogen parameters and benthic alga l 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 th e relationship between nut rients 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 to tal 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 st reams, but was -0.16 in cl ear streams. With the increased color and stronger light limitation to periphyton, phytoplankton appear more able to

utilize the available nutri ents than periphyton. Chl. a appeared to respond somewhat to phosphorus, but all of the respons es were statistically weak.

Further analysis of unshade d clear streams (i.e., color ≤ 40 and canopy cover ≤ 40%) indicate that TN and TIN were the variables having th e strongest correlation with algal abundance measurements (Figure B1-6, a-c). The analysis al so showed that TP concentration alone was not a strong predictor of the algal biomass rank. Howe ver 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 concen trations were ranked from 1 to 10 based on their range, mean, and standard deviation, and the ranked nutrient variables were combined (TN+

TP and NO

x 

### +TP) to test if the addition of TP impr oved the nutrient relationships with algal thickness. As indicated in Figure B1-6, d-e, th e combined nutrient variables have a stronger correlation to algal thickness than the individua l nutrient concentrations , potentially indicating nitrogen and phosphorus co-limitation for some st reams. This finding also indicates that both nitrogen (TN and NO

x 

### ) and phosphorus are significant in cont rolling algal thickness in streams. More details concerning these anal yses are provided in Appendix B-11.



### FDEP’s Conclusions

FDEP has conducted multiple analyses using a variet y of statistical techniques to investigate the effects of anthropogenic nutrient increases on the biological comm unities in Florida’s streams. These analyses were performed to define relations hips between nutrients a nd biological response

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

influence of nutrients on biol ogical indices such as the SC I, the SDI (currently under development), the individual metrics that compri se these indices, and ot her biological measures

such as chl. a , taxonomic composition of macroinvert ebrate and algal communities, and frequency of occurrence a nd abundance of algae (RPS).

The results of the analyses gene rally indicate that many of the biological measures evaluated exhibit a statisticallysignificant adverse response to nutrient enrichment, however, the relationships between the biologi cal response variables and nutr ient 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 relatio nships between measures of the biological communities and nutrient levels. While FDEP believes the effect of nutrients on theTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-8 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 crit eria to prevent adverse biological effects in

Florida streams.

The statistical significance indicates that numeric nutrient criteria shou ld be established and supports the decision to implement an alternativ e 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 th at could be used as wa ter quality criteria, the relationships that were determined, while relatively weak, do support th e values derived using the Nutrient Benchmark Approach. Both the an alysis of the RPS (re garding probability of increased algal thickness) and th e analysis of the s econd 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 genera ted using the Benchmark Distribution Approach.TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-9 Table B1-1. Summary of Multiple Linear Re gression 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 r 2

= 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 RegionTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-10 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 re lationships and darker red shading indicates stronger negative relationships. Values given are Spearman r values.TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-11 Figure B1-1. Example relationships between macr oinvertebrate response variables and nutrient

levels. TSIN is Total Soluble I norganic Nitrogen (ammonia plus NO 3 

### -NO 2 

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



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



### B1-13 Figure B1-3. Relationships between periphy ton abundance and selected environmental predictors. The smooth curves are the locally wei ghted smoothing lines. The vertical lines are the change points (solid lines) and thei r confidence intervals (dashed lines).TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



### B1-14 Figure B1-4. Relationships between nutrient concen trations 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 a nd TN, TP, and NOx

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

and color ≤ 40 PCU). Each dot represen ts a stream reach. The dashed curves are the loess regression lines 95% confidence limits; and the vertical lines are ch ange 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 Criter ia 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

### 2



## Statistical Analysis of Stream Data

Some Initial Results (All predictors except pH tr ansformed 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

### 3



## I) SCI07 Scores.

Notes:

a) TP, TN, TSIN, AN, Cond, KN, a nd 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

### 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 We isberg 2005, Applied Linear Regression, Chapter 7):

The log rule If the values of a variable rang e 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 cons iderably less than one order of magnitude, then any transformation of that variable is unlikely to be helpful.

### 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)

### 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.**

### 7



## Models:

1) With 9 Predictors (M issing 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 mini mizing 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**

### 8



## II) Clinger Taxa



## Notes:

d) TP, TN, TSIN, AN, Cond, KN, a nd 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)

### 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)

### 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)

### 11



## Models:

1) With 9 Predictors (Missi ng 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 manua lly by minimizing the Akaike Information Criterion (AIC). Wi th 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**

### 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)

### 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)

### 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)

### 15



## Models:

1) With 9 Predictors (Missi ng 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**

### 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

### 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

### 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 Colo r 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

### 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

pHPoll 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

ColorPoll 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 an d TP=0.565 are removed.

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

3) Outliers TN=5.88 a nd TN=5.51 are removed.

### 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**

### 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**

### 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

pHPoll 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

ColorPoll 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)

### 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**

### 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**

### 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)

### 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 Squa re (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**

### 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**

### 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

pHSaprobic % Cells

45678 40 60 80 100

Conductance, field (umhos/cm)Saprobic % Cells

0 100 200 300 400 500 40 60 80 100

ColorSaprobic % 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)

### 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 transfor med 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**

### 15



## 3) Response Sapr tran sformed 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**

### 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

pHVan 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

ColorVan 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)

### 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**

### 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**

### 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

pHTP 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

ColorTP 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)

### 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 identica l 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**

### 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 se nsitive 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**

### 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

pHTIN 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

ColorTIN 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)

### 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 diatom s 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**



### \

### 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 se nsitive 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**

### 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

pHN 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

ColorN 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)

### 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 l ogarithm 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**

### 27



## 3) Response 

## N Metab transformed by the Reci procal 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**

### 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

pHpH 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

ColorpH 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)

### 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 l ogarithm 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**

### 30



## 3) Response 

## pH Optima transformed by the Reci procal 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**

### 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

pHStream 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

ColorStream 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)

### 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**

### 33



## 3) Response Stream Diatom Index transf ormed 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 Strea m 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**

## Appendix 6- C

Statistical Analysis of Stream Data-Periphyton Metrics (Weaver Region Peninsula, Some Initial Results)

### 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

### 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 Colo r 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**

### 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

pHPoll 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

ColorPoll 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 a nd TP=2.39 are removed.

### 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**

### 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**

### 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

pHPoll 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

ColorPoll 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)

### 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**

### 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**

### 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)

### 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**

### 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**

### 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

pHSaprobic % Cells

5678 40 60 80 100

Conductance, field (umhos/cm)Saprobic % Cells

0 500 1000 1500 40 60 80 100

ColorSaprobic % 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)

### 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 transf ormed 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**

### 14



## 3) Response Sapr tran sformed 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**

### 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

pHVan Dam TSI

5678 1 2 3 4 5

Conductance, field (umhos/cm)Van Dam TSI

0 500 1000 1500 1 2 3 4 5

ColorVan 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)

### 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**

### 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**

### 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

pHTP 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

ColorTP 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)

### 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**

### 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 se nsitive 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**

### 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

pHTIN 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

ColorTIN 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)

### 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 diatom s 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**

### 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 se nsitive 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**

### 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

pHN 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

ColorN 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)

### 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**

### 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**

### 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

pHpH 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

ColorpH 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)

### 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**

### 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**

### 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

pHStream 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

ColorStream 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)

### 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**

### 32



## 3) Response Stream Diatom Index tran sformed 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 Strea m 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**

### 1



## 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

### 2



## 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

### 3



## I. The Detection Procedure

Niu et al. (2000) introduced an it erative procedure for detecting and modeling level-shift change points. The procedure is similar to that s uggested by Chang (1982) an d 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 {( , )
i i 

### X Y

, 1, 2, , i n

  

### } 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 { ,
i 

### X 1, 2, , i n

  

### } are distinct. If several '
i 

### Y s are corresponding to a

single X value, the median of the '
i 

### Y s is taken to be the response value for the X value.

 {( , ) i i 

### X Y

, 1, 2, , i n

  

### } are sorted according to the values of X from least to greatest.

For each integer 

### 1 l  , 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



### () () () () i i i 

### Y l lSl l     

, 1, 2, , i n

  

### , (1)

where for a fixed l , the ( )'
i 

### l s  are assumed to be independent an d identically distributed normal

random variables with mean zero and variance 2 

### ( ) l 

.

Step 2 . Calculate the values { 1 1 

### ( ) ( ) / ( ( )) L l l se l     

, 2, 3, , ( 1) l n



  

### } where 1 

### ( ( )) se l   is the

estimated standard error of 1 

### ( ) l  

.

Step 3 . Let 1 

### ( ) max{ (2), (3), , ( 1)} Ll L L Ln    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%) si gnificance level, based on the simula tion results of Chang et al. (1988).

If 1 

### ( ) L l is significant, we co nclude that the response Y has a change point at

1 l 

### X 

### with a levelshift 1 

### ( ) l  

.

Step 4 . Let *

11 1 

### () () ii i 

### Y Y lSl    

### . Repeat Steps 1-3 on the new response variable *

i 

### Y 

### for
detecting a possible second change point. Continue the process unt il no further change point can

be identified.

### 4

Step 5 . Suppose that k change points are detected in the response variable Y and the corresponding X values are

1 2 

### {, ,, }

k ll l 

### X X X

 

### . Fit the model

0 11 2 2 

### () () () i ii k i k i 

### Y Sl Sl Sl         

 , 1, 2, , i n

  

### . (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 de scribe the relationship between Y and X. In particular, if the scatter plot of observations { ( , )
i i 

### X Y

, 1, 2, , i n

  

### } shows a straight line or a smooth curve
pattern, a linear regression mode l or a nonlinear smooth-curve mode l should be fitted to the data instead of the step-function change point model in (2).

For the response variable Y and th e predictor variable X, the li near regression model has the

form:

0 1 i ii 

### Y X     

, 1, 2, , i n

  

### . (3)

If the relationship between Y and X is nonlinea r, many smooth-curve models may be considered. One of the choices is transforming the predicto r variable X and fitting a regression model. For example, we may use the natural logarithm transf ormation log(X) instead of X as the predictor variable and fit the regression model:

0 1 

### log( )
i i i 

### Y X     

, 1, 2, , i n

  

### . (4)

When different models are fitted to the observations { ( , )
i i 

### X Y

, 1, 2, , i n

  

### }, 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 base d 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 mode l (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 di stribution 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:

### 5

SBC(p) = 

#   2

1 

### ˆ log ( ) /( 1) n

i i i 

### n YY np

 

###    

#  + p  

### log(n), (5)

where 

### ˆ

i 

### Y 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 part s in (5), the first part is 

#   2

1 

### ˆ log ( ) /( 1) n

i i i 

### n YY np

 

###    

#  = 2 

### ˆ log n 


, which is a measure of the goodness-of-fit of the ca ndidate 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 fitt ed to a data set, we may get a perfect fit but the model will be useless for infe rence such as prediction. In statistics, fitting a model with too many unnecessa ry 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 ca ndidate 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 re sults of Total Phosphorus (TP) ch ange point analysis of stream periphyton metrics after adjusted for effects of other variable s on the responses. Specifically, with each periphyton metric as the response vari able and TP, TN, TIN, Conductivity, Color, pH as predictors, we select the best linear regressi on 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 valu es correspond to the same TP va lue, 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.

### 6



## 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

### 7

Change Points: TP=0.022 (the point after chan ge 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.

### 8



## 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 poi nt after change occurs) with the test statistic of 5.09 and confidence level over 95%;

Potential Change Point (just for your info rmation): TP=0.083 with the test

statistic of 1.72 and confidence le vel 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

### 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 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

### 10

The three fitted regression models are presented in Table 1. The SBC values for the change-point model, the linear regression model, and th e 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 Diatom s at the change point decreased about 35%.



## Table 1. Fitte d 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**

### 11

**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**

### 12



## 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 poi nt 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.

### 13



## 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 poi nt after change occurs) with the test

statistic of 4.3 and co nfidence level over 95%;

Potential Change Point (just for your info rmation): TP=0.078 with the test

statistic of 2.3 and confidence le vel 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** 

### 14

**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

### 15

The three fitted regression models are presented in Table 2. The SBC values for the change-point model, the linear regression model, and th e 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 chan ge point at TP=0.010 is extremely significant (with p-values =0.0001). The log(Poll Tolerant Di atoms) 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 (l og(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 (l og(Poll Tolerant Diat oms) 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** 

### 16

**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 to lerant 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

### 17

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 poi nt 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.

### 18



## 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 0.149 0.093



## Change Point: TP=0.015 (the poi nt after change occurs) with the test statistic of 4.32 and confidence level over 95%;

Potential Change Point (just for your info rmation): TP=0.090 with the test

statistic of 2.06 and confidence le vel 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** 

### 19

**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

### 20

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 m odel are -189.7, -181.2, and -187.1, respectively. Thus, the ch ange-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( OxyT ol)) at the change point decreased about 0.27.

. 

## Table 3. Fitted Regression Mode ls (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 Mo del (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

### 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

### 22



## Change Points: TP=0.018 (the poi nt 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.

### 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 poi nt after change occurs) with the test statistic of 4.283 and confidence level over 95%;

Potential Change Point (just for your info rmation): 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

### 24



## 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

### 25

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 m odel 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 fo r 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 (a rcsin(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**

### 26

**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**

### 27



## 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 poi nt 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.

### 28



## 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 poi nt after change occurs) with the test statistic of 6.02 and confidence level over 95%;

Potential Change Point (just for your info rmation): 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**

### 29



## 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

### 30

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 m odel 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 th e fitted change-point model, the change point at TP=0.022 is extremely significant (with p-va lues =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(V an 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(V an 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**

### 31

**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 Sensitiv e 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**

### 32



## 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 0.060 0.027



## Change Points: TP=0.022 (the poi nt 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.

### 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

### 34

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 m odel are -129.6, -118..9, and -127.1, respectively. Thus, the ch ange-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 Sens itive 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 (arcs in(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 (arcs in(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**

### 35

**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**

### 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 poi nt 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.

### 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 poi nt after change occurs) with the test statistic of 4.24 and confidence level over 95%;

Potential Change Point (just for your i nformation): TP=0.067 with the test

statistic of 1.78 and confidence le vel 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

### 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

### 39

The three fitted regression models are presented in Table 7. The SBC values for the change-point model, the linear regression model, and th e non-linear regression model are 384.2, 393.95, and 387.8, respectively. Thus, the ch ange-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 Diatom s at the change point decreased about 33%.



## Table 7. Fitted Regression Mo dels (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** 

### 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**

### 41



## 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 poi nt 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.

### 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

. 0 5 0

. 1 0 0

. 1 5 0

. 2 0 40 60 80 100 120

0.008 0.131 0.083



## Change Point: TP=0.022 (the poi nt after change occurs) with the test statistic of 6.45 and confidence level over 95%;

Potential Change Point (just for your info rmation): TP=0.082 with the test

statistic of 2.25 and confidence le vel 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** 

### 43

**F-statistic: 25.77 on 2 and 52 degrees of freedom, the p-value**

**is 1.673e-008**



## SBC=301.8

### 44



## 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

### 45

The three fitted regression models are presented in Table 8. The SBC values for the change-point model, the linear regression model, and th e non-linear regression model are 297.8, 314.3, and 301.3, respectively. Thus, the change-point model a nd the nonlinear model we re better than the linear model. Based on the fitted change-point m odel, the change point at TP=0.022 is extremely significant (with p-values =0.0000). The Stream Di atom 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 Mode l (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 Mode l (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**

### 46

**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**

### 47



## 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 poi nt 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.

### 48



## 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 poi nt after change occurs) with the test statistic of 4.39 and confidence level over 95%;

Potential Change Point (just for your info rmation): 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

### 49



## 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

### 50

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 ch ange-point model and the nonlinea r model were better than the linear model. Based on the fitted change-point m odel, 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**

### 51

**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**

### 52



## 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 poi nt 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.

### 53



## 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

### 54

The three fitted regression models are presen ted in Table 10. The SBC values for the changepoint model, the linear regression model, a nd the non-linear regressi on model are -326.8, -317.3, and -324.6, respectively. Thus, the change-poi nt 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**

### 55

**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 chan ge 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 to lerant 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 chan ge 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 chan ge 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.

### 56



## 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 chan ge 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 chan ge 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 chan ge 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 chan ge 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. “Estimati on 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.

### 57

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.

### 1



## 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

### 2



## 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

### 3

1. Quantile Regression

Quantile regression is a generalized approach of linear regression and usually provides a more complete analysis of a data set than lin ear 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 pict ure of the set. Ordinarily this is not done, and so regression often gives a rather incomple te 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 regressi on 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 applica tions of quantile regression have also been documented in recent years (e.g., Terrell et al. 1996; Ca de et al. 1999; McClain and Re x, 2001). Cade et al. (1999) pointed out that quantile regressi on is a very useful method for es timating 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 ch anges in a biological response variable (species biomass) as a function of limiting f actors (habitat conditions) that are measured and as a function of other limiting factors (non-hab itat factors such as weat her 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 pos itive linear function of habitat factors and a negative function of the interaction of habitat and no n-habitat factors, i.e.,

an interference interac tion model.” Cade et al. (1999) furt her 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 estimat ed change in means is small and homogeneous. If, however, we do not measure the non-habitat fa ctors, we cannot estimate the interaction. The resultant distribution of biomass has great er variation that increases with the level of habitat that would support more biomass if ha bitat 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 bi omass and the measured habitat factors most consistent with the relation expected if habitat is the active limiting fa ctor is near the upper ‘edge,’ rather that through the center of the data distribution .”

In this report, we briefly discuss the quantile regression us ing the notation in Koenker and Bassett (1982). Let Y 

### be a random variable with righ t continuous dist ribution 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)

### 4

Suppose that { , , , } Y Y Y

n 1 2 

###  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:

 ( ) inf{ | ( ) min!} Q y Yy

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 di stribution function 

### F y x (| ) where x is a row vector of exogenous variables. The first component of x is an intercept so that x i 1 

### 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 conducta nce (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 iden tically distributed with N (, ) 0 2 

###  

### . Then

the conditional distribution of Y 

### given log(Conductivity ) is



### F y Conductivity N Conductivity

( |log( )) ( log( ), )     

0 1 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 th e “sum of residuals”  

 i n

i i 

### Y x

 

# 

 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 a nd TP, TN, TIN, and specific conductance as independent variables. The loga rithm (Base e) transformation is performed on the four predictor

### 5

variables. The periphyton metrics are transformed using th e transformations chosen in Niu (2009). Only simple linear regression models w ith one predictor are c onsidered in this study.

Consider a periphyton metric denoted by y and a predictor, say Conductivity. For a given quantile  , the empirical conditiona l quantile function has the form:

 ( |log( )) ( ) ( ) log( ) Q Conductivity Conductivity

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 90 th 

### quantile regression as an example,

Y 90 

### =a 90 

### + b 90 

### X, (10)

where a 90 is the intercept of the 90 th quantile regression of Y on X and b 90 is the slope.



### The quantreg Package in the R computer language was us ed for computations ( http://cran.at.rproject.org/src/contri b/PACKAGES.html#quantreg ). The coefficients   0 

### ( ) and 

###   1 

### ( ) were estimated using the “rq” function from quantre g. The default estimation method in the “rq” function was chosen, which is the modified vers ion of the Barrodale and Robert algorithm for



### L

1 

### -regression, described in Koenker and d’Orey (1 987, 1994). This algorithm is quite efficient for problems up to several thousand observations.

A quantile version of the coefficient of determination (R 1 

### ) defined in Koenker and Machado (1999) is calculated, which is a natural analog of R 2 

### for classical least square regressions. R 1 

### 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, R 1 

### value for a given quantile is a measure of the scatter around the quantile regression line.

### 6

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 ( m g P/L )Poll sensitive diatoms

R1=0.13** R1=0.07**

01234 0 20 40 60 80 100

Total Nitro g en ( m g N/L )Poll sensitve diatoms

R1=0.01 R1=0.005

01234 0 20 40 60 80 100

TIN ( m g /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 an d TP=0.565 are removed. 2) Outliers Cond=1344 and Cond=1557 are removed. 3) Outliers TN=5.88 a nd TN=5.51 are removed.

### 7



## Quantile Regression Models:

1) PollSens on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 8



## 4) PollSens on log(Cond):

a. The 50 th 

## 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 85 th 

## 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

### 9



## II) Log(Pollution tolerant diatoms)

0.00 0.05 0.10 0.15 0.20 -4 -2 0 2 4

Total-P ( m g P/L )log(Poll Tol diatoms)

R^2=0.07** R^2=0.13**

01234 -4 -2 0 2 4

Total Nitro g en ( m g N/L )log(Poll Tol diatoms)

R^2=0.002 R^2=0.003

01234 -4 -2 0 2 4

TIN ( m g /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)

### 10



## Quantile Regression Models:

1) Log(PollTol) on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 11



## 3) Log(PollTol) on log(TIN):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 12



## III) arcsin(sqrt(Percentage R equiring 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 ( m g 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 Nitro g en ( m g 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 ( m g /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)

### 13



## Quantile Regression Models:

1) 

## Arcsin(sqrt(%R equiring high D.O)) on log(TP):

a) The 50 th 

## 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 85 th 

## 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(%R equiring high D.O)) on log(TN):

a) The 50 th 

## 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 85 th 

## 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

### 14



## 3) 

## Arcsin(sqrt(%R equiring high D.O)) on log(TIN):

a)The 50 th 

## 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 85 th 

## 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(%R equiring high D.O)) on log(Cond):

a)The 50 th 

## 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 85 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /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)

### 16



## Quantile Regression Models:



## 1)Arcsin(sqrt(Saprobic % Cells )) on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 17



## 3) 

## Arcsin(sqrt(Saprobic % Cells )) on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 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 ( m g P/L )sqrt(Van Dam TSI)

R1=0.18** R1=0.04**

01234 1.0 1.5 2.0 2.5

Total Nitro g en ( m g N/L )sqrt(Van Dam TSI)

R1=0.02 R1=0.01

01234 1.0 1.5 2.0 2.5

TIN ( m g /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)

### 19



## Quantile Regression Models:



## 1) sqrt(Van Dam TSI) on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 20



## 3) 

## sqrt(Van Dam TSI) on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 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 ( m g P/L )arcsin(sqrt(TP Sensitive Diatoms))

R1=0.16** R1=0.10**

01234 0.0 0.5 1.0 1.5

Total Nitro g en ( m g N/L )arcsin(sqrt(TP Sensitive Diatoms))

R1=0.06** R1=0.01

01234 0.0 0.5 1.0 1.5

TIN ( m g /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)

### 22



## Quantile Regression Models:



## 1) arcsin(sqrt(TP Sensitive Diatoms)) on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 23



## 3) 

## arcsin(sqrt(TP Sensitive Diatoms)) on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 24



## VII) TIN Sensitive Diatoms

0.00 0.05 0.10 0.15 0.20 0 20 40 60 80 100

Total-P ( m g P/L )Poll sensitive diatoms

R1=0.14** R1=0.11**

01234 0 20 40 60 80 100

Total Nitro g en ( m g N/L )TIN sensitve diatoms

R1=0.04** R1=0.01

01234 0 20 40 60 80 100

TIN ( m g /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)

### 25



## Quantile Regression Models:



## 1) TIN Sensitive Diatoms on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 26



## 3) 

## TIN Sensitive Diatoms on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /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)

### 28



## Quantile Regression Models:



## 1) (N Metab) -1 

## on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 29



## 3) 

## (N Metab) -1 

## on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /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)

### 31



## Quantile Regression Models:



## 1) (pH Optima) -1 

## on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 32



## 3) 

## (pH Optima) -1 

## on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 33



## X) Stream Diatom Index

0.00 0.05 0.10 0.15 0.20 0 20 40 60 80 100

Total-P ( m g P/L )Stream Diatom Index

R1=0.12** R1=0.13**

01234 0 20 40 60 80 100

Total Nitro g en ( m g N/L )Stream Diatom Index

R1=0.0 R1=0.003

01234 0 20 40 60 80 100

TIN ( m g /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)

### 34



## Quantile Regression Models:



## 1) Stream Diatom Index on log(TP):

a) The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 35



## 3) Stream Diatom Index on log(TIN):

a)The 50 th 

## 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 85 th 

## 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 50 th 

## 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 85 th 

## 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

### 36



## References:
Bassett, G. and Koenker, R. W. 1982a. Tests of Linear Hypotheses and L 1 

### Estimation.

Econometrica

, 50 :1577-1583.

Bassett, G. and Koenker, R. W. 1982b. An Empiri cal 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 Intro duction 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 Te sts 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 Re mark 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 Ő kologie, Morphologie, und Systematik der Brackenwasser-Diatomeen (The ecology, morphology and systematic s 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-S ea 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 St ream Data-Periphyton Metrics (Weaver Region Panhandle). Technical Report Submitted to the Flor ida Department of Environmental

Protection.

### 37

Terrell, J.W., Cade, B. S., Carpenter, J., and Thomson, J. M. 1996. Modeling Stream Fish Habitat Limitations from Wedged-Shaped Pa tterns of Variation in Standing Stock. Transactions of the American Fisheries Society 125 :104-117.

### 1



## 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

### 2



## 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

### 3

1. Quantile Regression

Quantile regression is a generalized approach of linear regression and usually provides a more complete analysis of a data set than lin ear 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 pict ure of the set. Ordinarily this is not done, and so regression often gives a rather incomple te 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 applica tions of quantile regression have also been documented in recent years (e.g., Terrell et al. 1996; Ca de et al. 1999; McClain and Re x, 2001). Cade et al. (1999) pointed out that quantile regressi on is a very useful method for es timating 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 ch anges in a biological response variable (species biomass) as a function of limiting f actors (habitat conditions) that are measured and as a function of other limiting factors (non-hab itat factors such as weat her 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 pos itive linear function of habitat factors and a negative function of the interaction of habitat and no n-habitat factors, i.e.,

an interference interac tion model.” Cade et al. (1999) furt her 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 estimat ed change in means is small and homogeneous. If, however, we do not measure the non-habitat fa ctors, we cannot estimate the interaction. The resultant distribution of biomass has great er variation that increases with the level of habitat that would support more biomass if ha bitat 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 bi omass and the measured habitat factors most consistent with the relation expected if habitat is the active limiting fa ctor is near the upper ‘edge,’ rather that through the center of the data distribution .”

In this report, we briefly discuss the quantile regression us ing the notation in Koenker and Bassett (1982). Let Y 

### be a random variable with righ t continuous dist ribution 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)

### 4

Suppose that { , , , } Y Y Y

n 1 2 

###  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:

 ( ) inf{ | ( ) min!} Q y Yy

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 di stribution function 

### F y x (| ) where x is a row vector of exogenous variables. The first component of x is an intercept so that x i 1 

### 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 lo garithm of Total Phosphorus (TP). If log(TP) and Y follow a

linear model

0 1 

### log( )
i i i 

### Y T P      , (4)

where the random errors  i 

### ’s are independent and iden tically distributed with N (, ) 0 2 

###  

### . Then

the conditional distribution of Y 

### given log(TP ) is

2

0 1 

### ( | log( )) ( log( ), ) F y TP N TP      

### . (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 th e “sum of residuals”  

 i n

i i 

### Y x

 

# 

 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 metric s as dependent variables and TP, TN, TIN,

### 5

and pH as independent variables. The logar ithm (Base e) transforma tion is performed on TP, TN, and TIN, while pH is not transformed. Th e 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 conditiona l quantile function has the form:

0 1 

### ˆ ( | log( )) ( ) ( ) log( )

i Y 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 90 th 

### quantile regression as an example,

Y 90 

### =a 90 

### + b 90 

### X, (10)

where a 90 is the intercept of the 90 th quantile regression of Y on X and b 90 is the slope.



### The quantreg Package in the R computer language was us ed for computations ( http://cran.at.rproject.org/src/contri b/PACKAGES.html#quantreg ). The coefficients   0 

### ( ) and 

###   1 

### ( ) were estimated using the “rq” function from quantre g. The default estimation method in the “rq” function was chosen, which is the modified vers ion of the Barrodale and Robert algorithm for



### L

1 

### -regression, described in Koenker and d’Orey (1 987, 1994). This algorithm is quite efficient for problems up to several thousand observations.

A quantile version of the coefficient of determination (R 1 

### ) defined in Koenker and Machado (1999) is calculated, which is a natural analog of R 2 

### for classical least square regressions. R 1 

### 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, R 1 

### value for a given quantile is a measure of the scatter around the quantile regression line.

### 6

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 ( m g 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 Nitro g en ( m g 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 ( m g /L )Poll sensitve diatoms

R1=0.006 R1=0.01

5678 0 20 40 60 80 100

p HPoll 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 a nd TP=2.39 are removed.

### 7



## Quantile Regression Models:

1) PollSens on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 8



## 3) PollSens on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 9



## 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )Sqrt(Poll Tol diatoms)

R1=0.0002 R1=0.0003

5678 0 2 4 6 8 10

p HSqrt(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]

### 10



## Quantile Regression Models:

1) Sqrt(PollTol) on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 11



## 3) Sqrt(PollTol) on log(TIN):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 12



## III) arcsin(sqrt(Percentage R equiring 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )Arcsin(sqrt(% Requiring high D.O))

R1=0.0004 R1=0.002

5678 0.0 0.5 1.0 1.5

p HArcsin(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]

### 13



## Quantile Regression Models:

1) 

## Arcsin(sqrt(%R equiring high D.O)) on log(TP):

a) The 50 th 

## 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 90 th 

## 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(%R equiring high D.O)) on log(TN):

a) The 50 th 

## 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 90 th 

## 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

### 14



## 3) 

## Arcsin(sqrt(%R equiring high D.O)) on log(TIN):

a)The 50 th 

## 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 90 th 

## 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(%R equiring high D.O)) on pH:

a)The 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )Arcsin(sqrt(Saprobic % Cells))

R1=0.0001 R1=0.003

5678 0.0 0.5 1.0 1.5

p HArcsin(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]

### 16



## Quantile Regression Models:



## 1)Arcsin(sqrt(Saprobic % Cells )) on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 17



## 3) 

## Arcsin(sqrt(Saprobic % Cells )) on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )Van Dam TSI R1=0.014* R1=0.008

5678 1 2 3 4 5

p HVan 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]

### 19



## Quantile Regression Models:



## 1) Van Dam TSI on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 20



## 3) 

## Van Dam TSI on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )TP Sensitive Diatoms

R1=0.0001 R1=0.003

5678 0 20 40 60 80 100

p HTP 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]

### 22



## Quantile Regression Models:



## 1) TP Sensitive Diatoms on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 23



## 3) 

## TP Sensitive Diatoms on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )TIN Sensitive Diatoms

R1=0.0007 R1=0.026

5678 0 20 40 60 80 100

p HTIN 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]

### 25



## Quantile Regression Models:



## 1) TIN Sensitive Diatoms on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 26



## 3) 

## TIN Sensitive Diatoms on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /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

p HReciprocal 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]

### 28



## Quantile Regression Models:



## 1) (N Metab) -1 

## on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 29



## 3) 

## (N Metab) -1 

## on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /L )Reciprocal of pH Optima

R1=0.0036 R1=0.030*

5678 0.1 0.2 0.3 0.4 0.5

p HReciprocal 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]

### 31



## Quantile Regression Models:



## 1) (pH Optima) -1 

## on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 32



## 3) 

## (pH Optima) -1 

## on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 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 ( m g 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 Nitro g en ( m g 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 ( m g /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

p HArcsin(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]

### 34



## Quantile Regression Models:



## 1) Arcsin(Sqrt( Stream Diatom Index)) on log(TP):

a) The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 35



## 3) 

## Arcsin(Sqrt( Stream Diatom Index)) on log(TIN):

a)The 50 th 

## 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 90 th 

## 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 50 th 

## 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 90 th 

## 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

### 36



## References:

Bassett, G. and Koenker, R. W. 1982a. Tests of Linear Hypotheses and L 1 

### Estimation.

Econometrica

, 50 :1577-1583.
Bassett, G. and Koenker, R. W. 1982b. An Empiri cal 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 Intro duction 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 Te sts 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 Re mark 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 Ő kologie, Morphologie, und Systematik der Brackenwasser-Diatomeen (The ecology, morphology and systematic s 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-S ea 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 St ream Data-Periphyton Metrics (Weaver Region Peninsula). Technical Report Submitted to the Flor ida 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 Pa tterns of Variation in Standing Stock. Transactions of the American Fisheries Society 125 :104-117.

## Appendix 6- G

Florida’s Nutrient Criteria Based on Rapid Periphyton Survey Data

## 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 endpoin ts.

RPSs used a 10 0 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/thickn ess 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)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) hi gher tur bidity and canopy cover

to lead to light limitation and reduce the abundance of benthic algal biomass, and 3) hi gher grazing also

to reduce algal biomass. Stream velocity was more complicated to predict since flow could increase

nutrient uptake rates for p eriphyton 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 drop pe d both

flow and temperature from further a nalysis. Information on grazers was available as scraper density

from the benthic macroinvertebrate sampling and showed a slightly positive correlation with algal

thickness (Ta ble 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 penetr ation
(canopy cover and water color) and nutrients (total N and P).

A theoretical model of algal biomass response to li ght and nutri ent concentration was represented with

the following equation (Yi is algal biomass):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 al gal 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 periphyt on thicknes s 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 Categ ory 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 thi ckness score and the type score (i.e., thickness score

* type score). All scores were assigned to each of the potential 99 monitoring points compr i sing 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 point s or non

‐ linear responses from Loess regression and change point analyses.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 0.29Figure 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 environme n tal 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 corr elated with color (Spearman correlations were 0.79, 0.80, and ‐ 0.52, respectively). These strong correlations may explain the unexpected correlations be tw een 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. Hi gh conductivity, TP, and

water column Chl a are often associated with watershed urbanization.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 NO 2+3
concentration was above 140 μ g/L and reached a peak when NO 2+3 concentrations reached 1100 μ g/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,

NO 2+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 thickne ss was strongly correlated with color, a factor that potentially led to light limitation

but also released algae from nutrient limitation since hig her 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 NO 2+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

NO 2+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

NO 2+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 andNO 2+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 NO 2+3 : TP ratio in the gradient study sites and found that more than 90% of the

samples had both DIN:TP and NO 2+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 le ss than 40% canopy cover and averaged algal thickness in the remaining

transects as the mean algal thickn ess 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 nutri ent concentration gradient.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 cl ear and

intermediate colored streams, but had comparable phytoplankton biomass to clear streams.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 to tal ni trogen) 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 l imitation.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.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 fi nd a relationship between

periphyton thickness and nutrient concentrations. In heavily shaded / colored streams, light limitation

becomes the dominant limiting factor to periph yton growt h 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 tre e 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 (c olored streams with limited or no tree canopy), we ma y expect phytoplankton chlorophyll to
respond to nutrient enrichment.

Due to co

‐ li nearity 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 th e 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 (Figur e 6a). However, N and P could be co

‐ limiting algal

growth in the stream system. To verify that, we standardized/scaled nutrient co ncen trations 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), in dicating 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 3.0.01 0.02 0.05 0.10 0.2001234

TP.rawAlgal thickness Spearman r= 0.19 

### a

0.2 0.5 1.0 2.0 5.001234

TN.rawAlgal thickness Spearman r= 0.43 

### b

0.002 0.020 0.200 2.00001234

NOx.rawAlgal thickness Spearman r= 0.5 

### c

4 6 8 10 12 14 16012345

TN PAlgal thickness Spearman r= 0.56



### d

4 6 8 10 12 14 16012345

NOx PAlgal 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 de viation; 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

represen ts a stream re ach. The dashed curves are the Loess regression lines 95% confidence limits;

and the vertical lines are ch ange 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 0.045b. 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 logist i c regression models were

constructed to examine the relationship between the probability of impact and TN, TP, canopy cover

and their i nteraction terms.

Table 4. Logistic regression models of probability of algal thickness impairment as a function of

nutrient and shading variables.

Akaike's information criterio n (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. Th e 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 accordi ng 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 indi cates 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. Th e Nitrate model (model 2) was more complicated due to significant interactions among predictor

variables, and was relativ ely 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=0.765Figure 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

impairme nt, 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).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.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 wer e 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

deter mined by manage ment.

b. Colored streams:

i. Periphyton thickness became increasingly limited by light and correlations with nutrients

were very weak; however, water colu mn 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 th e water.