Regression Equation

Sustainable Water Management Initiative 

Advisory Committee 

Presentation Title: 

Stream Categorization 

Date of Presentation: 21 June 2010 

Principle Author: 

Todd Richards, Massachusetts DFW 

The following presentation is offered for discussion purposes only and does not 

necessarily represent current statute, regulation, or policy positions of the 

Commonwealth of Massachusetts unless specifically acknowledged. 

This presentation is not to be cited as a reference. Its purpose is to foster open and 

broad discussion of the issues of sustainable water management as well as help 

assure public awareness of the discussions as of the date of the presentation. 

FOR DISCUSSION PURPOSES ONLY - NOT TO BE CITED 

1

Stream Categorization: 

Describing the Current 

Condition 

Pilot basins: 

SuAsCo 

Nashua 

Westfield 

FOR DISCUSSION PURPOSES ONLY - NOT TO BE CITED

Fish and Habitat Study 

Objectives 

1. Describe physical–basin characteristics 

(Basin size, elevation, slope, sand and gravel…) 

2. Describe human alteration factors 

(flow alteration, imperviousness, dams…) 

3. Relate fish community composition to physical basin 

characteristics and human alteration factors using appropriate 

statistical tools 

Physical Basin 

Characteristics 

Fish Community 

Characteristics 

Human 

Alteration 


Stream Categorization 

Step 1 - Not All Streams Are the Same 

– Group streams based on physical 

characteristics 

Step 2 - Use the Biology 

– Classify the current status of streams within 

each group based on fisheries data 


Fish Communities 

The Fish Tell the Story 

– Long-lived 

– Reflect stresses over time 

– Easily recognized and identified 

– Well-studied 

– Good indicators of the condition of the aquatic 

environment 


Rivers Should Have River Fish 

Communities 

What is a River Fish? 

Brook Trout 

Fallfish 

Creek Chubsucker Tesselated Darter Common Shiner 


Preliminary Assessment 

of Factors Influencing 

Riverine Fish Communities 

in Massachusetts 

by 

David Armstrong 

Sara Brandt 

U.S. Geological Survey 

Massachusetts-Rhode Island 

Water Science Center 

and 

Todd Richards 

Massachusetts DFW 


MDFW Fish Survey Database 

756 sites included in the analysis 

– Free Flowing Habitat (riffle/pool/run) 

– Wadeable Streams 

– 1998 to 2008 

Statewide distribution of sites 

Includes a range of values for all 

explanatory variables 


Preliminary Study 

Explanatory variables examined 

• Basin Characteristics 

• Drainage area 

• Mean elevation 

• Mean basin slope 

• Local channel slope 

• Percent sand and gravel 

• Outlet Longitude 

• Wetland area 

• Open water area 



Explanatory variables examined 

• Anthropogenic factors 

• Flow alteration 

• August median flow alteration 

(net depletion, net surcharging) 

• Water-use intensity 

• Annual ratio of returns to unimpacted flows 

• Annual ratio of withdrawals to unimpacted 

flows 

• Impervious cover 

• Dam density 



Response variables examined 

• Fish-community 

metrics 

• Fluvial Fish 

Relative Abundance 

Richness 

Percent 

• Coldwater fish 

• Relative Abundance 

• Percent 

• Indicator species 

• Brook Trout 

Relative Abundance 

Percent 

• White Sucker 

• Relative Abundance 

• Percent 


Preliminary Study Analytical methods 

• Quantile regression 

• Generalized linear modeling (GLM) 


Regression Equation 

DRAFT 

( Y ) = (1- π)( 

μ) 

E i 

γ0 

+ γ1z1 

+ γ2z2... 

γmzm 

e 

π = γ0 

+ γ1z1 

+ γ2z2... 

γmzm 

1+ e 

Probability Portion 

μ 

= 

e 

β 

0 

+ β1x1 

+ β2x2 

... β n x n 

Count Portion 

E(Y i ) = expected mean value of cpue or richness 

π = probability of zero from logistic processes 

μ= mean value from negative binomial count processes 

γ= coefficients of logistic equation 

β= coefficients of negative binomial equation 

z= covariates from logistic equation 

x= covariates from negative binomial equation 


Fluvial Abundance Regression 

Equation 

Probability portion (pi) 

– drainage area 

– longitude 

= 

The count portion (mu): 

– percent wetland 

– channel slope 

μ 

– longitude 

– impervious cover 

– percent alteration of August 

median streamflow 

γ0 

e 

1+ e 

+ γ 

+ γ 

... γ 

π γ + γ z + γ z ... γ 

= 

e 

FOR DISCUSSION PURPOSES ONLY - NOT TO BE CITED 

β 

0 

0 

1 

z 

1 

1 

DRAFT 

1 

2 

z 

2 

2 

2 

+ β1x1 

+ β2x2 

m 

z 

m 

m 

z 

m 

... β n x n

Model Validation 

Remove-One Model Validation 

Plot Observed vs Predicted 

Model Association in Line with Other 

Biological Models 


Plain English 

Keeping all other variables static, 

– a unit increase in impervious surface is 

associated with a 5.5 percent decrease in 

fluvial-fish relative abundance. 

– a unit increase in percent alteration of August 

median streamflow is associated with a 0.4 

percent decrease in fluvial-fish relative 

abundance 


Fluvial Density 

Fluvial Relative Abundance 

800 

DRAFT 

700 

600 

w estern MA 

central MA 

eastern MA 

500 

400 

300 

200 

100 

0 

0 20 40 60 80 100 

Percent net August depletion 


Basin-Specific Calculation 

Enter individual basin variables 

MWI 1429 Sub-basins 

Run Regression Equation 

Can be Site-Specific 


Baseline Impervious Cover 

“Straw” Recommendation 

– Lowest subbasin IC in Major Planning Basin 

– Recognizing an E/W IC pattern in MA 

Tech Subcommittee 

– Use Zero IC as “True Reference” 

– Use Categories of IC across state 

Need to decide before expanding from 

pilot basins 


Example Basin 11031: Nashua 


Variables: 

Drainage Area: 16 sqmi 

Wetland Area: 4.3% 

Channel Slope: 1% 

Longitude: 1.72 (sp - m) 

Baseline IC = 3% 

FOR DISCUSSION PURPOSES ONLY - 

NOT TO BE CITED


DRAFT 

Baseline Condition 


300 

250 

200 

150 

100 

50 

0 

0 20 40 60 80 100 

August Percent Alteration 


Categories 

Developed based on fluvial relative abundance 

regression equation 

Quantile Regression 

– Brook Trout – Immediate, dramatic response 

– Species Diversity – Loss of a species by 20% August 

Depletion 

Titan – Baker and King 

– Sensitive species have a strong and immediate 

response 

Published tolerances for species 


Brook Trout Relative Abundance 

DRAFT 



Brook Trout Relative Abundance 

DRAFT 


Quantile Regression 

Categories 

– Species Diversity – Loss of a species by 20% August Depletion 

DRAFT 


Categories 

TITAN - Baker and King 

– Species that Decrease with increasing flow alteration 

Brook trout 

Blacknose dace 

Sculpin 

Creek chub 

– Species that increase with increasing flow alteration 

Redfin pickerel 

Largemouth bass 

Bluegill 

Yellow Bullhead 

Native Fluvial Species 

Generalist Species 

Increasers 


Fish Community Response 

100% 

80% 

60% 

0-5% Biological Alteration 

- High quality streams 

- Sensitive species may 

be impacted 

40% 

20% 

0% 


BCG Language: Native structural, functional, and taxonomic 

integrity is preserved; within range of natural variability 



100% 

80% 

60% 

40% 

20% 


- Sensitive species decline 

rapidly 

- Species loss increasingly 

likely 

0% 


BCG Language: Some changes in fish community due to loss of some rare 

native species; shifts in relative abundance of species but some sensitive– 

species are common and abundant; ecosystem functions are fully maintained. 



100% 

80% 

60% 

40% 

20% 

0% 



- Sensitive species loss 

- Decline in more tolerant 

fluvial species 

- Further reductions in 

diversity 

BCG Language: Moderate changes in structure due to replacement of 

some sensitive–ubiquitous species by more tolerant species, but 

reproducing populations of some sensitive species are maintained. 



100% 

80% 

60% 

40% 

20% 

0% 


30 -50% Alteration 

- Replacement of sensitive 

species with tolerant 

individuals 

- Density of tolerant 

individuals reduced 

BCG Language: Sensitive taxa are markedly diminished; conspicuously 

unbalanced distribution of major groups from that expected; organism 

condition shows signs of physiological stress; system function shows 

reduced complexity and redundancy. 



100% 

80% 

60% 

40% 

20% 

0% 


>50% Biological Alteration 

1. Replacement of sensitive 

species with tolerant 

individuals 

2. Density of tolerant 

individuals reduced 

Extreme changes in structure; wholesale changes in species composition; 

extreme alterations from normal abundances and distributions; organism 

conditioning is often poor; ecosystem functions are severely altered. 




300 

250 

200 


5% Biological Loss 




150 

100 

50 

0 

0 20 40 60 80 100 





300 

250 

200 






150 

100 

50 

0 

4% 12% 25% 45% 

0 20 40 60 80 100 



280 Sub-basins 

Basin IC% Aug Dep% Biol Alt % Category 

12039 10.2 6.79 100 5 

12071 6.0 1.33 45 4 

11031 3.8 0.05 13 2 

11068 3.9 0.84 15 3 

12076 6.1 4.34 49 4 

11045 3.7 100 100 5 


Example Basin 11031 


Variables: 

Drainage Area: 16 sqmi 

Wetland Area: 4.3% 

Channel Slope: 1% 

Longitude: 1.72 (sp - m) 

Baseline IC = 3% 


NOT TO BE CITED




300 

250 

200 

150 

100 

50 

Baseline IC = 3% (Nashua) 

Actual IC = 3.8% 

0 

0 10 20 30 40 50 60 70 80 90 100 

% August Depletion 




300 




250 

200 

150 

Actual August % 

Depletion = .05% 

100 

50 

0 

0 10 20 30 40 50 60 70 80 90 100 



Abundance 



Fluvial Rela 

300 

15% Biological 

250 

200 

Actual August % 




300 




250 

200 

150 

2 

100 

50 

0 

0 10 20 30 40 50 60 70 80 90 100 


Total % Biological Alteration = 13% (Category 2) 

Alteration Due to IC = 12% 

Alteration Due to August Alteration = 1% 



Example Basin 19056: Baseline IC 1% 

600 

500 


400 


300 

200 

4 

100 

0 

0 10 20 30 40 50 60 70 80 90 100 

% August Alteration 

Total % Biological Alteration = 32% (Category 4) 

Alteration Due to IC = 20% 

Alteration Due to Flow Alteration = 12% 


11031 

Nashua 

Reference IC = 3% 


Number of Sub Basins 

Nashua 

Impervious Cover Baseline 

50 

40 

30 

20 

3%IC and existing flow 

0%IC andExisting Flow 

10 

0 

1 2 3 4 5 

Category 


SuAsCo 



Westfield 



Flow Alteration 


Impervious Cover 



Decreasers 

Categories 

Titan – Baker 

and King 

– Sensitive 

species have 

a strong and 

immediate 

response 

= “decreasers” 

= “increasers” 

Increasers 

Blacknose dace 

Sculpin 

Brook Trout 


NOT TO BE CITED

Regression Equation

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