1 2 3 4 5 6

40

35

30

25

20

15

10

5

0

Probability, in percent

Biological Condition Gradient

1 2 3 4 5 6

40

35

30

25

20

15

10

5

0

Biological Condition Gradient

Probability, in percent

U.S. Department of the Interior

U.S. Geological Survey

National Water-Quality Assessment Program

Scientific Investigations Report 2012–5030

Linking Urbanization to the Biological Condition 

Gradient (BCG) for Stream Ecosystems in the 

Northeastern United States Using a Bayesian

Network Approach
Cover. Left photograph—Example of a stream with low levels of urban stress, which is more likely to have biological condition in 

BCG tiers 1 or 2 as shown by the superimposed probability distribution in green (Thomas F. Cuffney, USGS, September 2011).

Right photograph—Example of a stream with high levels of urban stress, which is more likely to have biological condition in 

BCG tiers 5 or 6 as shown by the superimposed probability distribution in red (Michelle Moorman, USGS, April 2011).
Linking Urbanization to the Biological Condition Gradient 

(BCG) for Stream Ecosystems in the Northeastern 

United States Using a Bayesian Network Approach

By Roxolana Kashuba, Gerard McMahon, Thomas F. Cuffney, Song Qian, Kenneth Reckhow, 

Jeroen Gerritsen, and Susan Davies

Prepared in cooperation with Duke University

Scientific Investigations Report 2012–5030

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Kashuba, Roxolana, McMahon, Gerard, Cuffney, T.F., Qian, Song, Reckhow, Kenneth, Gerritsen, Jeroen, and 

Davies, Susan, 2012, Linking urbanization to the Biological Condition Gradient (BCG) for stream ecosystems in the 

Northeastern United States using a Bayesian network approach: U.S. Geological Survey Scientific Investigations 

Report 2012–5030, 48 p.

(Available online at http://pubs.usgs.gov/sir/2012/5030/)
iii

Acknowledgments

The authors would like to thank David Courtemanch and Thomas Danielson of the Maine 

Department of Environmental Protection for great investments of time and effort toward 

Biological Condition Gradient (BCG) discussion and extensive expert elicitation development 

exercises. 

James Coles and Nathaniel Plant of the U.S. Geological Survey provided discerning technical 

reviews that improved this report substantially. 

Finally, we owe all expert teams a large measure of gratitude for agreeing to share their 

considerable expertise and for their openness to new ideas and new ways of thinking.

v

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................2

Methods...........................................................................................................................................................3

USGS Urban Stream Data ...................................................................................................................3

Biological Condition Gradient.............................................................................................................3

Assigning BCG Tier Membership in the Northeastern United States.................................6

Bayesian Network Model....................................................................................................................6

Creating a Bayesian Network Model .......................................................................................8

Developing the Northeastern U.S. Bayesian Network Prior Model 

Using Expert Elicitation .................................................................................................8

Model Structure..................................................................................................................9

Variable Selection and Discretization ...........................................................................10

Conditional Probability Tables ........................................................................................11

Prior Weights.....................................................................................................................13

Updating the Prior Model with Data.......................................................................................15

Predicting Effects of Urbanization on Biota ............................................................................................18

Prior Bayesian Network Model........................................................................................................18

Data-Only Bayesian Network Model...............................................................................................20

Posterior Bayesian Network Model ................................................................................................24

Assessing the Value of a Bayesian Network Approach .......................................................................30

Benefits of Using a Bayesian Network for Urban Development Modeling ..............................30

Unresolved Issues ..............................................................................................................................31

Conclusions...................................................................................................................................................32

References Cited..........................................................................................................................................33

Appendix 1. Distribution Forms for Bayesian Updating .....................................................................35

Appendix 2. Supplemental Prior and Posterior Conditional Probability Tables, Data Tables, 

 and Bayesian Network Diagrams....................................................................................36
vi

Sidebars

1. Comparing Stream Biological Conditions Across Regions....................................................5

2. How Bayesian Updating Works................................................................................................16

Simple Example with Single Probability Parameter....................................................16

Bayesian Updating for Multiple Probability Parameters within a Bayesian 

Network CPT Row ...............................................................................................17

Figures

1. Conceptual diagram of the Effects of Urbanization on Stream Ecosystems (EUSE) 

National Water-Quality Assessment (NAWQA) Program study ...........................................2

2. Map showing locations of the nine metropolitan regions and surrounding areas 

of the Effects of Urbanization on Stream Ecosystems (EUSE) studies ................................3

3. Graph showing Biological Condition Gradient (BCG) tiers relative to increasing 

stressor gradient...........................................................................................................................4

4. Graph showing Midwest versus Appalachian stream conditions .......................................5

5. Directed acyclic graph (DAG) showing a simple Bayesian network with four nodes 

and four arrows.............................................................................................................................7

6. Example of simple conditional probability tables (CPT).........................................................7

7. Diagram showing parsimonious Northeast Bayesian network model structure.............10

8. Graph showing Bayesian updating of hypothetical, generic parameter θi ......................16

9. Charts showing Bayesian updating of parameters θ1, θ2, θ3, within a conditional 

probability table (CPT) row in a Bayesian network...............................................................17

10. Diagram showing prior predictive probabilities of occurrence for each level 

of each node under low urban development.........................................................................19

11. Diagram showing prior predictive probabilities of occurrence for each level 

of each node under high urban development........................................................................21

12. Diagram showing data-only predictive probabilities of occurrence for each level 

of each node under low urban development.........................................................................22

13. Diagram showing data-only predictive probabilities of occurrence for each level 

of each node under high urban development........................................................................23

14. Diagram showing posterior predictive probabilities of occurrence for each level 

of each node given an observation of high urban land cover and no management 

interventions................................................................................................................................25

15. Diagram showing posterior predictive probabilities of occurrence for each level 

of each node under causal inference: Managing flashiness to medium, while still 

observing high urban land cover .............................................................................................26

16. Diagram showing posterior predictive probabilities of occurrence for each level 

of each node under causal inference: Managing specific conductance to low, 

while still observing high urban land cover ...........................................................................27

17. Diagram showing posterior predictive probabilities of occurrence for each level 

of each node under causal inference: Managing flashiness to medium and specific 

conductance to low, while still observing high urban land cover......................................28
vii

Appendix Figures

2–1. Prior Northeast Bayesian network ..................................................................................................47

2–2. Data-only Northeast Bayesian network .........................................................................................48

Tables

1. Biological Condition Gradient (BCG) tier and attribute definitions.......................................4

2. Northeastern U.S. urbanization effects model expert teams................................................9

3. Nodes and variables chosen by experts to represent major system components 

in the Northeastern U.S. Bayesian network model...............................................................11

4. “Hydrology” node prior conditional probability table, data table, and posterior 

conditional probability table .....................................................................................................12

5. Probability range prior weight elicitation results for all child state probabilities 

in each of two randomly selected rows from each conditional probability table ...........14

6. Driver causal interventions most likely to improve Biological Condition Gradient 

(BCG) tier achievement likelihood given unobserved urban land cover state.................29

7. Charts showing excerpts from macroinvertebrate metric prior expert-elicited 

conditional probability tables ...................................................................................................30

Appendix Tables

2-1. “Habitat” node prior conditional probability table and prior weight (α0), data table, 

and posterior conditional probability table and posterior weights (α0+n).........................36

2–2. “Water quality” node prior conditional probability table and prior weight (α0), 

data table, and posterior conditional probability table and posterior weights (α0+n).....37

2–3. “Generic richness” node prior conditional probability table and prior weight (α0), 

data table, and posterior conditional probability table and posterior weights (α0+n).....38

2–4. “Filter feeder relative abundance” node prior conditional probability table 

and prior weight (α0), data table, and posterior conditional probability table 

and posterior weights (α0+n).....................................................................................................40

2–5. “P+E relative abundance” node prior conditional probability table and prior 

weight (α0), data table, and posterior conditional probability table 

and posterior weights (α0+n).....................................................................................................42

2–6. “BCG” node prior conditional probability table and prior weight (α0), data table, 

and posterior conditional probability table and posterior weights (α0+n).........................44
viii

Abbreviations

BCG Biological Condition Gradient 

BMP Best Management Practices 

CART Classification and regression tree 

CPT Conditional probability tables 

DAG Directed acyclic graph 

EPT Ephemeroptera (mayflies), Plecoptera (stoneflies), and 

Trichoptera (caddisflies)

EUSE Effects of Urbanization on Stream Ecosystems

MCMC Markov Chain Monte Carlo 

NAWQA National Water-Quality Assessment 

NECB New England Coastal Basins

NEWS New England Wadeable Streams 

OLR Ordered logistic regression 

P+E Plecoptera and Ephemeroptera

USEPA U.S. Environmental Protection Agency 

USGS U.S. Geological Survey 
Linking Urbanization to the Biological Condition Gradient 

(BCG) for Stream Ecosystems in the Northeastern 

United States Using a Bayesian Network Approach

By Roxolana Kashuba,1 Gerard McMahon,1 Thomas F. Cuffney,1 Song Qian,2 Kenneth Reckhow,2

Jeroen Gerritsen,3

 and Susan Davies4

Abstract

Urban development alters important physical, chemical, 

and biological processes that define urban stream ecosystems. 

An approach was developed for quantifying the effects of 

these processes on aquatic biota, and then linking those effects 

to endpoints that can be used for environmental management. These complex, interacting systems are challenging to 

model from a scientific standpoint. A desirable model clearly 

shows the system, simulates the interactions, and ultimately 

predicts results of management actions. Traditional regression 

techniques that calculate empirical relations between pairs of 

environmental factors do not capture the interconnected web 

of multiple stressors, but urban development effects are not 

yet understood at the detailed scales required to make mechanistic modeling approaches feasible. Therefore, in contrast to 

a fully deterministic or fully statistical modeling approach, a 

Bayesian network model provides a hybrid approach that can 

be used to represent known general associations between variables while acknowledging uncertainty in predicted outcomes. 

It does so by quantifying an expert-elicited network of probabilistic relations between variables. Advantages of this modeling approach include (1) flexibility in accommodating many 

model specifications and information types; (2) efficiency in 

storing and manipulating complex information, and to parameterize; and (3) transparency in describing the relations using 

nodes and arrows and in describing uncertainties with discrete 

probability distributions for each variable. 

In realization of the aforementioned advantages, a 

Bayesian network model was constructed to characterize the 

effect of urban development on aquatic macroinvertebrate 

stream communities through three simultaneous, interacting 

ecological pathways affecting stream hydrology, habitat, and 

water quality across watersheds in the Northeastern United 

States. This model incorporates both empirical data and expert 

knowledge to calculate the probabilities of attaining desired 

aquatic ecosystem conditions under different urban stress 

levels, environmental conditions, and management options. 

Ecosystem conditions are characterized in terms of standardized Biological Condition Gradient (BCG) management 

endpoints. This approach to evaluating urban developmentinduced perturbations in watersheds integrates statistical and 

mechanistic perspectives, different information sources, and 

several ecological processes into a comprehensive description 

of the system that can be used to support decision making. 

The completed model can be used to infer which management 

actions would lead to the highest likelihood of desired BCG 

tier achievement. For example, if best management practices 

(BMP) were implemented in a highly urbanized watershed to 

reduce flashiness to medium levels and specific conductance 

to low levels, the stream would have a 70-percent chance 

of achieving BCG Tier 3 or better, relative to a 24-percent 

achievement likelihood for unmanaged high urban land cover. 

Results are reported probabilistically to account for modeling 

uncertainty that is inherent in sources such as natural variability and model simplification error. 

Introduction

Urban development affects physical, chemical, and 

biological processes that shape the condition of stream 

ecosystems (fig. 1). Impervious surfaces disrupt patterns of 

water movement (Klein, 1979; Poff and others, 1997; 

McMahon and others, 2003), and the resulting flashy streamflows can alter the physical habitat of streams, as evident in 

channel scouring and incision (Booth, 1990), sedimentation 

(Wolman and Schick, 1967; Trimble, 1997), floodplain disconnection (Haase, 2003), and the removal of riparian habitat. 

Urban storm runoff also contains anthropogenic contaminants, 

such as industrial chemicals, pesticides, and human waste 

(Van Metre and others, 2000; Beck, 2005). Habitat and stream 

1

U.S. Geological Survey.

2

Nicholas School of the Environment, Duke University, Durham, N.C.

3

Tetra Tech, Inc., Owings Mills, Md.

4

Maine Department of Environmental Protection.
2 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Portland

Eugene

Salem

Regional

processes Regional environmental setting

Climate, geology, natural flora and fauna,

 historical land-use patterns

Salem

Watershed 

processes Urban development within a watershed

Built environment: Impervious cover, housing, roads

Stream-reach

processes

Hydrology Stream chemistry

Habitat

Aquatic biota

EXPLANATION

Stream-reach

process interactions

Direct effect

pathways

Figure 1. Conceptual diagram of the Effects of Urbanization on Stream Ecosystems (EUSE) National Water-Quality Assessment 

(NAWQA) Program study. Urban stream ecosystems include processes operating at regional, watershed, and stream-reach scales.

chemistry changes can destabilize stream-nutrient, energy, 

and temperature cycles (Jacobson, 2001; Sprague and others, 2006). This interacting suite of physical and chemical 

stream factors serves as stressors and can degrade the condition of aquatic biota (Jones and Clark, 1987; Yoder and others, 

1999). Understanding how a stream ecosystem will respond to 

management actions designed to mitigate the effects of urban 

development first requires understanding how processes are 

linked across spatial scales and how they can interact within 

a given level (indicated in fig. 1 by dashed lines for streamreach processes).

As used to understand and quantify the effects of urban 

development on stream macroinvertebrates, traditional 

regression techniques that only calculate empirical relations 

between pairs of environmental factors (Cuffney and others, 

2010) do not account for the complex interactions between 

these multiple stressors. In addition, regression models do not 

incorporate available and information-rich expert knowledge, 

nor do they systematically account for uncertainty associated 

with system complexity, imperfect scientific understanding, 

and environmental variability. 

To address the aforementioned concerns, the U.S. Geological Survey (USGS), in cooperation with Duke University, 

developed a Bayesian network approach to model the system of interacting stressors associated with urbanization and 

their effects on stream biota. This study advances the USGS 

mission by creating a tool that can be used to assess potential 

outcomes of different biological resource management strategies including an explicit incorporation and representation of 

uncertainty associated with those decisions. The study and 

refinement of such tools will enable the public to enjoy healthy 

aquatic resources by identifying sustainable urbanization practices that minimize negative effects on the environment. 

Purpose and Scope

This report presents a Bayesian network modeling 

approach to (1) understand the relation between urban development, reach-scale factors (stressors) that are affected by 

urban development, and the condition of aquatic biota; and 

(2) provide information that can be used to manage water 

quality. A Bayesian network is a probabilistic, graphical model 

that quantifies a network of relations between variables. This 

type of model is flexible in accommodating many model 

structural configurations and input information types, efficient 

in storing and manipulating complex information, efficient 

to parameterize, and transparent in the relations it describes 

through the use of nodes and arrows. In addition, uncertainty 

is clearly represented as discrete probability distributions 

across all possible values of each modeled variable.
Methods 3

To link scientific understanding to management decision 

making, the Biological Condition Gradient (BCG) (Davies and 

Jackson, 2006) framework is used as the response variable, or 

endpoint, for the Bayesian network model. The BCG defines 

six tiers of biological community condition that can be used 

by managers as reference points for assessing stream health 

and determining management actions. The use of Bayesian 

network models to predict BCG tier membership for individual streams supports management decision-making objectives, 

including 

1. Providing objective and replicable characterizations of 

the relation between urban development and endpoints for stream health that can be linked to 

management actions; 

2. Describing and quantifying how changes in stressors 

can lead to changes in a biological-resource endpoint, 

characterized by the BCG; and

3. Supporting management decision making by calculating the probability of attaining aquatic ecosystem 

endpoints (BCG tiers) assuming different levels of 

urban stressors, environmental conditions, and 

ultimately, management options.

This model provides a realistic and applied method for 

resource managers to understand the multiple stressors affecting biological communities and evaluate alternative solutions 

that make sense from an ecological perspective. 

The scope of this report is limited to a description of a 

parsimonious eight-node Bayesian network model constructed 

using the New England Coastal Basins (NECB) subset of the 

USGS Effects of Urbanization on Stream Ecosystems (EUSE) 

data (Cuffney and Falcone, 2008). This report excludes discussion of the original Bayesian network urbanization modeling 

methods development process and justification, which focused 

on the Southeast United States (Kashuba, 2010). The focus of 

this report centers on model application and, as such, excludes 

the details of statistical methods innovations in the parameterization and understanding of Bayesian network modeling.

Methods

This section describes data-collection design, biological endpoint standardization and assignment, and the process 

involved in building and updating a Bayesian network model.

USGS Urban Stream Data

A set of nine watershed studies designed to investigate 

the Effects of Urbanization on Stream Ecosystems (EUSE) 

was conducted in major U.S. metropolitan areas during 

1999–2004 as part of the USGS National Water-Quality 

Assessment (NAWQA) Program (fig. 2; Tate and others, 

2005; Giddings and others, 2009). These studies assessed the 

Dallas

Boston

Denver

Raleigh

Atlanta

Portland

Milwaukee

Birmingham

Salt Lake City

Figure 2. Locations of the nine metropolitan regions and 

surrounding areas of the Effects of Urbanization on Stream 

Ecosystems (EUSE) studies.

physical, chemical, and biological conditions of streams across 

a range of urban development with a common design that 

used standardized measures of urban intensity (Cuffney and 

Falcone, 2008), methods of collection and processing samples, 

and techniques for data analysis (Fitzpatrick and others, 1998; 

Moulton and others, 2002). Within each of the nine metropolitan areas, data were collected at approximately 30 similarly 

sized watersheds. By substituting space for time, the EUSE 

studies quantified many environmental and biological stream 

changes that occur as urban development progresses within 

a watershed. The EUSE study conducted in the Northeastern 

United States, which included the Boston metropolitan area 

(fig. 2), was designated the NECB EUSE study; data from this 

study were used in the modeling effort described herein. New 

England was chosen as the area of focus to take advantage 

of the regional expertise of local biologists who were instrumental in developing the BCG concept (Davies and Jackson, 

2006). 

Biological Condition Gradient 

The BCG provides a framework for assessing stream 

health in terms of the condition of resident aquatic biota 

(fig. 3; table 1; Davies and Jackson, 2006). The biological condition of a stream is reported in terms of six tiers that represent 

biological condition endpoints ranging from natural (Tier 1) 

to highly disturbed (Tier 6); these endpoints are suitable for 

determining whether Clean Water Act water-quality standards 

are attained. 

The assignment of a stream to a BCG tier relies on 

the exercise of scientific judgment, dependent on regional 

expertise. Given a taxonomic group of interest (for example, 

macroinvertebrates), experts determine the community characteristics associated with each of 10 BCG attribute classes 

that are appropriate for a given region of the country (table 1). 

The overall assignment of a stream to a BCG tier is done by 
4 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach Biological Condition Gradient

Level of exposure to stressor

Watershed, habitat, flow regime,

and water chemistry as naturally 

occur.

Chemistry, habitat and (or) flow

regime severely altered from

natural conditions.

Natural structural, functional, and

taxonomic integrity is preserved.

Structure and function similar to natural 

community with some additional taxa 

and biomass; ecosystem level functions 

are fully maintained.

Evident changes in structure due to 

loss of some rare native taxa; shifts 

in relative abundance; ecosystem 

level functions fully maintained.

Moderate changes in structure due to

replacement of some sensitive 

ubiquitous taxa by more tolerant taxa; 

ecosystem functions largely maintained.

Sensitive taxa markedly diminished; 

conspicuously unbalanced distribution 

of major taxonomic groups; ecosystem 

function show reduced complexity and 

redundancy.

Extreme changes in structure and 

ecosystem function; wholesale 

changes in taxonomic composition; 

extreme alterations from normal 

densities.

Tiers of biological condition

1

2

3

4

5

6

Figure 3. Biological Condition Gradient (BCG) tiers relative to increasing stressor gradient (modified from Davies and Jackson, 

2006). The six BCG tiers are defined in terms of biotic community structure and ecosystem function as listed in table 1.

Table 1. Biological Condition Gradient (BCG) tier and attribute definitions.

[From Davies and Jackson (2006). The six BCG tiers are expressed graphically across increasing 

exposure to stressors in figure 3]

Tier Structure of biotic community Ecosystem function

1 Natural or native condition Natural or native condition

2 Minimal changes Minimal changes

3 Evident changes Minimal changes

4 Moderate changes Minimal changes

5 Major changes Moderate changes

6 Severe changes Major loss

Attribute Characteristics

I Historically documented, sensitive, long-lived or regionally endemic taxa

II Sensitive–rare taxa

III Sensitive–ubiquitous taxa

IV Taxa of intermediate tolerance

V Tolerant taxa

VI Nonnative or intentionally introduced taxa

VII Organism condition

VIII Ecosystem function

IX Spatial and temporal extent of detrimental effects

X Ecosystem connectance
Sidebar 1. Comparing Stream Biological Conditions Across Regions 5

Sidebar 1. Comparing Stream Biological Conditions Across Regions 

A major challenge in assessing relative biological conditions for streams in different parts of the country is setting 

expectations for the assessed sites that account for regional differences in the best available, or “reference,” conditions of 

aquatic biota (Herlihy and others, 2008). Macroinvertebrate samples from a U.S. Environmental Protection Agency (USEPA) 

study of the Temperate Plains region, which includes extensive agricultural lands in the eastern Dakotas, through Iowa, 

Minnesota, Missouri, Kansas, and Nebraska, to Indiana and Ohio, can be interpreted in a way that indicates that 62 percent of 

the stream length in this region was in good or fair condition. In contrast, macroinvertebrate sample data from the Northern 

Appalachians region, which includes all the New England states, most of New York, the northern half of Pennsylvania, 

and northeastern Ohio, can be interpreted in a way that indicates that only 

28 percent of the stream length was in good or fair condition. A conclusion 

that could be drawn from these data, collected as part of the USEPA Wadeable 

Streams Assessment, is that the overall biological condition of streams in 

the Midwestern agricultural region is better than the condition of streams in 

the largely forested Appalachian region (fig. 4; U.S. Environmental Protection 

Agency, 2006).

A likely reason for the larger percentage of good and fair stream reaches 

in the Temperate Plains in comparison to the Northern Appalachians is the 

relative difference in the observed biological condition of the reference 

streams in the two regions. Reference streams were selected on the basis 

of the “best available conditions,” those conditions generally present in 

undisturbed watersheds. Macroinvertebrate communities in these streams 

typically have more sensitive species than streams in watersheds that have 

been subject to some degree of human disturbance. However, much of the 

Temperate Plains has been altered by human disturbance, such as agricultural 

activity, and reference streams meeting the criterion of “best available 

conditions” had relatively fewer sensitive species than did reference streams 

in the Northern Appalachians. 

In essence, the regional difference in disturbance led to unequal 

starting points for comparing streams in the Temperate Plains with those 

in the Northern Appalachians. In terms of the Effects of Urbanization on Stream Ecosystems (EUSE) design, the relatively 

limited range of biological conditions in the Temperate Plains streams, including reference streams, resulted in a “truncated 

gradient” in comparison to the Northern Appalachian streams, where reference streams were more likely to have sensitive 

species. Therefore, for a given level of disturbance in a watershed (that is, moving away from reference conditions) a stream 

in the Northern Appalachian region would be likely to show greater departure from reference conditions compared to a 

stream in the Temperate Plains region. Additionally, a truncated gradient for the Temperate Plains region is consistent with the 

EUSE finding that agricultural land use in watersheds in the Milwaukee, Dallas, and Denver study areas had probably led to a 

reduction in the number of sensitive species in streams prior to urban development (Kashuba and others, 2010). 

An issue of potential concern for management in using least-disturbed streams to define “reference conditions” is that 

the qualities of a healthy stream can vary greatly among regions. In cases where assessments of stream health are based 

on regionally distinct reference biological communities, they are often difficult to compare across regions. This situation 

can occur, for example, when tolerant species dominate the biological community in the least-disturbed streams of a region 

because sensitive species have been lost from prior land-use disturbances. One solution that addresses this inconsistency 

is the use of a Biological Condition Gradient (BCG) (Davies and Jackson, 2006). The BCG provides a frame of reference for 

assessing stream biological conditions that can be applied in all parts of the United States. Best available stream conditions 

have reference conditions in BCG Tiers 1 or 2 in parts of the country that include high-quality biological communities. Other 

parts of the country, with degraded biological communities, may have reference conditions in BCG Tiers 3 or 4. Informative 

cross-regional comparisons can only be made when they are based on a common frame of reference.

100

90

80

70

60

50

40

30

20

10

0

Percentage of stream length

EXPLANATION

Not assessed

Poor

Fair

Good

Northern

Appalachian

Wadeable Streams Assessment

ecoregions

Temperate

Plains

Figure 4. Midwest versus Appalachian 

stream conditions. 
6 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

characterizing the organisms found in a biological sample in 

terms of these attributes (table 1). This characterization can 

be done by designating the appropriate attribute category for 

individual organisms (for example, sensitive rare taxa) or using 

metrics that provide summaries of the community composition. 

Experts determine the set of metrics that are best suited to represent the attributes for a given region and the appropriate range 

of metric values associated with each tier. A stream is assigned 

by experts to a BCG tier by weighing evidence from specific 

organisms and summary metrics. For example, a site with many 

sensitive, rare taxa belonging to Attribute II and few tolerant 

taxa belonging to Attribute V may be assigned a BCG Tier 2, 

reflecting a judgment that the overall structure of that site’s 

biotic community differs minimally from the natural condition. 

Implementation of a BCG framework allows waterquality managers to identify and protect waters of exceptional 

quality and detect incremental improvement or degradation 

in a stream at a finer scale than currently practiced. Managers 

can also use the BCG to set realistically attainable restoration 

goals, diagnose problems and causes with increased detection 

sensitivity, and find problems early and correct them while 

they are still local (Davies and Jackson, 2006). The BCG 

attempts to facilitate comparisons among regions by taking 

into account regional differences in the distribution of fauna 

and differences in methods of data collection and parameterization used by State and Federal agencies that monitor 

biological conditions (Davies and Jackson, 2006) (sidebar 1).

Assigning BCG Tier Membership in the 

Northeastern United States

In the Northeastern United States, substantial effort has 

been exerted to derive expert consensus on the classification 

of macroinvertebrate taxa into BCG attributes associated with 

community structure (Attributes I–VI; table 1). Based on 

extensive previous work conducted in the Northeastern United 

States by the U.S. Environmental Protection Agency (USEPA) 

(Snook and others, 2007; Yoder and Barbour, 2009), Tetra 

Tech Inc. (Gerritsen, 2008), and the State of Maine (Shelton 

and Blocksom, 2004), some 700 taxa sampled in the EUSE 

NECB data, hereafter referred to as EUSE Northeast data, 

were classified by attribute characteristics. These characteristics relate to the relative sensitivity of specific macroinvertebrates in the Northeast, but the same taxa would need to 

be re-classified for other ecoregions. For example, caddisfly 

Oecetis is classified as a genus of intermediate tolerance 

(Attribute IV) in the Northeast but as a sensitive-ubiquitous 

genus (Attribute III) in the Midwest (Barbour and others, 

1999). BCG Attributes VII–X describe ecological function and 

are much more challenging to measure than those involving 

community structure. Therefore, these attributes have not yet 

been characterized in implementations of the BCG framework 

(Gerritsen, 2008).

Once EUSE Northeast taxa were classified, biological experts were given 30 spreadsheets (one for each NECB 

stream sampled) that characterized each site’s macroinvertebrate community with a list of taxa found at that site, sorted 

and color-coded by attribute. In addition, spreadsheets also 

contained 20 standard macroinvertebrate metrics describing 

the richness and abundance of common indicator groups of 

taxa (Ephemeroptera, Plecoptera, and Trichoptera (EPT), Chironomidae, Oligochaeta, and so forth). Using their long-term 

career experience in judging biological condition, experts used 

this information to assign one BCG tier (Tier 1–6) to each 

NECB site. Tiers were first assigned individually, and final 

assignments were reached through expert group discussion 

and consensus. These assignments were then considered part 

of the EUSE Northeast dataset.

To operationalize the BCG approach, results from implementing the BCG framework need to be incorporated into 

a model that predicts membership in a BCG tier for a given 

stream as a function of watershed processes. These processes 

are affected by the degree of urban development in the watershed, which interacts with stressors such as hydrology and 

stream chemistry, and affects the aquatic biota found in the 

streams.

Bayesian Network Model

Conventional bivariate analysis of stream ecosystem 

data is often focused on relations between single pairs of 

environmental factors, without incorporating the influence 

of additional interconnected factors or previous ecological 

information about the system. Multiple factors associated with 

reach-scale hydrology, habitat, and water chemistry processes 

can act as stressors that affect the biological community, either 

through direct pathways (solid arrows) or through interactions 

among the processes (dashed arrows) (fig. 1). A Bayesian network modeling approach (Pearl, 1988) examines the relations 

among the processes by dissecting this complex system into 

smaller sets of directly related factors. 

The two main components of a Bayesian network are 

“nodes,” representing important concepts (processes and their 

factors), and “arrows,” representing relations between those 

concepts in the form of conditional probabilities (that is, the 

likelihood of any particular outcome depends on the occurrence of preceding events). To depict the structure of a model, 

these nodes and arrows are combined into a graphical representation with the use of a directed acyclic graph (DAG). As 

shown in figure 5, for example, Urban development can indirectly affect Biological condition by first disrupting Physical 

condition and Chemical condition. The relations among these 

four major concepts are depicted with a DAG through a set of 

nodes connected by ordered arrows where no pathway following the arrows goes through the same node twice; that is, there 

are no cycles (feedback loops) in the model. A DAG describing this system, therefore, uses four nodes and four arrows.

A node from which an arrow points is called a “parent” 

node and a node toward which an arrow points is called a 

“child” node. Therefore, Urban development is the parent of 
Methods 7

Biological

condition

Chemical

condition

Physical

condition

Urban

development

Figure 5. Directed acyclic graph (DAG) showing a simple 

Bayesian network with four nodes and four arrows.

both Physical condition and Chemical condition. This notation 

means that the physical condition and chemical condition are 

both conditional upon a watershed’s urban development level. 

Child nodes relative to one concept can then be parent nodes 

of another concept. That is, in addition to being children of 

Urban development, Physical condition and Chemical condition are both also parents of Biological condition. 

This modeling structure allows for the deconstruction 

of a complicated system into sets of direct relations between 

every parent node and its children, so that child nodes can then 

be modeled as parents of subsequent child nodes to eventually 

link the entire system into one probabilistic network. Representing a network of associations as a series of conditional 

relations such as these reduces the difficulty of parameterizing such a model and also greatly increases the amount of 

information obtainable from model output. One needs only to 

specify relations between directly linked factors in order to be 

able to create a Bayesian network that describes the interrelations among all factors simultaneously. The effect of changing 

one factor can then be measured on all remaining factors. 

To turn this qualitative model structure into a quantified Bayesian network, conditional probability tables (CPT) 

are defined, either using expert knowledge or existing data. 

For every possible combination of parent node values, a CPT 

indicates a probability distribution for values likely to occur at 

each child node. In a simplified example where urban development can be classified as either low or high, and Urban development is the single parent of Physical condition, the CPT for 

Physical condition has two rows: low and high urban development (fig. 6). Each row provides the probability of observing 

either good or poor physical condition given a known level of 

urban development. The probabilities in each row must add up 

to 100 percent, because each row describes a complete distribution across all possible child node values. The first row of 

this CPT, relating Urban development and Physical condition, 

indicates that if Urban development is low, there is a 90 percent chance that Physical condition is good, and a 10 percent 

chance that Physical condition is poor. Put differently, if 

100 streams were selected from watersheds having low urban 

land cover, 90 streams are likely to have good physical characteristics, but 10 could have poor characteristics.

Biological

condition

Chemical

condition

Physical

condition

Urban

development

If Physical

condition is... 

and Chemical 

condition is... 

good poor 

good good 95% of the time 5% of the time

good poor 25% of the time 75% of the time 

poor good 30% of the time 70% of the time 

poor poor 1% of the time 99% of the time 

Biological

condition will be...

Physical condition as PARENT node:

p(Biological condition|Physical condition, Chemical condition)

If Urban

development is... 

good poor 

low 90% of the time 10% of the time

high 10% of the time 90% of the time 

Physical 

condition will be...

Physical condition as CHILD node:

p(Physical condition|Urban development)

Figure 6. Example of simple conditional probability tables (CPT). The relation between each child node and its parents 

(left) is specified with a CPT (right). The upper CPT describes the relation when Urban development is the parent node 

and Physical condition is the child node. The lower CPT describes the relation when Physical condition is the parent 

node (along with the Chemical condition parent node) and Biological condition is the child node.
8 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

A primary advantage of the Bayesian network over traditional methods of causal analysis is the ability to simultaneously model interacting system components. In the simplified 

example, Biological condition is affected by both Physical 

condition and Chemical condition, so the associated CPT 

shows four probability distributions for Biological condition that account for all possible combinations of physical 

and chemical stream states (fig. 6, lower table). The first row 

of the CPT for Biological condition indicates a 95-percent 

chance that Biological condition is good if Physical condition and Chemical condition are both good. The probability of 

observing good Biological condition decreases to 30 percent 

or 25 percent, respectively, if either Physical condition or 

Chemical condition is poor and decreases to 1 percent if both 

Physical condition and Chemical condition are poor.

Creating a Bayesian Network Model

Creating a Bayesian network involves two major steps: 

(1) developing an initial model and distributions, known as 

the prior model, because it is built from information known 

prior to the inclusion of a specific dataset, and (2) updating the prior model with data to obtain the posterior model, 

which is the model form after data have been incorporated. 

All aspects of the prior model used for the present study were 

based on elicitations from subject experts such as scientists 

and resource managers. The information obtained included the 

model structure (arrangement of nodes and arrows), variable 

selection and discretization (division of a continuous measurement into discrete categories), conditional probabilities 

(the probabilities that child nodes will have certain values 

conditional upon the states of parent nodes), and prior weights 

(the influence of prior information on the model, relative to 

the influence of data). The prior model is then updated with 

the EUSE Northeast data to create the posterior model. As 

per Bayesian philosophy (Bayes, 1763), prior knowledge of 

how a system works is updated when additional information 

about the system is available. Upon completion, this posterior 

model can be used to better understand the relations within 

the parameterized network of nodes through the propagation 

of “evidence,” also called predictive or diagnostic probability 

calculation (Jensen and Nielsen, 2007). By setting the value 

of any parent (driver) node, a Bayesian network can predict, 

in distribution form, the likely values of all child (endpoint) 

nodes ultimately affected by changes to that driver. A Bayesian 

network can also “diagnose” the likely distributions of parent 

nodes required to cause a set child node value. In both cases 

(either following the arrow from parent to child, or in reverse), 

using the probabilistic relations between the nodes and Bayesian statistics, the Bayesian network will update what is known 

about a node on the basis of actual or hypothetical evidence 

about another node. The Bayesian networks presented in this 

report were built using Hugin software (Hugin, 2008).

Developing the Northeastern U.S. Bayesian 

Network Prior Model Using Expert Elicitation 

Expert elicitation specifically refers to the translation of 

expert knowledge into a probabilistic framework (Morgan and 

Henrion, 1990; Winkler, 2003; Reckhow and others, 2005; 

O’Hagan and others, 2006). Scientists often prefer to describe 

the model development process as objective, without acknowledging that model and parameter selections are made by way 

of implicit expert judgment. Expert elicitation, in contrast, is 

an explicit incorporation of expert judgment into the modeling 

process. The goal is to codify expert knowledge, appropriately 

recognizing the degree of uncertainty in that knowledge, and 

then use that knowledge directly in model development and 

parameterization. Using expert elicitation in model development thus focuses on the science of the problem by confirming 

or denying expected relations (hypothetico-deductive reasoning), instead of calculating statistics for all possible models 

and variable combinations without clear purpose.

Expert knowledge is essential to the development of the 

prior portion of the Bayesian network modeling construct 

described herein. Unlike data gleaned from a single study, 

experts provide an integrated estimate of system relations and 

uncertainties based on all information obtained and synthesized over their respective careers. Weighting prior knowledge 

in which experts have high confidence more heavily than lowconfidence knowledge can help address known problematic 

data concerns. 

To develop this Northeastern U.S. Bayesian network 

prior model, multiple groups of experts were recruited that had 

long-term experience in urban planning, water management, 

water chemistry, basin-scale habitat evaluation, and aquatic 

ecology (table 2). Following a specific methodology that 

was designed for creating an informed expert prior Bayesian 

network (Kashuba, 2010), model structure, variable selection 

and discretization, conditional probabilities, and prior weights 

were elicited from these groups of subject matter experts. 
Methods 9

Table 2. Northeastern U.S. urbanization effects model expert teams.

Biologists and aquatic ecologists

Susan P. Davies, Maine Department of Environmental Protection

David L. Courtemanch, Maine Department of Environmental Protection

Thomas J. Danielson, Maine Department of Environmental Protection

Susan K. Jackson, U.S. Environmental Protection Agency, Headquarters

Jeroen Gerritsen, Tetra Tech, Inc.

James F. Coles, U.S. Geological Survey, New Hampshire–Vermont Water Science Center

Thomas F. Cuffney, U.S. Geological Survey, North Carolina Water Science Center

Amanda H. Bell, U.S. Geological Survey, Wisconsin Water Science Center

Water management assessors

Peter K. Weiskel, U.S. Geological Survey, Massachusetts–Rhode Island Water Science Center

Marilee A. Horn, U.S. Geological Survey, New Hampshire–Vermont Water Science Center

Karen M. Beaulieu, U.S. Geological Survey, Connecticut Water Science Center 

Marcus C. Waldron, U.S. Geological Survey, Massachusetts–Rhode Island Water Science Center

Habitat scientists

Faith A. Fitzpatrick, U.S. Geological Survey, Wisconsin Water Science Center

Marie C. Peppler, U.S. Geological Survey, Wisconsin Water Science Center

Barbara C. Scudder, U.S. Geological Survey, Wisconsin Water Science Center

David S. Armstrong, U.S. Geological Survey, Massachusetts–Rhode Island Water Science Center

Urban planners and managers

Paul E. Sturm, Center for Watershed Protection 

William Stack, City of Baltimore Department of Public Works, Water Quality Management Service 

Kernell G. Ries, U.S. Geological Survey, Maryland Water Science Center

Ronald E. Bowen, Anne Arundal County, Maryland, Department of Public Works

Janis S. Markusic, Anne Arundal County, Maryland, Department of Public Works

Christopher Victoria, Anne Arundal County, Maryland, Department of Public Works

Joseph MacDonald, American Planning Association

Karen Cappiella, Center for Watershed Protection 

Hala E. Flores, Anne Arundal County, Maryland, Department of Public Works

Model Structure

Model structure refers to the arrangement of Bayesian 

network nodes and arrows. The goal of structure elicitation 

is to construct a diagram of nodes and arrows that represent 

the chain of events through which urban development affects 

aquatic macroinvertebrate communities. Initial model structure 

was elicited by way of textual analysis of the transcript from 

an open-ended causal narrative interview with a USGS career 

ecologist. Using this causal map development method (Nadkarni and Shenoy, 2004), the expert was asked to describe, 

step by step, how elements of urban development contribute 

to a biologically degraded stream condition. Then, formal 

textual analysis identified major concepts and causal relations between concepts. A “concept” is a single idea, such as 

“urban development” or ”habitat.” Environmental processes 

are represented in the causal relations between concepts, for 

example, channel incision is one way in which urban development affects habitat. To model the environmental processes 

discussed in the interview, elicited concepts and relations were 

converted into structure nodes and arrows, respectively. In 

model structure development, it is important to eliminate reiteration of the same concepts, clearly define causal pathways, 

avoid scale mismatch between concepts, and balance model 

complexity with an ability to parameterize (Reckhow, 1999). 

Therefore, in an iterative process of expert feedback from all 

subject matter groups, the initial causal map was pared down 

to a parsimonious Northeast model structure that was affirmed 

by expert consensus to represent key processes and causal 

influences at the selected scale, while also being of sufficiently 

manageable size to allow for parameterization (fig. 7). 

Macroinvertebrate metrics were selected using a twopronged approach. After the process of BCG tier assignment 

(described earlier), experts were asked to identify the three 

most vital macroinvertebrate metrics whose values influenced 

assessment of biological condition. Simultaneously, classification and regression tree (CART) and ordered logistic 

regression (OLR) models were constructed to evaluate which 

metrics were most predictive of BCG in the USEPA New 

England Wadeable Streams (NEWS) dataset (Snook and others, 2007). The three top macroinvertebrate metrics identified 

by both experts and statistical analysis were chosen for use 

in the Bayesian network model: generic richness, filter feeder 

relative abundance, and Plecoptera and Ephemeroptera (P+E) 

relative abundance (fig. 7).
10 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Habitat

Water

chemistry Hydrology

Urban

development

Plecoptera + 

Ephemeroptera (P+E)

relative abundance

Generic

richness

Filter feeder

relative abundance

Biological Condition

Gradient (BCG)

Variable Selection and Discretization

Model structure development involves only identifying 

major qualitative concepts (nodes) and their causal connections with each other (arrows). To transform such a causal 

map into a Bayesian network, a quantifiable variable must be 

assigned to each node, and each assigned continuous variable 

must be converted into a discrete number of mutually exclusive categories. For each model node, experts rely on career 

experience, inter-expert discussion, and consensus building to 

select an EUSE Northeast dataset variable that best represents 

the intended concept of that node (table 3). The choice of how 

many categories a variable should be split into involves a 

tradeoff between the model’s discriminatory strength and the 

accuracy of (potentially complex) parameterization. Having 

few categories limits the ability of the model to differentiate 

between different states of a node and to evaluate changes to 

the variable and the system. As a variable is split into more 

Figure 7. Parsimonious Northeast Bayesian network model structure.

categories, however, it becomes more difficult to establish 

dependencies between model variables (Uusitalo, 2007) 

because parameter space expands rapidly. In addition, based 

on lessons learned during method development (Kashuba, 

2010), experts often have difficulty distinguishing between 

the middle two of four categories; therefore, each continuous 

variable was split into three categories. For the two selected 

discrete variables (dominant substrate and BCG), model 

categories were chosen to mimic natural, discrete categories; 

dominant substrate is binary (either fine or coarse), and BCG 

has six tiers (table 3). 

Ideally, each category should represent a group of 

values similar to one another and distinct from other categories, because after discretization, every value within a single 

category will be treated identically by the model. In the 

absence of clear ecological or resource management dividing lines (which dominant substrate and BCG have), this 
Methods 11

Table 3. Nodes and variables chosen by experts to represent major system components in Northeastern U.S. Bayesian 

network model. 

[%, percent, >, greater than, P+E, Plecoptera and Ephemeroptera; BCG, Biological Condition Gradient]

Node Variable: units Discrete categories

Low Medium High

Urban development Urban land cover: percentage urban land 

cover in basin area 0–7% >7–31% >31–100%

Hydrology Flashiness: rises greater than 7 times the 

annual median rise 0 1–3 4+

Habitat Substrate: dominant (>50% of transects) 

substrate type

Fine

(sand and smaller)

Coarse

(gravel and larger)

Water quality

Specific conductance: at low base flow, 

microsiemens per centimeter at 25 degrees 

Celsius

0–139 >139–269 >269

Generic richness Generic richness: total number of taxa at the 

genus taxonomic level 0–14 15–37 38+

Filter feeder relative 

abundance

Filter feeder relative abundance: percent of 

total abundance that are filter feeders 0–30% >30–60% >60–100%

P+E relative abundance

P+E relative abundance: percentage of total 

abundance that are Plecoptera and 

Ephemeroptera

0–5% >5–20% >20–100%

BCG Biological Condition Gradient discrete scale 

of 1 (best) to 6 (worst) 1 2 3 4 5 6

Conditional Probability Tables 

Just as variable selection and discretization explicitly 

define model nodes, CPTs explicitly define the relations 

between the nodes (which are represented by arrows). In a 

Bayesian network, a node is modeled in terms of the probabilities that a sample (in this case, a stream measurement) would 

belong to each of its categories. This probability distribution across the states of a given node changes depending on 

the states of nodes that influence it. Rephrasing in Bayesian 

network parlance, child nodes (into which arrows point) are 

conditionally dependent on their parent nodes (from which 

arrows point). For example, the likelihood of observing high, 

medium, or low flashiness in a stream is conditional on the 

level of urban development in the stream’s watershed. Therefore, the Hydrology child node is parameterized conditional 

on its Urban development parent node. The Bayesian network 

structure specifies, through its arrow placement, the set of 

CPTs required by the model, where a CPT is created for every 

child node conditional on its parents.

Within each CPT, a probability distribution across all 

possible states of a child node must be elicited for every possible combination of parent node states. For example, the CPT 

for the Hydrology node conditional on the Urban development

node has a separate distribution across high, medium, and 

low flashiness for each of the three possible states of urban 

land-cover percentage (table 4A). Each of these distributions 

across child node states is represented in its own CPT row and 

unambiguous distinction between categories is difficult to 

achieve. Therefore, because no clear thresholds existed for 

the seven continuous variables requiring discretization, an 

adaptive, two-criterion category-definition methodology was 

created. This approach starts with defining category endpoints 

such that each category contains an equal frequency of available data. These initial category endpoints are then adjusted 

as ecologically important cutoff points are identified during 

conditional probability elicitation. Applying this methodology, the 30 EUSE Northeast data points for each continuous 

variable were split such that values less than the 33rd percentile defined the “low” category, values between the 33rd and 

67th percentiles defined the “medium” category, and values 

greater than the 67th percentile defined the “high” category. 

Experts were asked whether these three category definitions 

accurately represented what would be considered ecologically “low,” “medium,” or “high” for each variable, and initial 

endpoint adjustments were made based on expert feedback. 

During conditional probability elicitation, experts refined 

their definitions of each category in the context of describing 

the behavior of variables in relation to other variables. For 

example, the definition of low generic richness was narrowed 

from 0–23 genera to 0–14 genera when it was determined that 

the original range of values was too broad to have a consistent 

effect on BCG tier classification. All generic richness values 

defined as low based on frequency did not belong to the same 

category ecologically, so the category definition was adjusted. 
12 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Table 4. “Hydrology” node prior conditional probability table and prior weight (α0), 

data table, and posterior conditional probability table and posterior weights (α0

+n).

A. Prior conditional probability table 

[Flashiness categories in probability units and α0 in equivalent data points; rows selected for prior 

weight elicitation are highlighted in gray]

Urban land 

cover

Flashiness greater than 7 times the median

Low Medium High α0

Low 0.20 0.70 0.10 9.72

Medium 0.15 0.55 0.30 9.72

High 0.10 0.40 0.50 9.72

B. Data table 

[Flashiness counts and n total number of samples per parent state combination]

Urban land 

cover

Flashiness greater than 7 times the median

Low Medium High n

Low 1 8 1 10

Medium 1 5 4 10

High 2 4 4 10

C. Posterior conditional probability table

[Flashiness categories in probability units and α0+ n in equivalent data points]

Urban land 

cover

Flashiness greater than 7 times the median

Low Medium High α0

+n

Low 0.149 0.751 0.100 19.72

Medium 0.125 0.525 0.351 19.72

High 0.151 0.400 0.449 19.72

described by its own Dirichlet prior distribution (Jensen and 

Nielsen, 2007) (app. 1, eqs. 1.1, 1.2). A Dirichlet distribution 

describes the probabilities of each of three or more mutually 

exclusive events occurring.

To fully characterize the seven CPTs defined by this 

8-node, 17-arrow Bayesian network model (fig. 7), 102 such 

Dirichlet distributions are required, collectively composed 

of a total of 378 Dirichlet θi

 parameters (where i = 1, 2, or 3 

for all nodes except Habitat, which has two states, or BCG, 

which has six). Nodes with no parents, called “marginal 

nodes,” (such as Urban development) are simply assigned an 

unbiased flat distribution across all possible discrete states, 

such that every state has an equal probability of occurrence. 

Dirichlet distributions for the urban development node are 

never explicitly reported because urban land cover is simply 

distributed equally (0.33 per node state), by design, for both 

the prior distribution and the data distribution and, hence, the 

posterior distribution. The roles of prior, data, and posterior 

are described in further detail later as part of the discussion on 

updating the prior model with data.

The CPTs should be elicited following a systematic, prescribed process designed to guide the experts through a rational, judicious evaluation of their expertise. There are several 

documented direct and indirect probability elicitation methods 

for binomial distributions (Winkler, 1967, 2003; Morgan and 

Henrion, 1990); however, the literature remains sparse on ideal 

elicitation methods for the multinomial distributions used in 

this model. Therefore, an adaptation of the direct fixed value 

elicitation method (Clemen, 1991) was developed to apply 

to multinomial elicitations, following the five steps of the 

Stanford Research Institute Elicitation Protocol (Spetzler and 

von Holstein, 1975) to attempt to minimize bias and error. To 

start this elicitation, experts are familiarized with the problem 

context (a process called “motivating”) and specific questions 

of interest (“structuring”) and are then asked to summarize 

and review relevant expert knowledge qualitatively (“conditioning”). After experts are appropriately prepared, prior 
Methods 13

probabilities are assigned (“encoding”) and tested to ensure 

they correctly capture the experts’ opinions (“verifying”). 

Encoding was conducted in frequency units rather than 

probability units to facilitate human conceptualization of the 

information required (Morgan and Henrion, 1990). Using 

direct fixed value multinomial-adapted elicitation, experts 

were asked to divide a fixed total of events into categories 

according to their expected likelihood of occurrence. For 

example, for the first row of the Hydrology child node conditional on the Urban development parent node, the experts are 

asked the following: 

Assume the watersheds of 100 streams in the Northeastern United States are known to have 0–7 percent 

(low) urban land cover. Assume all other stream 

features are randomly distributed as if you took a 

random sample of northeastern streams with low 

urban land cover. How many of those 100 streams 

would you expect to have low flashiness (no rises 

greater than 7 times the median in a year), medium 

flashiness (between 1 and 3 rises), or high flashiness 

(more than 4 rises)? 

Experts were encouraged to discuss this question until consensus was reached. In this example, experts agreed to report that, 

out of 100 streams in watersheds with low urban land cover, 

they would expect 20 of those streams to have low flashiness, 

70 streams to have medium flashiness, and 10 streams to have 

high flashiness (table 4A, first row). This same exercise was 

then conducted for the remaining possible Urban development parent node states (that is, medium and high) and then 

also for each CPT row (that is, parent node state combination) 

of the remaining six child nodes. For the three macroinvertebrate metric nodes and BCG node, a total of 1,000 streams 

were postulated to allow for the assignment of very unlikely 

probabilities of less than 1 percent. Frequency results were 

converted into probabilities and normalized when the reported 

total did not equal 100 or 1,000 exactly. The complete elicited 

prior CPT for child node Hydrology is reported in table 4A. All 

other prior CPTs are provided in appendix 2, tables 2–1A to 

2–6A.

Prior Weights

Prior weights were elicited to determine how much to 

weight prior knowledge relative to data during Bayesian 

updating (described later). Prior weights are reported in units 

of “equivalent data points” to allow for comparison with data 

weight reported as a number of actual data points. After evaluation of three different prior weight-elicitation methods, the 

probability range method (Cowell and others, 1999) was found 

to show lowest within-method variability, most consistent 

prior weights among nodes, and was most intuitive for experts 

to communicate (Kashuba, 2010). This method asks experts 

to provide a range of values that represents their certainty 

about a given parameter. For example, experts reported in CPT 

elicitation that, of 100 streams having low urban land cover, 

they would expect 20 to have low flashiness. When asked to 

provide a certainty range of values, they responded that they 

would not be surprised if there were as few as 5 or as many 

as 35 streams that had low flashiness in a sample of 100 low 

urban land-cover streams (table 5, first row). The premise of 

the probability range elicitation method is that small reported 

probability ranges correspond to high certainty (that is, high 

prior weight), and large ranges correspond to high uncertainty 

(low prior weight).

The width of an elicited range has been determined to be 

approximately two standard deviations long around a Dirichlet θi

 value (app.1, eq. 1.1) (Spiegelhalter and others, 1994), 

that is, one standard deviation is equivalent to one-half the 

length of the range. Eliciting a prior probability and an uncertainty range of probabilities for a CPT cell, therefore, provides 

values for expected mean (E[θi ]) and expected variance 

(var[θi ]), respectively, for the Dirichlet parameter, θi. Equations for the Dirichlet expected value and Dirichlet expected 

variance can then be solved for prior weight, α0, (app. 1, 

eqs. 1.3–1.5) (Kashuba, 2010). In the example reported earlier, 

E[θi ] = 0.20, a range of 0.30 translates to a standard deviation 

of 0.15, so var[θi ] = 0.0225, resulting in α0 = 6.11 for the CPT 

cell representing the probability of observing low flashiness 

given low urban land cover (table 5, first row). Probability ranges were elicited and prior weights were calculated 

in this way for two random rows of each child node’s CPT 

(highlighted in table 4A for Hydrology child node, and app. 

2, tables 2–1A to 2–6A for remaining child nodes). These celllevel prior weight values were then averaged across a child 

node for stability (table 5). Node-averaged prior weights are 

also reported with elicited CPTs in table 4A and appendix 2, 

tables 2–1A to 2–6A. For example, the prior weight for the 

Hydrology child node, 9.72 (table 4A, table 5), is the mean of 

the six elicited probability ranges for the low and high urban 

land cover CPT rows (table 5, first six rows).
14 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

Table 5. Probability range prior weight elicitation results for all child state probabilities in each of two randomly selected rows from 

each conditional probability table.—Continued

[P+E, Plecoptera and Ephemeroptera; BCG, Biological Condiiton Gradient]

Child node 

(variable)

Parent node

variable states 

(category definition)

Child 

variable 

state

Prior 

expected 

value 

(E[θi ])

Elicited 

prior 

probability

range

Standard 

deviation 

calculated 

from range 

Calculated prior 

weight 

(α0)

Hydrology 

(Flashiness)

Urban land cover

Low

Low 0.20 0.05–0.35 0.15 6.11

Medium 0.70 0.50–0.80 0.15 8.33

High 0.10 0.02–0.18 0.08 13.98

High

Low 0.10 0.02–0.18 0.08 13.06

Medium 0.40 0.30–0.60 0.15 9.67

High 0.50 0.30–0.65 0.18 7.16

Mean ± within–method standard deviation 9.72 ± 3.19

Habitat 

(Substrate)

Urban land cover Flashiness

Low High Fine 0.05 0–0.12 0.06 12.19

Coarse 0.95 0.85–1 0.08 7.44

High Low Fine 0.40 0.20–0.60 0.20 5.00

Coarse 0.60 0.40–0.80 0.20 5.00

Mean ± within–method standard deviation 7.41 ± 3.39

Water 

quality 

(Specific 

conductance)

Urban land cover Flashiness

Low Low

Low 0.85 0.75–0.95 0.10 11.75

Medium 0.10 0.02–0.20 0.09 10.11

High 0.05 0–0.10 0.05 18.00

High Low

Low 0.02 0–0.05 0.03 30.36

Medium 0.23 0.05–0.30 0.13 10.33

High 0.75 0.65–0.95 0.15 7.33

Mean ± within–method standard deviation 14.65 ± 8.48

Generic 

richness

Flashiness Substrate Conductance

Medium Coarse Medium

Low 0.100 0.010–0.200 0.095 8.97

Medium 0.350 0.100–0.900 0.400 0.42

High 0.550 0.300–0.800 0.250 2.96

High Fine High

Low 0.900 0.500–0.999 0.250 0.45

Medium 0.099 0.050–0.800 0.375 –0.37

High 0.001 0–0.100 0.050 –0.60

Mean ± within–method standard deviation 1.97 ± 3.65

Filter 

feeder relative 

abundance

Flashiness Substrate Conductance

Low Fine High

Low 0.440 0.200–0.800 0.300 1.74

Medium 0.550 0.200–0.800 0.300 1.75

High 0.010 0.001–0.150 0.075 0.78

High Coarse High

Low 0.200 0.100–0.600 0.250 1.56

Medium 0.500 0.100–0.800 0.350 1.04

High 0.300 0.100–0.600 0.250 2.36

Mean ± within–method standard deviation 1.54 ± 0.56

( var[ ] θi )
Methods 15

Updating the Prior Model with Data

The mechanism of Bayesian network updating and, 

hence, the ability to combine expert judgment with data 

derives from the principles of Bayes Theorem (Bayes, 1763):

p x p px ( ) ( ) ( ), θ θθ ∝

where

p(θ)	 is the prior probability distribution of θ, the 

parameter set of interest, 

p(x|θ)	 is the likelihood function characterizing x, the 

data, given θ, and 

p(θ|x)	 is the posterior probability distribution of θ, 

given the data, x, which is a combination 

of the prior information and the data 

collected.

(1)

In general, Bayesian analysis attempts to gain understanding about the distribution of all possible values of a 

parameter set of interest, θ. This distribution, p(θ), is originally 

constructed from information available prior to the collection of a specific dataset. Once data are available, the likelihood function, p(x|θ), calculates the likelihood of observing 

those data given each possible value of θ. To update the prior 

information with the additional information from the data, the 

prior distribution is multiplied by the data likelihood function, 

resulting in a posterior distribution of θ, conditional upon the 

data observed. This posterior distribution, p(θ|x), is essentially a weighted average of the prior information and the data 

(sidebar 2).

Table 5. Probability range prior weight elicitation results for all child state probabilities in each of two randomly selected rows from 

each conditional probability table.—Continued

[P+E, Plecoptera and Ephemeroptera; BCG, Biological Condiiton Gradient]

Child node 

(variable)

Parent node

variable states 

(category definition)

Child 

variable 

state

Prior 

expected 

value 

(E[θi ])

Elicited 

prior 

probability

range

Standard 

deviation 

calculated 

from range 

Calculated prior 

weight 

(α0)

P+E relative 

abundance

Flashiness Substrate Conductance

Low Coarse Medium

Low 0.100 0.050–0.300 0.125 4.76

Medium 0.600 0.450–0.900 0.225 3.74

High 0.300 0.200–0.600 0.200 4.25

Medium Coarse Low

Low 0.010 0.001–0.100 0.050 3.04

Medium 0.390 0.200–0.600 0.200 4.95

High 0.600 0.500–0.800 0.150 9.67

Mean ± within–method standard deviation 5.07 ± 2.36

BCG

Generic 

richness

Filter feeder 

relative 

abundance

P+E relative 

abundance

Low High High

1 0.001 0–0.005 0.002 159.48

2 0.001 0–0.005 0.002 159.48

3 0.001 0–0.020 0.010 9.03

4 0.498 0.299–0.697 0.199 5.30

5 0.498 0.299–0.697 0.199 5.30

6 0.001 0–0.100 0.050 –0.60

High High High

1 0.050 0.030–0.151 0.004 12.21

2 0.050 0.040–0.100 0.001 51.83

3 0.450 0.350–0.549 0.010 23.80

4 0.350 0.250–0.450 0.010 21.79

5 0.100 0.050–0.150 0.002 35.04

6 0.001 0–0.002 0.000001 999.00

Mean ± within–method standard deviation 123.47 ± 281.42

( var[ ] θi )
16 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

Sidebar 2. How Bayesian Updating Works

Simple Example with Single Probability Parameter 

Bayesian updating is the process of revising a prior distribution of one or more parameters using newly obtained data 

that contain information about those parameters. This simple example shows how to estimate the probability that a random 

stream in the northeastern United States has good biological 

condition. This probability can be represented by the 

parameter, θi. Prior information about θi (from either expert 

knowledge or previous data) can be summarized in this 

case by a beta distribution centered on 0.50 with a standard 

deviation of 0.2 (fig. 8, solid red distribution). This prior 

information is known with a prior weight (hypothetical sample 

size) of 6. This means that, prior to data collection, analysts 

believe there is a 50-percent chance that a random stream in 

the northeastern United States has good biological condition, 

and the certainty of that probability estimate is equivalent 

to the certainty of observing six streams, of which three had 

good biological condition. This prior distribution summarizes 

everything known, and how well it was known, before data 

were collected.

The biological condition of 10 random streams in the 

Northeast are then sampled. The data collected indicate 

that 7 of these 10 streams have good biological condition. 

This means the data are assumed to belong to a binomial 

likelihood distribution centered on the maximum likelihood 

estimate of 0.70 for parameter θi (fig. 8, dashed blue 

distribution). Making an inference about parameter θi based 

on these data alone, there is a 70-percent chance that a 

random stream in the northeastern United States has good 

biological condition with a certainty equivalent to 10 samples. 

Given the sources just described, there are two different 

types of information from which two different conclusions 

can be drawn concerning the probability that a stream in the 

Northeast United States has good biological condition. There 

is slightly more certainty in the conclusions drawn from the 

10 sample units of recently collected data, but that does not 

mean that the 6 sample units of information available prior to 

collecting data should be discounted. 

Ideally, the greatest certainty would be associated with 

a conclusion that could be drawn from both aforementioned 

sources of information. This combining of information is exactly what Bayesian updating allows one to do. By taking a weighted 

average of prior information and data, a posterior (beta) distribution for parameter θi is calculated with an expected value of 

0.625 (fig. 8, solid purple distribution). An analyst can now infer that the probability of a stream in the northeastern United States 

having good biological condition is closer to 62.5 percent, with a certainty equivalent to 16 samples. This greater certainty of the 

posterior state of knowledge is represented by a smaller standard deviation of 0.1 (fig. 8, solid purple distribution) relative to the 

prior distribution standard deviation of 0.2 (fig. 8, solid red distribution).

0.0 0.2 0.4 0.6 0.8 1.0

0

1

2

3

4

θi

Probability density

Prior: p(θi) → 0.50

Data: xi /n = 7/10 → 0.70

Posterior: p(θi

|xi) → 0.625

Figure 8. Bayesian updating of hypothetical, generic 

parameter θi (which can represent a probability between 

0 and 1). The expected value of the prior distribution (red), 

p(θi), is 0.50. Collected data (blue) shows 7 of 10 samples 

(where xi is number of positive draws and n is total sample 

size), resulting in a maximum likelihood estimate of 0.70. 

The posterior distribution (purple), p(θi|xi), averages prior 

information with data, weighting by prior weight (6) and 

sample size (10), respectively, and yielding an expected 

value of 0.625. Because sample size was slightly greater 

than prior weight, the posterior expected value is slightly 

closer to the maximum likelihood estimate than to the prior 

expected value.
Sidebar 2. How Bayesian Updating Works 17

Bayesian Updating for Multiple Probability Parameters within a Bayesian Network CPT Row 

In the context of a Bayesian network, Bayesian updating of parameters applies to each parameter in each conditional probability table (CPT). Rather than using the distribution forms that describe the probability of a single outcome occurring (that is, beta prior 

and posterior distributions for the parameter, θ, and binomial likelihood for the data), each row in the conditional probability table 

uses the distribution forms that describe the probability of one of multiple outcomes occurring. The distribution form for multiple 

(for example, three) possible outcomes is Dirichlet prior and posterior distributions for the parameters, θ1, θ2, θ3, and multinomial 

likelihood for the data, as described in the discussion of model updating with prior data and equations 1.1–1.9 (appendix 1).

The different distribution forms just described follow identical Bayesian principles. Each cell in a CPT shows the expected 

value of the probability that a stream will fall into that child node category given that it belongs to the parent node category for that 

row. For example, the first row of the prior CPT for the Hydrology child node shows that for a stream in a watershed with low urban 

development (parent node category), there is an expected 20-percent chance that stream will have low flashiness, a 70-percent 

chance that stream will have medium flashiness, and a 10-percent chance that stream will have high flashiness (fig. 9, top prior 

row, from table 4A, first row). Similar to the single probability example described earlier, these three probabilities are constructed 

from (expert) knowledge obtained prior to data collection. These three values are considered the expected prior values for 

Dirichlet parameters, θ1, θ2, θ3. The expert-elicited prior weight indicates that this knowledge is equivalent in certainty to 8.3 

hypothetical samples. This prior weight is represented in Dirichlet terminology as α0 (appendix 1, equations 1.1–1.9).

Additionally, Effects of Urbanization on Stream Ecosystems (EUSE) Northeast data measuring flashiness and urban 

land cover are also available to make inference on the likely values of θ1, θ2, θ3. In this case, data show that of 10 streams in 

watersheds having low urban land cover, 1 has low flashiness, 8 have medium flashiness, and 1 has high flashiness (fig. 9, 

middle data row, from table 4B, first row). The maximum likelihood values for θ1, θ2, and θ3, given these data, (from assumptions 

specific to a multinomial distribution) are 0.10, 0.80, and 0.10, respectively. Bayesian updating is then used to combine these 

two sets of information into a posterior conditional probability table that lists the expected values for parameters θ1, θ2, and θ3, 

given both prior information and data, weighting by the prior weight, α0, and sample size, n, respectively (fig. 9, bottom posterior 

row, from table 4C, first row). In this case, because the sample size is slightly greater than the prior weight, posterior expected 

values of the probabilities of having low or medium flashiness given low urban land cover are calculated slightly closer to 

the maximum likelihood values of the data compared to the expected values of the prior distribution. The posterior probability 

of high flashiness remains 

unchanged because both the 

prior distribution and the data 

likelihood have the same 0.10 θ3

value. This Bayesian updating 

process is followed for every CPT 

row in the model. 

Figure 9. Bayesian updating 

of parameters θ1, θ2, θ3, within a 

conditional probability table (CPT) 

row in a Bayesian network. The 

posterior expected values, E[θ1|x1], 

E[θ2|x2], and E[θ3|x3], are each 

the weighted average of the prior 

expected values (E[θ1], E[θ2], and 

E[θ3]) and the maximum likelihood 

estimates from the data (x1/n, x2/n, 

and x3/n), weighted by the prior 

weight (α0) and sample size (n), 

respectively.

PRIOR

Urban development: 

Percent urban land cover

Hydrology: 

Flashiness greater than 7 times the annual median rise

Low 

(0–7%)

Low

(0 rises)

Medium

(1–3 rises)

High

(4+ rises)

Prior 

weight

0.20 0.70 0.10 8.3

DATA

E[θ1] E[θ2 ] E[θ3] α0

Urban development: 

Percent urban land cover

Hydrology: 

Flashiness greater than 7 times the annual median rise

Low

(0–7%)

Low

(0 rises)

Medium

(1–3 rises)

High

(4+ rises)

Sample 

size

1 8 1 10

POSTERIOR

x1 x2 x3 n

Urban development: 

Percent urban land cover

Hydrology: 

Flashiness greater than 7 times the annual median rise

Low

(0–7%)

Low 

(0 rises)

Medium

(1–3 rises)

High

(4+ rises)

Posterior 

weight

0.15 0.75 0.10 18.3

E[θ1 | x1 ] E[θ2 | x2] E[θ3 | x3] α0+ n
18 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

In theory, prior parameter distributions can take any 

functional form conceivable. However, if the posterior distribution function cannot be calculated analytically (for a given 

combination of prior distribution and data likelihood function), numerical approximation techniques such as Markov 

Chain Monte Carlo (MCMC) sampling are often computationally laborious and time intensive (Lunn and others, 2000). If, 

instead, the prior distribution and the data likelihood function 

belong to what is called a conjugate family, then a posterior 

solution of the same functional form as the prior distribution is 

guaranteed. 

In the context of a Bayesian network, the parameter sets 

of interest are the probabilities that a node’s value will fall 

within each of its possible discrete categories. These probabilities, represented by different θi

 parameters, can be modeled using a Dirichlet distribution, as explained earlier in the 

discussion of prior model development using expert elicitation. For example, a node representing urban development has 

three possible categories: high (>31–100 percent urban land 

cover), medium (>7–31 percent) and low (0–7 percent). The 

prior probability that a random Northeastern U.S. watershed 

has high, medium, or low urban land cover can be described 

by parameters θ1, θ2, and θ3, respectively. 

Continuous data collected by measuring the urban landcover percentages of a random sample of watersheds can be 

converted into discrete data by placing the samples into the 

three defined urban land-cover categories and reporting number of samples in each category rather than each sample’s original continuous value. In this way, 30 continuous x values (for 

example, 0.9, 1.1, 1.8, 2.4, 2.4, 2.6, 3.2, 3.3, 4.9, 6.4, 8.0, 8.0, 

10.3, 15.4, 18.3, 21.5, 23.5, 24.4, 28.5, 30.6, 34.7, 35.7, 38.6, 

43.3, 44.7, 50.2, 53.7, 60.1, 64.4, and 76.4 percent urban land 

cover) can be reported, instead, as three discrete x values (for 

example, 10, 10, and 10 samples in categories high, medium, 

and low urban development, respectively). Data in this discrete form can be described using the multinomial likelihood 

function (app. 1, eqs. 1.6–1.7). The Dirichlet-multinomial 

family is conjugate, which means that if the Dirichlet distribution is used to quantify prior knowledge about the possible 

values of θ1, θ2, and θ3, and multinomial data are collected, 

then the posterior distribution combining prior knowledge and 

data will also be of the Dirichlet form. To calculate this posterior distribution, the Dirichlet prior distribution is multiplied 

by the multinomial likelihood function as specified by Bayes 

Theorem (eq. 1), resulting in a Dirichlet posterior distribution 

with new coefficient values (app. 1, eqs. 1.8–1.9). 

The Dirichlet posterior estimates are a weighted average 

of prior estimates and data estimates. Hypothetically, assume 

the expected value of θ1 from the Dirichlet prior distribution 

was 0.20 with a prior weight of 5 and data showed that 4 out 

of 10 samples fell into category 1. The posterior expected 

value of θ1 calculated from the Dirichlet posterior distribution 

would then be the average of 0.20 weighted by 5 and 0.40 

weighted by 10, or 0.33. This posterior expected value of θ1, 

0.33, is the average of 0.20 and 0.40, where 0.40 has twice the 

weight of 0.20, as specified by the prior weight relative to the 

data weight (sample size). In this way, prior and data information are combined, appropriately weighted (sidebar 2). In other 

words, the prior expected value of θ1 (0.20) is updated with 

information from collected data to yield a posterior expected 

value of 0.33. Specific to the Hydrology child node discussed 

above, the expert elicited prior CPT shows that a watershed 

with low urban land cover, flashiness is 20 percent likely to 

be low, 70 percent likely to be medium, and 10 percent likely 

to be high (table 4A). The EUSE Northeast data show that, of 

10 watersheds with low urban land cover, 1 had low flashiness, 

8 had medium flashiness, and 1 had high flashiness (table 4B). 

Therefore, the posterior CPT for the Hydrology child node 

shows expected values of 14.9 percent low, 75.1 percent 

medium, and 10.0 percent high flashiness, which are each an 

average of the prior probabilities and the data, weighted by the 

prior weight and sample size, respectively (table 4C).

Predicting Effects of Urbanization 

on Biota

Once a prior Bayesian network is built and updated with 

data, the resulting posterior Bayesian network is used to investigate potential results of applying management practices on 

biological condition. Drawbacks of using only data to parameterize this Bayesian network are presented.

Prior Bayesian Network Model

The final prior Bayesian network combines elicited 

model structure, variables, CPTs, and prior weights into a 

single representation of node relations and uncertainties (app. 

2, fig. 2–1). The model shows marginal probability distributions for each of the eight nodes; marginal probabilities are 

unconditional probabilities for each variable that are calculated by integrating out information about its parent variables. 

Conditional probabilities and prior weight information are 

embedded in the arrows pointing from parent to child nodes. 

For each node in a parameterized Bayesian network like figure 2–1 (app. 2), the horizontal blue bars depict the probability 

of a Northeast stream sample falling within each node state, 

with longer bars corresponding to higher probabilities. The 

numeric column superimposed on these bars lists these probability values as percentages. This prior network can provide 

information such as the probability of observing a “minimally 

changed” BCG Tier 2 condition in a random Northeastern 

U.S. stream is 13.47 percent. More usefully than making an 

average inference for a random stream, hypothetical “evidence” can be entered into the network (shown with horizontal 

red bars) and propagated to predict the effects of one variable 

state change on the rest of the system. For example, under 

conditions of low urban land cover, the predictive probability 

of observing BCG Tier 2 condition increases to 22.78 percent 

(fig. 10). 
Predicting Effects of Urbanization on Biota 19

1

2

3

4

5

6

6.88

22.78

31.95

24.40

11.44

2.55

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

10.50

89.50

Low

Medium

High

89.50

6.60

3.90

Low

Medium

High

20.00

70.00

10.00

Low

Medium

High

9.49

54.68

35.84

Low

Medium

High

48.70

40.68

10.62

Low

Medium

High

11.20

41.30

47.50

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

100.00

0.00

0.00

Low

Medium

High

Figure 10. Prior predictive probabilities of occurrence for each level of each node under low urban development. [Probabilities 

are represented as percentages, numerically and graphically (horizontal colored bars). Factor levels are defined in table 3.]
20 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

In addition, when urban land cover is known to be low, 

the prior predictive probabilities indicate an increased likelihood of observing stable hydrology, coarse habitat, lowconductance water quality, high macroinvertebrate generic 

richness, low filter feeder relative abundance, and high P+E 

relative abundance. These predictions are reversed under 

conditions of high urban land cover, with the probability of 

observing BCG Tier 2 condition decreasing to 5.69 percent 

(fig. 11). Not only does the Bayesian network illustrate the 

direction and magnitude of expected change for every node, it 

also incorporates uncertainties about those changes by reporting results in the form of (discrete) distributions. 

Data-Only Bayesian Network Model

Instead of using expert elicitation, a Bayesian network 

can be parameterized using data alone. Data collected for 

the 30 EUSE Northeast watersheds can be discretized and 

organized according to model-structure-specified data tables 

(table 4B for Hydrology child node; app. 2, tables 2–1B to 

2–6B for remaining child nodes). Converting these data tables 

to probabilities creates the CPTs required to specify a dataonly Bayesian network model. For the sake of comparison, 

this data-only model (fig. 2–2) was evaluated. Functionally, creating such a Bayesian network requires updating an 

uninformed prior distribution with the dataset, such that the 

posterior model reflects only information from the data.

A major problem with using a data-only approach for 

this model is the small sample size (30 watersheds, per CPT) 

relative to the large number of model parameters (378 θi probabilities to define, total). Because of this disparity, many of the 

variable-state combinations the model attempts to characterize 

are not represented in the dataset because they were not measured; these include all CPT rows created from data rows in 

table 4B and appendix 2, tables 2–1B to 2–6B for which n=0. 

One such missing component is the fine-sediment-dominated 

stream. Streams in the Northeastern United States tend to be 

geomorphologically coarser, in general, than streams in EUSE 

studies in other parts of the country, such as in agriculturalrunoff-dominated regions of the Midwest. Because high levels 

of fine sediments are uncommon in the Northeast, no such 

stream was observed during EUSE Northeast data collection in 

this region. Consequently, no data are available to characterize 

any of the CPT probability rows conditional on fine-sedimentdominated habitat when Habitat is acting as a parent node (a 

total of 81 θi probabilities, created from data tables 2–3B to 

2–5B in app. 2) nor any of the CPT for the Habitat child node 

(18 θi probabilities, created from data table 2–1B in app. 2), 

even though expert biologists emphasized the role of fine sediments in degrading the macroinvertebrate condition. Because 

of the lack of data, the Habitat node in the data-only model 

never changes state from 100 percent “coarse.”

Similarly, no streams with “low” generic richness (less 

than 15 genera) were sampled, probably because the EUSE 

Northeast study did not include watersheds containing more 

than 77 percent urban land cover. In the Northeast, many of 

the most urbanized streams have been converted into concrete 

culverts or underground pipes. These streams were consciously not sampled as part of EUSE because they were not 

considered natural stream systems. This exclusion resulted 

in undersampling of highly urbanized streams, which are 

the ones most likely to have “low” generic richness. Consequently, any CPT cell involving low generic richness as a 

child or parent state could not be characterized by the data 

(72 θi probabilities, created from data tables 2–3B and 2–6B in 

app. 2).

In addition to the two systematic data gaps just identified, many of the remaining parent-state combinations have 

no data equivalent, with random data gaps increasing as node 

complexity increases. For the BCG node that has three parents 

with three states each, only 7 of the 27 parent state combinations have available data (app. 2, table 2–6B). This result is 

observed because (1) some parent state combinations are more 

likely to occur than others (for example, 10 of 30 Northeast 

streams had a parent state combination of medium generic 

richness, high filter-feeder relative abundance, and low P+E 

abundance); and (2) small sample sizes often do not capture 

rare state combinations.

Paradoxically, the effect of parameterizing a Bayesian network with limited data is an inflated certainty in the 

marginal distributions of some nodes; for example, Habitat

shows 100 percent coarse substrate (fig. 2–2). In addition, 

when small-sample-sized data are used to calculate CPTs, 

node distributions exhibit extreme responses to evidence 

propagation. For example, in cases of low urban land cover, 

the data-only model predictive probability of observing BCG 

Tier 2 (53.86 percent, fig. 12) is much greater than the expertprior model prediction (22.78 percent, fig. 10), and much less 

than the expert-prior model prediction in cases of high urban 

land cover (0 percent, fig. 13, relative to 5.69 percent, fig. 11). 

This result can be traced to the abundance of data-gap-induced 

CPT zeros in the data-only model, which are probabilistically interpreted as a total certainty of nonoccurrence. This 

false certainty unrealistically distorts prediction magnitude. 

Although the direction of change is the same in both models, 

showing that experts and data agree on the direction of variable relations, available data alone are insufficient to adequately parameterize this model. In this situation, there would 

be very little confidence in the final model if substantial expert 

information were not included in the prior distributions. 
Predicting Effects of Urbanization on Biota 21

1

2

3

4

5

6

1.19

5.69

13.62

30.48

37.66

11.36

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

23.30

76.70

Low

Medium

High

7.20

20.60

72.20

Low

Medium

High

10.00

40.00

50.00

Low

Medium

High

47.59

38.23

14.17

Low

Medium

High

30.18

41.00

28.82

Low

Medium

High

49.01

44.12

6.86

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

0.00

0.00

100.00

Low

Medium

High

Figure 11. Prior predictive probabilities of occurrence for each level of each node under high urban development. [Probabilities 

are represented as percentages, numerically and graphically (horizontal colored bars). Factor levels are defined in table 3.]
22 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

1

2

3

4

5

6

3.75

53.86

20.52

10.37

6.75

4.75

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

0.00

100.00

Low

Medium

High

80.00

20.00

0.00

Low

Medium

High

10.00

80.00

10.00

Low

Medium

High

0.00

23.75

76.25

Low

Medium

High

40.00

45.00

15.00

Low

Medium

High

5.00

63.75

31.25

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

100.00

0.00

0.00

Low

Medium

High

Figure 12. Data-only predictive probabilities of occurrence for each level of each node under low urban development. 

[Probabilities are represented as percentages, numerically and graphically (horizontal colored bars). Factor levels are defined in 

table 3.]
Predicting Effects of Urbanization on Biota 23

1

2

3

4

5

6

0.00

0.00

10.73

39.77

33.52

15.97

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

0.00

100.00

Low

Medium

High

0.00

30.00

70.00

Low

Medium

High

20.00

40.00

40.00

Low

Medium

High

0.00

100.00

0.00

Low

Medium

High

0.00

6.00

94.00

Low

Medium

High

60.67

39.33

0.00

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

0.00

0.00

100.00

Low

Medium

High

Figure 13. Data-only predictive probabilities of occurrence for each level of each node under high urban development. 

[Probabilities are represented as percentages, numerically and graphically (horizontal colored bars). Factor levels are defined in 

table 3.]
24 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

Posterior Bayesian Network Model

Using Dirichlet-multinomial updating, as described 

earlier, the expert-elicited prior model was updated with the 

EUSE Northeast data to create the posterior model. Posterior 

conditional probability tables, which are a weighted average of prior information and data, are calculated for every 

child node in the model (tables 4C and app. 2, tables 2–1C

to 2–6C). To evaluate relations described by the posterior 

model, it is easier to interactively manipulate the Bayesian 

network than to interpret the static, multidimensional series 

of CPTs. By entering the hypothetical evidence about each 

node in turn, system trends can be more clearly understood 

than from discrete tables of numbers. For example, as specific 

conductance increases, generic richness decreases, filter feeder 

relative abundance increases, and P+E relative abundance 

decreases. This means that as water quality becomes impaired, 

macroinvertebrate communities become less diverse because 

the sensitive taxa are lost and the overall community becomes 

more contaminant-tolerant. The posterior Bayesian network 

also quantifies the relative magnitudes of system changes. For 

example, flashiness seems to affect filter-feeder relative abundance more than generic richness. 

To investigate the potential effect of applying best management practices (BMPs) to urban landscapes, a technique 

known as causal intervention modeling (Pearl, 2000) is used. 

Thus far, the posterior network as described has been used to 

predict states of system variables, conditional upon observing one of the variables. For example, if it is observed that a 

stream is located in a watershed with high urban land cover, 

the posterior Bayesian network predicts a 24.46 percent likelihood of that stream achieving BCG Tier 3 or better biological 

condition (fig. 14). However, if the objective is to use this 

model to predict the likelihood of achieving a “good” biological condition as a result of a management action (such as an 

implemented BMP), this action is no longer a simple observation of the system, but rather, an intervention to the system. 

To model such an intervention to a particular node, all arrows 

pointing to that node must be removed to show that parent 

nodes are no longer predicting the value of that child node; 

instead, the external intervention is now determining the childnode state. The statistics of how those parent nodes would 

have likely affected that child node are no longer relevant 

because a definitive intervention, further down the causal 

chain of events, is being simulated instead.

In the case of modeling effects of urban development, 

ideally, BMP nodes would be explicitly included, and the 

effects of those BMPs on the hydrology, habitat, and water 

quality of a system would be quantified. Without specific 

information on those relations, at the very least, it is known 

that implementation of a BMP would disrupt the relations 

between urban development and hydrology, habitat, and water 

quality, which are currently modeled in the absence of BMPs. 

Therefore, it is logically appropriate (as well as statistically 

correct) to remove the arrows to simulate the effects of a BMP 

on each of these three system drivers, because the relation 

originally modeled would no longer apply.

 In terms of notation, the arrow between Urban development and Hydrology in the model represents the current understanding and quantification of that relation across watersheds 

having different levels of urban development in the absence 

of BMPs developed from expert knowledge and collected 

data. However, managers may want to know which BMPs 

would ultimately improve the biotic condition of a stream the 

most and data to assess that question directly are not currently 

available. It can be assumed that BMPs would change the 

relation (that is, the arrow) between urban development and 

hydrology, ideally reducing flashiness relative to a particular 

level of urban development. Because this new, BMP-mediated 

relation between urban land cover and hydrology is unknown, 

it cannot be modeled directly. Instead, the arrow specifying the 

current relation between Urban development and Hydrology

(in the absence of BMPs) is removed, and it is assumed that 

some BMP is able to reduce flashiness from high to medium. 

The effects of that hypothetical reduction on the rest of the 

model can then be investigated. When using the technique just 

described to simulate the effects of a BMP that reduces flashiness to medium (shown with a horizontal green bar), while 

still observing high urban land cover (horizontal red bar), 

the likelihood of achieving BCG Tier 3 or better increases to 

28.56 percent (fig. 15) relative to 24.46 percent for an unmanaged watershed with high urban land cover (fig. 14). 

Alternately, if a BMP is implemented that reduces specific conductance to “low,” while still observing high urban 

land cover, BCG Tier 3 or better attainment is 56.62 percent 

likely (fig. 16). If both flashiness and specific conductance are 

managed, this likelihood increases to 69.69 percent (fig. 17).

Ultimately, managers would likely use this model to 

determine which manipulation to the system will yield the 

greatest chance of attaining a “good” BCG tier. Averaging across all possible urban land cover scenarios, BCG 

attainment probabilities were determined for each possible 

combination of management actions (affecting one, two, or 

three stressor nodes), and sorted in table 6 according to the 

best BCG Tier 3 or better probability achieved. The greatest 

likelihood of attaining BCG Tier 3 or better (79.55 percent) is 

obtained by managing to achieve medium flashiness, coarse 

substrate, and low conductance (rank 1, table 6). Conversely, 

BCG is least likely to be Tier 3 or better (2.33 percent) if management actions cause high flashiness, fine substrate, and high 

conductance (rank 47, table 6). 
Predicting Effects of Urbanization on Biota 25

1

2

3

4

5

6

0.81

4.75

18.90

37.15

31.06

7.34

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

24.46% 

Likelihood of attaining 

BCG Tier 3 or better

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

16.72

83.28

Low

Medium

High

5.37

23.37

71.27

Low

Medium

High

15.07

40.00

44.93

Low

Medium

High

22.84

67.87

9.29

Low

Medium

High

16.14

23.13

60.73

Low

Medium

High

51.43

43.12

5.46

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

0.00

0.00

100.00

Low

Medium

High

Figure 14. Posterior predictive probabilities of occurrence for each level of each node given an observation of high urban land 

cover and no management interventions. [Probabilities are represented as percentages, numerically and graphically (horizontal 

colored bars). Factor levels are defined in table 3.]
26 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

1

2

3

4

5

6

0.87

5.35

22.34

38.71

27.02

5.71

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

28.56% 

Likelihood of attaining 

BCG Tier 3 or better

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

17.53

82.47

Low

Medium

High

3.93

28.01

68.07

Low

Medium

High

0.00

100.00

0.00

Low

Medium

High

19.08

67.20

13.72

Low

Medium

High

14.64

17.98

67.37

Low

Medium

High

38.83

53.46

7.71

Reduce Flashiness

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

0.00

0.00

100.00

Low

Medium

High

Figure 15. Posterior predictive probabilities of occurrence for each level of each node under causal inference: Managing 

flashiness to medium, while still observing high urban land cover. [Probabilities are represented as percentages, numerically and 

graphically (horizontal colored bars). Factor levels are defined in table 3.]
Predicting Effects of Urbanization on Biota 27

1

2

3

4

5

6

5.97

20.89

29.76

22.84

16.97

3.56

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

56.62% 

Likelihood of attaining 

BCG Tier 3 or better

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

16.72

83.28

Low

Medium

High

100

0.00

0.00

Low

Medium

High

15.07

40.00

44.93

Low

Medium

High

12.83

31.82

55.36

Low

Medium

High

52.22

43.37

4.41

Low

Medium

High

19.53

46.65

33.82

Improve water

chemistry

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

0.00

0.00

100.00

Low

Medium

High

Figure 16. Posterior predictive probabilities of occurrence for each level of each node under causal inference: Managing 

specific conductance to low, while still observing high urban land cover. [Probabilities are represented as percentages, 

numerically and graphically (horizontal colored bars). Factor levels are defined in table 3.]
28 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

1

2

3

4

5

6

7.87

26.83

34.99

19.76

8.40

2.14

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

69.69% 

Likelihood of attaining 

BCG Tier 3 or better

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

17.53

82.47

Low

Medium

High

7.18

25.06

67.76

Low

Medium

High

54.85

45.01

0.15

Low

Medium

High

9.09

51.04

39.88

Hydrology

(flashiness)

Probability of

occurring (%)

Factor

level

Low

Medium

High

0.00

100.00

0.00

Reduce flashiness

Water chemistry

(specific conductance)

Probability of

occurring (%)

Factor

level

Low

Medium

High

100

0.00

0.00

Improve water

chemistry

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

0.00

0.00

100.00

Low

Medium

High

Figure 17. Posterior predictive probabilities of occurrence for each level of each node under causal inference: Managing 

flashiness to medium and specific conductance to low, while still observing high urban land cover. [Probabilities are represented 

as percentages, numerically and graphically (horizontal colored bars). Factor levels are defined in table 3.]
Predicting Effects of Urbanization on Biota 29

Table 6. Driver causal interventions most likely to improve Biological Condition Gradient 

(BCG) tier achievement likelihood given unobserved urban land cover state. 

[BCG goal is the combined probabilities of attaining BCG Tiers 1, 2, or 3; %, percent; BMP, best 

management practice]

Rank Flashiness Substrate Conductance BCG goal 

(% achievement)

Nodes 

managed

1 Medium Coarse Low 79.55 3

2 Medium NoBMP Low 73.47 2

3 NoBMP Coarse Low 68.32 2

4 NoBMP NoBMP Low 63.39 1

5 Low Coarse Low 62.36 3

6 Low NoBMP Low 54.98 2

7 Medium Coarse NoBMP 50.48 2

8 High Coarse Low 50.22 3

9 High NoBMP Low 47.66 2

10 Medium NoBMP NoBMP 47.45 1

11 NoBMP Coarse NoBMP 45.26 1

12 Low Coarse NoBMP 43.97 2

13 Low Coarse Med 42.38 3

14 Low NoBMP NoBMP 38.82 1

15 Low NoBMP Med 36.65 2

16 Medium Coarse Med 36.23 3

17 Medium NoBMP Med 34.15 2

18 High Coarse NoBMP 33.06 2

19 NoBMP Coarse Med 31.89 2

20 High NoBMP NoBMP 31.45 1

21 NoBMP NoBMP Med 29.77 1

22 Low Fine Low 29.19 3

23 Low Coarse High 28.66 3

24 Medium Coarse High 27.92 3

25 Medium NoBMP High 25.76 2

26 NoBMP Coarse High 25.66 2

27 Low NoBMP High 24.94 2

28 NoBMP NoBMP High 23.59 1

29 Medium Fine Low 23.35 3

30 NoBMP Fine Low 22.28 2

31 High Coarse High 20.05 3

32 Low Fine NoBMP 19.09 2

33 High Coarse Med 18.85 3

34 High NoBMP High 18.68 2

35 High NoBMP Med 18.04 2

36 High Fine Low 17.01 3

37 Medium Fine Med 16.82 3

38 Low Fine Med 16.64 3

39 Medium Fine NoBMP 16.57 2

40 NoBMP Fine NoBMP 14.99 1

41 NoBMP Fine Med 14.30 2

42 Low Fine High 11.96 3

43 High Fine NoBMP 10.21 2

44 High Fine Med 8.52 3

45 Medium Fine High 7.96 3

46 NoBMP Fine High 6.84 2

47 High Fine High 2.33 3
30 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Assessing the Value of a Bayesian 

Network Approach

Knowing the relative influence of different changes to 

an environmental system on its components can be valuable 

from a management perspective. A manager can use a Bayesian network to assess the relative effect of different model 

drivers on a desired endpoint, such as BCG tier, to determine 

which management actions lead to the greatest improvement. 

In contrast to traditional model prediction, a Bayesian network 

provides a more holistic approach to endpoint evaluation 

because it accounts for multiple interactions among variables 

simultaneously. In addition, the use of Bayesian networks for 

causal inference incorporates uncertainties that are encoded 

by the network when predicting driver effects on the endpoint, and results are reported probabilistically for clearer 

characterization. 

Benefits of Using a Bayesian Network for Urban 

Development Modeling

Using a Bayesian network to evaluate and rank the potential effects of management interventions has two unique benefits: (1) ability to model nonlinearities and interactions and 

(2) model-wide uncertainty incorporation. Many nonlinearities 

and interactions exist in the process of urbanizing watersheds 

affecting stream biology. For example, a causal intervention 

resulting in low flashiness actually predicts a smaller chance 

of BCG Tier 3 or better attainment than medium flashiness 

(38.82 percent relative to 47.45 percent; rank 14 and 10, 

respectively, table 6). Ecologically, this makes sense because 

low flashiness could be indicative of stagnant flows (such as 

wetland-dominated streams), which may not be optimal for 

macroinvertebrates. Moreover, the prior CPTs elicited from 

experts for the macroinvertebrate metrics show that experts 

designed the system to work this way (table 7). This form 

of model construction acknowledges that biotic response is 

complicated and a function of the interaction between many 

different drivers, nor is it a simple monotonic relation in which 

a biotic response always moves in the same direction relative 

to increasing drivers. A Bayesian network is able to capture 

this real-world complexity in a way that simple linear models 

cannot. 

Another example of a system complexity modeled effectively by a Bayesian network is the nonlinear effect of conductance on a BCG Tier. Specifically, BCG attainment likelihood 

does not improve as greatly when managing to reduce specific 

conductance from high to medium as when managing to 

reduce specific conductance from medium to low. Managing 

for low conductance may actually be the management action 

Table 7. Excerpts from macroinvertebrate metric prior expert-elicited conditional probability tables. 

[Experts often report that Medium flashiness results in the greatest probability of “best” invert metric relative to “low” or “high” 

flashiness (shown here in frequency units out of 1,000). <, less than; %, percent] 

Given: How would you distribute 1,000 streams?

Flashiness Substrate Conductance Generic richness

<15 15–37 38+

Low Fine Low 300 600 100

Medium Fine Low 400 400 200

High Fine Low 500 400 100

Flashiness Substrate Conductance Generic richness

<15 15–37 38+

Low Coarse High 350 550 100

Medium Coarse High 333 333 333

High Coarse High 590 400 10

Flashiness Substrate Conductance P+E relative abundance

<5% 5–20% 20% +

Low Coarse Medium 100 600 300

Medium Coarse Medium 10 600 390

High Coarse Medium 500 450 50

Flashiness Substrate Conductance P+E relative abundance

<5% 5–20% 20% +

Low Fine Low 400 550 50

Medium Fine Low 500 400 100

High Fine Low 490 500 10
Assessing the Value of a Bayesian Network Approach 31

most effective at achieving good biological quality; conductance is low in eight of the top nine BCG tier probabilities 

(table 6). This is similar to a threshold effect in that reducing 

specific conductance does not appear to help until a threshold point, which the model defines as 139 microsiemens per 

centimeter. The added complexity is a result of interactions 

among nodes such that the influence of low conductance is 

only true at medium or low flashiness and coarse substrate. At 

other flashiness and substrate states, low conductance does not 

increase biological condition status substantially; for example, 

when substrate is fine, low flashiness states are further down 

the BCG probability ranking list, at ranks 22, 29, 30, 36 

(table 6). These permutations and influences are much more 

challenging to account for using a non-network model than a 

network model.

A second benefit of using a Bayesian network is that 

it accounts for these nonlinearities while simultaneously 

incorporating uncertainty in its predictions. The BCG output 

is reported as a probability of attainment to indicate the actual 

certainty with which model predictions are known. Therefore, 

a high probability of desirable BCG attainment is difficult to 

achieve for two reasons:

1. The network of stream ecosystem processes is 

complex, and it is unrealistic to expect fixes applied 

to just one node to rectify the entire problem. There 

are many interacting factors that ultimately affect 

biological condition, and a higher probability of 

attainment requires that multiple entities probably 

need to be managed. The best case scenario the current model can predict is about 80 percent attainment 

of BCG Tier 3 or better, but this requires managing 

all three drivers (table 6).

2. There is still much uncertainty and variability that 

this model is incorporating, including random variability, model simplification error, imperfect knowledge about how the stream ecosystem works, and 

potentially inaccurate assumptions. Consequently, it 

is not surprising that the model does not yield “perfect” high-attainment predictions. Given the limitations of what is known and unknown about a particular stream ecosystem, it is still not entirely certain 

that adjusting the flashiness, substrate, or specific 

conductance will allow a manager to achieve the 

desired biological endpoint. In all likelihood, many 

other factors can affect the endpoint, and the uncertainty in model output is realistically estimated. The 

level of uncertainty reported is typical for complex 

environmental questions. Model output quantifies 

how well the current state of subject-related expertise and data can predict the result of management 

efforts on the environment. This type of information 

is more useful and credible than overconfident model 

results reported with no accompanying uncertainty 

estimates.

Unresolved Issues

In addition to exploring the aforementioned benefits of 

applying a Bayesian network approach, this modeling effort 

also identified several currently unresolved issues. Primary 

among these is defining data needs relative to the number of 

CPT parameters specified by the model structure and discretization scheme. Unlike continuous functions in which 

a few parameters can describe relations between variables 

completely, each discrete combination of possible values in a 

Bayesian network has to be specified separately. This means 

that even Bayesian networks with few nodes, arrows, and 

variable categories require many parameters. Although this 

model format is undeniably an advantage in situations where 

functional relations between variables are unknown, it also 

requires large sample sizes in order to be confident of exclusively using data for parameterization. Assessing data requirements is important because data gaps often result in false 

certainties. This happens because each CPT row represents 

a discrete multinomial distribution, and the use of only one 

data point to define that distribution will change the expected 

values across categories from flat to extreme probabilities. For 

example, a probability of 0.33 for each of three categories will 

change to a probability of 0 for two categories and 1 for the 

third, if the one data point used for distribution specification 

falls in the third category. This problem is resolved with the 

use of prior expert knowledge to supplement collected data. To 

parameterize Bayesian networks with data alone, future studies are needed to establish relations between model confidence 

and data sample size for a given number of CPT parameters. 

Until such relations are established, however, Bayesian network users need to be aware of this potentially confounding 

issue.

A second concern with Bayesian network creation is the 

transformation of continuous variables into discrete ones. 

There is no clear method for selecting the optimal number 

of bins and bin interval endpoints during Bayesian network 

parameterization. Criteria that can be considered include scientifically based cutoffs, equivalent data frequencies across all 

bins, equal interval lengths across all bins, and moment matching with data. Further research is needed to better understand 

the benefits and drawbacks of these potential criteria, evaluate 

the sensitivity of model outputs to these different modeling choices, and obtain consensus on the appropriate type of 

method to use for a given modeling situation. 

A third issue with using the Bayesian network approach 

is the lack of consensus on the ideal expert elicitation methodology, particularly for multinomial probabilities. Most 

probability elicitation literature focuses on assessing single 

probabilities within a binomial framework (Morgan and 

Henrion, 1990; Winkler, 2003; Reckhow and others, 2005; 

O’Hagan and others, 2006). When a discrete variable is composed of more than two categories, specifying a probability 

(p) no longer signifies that the remaining category is assigned 

the remaining probability (1-p), making a multinomial distribution more complicated to conceptualize than a binomial 
32 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

distribution. As such, it is not clear which format for elicitation 

questions best accesses and represents expert knowledge with 

more than one degree of freedom.

A related fourth question concerns the elicitation of 

prior weights. The question of how to best assess the strength 

of prior knowledge is a topic of active research. Similar to 

elicitation of the knowledge itself, the goal of prior weight 

determination is to find a method that best captures expert certainty; however, it is unclear which criteria should be used to 

make that assessment. Other uncertainties include (1) the scale 

at which weights are most reliably appraised (CPT cell, row, 

or entire node), and (2) how to minimize or correct for known 

human biases (in interpreting extremes, anchoring judgments, 

and so forth). It is unknown what contributes to the variability 

in reported weights for a given set of knowledge and how to 

minimize that variability.

Conclusions

This effort of Bayesian network model development 

and updating for the Northeast accomplished three major 

objectives. First, an innovative method of modeling multiple 

ecological compartments was devised and implemented. Second, this multicompartment system was linked to a management context with a meaningful endpoint. Third, the effects of 

potential management interventions on this explicitly defined 

biological standard were evaluated. Bayesian network analysis 

also filled many previous data-analysis voids by (1) utilizing 

full-system-level parameterization and understanding, (2) thoroughly characterizing uncertainty, (3) integrating multiple 

sources of information, (4) supplementing insufficient data 

sample size, and (5) allowing customizing the model to fit data 

structure and problem context by means of the flexibility of 

Bayesian modeling assumptions.

Specifically, the posterior Bayesian network model demonstrated the utility of incorporating existing expert knowledge as a means of addressing data gaps. The network format 

of a conceptual model is a useful way to visualize and communicate understanding about how a system works. A Bayesian 

network goes a step further and quantifies that understanding 

using all available information. Using the BCG as a model and 

management endpoint allows for a standardized interpretation 

of biological condition. Predicting BCG using a probabilistic 

approach allows one to represent model output realistically 

and aids decision makers in risk assessment.

Causal inference demonstrates the predictive difference 

between observing a variable and manipulating a variable. 

From this evaluation it was learned that managing for low 

rather than medium conductance is vital to achieving a healthier stream. Overall, however, this model confirmed that there 

is a complex, nonlinear, interacting set of relations between 

stressors, and that these complexities are well-modeled using 

a Bayesian network. The complexity of the system is so great 

that this model cannot predict any more than about an 80-percent certainty of achieving BCG objectives, even if all three 

major stressors are managed.

From the model results presented herein, it can be concluded that information from experts and collected data are 

in agreement on the general directions of change imposed by 

urban development on hydrology, habitat, water quality, and 

the biological condition of a stream. In both the expert and 

data-only models and, hence, in the posterior model, higher 

urban development levels increased the certainty of observing 

flashy, fine-substrate-dominated, high conductance streams 

with poor biological condition. The magnitudes of these system changes relative to each other remain uncertain, however, 

and require further study.

In reinterpreting the Northeast portion of the EUSE 

dataset, this Bayesian network quantifies the simultaneous 

influences of multiple aspects of urban development on macroinvertebrate condition while also quantifying the uncertainty 

in those relations. Using this framework provides the ability to think of these relations between variables in terms of 

an interactive cause-and-effect network rather than a list of 

model parameters with error bars. The effects of a change in a 

variable on all other nodes in the system can now be modeled, 

enabling multidimensional data interpretation in a manner 

not previously possible. In addition, outcomes are predicted 

in terms of the probability of attaining each BCG tier, which 

gives the model user a more realistic understanding of outcome likelihood rather than a pseudo-confident exact prediction. Managers can use this Bayesian network to predict the 

results of possible actions on biological condition and to make 

quantitative, risk-based decisions in terms of a meaningful and 

defined aquatic goal, the BCG tier.

The posterior model shows that, of the three drivers of 

biological change, management actions that reduce specific 

conductance to low levels have the greatest likelihood of 

“good” BCG tier achievement, but not in conjunction with fine 

substrate and, to a lesser extent, high flashiness. In actuality, 

the drivers follow complex, nonlinear, interacting relations 

with biological condition, and more than one driver will likely 

have to be managed to achieve desired BCG endpoints with 

greater certainty. 

Due to the adaptive nature of Bayes Theorem, as more 

data are collected for this Northeast stream urban development model, the current posteriors become the new priors and 

the model is further informed. This flexible construct allows 

the model to “learn” as more data are incorporated. Using 

this modeling framework, the process of scientific hypothesis 

creation and verification can be quantified in a transparent 

manner. This is a means of clearly presenting which expert 

prior assumptions were included in a particular iteration of 

the model, instead of not reporting implicit expert input and 

erroneously referring to model building as “objective.” As 

more data on the system become available over time, they can 

override less accurate scientific assumptions and fortify correct ones, leading to a much more systematic implementation 

of the scientific process.
References Cited 33

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Appendixes 35

Appendix 1. Distribution Forms for Bayesian Updating

Dirichlet prior distribution:

1

3

1

2

1

1321

1 2 3 ( ,, ) −−− ∝ ααα p θθθθθθ (1.1)

0

3

1

∑ = ααi=

i (1.2)

 

where 

−θθ 31 are the probabilities of a sample belonging to categories 1–3, respectively;

−αα 31 are coefficients describing the possible values of −θθ 31 , respectively; and 

α 0 is the sum of −αα 31 , also known as total prior weight or equivalent sample size.

Solve for prior weight, α 0 , by means of equations for Dirichlet expected value and Dirichlet expected variance:

0

[ ]

α

α θ i E i = (1.3)

 

 

)1(

)( var[ ]

0

2

0

0

+

− = ααααα θ i i

i (1.4)

 

var[ ]

[ ] [ ] var[ ] 2

0

i

i EE i i

θ

θθθ

α −− = (1.5)

Multinomial likelihood function:

321

321321321 ( ,,|,, ) xxx xxxp ∝ θθθθθθ (1.6)

∑=

=

3

i 1

i nx (1.7)

 

where

31 − xx are the counts of samples belonging to each of three categories, respectively,

n is the sum of all counts (that is, total sample size), and 

−θθ 31 are the probabilities of a sample belonging to categories 1–3, respectively.

Dirichlet posterior distribution:

1

3

1

2

1

1321321

11 22 33 ( ,,|,, ) −+−+−+ ∝ α α α θθθ θθθ x x x p xxx (1.8)

∑=

+=+

3

1

0 )( i

ii αα nx (1.9)

 

where 

−θθ 31 are the probabilities of a sampled basin belonging to categories 1–3, respectively;

−αα 31 are prior coefficients describing the possible values of −θθ 31 , respectively;

α 0 is the sum of −αα 31 , also known as total prior weight or equivalent sample size;

31 − xx are the counts of sampled basins belonging to each of three categories, respectively; and

n is the sum of all counts (that is, total sample size).
36 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Appendix 2. Supplemental Prior and Posterior Conditional 

Probability Tables, Data Tables, and Bayesian Network Diagrams

Table 2–1. “Habitat” node prior conditional probability table and prior weight (α0), data table, and posterior conditional probability 

table and posterior weights (α0

+n).

A. Prior conditional probability table 

[Substrate categories in probability units and α0 in equivalent data points; rows selected for prior 

weight elicitation are highlighted]

Urban land 

cover

Flashiness

Dominant substrate

Fine Coarse α0

Low Low 0.15 0.85 7.41

Low Medium 0.10 0.90 7.41

Low High 0.05 0.95 7.41

Medium Low 0.25 0.75 7.41

Medium Medium 0.17 0.83 7.41

Medium High 0.12 0.88 7.41

High Low 0.40 0.60 7.41

High Medium 0.27 0.73 7.41

High High 0.17 0.83 7.41

B. Data table 

[Substrate counts and n total number of samples per parent state combination]

Urban land 

cover

Flashiness

Dominant substrate

Fine Coarse n

Low Low 0 1 1

Low Medium 0 8 8

Low High 0 1 1

Medium Low 0 1 1

Medium Medium 0 5 5

Medium High 0 4 4

High Low 0 2 2

High Medium 0 4 4

High High 0 4 4

C. Posterior conditional probability table 

[Substrate categories in probability units and α0+n in equivalent data points]

Urban land 

cover

Flashiness

Dominant substrate

Fine Coarse α0

+n

Low Low 0.132 0.868 8.41

Low Medium 0.048 0.952 15.41

Low High 0.044 0.956 8.41

Medium Low 0.220 0.780 8.41

Medium Medium 0.102 0.898 12.41

Medium High 0.078 0.922 11.41

High Low 0.315 0.685 9.41

High Medium 0.175 0.825 11.41

High High 0.110 0.890 11.41
Appendixes 37

Table 2–2. “Water quality” node prior conditional probability table and prior weight (α0), data table, and posterior conditional 

probability table and posterior weights (α0

+n). 

A. Prior conditional probability table 

[Specific conductance categories in probability units and α0 in equivalent data points; rows selected 

for prior weight elicitation are highlighted]

Urban land 

cover

Flashiness Specific conductance at low base flow

Low Medium High α0

Low Low 0.85 0.10 0.05 14.65

Low Medium 0.90 0.06 0.04 14.65

Low High 0.95 0.04 0.01 14.65

Medium Low 0.20 0.50 0.30 14.65

Medium Medium 0.25 0.50 0.25 14.65

Medium High 0.30 0.50 0.20 14.65

High Low 0.02 0.23 0.75 14.65

High Medium 0.05 0.22 0.73 14.65

High High 0.10 0.19 0.71 14.65

B. Data table

[Specific conductance counts and n total number of samples per parent state combination]

Urban land 

cover

Flashiness Specific conductance at low base flow

Low Medium High n

Low Low 0 1 0 1

Low Medium 7 1 0 8

Low High 1 0 0 1

Medium Low 0 1 0 1

Medium Medium 1 3 1 5

Medium High 1 1 2 4

High Low 0 0 2 2

High Medium 0 2 2 4

High High 1 1 3 4

C. Posterior conditional probability table

[Specific conductance categories in probability units and α0+n in equivalent data points]

Urban land 

cover

Flashiness Specific conductance at low base flow

Low Medium High α0

+n

Low Low 0.796 0.158 0.047 15.65

Low Medium 0.891 0.083 0.026 22.65

Low High 0.953 0.037 0.009 15.65

Medium Low 0.187 0.532 0.281 15.65

Medium Medium 0.237 0.525 0.237 19.65

Medium High 0.289 0.446 0.264 18.65

High Low 0.018 0.202 0.780 16.65

High Medium 0.039 0.280 0.681 18.65

High High 0.079 0.203 0.719 18.65
38 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Table 2–3. “Generic richness” node prior conditional probability table and prior weight (α0), data table, and posterior conditional 

probability table and posterior weights (α0

+n).

A. Prior conditional probability table

[Richness categories in probability units and α0 in equivalent data points; rows selected for prior weight elicitation are highlighted]

Flashiness Substrate Conductance

Generic richness

Low Medium High α0

Low Fine Low 0.300 0.600 0.100 1.97

Low Fine Medium 0.400 0.500 0.100 1.97

Low Fine High 0.600 0.390 0.010 1.97

Low Coarse Low 0.010 0.490 0.500 1.97

Low Coarse Medium 0.100 0.350 0.550 1.97

Low Coarse High 0.350 0.550 0.100 1.97

Medium Fine Low 0.400 0.400 0.200 1.97

Medium Fine Medium 0.500 0.400 0.100 1.97

Medium Fine High 0.700 0.299 0.001 1.97

Medium Coarse Low 0.010 0.600 0.390 1.97

Medium Coarse Medium 0.100 0.350 0.550 1.97

Medium Coarse High 0.333 0.333 0.333 1.97

High Fine Low 0.500 0.400 0.100 1.97

High Fine Medium 0.600 0.390 0.010 1.97

High Fine High 0.900 0.099 0.001 1.97

High Coarse Low 0.300 0.600 0.100 1.97

High Coarse Medium 0.450 0.500 0.050 1.97

High Coarse High 0.590 0.400 0.010 1.97

B. Data table 

[Richness counts and n total number of samples per parent state combination]

Flashiness Substrate Conductance

Generic richness

Low Medium High n

Low Fine Low 0 0 0 0

Low Fine Medium 0 0 0 0

Low Fine High 0 0 0 0

Low Coarse Low 0 0 0 0

Low Coarse Medium 0 1 1 2

Low Coarse High 0 2 0 2

Medium Fine Low 0 0 0 0

Medium Fine Medium 0 0 0 0

Medium Fine High 0 0 0 0

Medium Coarse Low 0 1 7 8

Medium Coarse Medium 0 6 0 6

Medium Coarse High 0 3 0 3

High Fine Low 0 0 0 0

High Fine Medium 0 0 0 0

High Fine High 0 0 0 0

High Coarse Low 0 0 2 2

High Coarse Medium 0 2 0 2

High Coarse High 0 5 0 5
Appendixes 39

Table 2–3. “Generic richness” node prior conditional probability table and prior weight (α0), data table, and posterior conditional 

probability table and posterior weights (α0

+n).—Continued

C. Posterior conditional probability table

[Richness categories in probability units and α0+n in equivalent data points]

Flashiness Substrate Conductance

Generic richness

Low Medium High α0

+n

Low Fine Low 0.300 0.600 0.100 1.97

Low Fine Medium 0.400 0.500 0.100 1.97

Low Fine High 0.600 0.390 0.010 1.97

Low Coarse Low 0.010 0.490 0.500 1.97

Low Coarse Medium 0.050 0.426 0.525 3.97

Low Coarse High 0.174 0.777 0.050 3.97

Medium Fine Low 0.400 0.400 0.200 1.97

Medium Fine Medium 0.500 0.400 0.100 1.97

Medium Fine High 0.700 0.299 0.001 1.97

Medium Coarse Low 0.002 0.219 0.779 9.97

Medium Coarse Medium 0.025 0.839 0.136 7.97

Medium Coarse High 0.132 0.736 0.132 4.97

High Fine Low 0.500 0.400 0.100 1.97

High Fine Medium 0.600 0.390 0.010 1.97

High Fine High 0.900 0.099 0.001 1.97

High Coarse Low 0.149 0.298 0.553 3.97

High Coarse Medium 0.223 0.752 0.025 3.97

High Coarse High 0.167 0.830 0.003 6.97
40 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Table 2–4. “Filter feeder relative abundance” node prior conditional probability table and prior weight (α0), data table, and posterior 

conditional probability table and posterior weights (α0

+n).

A. Prior conditional probability table

[Relative abundance categories in probability units and α0 in equivalent data points; rows selected for prior weight elicitation are 

highlighted]

Flashiness Substrate Conductance

Filter feeder relative abundance

Low Medium High α0

Low Fine Low 0.600 0.390 0.010 1.54

Low Fine Medium 0.550 0.440 0.010 1.54

Low Fine High 0.440 0.550 0.010 1.54

Low Coarse Low 0.001 0.600 0.399 1.54

Low Coarse Medium 0.001 0.299 0.700 1.54

Low Coarse High 0.010 0.290 0.700 1.54

Medium Fine Low 0.700 0.299 0.001 1.54

Medium Fine Medium 0.700 0.299 0.001 1.54

Medium Fine High 0.500 0.400 0.100 1.54

Medium Coarse Low 0.600 0.390 0.010 1.54

Medium Coarse Medium 0.250 0.500 0.250 1.54

Medium Coarse High 0.100 0.400 0.500 1.54

High Fine Low 0.800 0.199 0.001 1.54

High Fine Medium 0.800 0.199 0.001 1.54

High Fine High 0.750 0.200 0.050 1.54

High Coarse Low 0.700 0.290 0.010 1.54

High Coarse Medium 0.300 0.400 0.300 1.54

High Coarse High 0.200 0.500 0.300 1.54

B. Data table 

[Relative abundance counts and n total number of samples per parent state combination]

Flashiness Substrate Conductance

Filter feeder relative abundance

Low Medium High n

Low Fine Low 0 0 0 0

Low Fine Medium 0 0 0 0

Low Fine High 0 0 0 0

Low Coarse Low 0 0 0 0

Low Coarse Medium 0 1 1 2

Low Coarse High 0 0 2 2

Medium Fine Low 0 0 0 0

Medium Fine Medium 0 0 0 0

Medium Fine High 0 0 0 0

Medium Coarse Low 4 4 0 8

Medium Coarse Medium 0 0 6 6

Medium Coarse High 0 0 3 3

High Fine Low 0 0 0 0

High Fine Medium 0 0 0 0

High Fine High 0 0 0 0

High Coarse Low 1 1 0 2

High Coarse Medium 0 0 2 2

High Coarse High 0 1 4 5
Appendixes 41

Table 2–4. “Filter feeder relative abundance” node prior conditional probability table and prior weight (α0), data table, and posterior 

conditional probability table and posterior weights (α0

+n).—Continued

C. Posterior conditional probability table

[Relative abundance categories in probability units and α0+n in equivalent data points]

Flashiness Substrate Conductance

Filter feeder relative abundance

Low Medium High α0

+n

Low Fine Low 0.600 0.390 0.010 1.54

Low Fine Medium 0.550 0.440 0.010 1.54

Low Fine High 0.440 0.550 0.010 1.54

Low Coarse Low 0.001 0.600 0.399 1.54

Low Coarse Medium 0.000 0.413 0.587 3.54

Low Coarse High 0.004 0.126 0.869 3.54

Medium Fine Low 0.700 0.299 0.001 1.54

Medium Fine Medium 0.700 0.299 0.001 1.54

Medium Fine High 0.500 0.400 0.100 1.54

Medium Coarse Low 0.516 0.482 0.002 9.54

Medium Coarse Medium 0.051 0.102 0.847 7.54

Medium Coarse High 0.034 0.136 0.830 4.54

High Fine Low 0.800 0.199 0.001 1.54

High Fine Medium 0.800 0.199 0.001 1.54

High Fine High 0.750 0.200 0.050 1.54

High Coarse Low 0.587 0.409 0.004 3.54

High Coarse Medium 0.131 0.174 0.695 3.54

High Coarse High 0.047 0.271 0.682 6.54
42 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach

Table 2–5. “P+E relative abundance” node prior conditional probability table and prior weight (α0), data table, and posterior 

conditional probability table and posterior weights (α0

+n).

A. Prior conditional probability table

[Relative abundance categories in probability units and α0 in equivalent data points; rows selected for prior weight 

elicitation are highlighted]

Flashiness Substrate Conductance

P+E relative abundance

Low Medium High α0

Low Fine Low 0.400 0.550 0.050 5.07

Low Fine Medium 0.700 0.290 0.010 5.07

Low Fine High 0.700 0.299 0.001 5.07

Low Coarse Low 0.010 0.390 0.600 5.07

Low Coarse Medium 0.100 0.600 0.300 5.07

Low Coarse High 0.300 0.600 0.100 5.07

Medium Fine Low 0.500 0.400 0.100 5.07

Medium Fine Medium 0.550 0.400 0.050 5.07

Medium Fine High 0.699 0.300 0.001 5.07

Medium Coarse Low 0.010 0.390 0.600 5.07

Medium Coarse Medium 0.010 0.600 0.390 5.07

Medium Coarse High 0.400 0.550 0.050 5.07

High Fine Low 0.490 0.500 0.010 5.07

High Fine Medium 0.700 0.290 0.010 5.07

High Fine High 0.700 0.299 0.001 5.07

High Coarse Low 0.400 0.400 0.200 5.07

High Coarse Medium 0.500 0.450 0.050 5.07

High Coarse High 0.600 0.399 0.001 5.07

B. Data table 

[Relative abundance counts and n total number of samples per parent state combination]

Flashiness Substrate Conductance

P+E relative abundance

Low Medium High n

Low Fine Low 0 0 0 0

Low Fine Medium 0 0 0 0

Low Fine High 0 0 0 0

Low Coarse Low 0 0 0 0

Low Coarse Medium 0 2 0 2

Low Coarse High 1 1 0 2

Medium Fine Low 0 0 0 0

Medium Fine Medium 0 0 0 0

Medium Fine High 0 0 0 0

Medium Coarse Low 0 5 3 8

Medium Coarse Medium 3 3 0 6

Medium Coarse High 1 2 0 3

High Fine Low 0 0 0 0

High Fine Medium 0 0 0 0

High Fine High 0 0 0 0

High Coarse Low 0 1 1 2

High Coarse Medium 2 0 0 2

High Coarse High 4 1 0 5
Appendixes 43

Table 2–5. “P+E relative abundance” node prior conditional probability table and prior weight (α0), data table, and posterior 

conditional probability table and posterior weights (α0+n).—Continued

C. Posterior conditional probability table

[Relative abundance categories in probability units and α0+n in equivalent data points]

Flashiness Substrate Conductance

P+E relative abundance

Low Medium High α0+n

Low Fine Low 0.400 0.550 0.050 5.07

Low Fine Medium 0.700 0.290 0.010 5.07

Low Fine High 0.700 0.299 0.001 5.07

Low Coarse Low 0.010 0.390 0.600 5.07

Low Coarse Medium 0.072 0.713 0.215 7.07

Low Coarse High 0.357 0.572 0.072 7.07

Medium Fine Low 0.500 0.400 0.100 5.07

Medium Fine Medium 0.550 0.400 0.050 5.07

Medium Fine High 0.699 0.300 0.001 5.07

Medium Coarse Low 0.004 0.534 0.462 13.07

Medium Coarse Medium 0.276 0.546 0.179 11.07

Medium Coarse High 0.375 0.593 0.031 8.07

High Fine Low 0.490 0.500 0.010 5.07

High Fine Medium 0.700 0.290 0.010 5.07

High Fine High 0.700 0.299 0.001 5.07

High Coarse Low 0.287 0.428 0.285 7.07

High Coarse Medium 0.641 0.323 0.036 7.07

High Coarse High 0.699 0.300 0.001 10.07
44 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

Table 2–6. “BCG” node prior conditional probability table and prior weight (α0), data table, and posterior conditional probability table 

and posterior weights (α0+n).

A. Prior conditional probability table 

[BCG tier categories in probability units and α0 in equivalent data points; rows selected for prior weight elicitation are highlighted]

Generic 

richness

Filter 

feeder 

relative 

abundance

P+E 

relative 

abundance

BCG tier

1 2 3 4 5 6 α0

Low Low Low 0.001 0.001 0.001 0.127 0.571 0.299 123.47

Low Low Medium 0.001 0.001 0.001 0.127 0.571 0.299 123.47

Low Low High 0.001 0.001 0.001 0.127 0.571 0.299 123.47

Low Medium Low 0.001 0.001 0.001 0.225 0.572 0.200 123.47

Low Medium Medium 0.001 0.001 0.001 0.299 0.598 0.100 123.47

Low Medium High 0.001 0.001 0.001 0.498 0.498 0.001 123.47

Low High Low 0.001 0.001 0.001 0.001 0.598 0.398 123.47

Low High Medium 0.001 0.001 0.001 0.575 0.384 0.038 123.47

Low High High 0.001 0.001 0.001 0.498 0.498 0.001 123.47

Medium Low Low 0.001 0.001 0.001 0.299 0.598 0.100 123.47

Medium Low Medium 0.010 0.196 0.294 0.490 0.010 0.001 123.47

Medium Low High 0.099 0.297 0.396 0.198 0.010 0.001 123.47

Medium Medium Low 0.001 0.010 0.296 0.494 0.198 0.001 123.47

Medium Medium Medium 0.050 0.300 0.300 0.300 0.050 0.001 123.47

Medium Medium High 0.150 0.399 0.399 0.050 0.001 0.001 123.47

Medium High Low 0.001 0.001 0.050 0.449 0.449 0.050 123.47

Medium High Medium 0.001 0.050 0.449 0.449 0.050 0.001 123.47

Medium High High 0.001 0.050 0.449 0.449 0.050 0.001 123.47

High Low Low 0.001 0.001 0.001 0.100 0.896 0.001 123.47

High Low Medium 0.105 0.420 0.420 0.053 0.001 0.001 123.47

High Low High 0.199 0.499 0.299 0.001 0.001 0.001 123.47

High Medium Low 0.001 0.001 0.249 0.499 0.249 0.001 123.47

High Medium Medium 0.001 0.091 0.454 0.408 0.045 0.001 123.47

High Medium High 0.100 0.200 0.499 0.200 0.001 0.001 123.47

High High Low 0.001 0.001 0.050 0.449 0.449 0.050 123.47

High High Medium 0.001 0.001 0.100 0.449 0.449 0.001 123.47

High High High 0.050 0.050 0.450 0.350 0.100 0.001 123.47
Appendixes 45

Table 2–6. “BCG” node prior conditional probability table and prior weight (α0), data table, and posterior conditional probability table 

and posterior weights (α0+n).—Continued

B. Data table

[BCG tier counts and n total number of samples per parent state combination]

Generic 

richness

Filter 

feeder 

relative 

abundance

P+E 

relative 

abundance

BCG tier

1 2 3 4 5 6 n

Low Low Low 0 0 0 0 0 0 0

Low Low Medium 0 0 0 0 0 0 0

Low Low High 0 0 0 0 0 0 0

Low Medium Low 0 0 0 0 0 0 0

Low Medium Medium 0 0 0 0 0 0 0

Low Medium High 0 0 0 0 0 0 0

Low High Low 0 0 0 0 0 0 0

Low High Medium 0 0 0 0 0 0 0

Low High High 0 0 0 0 0 0 0

Medium Low Low 0 0 0 0 0 0 0

Medium Low Medium 0 0 0 0 0 0 0

Medium Low High 0 0 0 0 0 0 0

Medium Medium Low 0 0 0 0 0 1 1

Medium Medium Medium 0 0 1 0 0 0 1

Medium Medium High 0 0 0 0 0 0 0

Medium High Low 0 0 0 2 6 2 10

Medium High Medium 0 0 2 6 0 0 8

Medium High High 0 0 0 0 0 0 0

High Low Low 0 0 0 0 0 0 0

High Low Medium 0 1 0 0 0 0 1

High Low High 0 4 0 0 0 0 4

High Medium Low 0 0 0 0 0 0 0

High Medium Medium 0 3 2 0 0 0 5

High Medium High 0 0 0 0 0 0 0

High High Low 0 0 0 0 0 0 0

High High Medium 0 0 0 0 0 0 0

High High High 0 0 0 0 0 0 0
46 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

Table 2–6. “BCG” node prior conditional probability table and prior weight (α0), data table, and posterior conditional probability table 

and posterior weights (α0+n).—Continued

C. Posterior conditional probability table

[BCG tier categories in probability units and α0+n in equivalent data points]

Generic 

richness

Filter 

feeder 

relative 

abundance

P+E 

relative 

abundance

BCG tier

1 2 3 4 5 6 α0

+n

Low Low Low 0.001 0.001 0.001 0.127 0.571 0.299 123.47

Low Low Medium 0.001 0.001 0.001 0.127 0.571 0.299 123.47

Low Low High 0.001 0.001 0.001 0.127 0.571 0.299 123.47

Low Medium Low 0.001 0.001 0.001 0.225 0.572 0.200 123.47

Low Medium Medium 0.001 0.001 0.001 0.299 0.598 0.100 123.47

Low Medium High 0.001 0.001 0.001 0.498 0.498 0.001 123.47

Low High Low 0.001 0.001 0.001 0.001 0.598 0.398 123.47

Low High Medium 0.001 0.001 0.001 0.575 0.384 0.038 123.47

Low High High 0.001 0.001 0.001 0.498 0.498 0.001 123.47

Medium Low Low 0.001 0.001 0.001 0.299 0.598 0.100 123.47

Medium Low Medium 0.010 0.196 0.294 0.490 0.010 0.001 123.47

Medium Low High 0.099 0.297 0.396 0.198 0.010 0.001 123.47

Medium Medium Low 0.001 0.010 0.294 0.490 0.196 0.009 124.47

Medium Medium Medium 0.050 0.297 0.305 0.297 0.050 0.001 124.47

Medium Medium High 0.150 0.399 0.399 0.050 0.001 0.001 123.47

Medium High Low 0.001 0.001 0.046 0.430 0.460 0.061 133.47

Medium High Medium 0.001 0.047 0.437 0.467 0.047 0.001 131.47

Medium High High 0.001 0.050 0.449 0.449 0.050 0.001 123.47

High Low Low 0.001 0.001 0.001 0.100 0.896 0.001 123.47

High Low Medium 0.104 0.425 0.417 0.052 0.001 0.001 124.47

High Low High 0.193 0.514 0.290 0.001 0.001 0.001 127.47

High Medium Low 0.001 0.001 0.249 0.499 0.249 0.001 123.47

High Medium Medium 0.001 0.111 0.452 0.392 0.044 0.001 128.47

High Medium High 0.100 0.200 0.499 0.200 0.001 0.001 123.47

High High Low 0.001 0.001 0.050 0.449 0.449 0.050 123.47

High High Medium 0.001 0.001 0.100 0.449 0.449 0.001 123.47

High High High 0.050 0.050 0.450 0.350 0.100 0.001 123.47
Appendixes 47

1

2

3

4

5

6

3.74

13.47

22.58

28.24

25.10

6.87

Urban

development

Development in

watershed (%)

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Urban

 category 

Percentage of

watersheds

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

0-7

7-31

> 31

33.33

33.33

33.33

Fine

Coarse

16.83

83.17

Low

Medium

High

40.82

25.73

33.45

Low

Medium

High

Low

Medium

High

15.00

55.00

30.00

Low

Medium

High

28.44

45.49

26.07

Low

Medium

High

38.02

40.61

21.37

Low

Medium

High

29.91

44.47

25.62

Figure 2–1. Prior Northeast Bayesian network. [Probabilities are represented as percentages, numerically and graphically 

(horizontal colored bars). Factor levels are defined in table 3.]
48 Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern U.S. Using a Bayesian Network Approach 

1

2

3

4

5

6

1.67

23.04

15.37

26.72

22.07

11.13

Hydrology

(flashiness) Water chemistry

(specific conductance)

Habitat

(substrate)

Generic richness

(number of taxa)

Filter feeder 

(relative abundance)

Plecoptera + Ephemeroptera

(P+E)(relative abundance)

Biological Condition

Gradient (BCG)

Likelihood of

attainment (%)

BCG

Tier

Probability of

occurring (%) Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Probability of

occurring (%)

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Factor

level

Fine

Coarse

0.00

100.00

Low

Medium

High

33.33

33.33

33.33

Low

Medium

High

13.33

56.67

30.00

Low

Medium

High

0.00

66.67

33.33

Low

Medium

High

16.67

23.33

60.00

Low

Medium

High

36.67

50.00

13.33

Urban

development

Development in

watershed (%)

Urban

 category 

Percentage of

watersheds

0-7

7-31

> 31

33.33

33.33

33.33

Low

Medium

High

Figure 2–2. Data-only Northeast Bayesian network (uninformed prior updated with data). [Probabilities are represented as 

percentages, numerically and graphically (horizontal colored bars). Factor levels are defined in table 3.]
Manuscript approved on February 3, 2012.

Prepared by:

USGS Science Publishing Network

Edited by Michael Deacon

Layout by Kay P. Naugle

For additional information regarding this publication, contact:

Roxolana O. Kashuba, Hydrologist

USGS North Carolina Water Science Center

3916 Sunset Ridge Road

Raleigh, NC 27607

phone: 919-571-4088

e-mail: rkashuba@usgs.gov

Or visit the Effects of Urbanization on Stream Ecosystems (EUSE) NAWQA 

Project Web site at:

http://water.usgs.gov/nawqa/urban/

A PDF version of this publication is available online at 

http://pubs.usgs.gov/sir/2012/5030/
Kashuba and others—Linking Urbanization to the BCG for Stream Ecosystems in the Northeastern United States Using a Bayesian Network Approach—Scientific Investigations Report 2012–5030