Use of Predictive Models in Aquatic Biological

Assessment:

theory and application to the Colorado REMAP/NAWQA

datasetCharles P. Hawkins

Aquatic, Watershed, and Earth ResourcesUtah State University

Basic Concepts• Predictive models base

assessments on the compositional similarity between observed and expected biota.

• Major issues:–Understanding the units of measure.

–Predicting the expected taxa.

Basic Concepts(The Expected Taxa)

SpeciesReplicate Sample Number Freq

(Pc)1 2 3 4 5 6 7 8 9 10

A * * * * * * * * * * 1.0

B * * * * * * * * 0.8

C * * * * * 0.5

D * * * * * 0.5

E * 0.1

Sp Count

3 3 3 2 4 3 2 2 4 3 2.9Species Richness is the Unit of Currency.E = ∑ Pc = number of species / sample = 2.9.

O/E as a Measure of Impairment

Expected Biota Observed Biota

Species Pc O1 O2 O3 O4

A 1.0 * * * *

B 0.8 * *

C 0.5 *

D 0.5 *

E 0.1

F 0 *

Expected Sp Count 2.9 3 2 2 1

O/E 1.03 0.69 0.69 0.34

Environmental Gradient

Pro

babili

ty o

f C

aptu

reThis is the Challenge:

Estimating the Probabilities of Capture of Many Different Taxa that Exhibit Individualistic

Distributions

The basic approach to modeling pc’s and estimating E was worked out by Moss et

al.*

River InVertebrate Prediction and Classification System

(RIVPACS)

*Moss, D., M. T. Furse, J. F. Wright, and P. D. Armitage. 1987. The prediction of the macro-invertebrate fauna of unpolluted running-water sites in Great Britain using environmental data. Freshwater Biology 17:41-52.

RIVPACS-type Models: 9 Steps1. Establish a network of reference sites.

2. Establish standard sampling protocols.

3. Classify sites based on biological similarity.

4. Calculate taxa frequencies of occurrence (Fi,g) within each class.

5. Derive a model for estimating probabilites of a site belonging to each group (Pg).

6. Estimate pc’s by weighting Fi,g by Pg.

For each assessed site:

7. Sum pc’s to estimate E.

8. Calculate O/E.

9. Determine if observed O/E is different from reference?

Creating RIVPACS Models1. Establish a

network of reference sites that span the range of environmental conditions in the region of interest.

Creating RIVPACS Models2. Use standard protocols to sample biota

and habitat features.

Creating RIVPACS Models3. Classify sites in terms of their

compositional similarity.

Dissimilarity0 0.2 0.4 0.6 0.8 1

Gro

up

A

D

B

C

Cluster analysis shows

4 ‘groups’ of sites

Creating RIVPACS Models4. Estimate frequencies of occurrence

of each taxon in each biotic group.

Group

Sp 1 Sp 2 Sp 3 Sp 4 Sp 5 Sp 6

A 0.33 0.89 0 0.25 1.00 0

B 0.80 0.99 0.21 0.36 0.87 0

C 0.60 0 0.16 0.28 0.98 0.05

D 0.10 0.54 0.09 0.29 1.00 0

Creating RIVPACS Models4. Estimate frequencies of occurrence of

each taxon in each biotic group.

Color Group Species 1 freq.

Red Group A

0.33

Green Group B

0.80

Yellow Group C

0.60

Blue Group D

0.10

Creating RIVPACS Models

New site

When we go to a new site, how do we know which biological group it should belong to?

5. Derive a model from environmental features (not biology) to predict the probabilities that a new site belongs to each of the biological groups.

Discriminant Function Model (for example):

Group is predicted by elevation, watershed area, geology

Creating RIVPACS Models

6. Develop site-specific ferquencies for each taxon to occur at the new site

New site

• Model predicts the probability that the new site is a member of each of the groups

• These probabilities are used to adjust site-specific frequencies of occurrence

Creating RIVPACS Models

7. Sum pc’s to estimate the number of taxa (E) that should be observed at the site based on standard sampling.

Species Pc

1 0.70

2 0.92

3 0.86

4 0.63

5 0.51

6 0.32

7 0.07

8 0.00

E 4.01

Creating RIVPACS Models

8. Calculate O/E by comparing the number of predicted taxa that were collected (O) with E.

Species Pc O

1 0.70 *

2 0.92 *

3 0.86

4 0.63

5 0.51 *

6 0.32

7 0.07

8 0.00

E 4.01 3

O/E = 3 / 4.01 = 0.75

Creating RIVPACS Models9. Determine if the O/E value is

significantly different from the reference condition by comparing against model predictions and error.

1E

O

O/E

Intermission

What’s confusing so far?

Applying RIVPACS to Colorado:

REMAP and NAWQA data 47 Reference Sites

37 REMAP sites10 NAWQA sites112 Taxa used in the model

123 Test Sites/Samples68 REMAP55 NAWQA

D

C

F

G

P

A

B

Spatial Distribution of Reference SitesColors indicate 7 different biologically defined ‘classes’

Circles = REMAP, Stars = NAWQA

Predictor Variablesin the Colorado Model

Variable F-valueDay Past 1 Jan 12.35Latitude 6.44Stream Length (log)

3.61

Substrate D50 (log) 2.83

% Ks Basin Lithology

2.61

0 10 20 30Expected # Taxa

0

10

20

30

Obs

erve

d #

Tax a

r2 = 0.66

0.0 0.5 1.0 1.50.0 0.5 1.0 1.5O/E

The Distribution of Estimated O/E

Values for Reference SitesMean = 1.00

SD = 0.1610th Percentile = 0.8490th Percentile = 1.16

D

C

F

G

P

A

B

Spatial Distribution of ‘Test’ SitesCircles = REMAP Sites, Stars = NAWQA Sites

Assessments could not be made on 16 of 118 samples (14% of total) because values of predictor variables were outside of the experience of the model.

0.0 0.5 1.0 1.50.0 0.5 1.0 1.5O/E

The Distribution of Estimated O/E Values for Test

Samples77% of test samples had O/E values outside the threshold values of 0.84 and 1.16.

Mean O/E ValuesREMAP: 0.67NAWQA: 0.69

D

C

F

G

P

A

B

Blue:>0.84 and <1.16Yell: 0.64–0.84, >1.16Red: <0.64Gray: No Assessment

Colorado Test SiteO/E values

Relationships between O/Eand

Potential Stressors

0 1 2 3 40.0

0.5

1.0

1.5

log Dissolved Copper (ug/L)

O/E

O/E Response to Stressors

Response to dissolved copper shows 2 thresholds:~ 2.5 and 30 ug/L.