1. Aquatic, Watershed, and Earth Resources
Use of Predictive Models in Aquatic Biological Assessment: theory and application to the Colorado REMAP/NAWQA dataset
Charles P. Hawkins
Aquatic, Watershed, and Earth Resources
Utah State University

2. 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.

3. Basic Concepts (The Expected Taxa)
Species
Replicate Sample Number
Freq
(Pc) 1 2 3 4 5 6 7 8 9 10 A *
1.0 B
0.8 C
0.5 D E
0.1
Sp Count
2.9
Species Richness is the Unit of Currency.
E = ∑ Pc =  number of species / sample = 2.9.

4. 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 E
0.1 F
Expected Sp Count
2.9 3 2 1
O/E
1.03
0.69
0.34

5. Environmental Gradient Probability of Capture
This is the Challenge:
Estimating the Probabilities of Capture of Many Different Taxa that Exhibit Individualistic Distributions
Environmental Gradient
Probability of Capture

6. 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 The prediction of the macro-invertebrate fauna of unpolluted running-water sites in Great Britain using environmental data. Freshwater Biology 17:41-52.

7. RIVPACS-type Models: 9 Steps
Establish a network of reference sites.
Establish standard sampling protocols.
Classify sites based on biological similarity.
Calculate taxa frequencies of occurrence (Fi,g) within each class.
Derive a model for estimating probabilites of a site belonging to each group (Pg).
Estimate pc’s by weighting Fi,g by Pg.
For each assessed site:
Sum pc’s to estimate E.
Calculate O/E.
Determine if observed O/E is different from reference?

8. Creating RIVPACS Models
Establish a network of reference sites that span the range of environmental conditions in the region of interest.

9. Creating RIVPACS Models
Use standard protocols to sample biota and habitat features.

10. Creating RIVPACS Models
Classify sites in terms of their compositional similarity.
Dissimilarity
Group A D B C
0.2
0.4
0.6
0.8 1
Cluster analysis shows
4 ‘groups’ of sites

11. Creating RIVPACS Models
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
0.25
1.00 B
0.80
0.99
0.21
0.36
0.87 C
0.60
0.16
0.28
0.98
0.05 D
0.10
0.54
0.09
0.29

12. Creating RIVPACS Models
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

13. Creating RIVPACS Models
When we go to a new site, how do we know which biological group it should belong to?
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
New site

14. Creating RIVPACS Models
Develop site-specific ferquencies for each taxon to occur at the 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
New site

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

16. Creating RIVPACS Models
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
Creating RIVPACS Models
Calculate O/E by comparing the number of predicted taxa that were collected (O) with E.
O/E = 3 / 4.01 = 0.75

17. Creating RIVPACS Models
Determine if the O/E value is significantly different from the reference condition by comparing against model predictions and error. O 1 E
O/E

18. Intermission What’s confusing so far?

19. Applying RIVPACS to Colorado: REMAP and NAWQA data
47 Reference Sites
37 REMAP sites
10 NAWQA sites
112 Taxa used in the model
123 Test Sites/Samples
68 REMAP
55 NAWQA

20. Spatial Distribution of Reference Sites
Colors indicate 7 different biologically defined ‘classes’
Circles = REMAP, Stars = NAWQA

21. Predictor Variables in the Colorado Model
F-value
Day Past 1 Jan
12.35
Latitude
6.44
Stream Length (log)
3.61
Substrate D50 (log)
2.83
% Ks Basin Lithology
2.61

22. r2 = 0.66

23. The Distribution of Estimated O/E Values for Reference Sites
Mean = 1.00
SD = 0.16
10th Percentile = 0.84
90th Percentile = 1.16
O/E

24. Spatial Distribution of ‘Test’ Sites
Circles = 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.

25. The Distribution of Estimated O/E Values for Test Samples
Mean O/E Values
REMAP: 0.67
NAWQA: 0.69
The Distribution of Estimated O/E Values for Test Samples
77% of test samples had O/E values outside the threshold values of 0.84 and 1.16.
O/E

26. Blue: >0.84 and <1.16
Yell: –0.84, >1.16
Red: <0.64
Gray: No Assessment
Colorado Test Site
O/E values

27. Relationships between O/E and Potential Stressors

28. O/E Response to Stressors
Response to dissolved copper shows 2 thresholds:
~ 2.5 and 30 ug/L.
O/E
log Dissolved Copper (ug/L)