1. Combinations (= multimetrics)
First developed by Jim Karr for fish
Index of Biotic Integrity
Based on the concept of economic indices
Regardless, the idea is that no single measure will indicate the status of a site therefore, it’s necessary to combine a number of different measures (=metrics)
Metrics are chosen that represent a range of response types (e.g., richness, % composition, diversity, ffg, biotic indices)
They also are chosen to maximize differences between reference and impaired sites which need to be pre-defined.
These individual measures are scaled and combined additively (most often) and then often rescaled to range from 1 to 10
Identifying impairment is based on a sites “value” relative to the established range
Well …
If one measure is intractable – maybe adding up a bunch will make sense???
It’s really not that bad – sorry.
Go back to similarity slide

2. Many many methods are used
Multivariate Methods
Many many methods are used

3. Classification Similarities measures Clustering algorithms But …
Many types
Think about the anticipated effect
Clustering algorithms
Most common Unweighted pair-group with arithmetic averages (UPGMA)
But …
Many types of
Similarity measures and clustering algorithms
Dichotomous
In or out of a group

4. Ordination sa1 sa2 sa3 sa4 sp1 4 2 89 sp2 3 5 sp3 1 562 89
sp2 3 5
sp3 1 56
Many different types
Principal objectives
Reduce the dimensionality of species X sample and or environmental X sample data
Determine trends in space and time
Develop a species X sample correlate to real or derived environmental variables

5. Ordination

6. Ordination in species space

7. A site ordination

8. Uses/methods of Ordination
Inference
Species distributions are used to infer environmental variables
Temperature in Montana
Indirect gradient analysis
Variation in species distributions are determined
Without a priori knowledge regarding “controlling” environmental gradients
Often then related to environmental variables
Many different methods
Direct gradient analysis
Often synonymous with constrained ordination
Searches for gradients in species data which are a “direct” function of environmental data
Sometimes “constrained” within the limits of the environmental data
Correspondence Analysis, Canonical Correlation Analysis (CCA)

10. Two (of the many) methods of assessment
Univariate approaches
IBI = multimetrics
Index of Biotic Integrity
RBP
Rapid Bioassessment Protocol
Multivariate
Endless methods but …
RIVPACS
River Invertebrate Prediction and Classification System
All methods “require” the collection of physical/chemical data
RBP  generally metric-driven
RIVPACS  species-driven

11. RBP
An a priori site classification is performed to establish two groups - impaired and least impaired (reference)
Physical/chemical/habitat (e.g., VHA) data are used
Species X site data are collected
Various levels of effort (fixed count size and taxonomic) are used (RBP I, II, III)
Metrics are derived
Richness, FFG, Biotic indices, …
Metrics are chosen based on their ability to differentiate impaired from reference
They could be chosen based on a hypothesized response to a known stressor – but …
Chosen metrics are added to form a multimetric and rescaled
Sites are classified into levels of impairment

16. RIVPACS
Inverts are collected from least impaired sites that represent the “total” range of sites to be “tested”
“Reference” sites
Physical/chemical/habitat data are collected at each site
Relatively little data are needed
Sites are classified into similar groups based on their species composition
Using a classification routine (e.g., TWINSPAN, UPGMA w/ % similarity)
The probability of a site being a member of a group is determined by Multiple Discriminant Function Analysis
MDFA differs from MLR in that dependent variables are discrete not continuous
Using p/c/h data that are not impacted by humans
The probability of occurrence at a site of each species is calculated as:
= Σ probability of a site belonging to a group X proportion of the sites within each group a species occurs  sum across all groups
“Delete” rare species
Choose a probability of occurrence of a species (e.g., p>.75 or .5)
List the number of taxa predicted based on the above probability of occurrence and sum their probabilities to form the number of taxa Expected
Collect inverts using the same effort from “test” sites
Compare as Taxa observed/taxa expected (O/E)

17. Compare and Contrast Multimetric RIVPACS “Reference” sites are needed
P/C/H data are needed
Metrics are calculated and compared between ref and test
Multimetric is “formed”
Test sites are compared to reference sites
RIVPACS
“Reference” sites are needed
P/C/H data are needed
Multivariate analyses are used to determine probability of occurrence of individual taxa
Species presence of test sites are compared to “reference” sites
Both methods need to establish a measure of how different is different

18. The (End) Beginning Read (critically) as much as possible
LEARN your stats
Question virtually everything
But also search for the answer
Think critically
Think – “if I were a bug”
Integrate all you’ve learned and ask:
Does it make sense?

19. Jaccard Coefficient

20. Percentage Similarity