1. Part 1 Putting things in order: Ordination as a tool for analyzing complex data sets

2. Historical Vegetation Analysis
Tabulation
What I found where….
Defining Gradients Before Data Collection
ETC.

3. The purposes of ordination... (Gauch 1982)
...to summarize community data by producing a low-dimensional ordination space in which similar species and samples are close together .....
...a means for producing effective, low-dimensional summaries from field data...by objective means

4. A Brief History of the Approach
Bray and Curtis (1957) Eco. Monographs
Principal Components Analysis (PCA)
Reciprical Averaging (RA)
Detrended Correspondence Analysis (DCA)
Canonical Correspondence Analysis

5. Bray and Curtis / Polar Ordination
Researcher defines endpoints or “poles”
arithmatically or “arbitrarily”
either species or sample
Other points are located between these based on similarity

6. Example: Polar Ordination

7. Principle Components Analysis (PCA)
First technique which defined relationships directly from data matrix
First to integrate species and sample scores
Goodall (1954) the “whole vegetation to be used… for the indication and indirect measurement of environmental complexes”

8. PCA Example

9. Detrended Correspondence Analysis (DCA)

10. DCA-Arch Removal

11. DCA Example

12. Cannonical Correspondence Analysis (CANOCO)

13. Canonical Correspondence Analysis (CCA) analyses the species matrix and the environmental matrix at the same time.
Thus you should ONLY use this when you want to understand, specifically, the relationships…
If you are interested in community structure, this is not the correct approach…

16. Non-metric multidimensional scaling
NMS, or NMDS is the analysis approach du jour partly because analyses are fashionable, and folks are just jumping in line, but mostly because the approach does not require multidimensional normality, and it can handle zeros in the matrix relatively well. As you might imagine, many matricies have a LOT of zeros!
There are a few things you need to know:
(1) NMS involves a randomization/resampling procedure.
(2) The number of axes is set by the process
(3) The axis that explains the most variation might not be the 1st axis
(4) You CAN assess environmental factors, but that is a wholly unique 2nd step…not the same as CCA
(5) Instead of p-values, here you want to minimize stress & instability