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

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

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

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

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

Example: Polar Ordination

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”

PCA Example

Detrended Correspondence Analysis (DCA)

DCA-Arch Removal

DCA Example

Cannonical Correspondence Analysis (CANOCO)

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…

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