Community Ordination and
Gamma Diversity
Techniques
James A. Danoff-Burg
Dept. Ecol., Evol., & Envir. Biol.
Columbia University
Ordination vs. Cardinal Indices
Cardinal Indices treat all species equally
What we’ve been doing thus far
Disproportionate influence was accorded to
superabundant species
• Purely as a consequence of the index calculation
Ordinal Indices allows for extra weight to
some species
Incorporate other biological information
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Uses for Ordination
Type of biological information to include
Rare species
Species of conservation importance
Taxonomically diverse communites
• Weight those with many unique lineages
• Weight those with disparate lineages
Keystone species
Commercially valuable species
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Methods of Ordination
Many methods of ordination
All involve assigning a weight to a each species
Abundance can also be involved in weighting system
Weighting is done according to desires of
researcher
Rarity
Conservation importance
Taxonomic uniqueness
Keystone species
After weighting
Can then do straight diversity analyses on these
weighted values
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Weighting – an Example
Taxonomically – two possible methods (Stiling 1996)
l Sl/l %
Branch Value w %
Branching
1
6.25
4
3.5
10.7
1
6.25
4
3.5
10.7
2
12.5
3
4.67 14.3
4
25
2
7
21.4
8
50
1
14
42.9
16
100
14
32.7
100
Places great weight on
taxonomically rare species
Lecture 7 – Community Ordination & Gamma Diversity
Information
Index
Places more equal weight on
taxonomically rare species
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Gamma Diversity
Comparisons across ecosystems within a
biome or larger region
Usually want to determine the degree of similarity
between disparate habitats
Similarity determined by shared species
Usually done using community ordination
analyses
Also interested in explaining why similarities
exist
Usually abiotic or landscape features
Most work has been done on plants
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Data in Ordination Analyses
When comparing sites, use similar data to
what we’ve used thus far
Richness
Abundance
Ordinal weights of each species
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Community Ordination
Techniques
Methods of analysis
Cluster Analysis
Indicator Species Analysis (ISA)
Principal Components Analysis (PCA)
• Sometimes called Principle Components Analysis
Canonical Correspondence Analysis (CCA)
Detrended (Canonical) Correspondence Analysis
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Cluster Analysis
 Stream similarity
by invertebrates
 Used least
impaired sites
Stribling, et al. (1998)
 Natural species
distributions, not
human
disturbance
created clusters
 Site clusters
were best
explained by
ecoregion
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Indicator Species Analysis
Description
a simple procedure for identifying those species that
show strongly preferential distributions with respect to
predefined groups
Predefined Groups
• might be those identified by cluster analysis
• might be clustered in terms of environmental variables
• might be treatment levels in an experimental design
Result is that those species that best coincide with the
predefined groups have highest values
Resources on ISA
 http://www.env.duke.edu/landscape/classes/env358/mv_lab6.pdf
 http://wiseman.brandonu.ca/article2.htm
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Principal Components
Analysis
PCA
Takes a set of variables and defines new variables
that are linear combinations of the initial variables
Extracts most variance from data
• Plots sample points in an n-dimensional cloud
• Longest axis of the cloud is the primary axis
Need to plot the data points to determine meaning of
axes
• Not always clear
• Can be many explanatory factors
Correlating multiple dependent variables with each
other
Mostly exploratory
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
PCA Example
 PCA of human disturbance measures using
diatoms
 Many different types of human disturbance
within each watershed
 Bryce et al. (1999)
 Summarize the risk of human disturbance in a
watershed
 Created a disturbance index PCA
 Different combinations of variables were tested
the set that best approximated the subjective
disturbance index
 PCA axis1 correlated with
 chloride, total N, riparian condition measures,
road density, % urban, forest, agriculture, and
mine cover
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Canonical Correspondence
Analysis
Method
Takes 2 sets of variables
• Multiple dependent variables
• Multiple independent variables
Creates new variables for each set such that the
correlation of the new variables is maximized
You give the model 2 sets of variables and the
model returns pairs of new variables
• made from linear combinations of the original variables
• Each new variable includes those that are the most
highly correlated
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
CCA Example
 Hill, et al. (in review)
 Exploratory evaluation of the
relationship between
measures of human
disturbance and candidate
diatom metrics
 Determined canonical
axes for both sets of
variables (DV & IV)
 First canonical axis
• derived from human
disturbance measures
• test for differences in
genus- and species-level
identification of diatoms
Diatom species that tolerate nutrient enrichment (Eutraphentic taxa)
increased significantly with human disturbance – but number of genera did not.
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Detrended Canonical
Correspondence Analysis
 Floral analysis along the
Hood River in Canada
 Sites found on uplifted marine
sediments (below 150 m)
separate out as floristically
distinct from sites found above
the uplifted sediments.
 All sites share a large
percentage of species (30%)
 Separation along the first axis
is related to gradients in soil
pH and a complex gradient in
elevation.
 Separation along the second
DCA axis is unexplained
 Hood (1995)
Lecture 7 – Community Ordination & Gamma Diversity
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu