Transcript Document

ORDINATION
What is it?
What kind of biological questions can we answer?
How can we do it in CANOCO 4.5?
Some general advice on how to start analyses.
How different or similar
is the vegetation at
these two places?
What are the patterns
within each of them?
Biomass
Productivity
Diversity
Species composition
Ordination
• Analyses of data with many response
variables
• Search for patterns
• We can also quantify and test the effect
of one or many predictor variables
(tomorrow!!)
But first: do communities exist?
A short answer after a long debate:
No.
Compositional variation in nature tends to be gradual.
How can we analyse species
composition?
Within some defined
environment or area
we sample a number
of plots and register
the species present
Site 1
Site 2
Site 3
Site 4
Site 5
.......
Pinus
3
5
0
4
3
....
Tsuga
10
1
2
8
5
....
SPECIES SPACE
Site 1
10
Site 4
Tsuga
Site 5
Site 3
Pinus
Tsuga
Acer
Betula
Site 1
3
10
2
4
Site 2
5
1
2
8
Site 3
0
2
5
6
Site 4
4
8
6
5
Site 5
3
5
1
0
.......
....
....
....
....
Site 2
0
0
Pinus
10
Site space
10
Betula
site 2
Pine
Pinus
Tsuga
Acer
Betula
Site 1
3
10
2
4
Site 2
5
1
2
8
Site 3
0
2
5
6
Site 4
4
8
6
5
Site 5
3
5
1
0
.......
....
....
....
....
Tsuga
Acer
0
0
Site 1
10
Data dimensions
• The sites differ in species abundances
• Each species is a variable – a dimension –
– in a dataset with n species the differences between plots can
be described exactly by their positions in a n-dimensional
space
• Species are not distributed independently of
each other
– They respond to the same factors, affect each other…
• Can we somehow find a few dimensions that
capture the bulk of the compositional
information?
Site 1
10
Site 4
Tsuga
Site 5
Site 3
Site 2
0
0
Pinus
10
This line describes the relative positions of sites
along one dimension that captures the largest
fraction possible of the variation in species
composition
We have done a Principal Component Analysis!!!!
Linear vs. Unimodal methods
• In the examples above we assumed that species
abundance and the environment is linearly related
• This is sometimes true! (when we are within a ca.
1-2.5 SD ’window’ along an environmental gradient)
Linear vs. Unimodal methods
• But what if we want to analyse the whole gradient?
• A linear-based method will give a ’wrong’ solution!
(which would give us a statistical artifact called the
’horseshoe effect’)
• There are unimodal-based methods (CA, DCA, …)
Correspondence analysis (CA)
when the response is unimodal
Sample where the species is present.
(size indicates abundance)
Weigthed average
optimum of this
species
In the same way you can find the optimum of a sample:
the weighted average of the species it contains
Species present in the sample.
(size indicates abundance)
Weigthed average
optimum of the
sample
Weighted averaging
• species scores are weighted averages
of site scores
– the weights are related to how common the
species are in the sites
• site scores are weighted averages of
species scores
– the weights are (again) related to how commmon the
species are in the sites
ITERATIVE
METHOD!
The arch problem
• After the first CA axis is constructed, the program will
start ’looking for’ a second, uncorrelated axis.
• If no ’real’ gradient exists in the data, it will tend to
’find’ the folded axis 1 (which by definition
uncorrelated, and half the lenght of the first axis)
Identifying the arch problem
…and handling it
• The problem is easily identified by inspecting
– The CA ordination diagram
• can you see an arch in the plot positions along axis 2?
– The eigenvalues of the first and second axes
• Is the eigenvalue of axis 1 ca. 2* that of axis 2)
• The problem can be removed by detrending
– Detrend by segments in indirect methods
PCA
CA
The magic
behind the
ordination
diagrams
Biplot interpretation
• Species and sample positions along the
axes can be presented as ordinaion
diagrams
• These diagrams tell us something about
the species composition the samples
• Interpretation differs between ordination
diagrams from linear methods (PCA)
and unimodal methods (CA)!
PCA
PCA
PCA
PCA
Etc.........
CA
Decreasing probability
of occurrence
CA
Decreasing probability
of occurrence
Summary
• unimodal vs. linear methods
• detrending in unimodal methods
• biplot vs. centroid interpretation