Transcript Chapter 20

CHAPTER 20
Detrended Correspondence Analysis
Tables, Figures, and Equations
From: McCune, B. & J. B. Grace. 2002. Analysis of
Ecological Communities. MjM Software Design,
Gleneden Beach, Oregon http://www.pcord.com
Figure 20.1. Detrending by segments. In this simplified example, a
CA ordination axis is divided into an arbitrary number of segments
(four in this case), then the sample unit scores on the vertical axis are
centered on zero, within each segment, analogous to sliding the
segments with respect to each other.
Figure 20.2. Segmenting a species ordination as the basis for
rescaling in DCA. The arrows indicate the boundaries of
segments. Circles are species. For each segment, DCA
calculates the within-sample variance for species whose
points occur within that segment. The lengths of the
segments are then stretched to equalize those within sample
variances. After rescaling, species tend to rise and fall (full
turnover) over four standard deviations.
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Axis 2
DCA
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Axis 1
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0
Figure 20.3. Detrended correspondence analysis of a data set
with known underlying structure. The lines connect sample
points along the major environmental gradient. The minor
secondary gradient is nearly orthogonal to the major
gradient. In the perfect ordination, the points would form a
horizontally elongate rectilinear grid (inset).
NM S
Axis 2
Axis 2
DCA
Axis 1
Axis 1
Figure 20.4. Comparison of DCA and NMS ordinations of a
data set with known underlying structure, containing two strong
gradients. DCA crumpled and folded the grid and while NMS
more successfully extracted the underlying structure. Inset: the
ideal result is a regular 10  10 grid.
NM S
Axis 2
Axis 2
DCA
Axis 1
Axis 1
Figure 20.5. Comparison of DCA and NMS ordinations of a data set with
known underlying structure, containing two strong gradients, one with a
discontinuity in the sample. The data set is the same as for Figure 20.4
except for the introduction of this discontinuity. The discontinuity is
barely recognizable in DCA while NMS successfully showed it, visible as
relatively broad segments roughly parallel to Axis 1. Inset: the ideal result
is a regular grid with a gap down the middle.