Detrended correspondence analysis

Lecture graphics

Detrended correspondence analysis (i.e., detrended reciprocal averaging)

developed in software form (DECORANA) in 1979

published in a journal in 1980 (Hill & Gauch Vegetatio 42:47-58)

Goals are to remove "arch" effect and compression of first-axis ends

Method:

To get rid of "arch", divide axis 1 into several segments, and adjust axis 2 to have a mean of 0 in each segment

To calculate a third DCA axis, sample scores are detrended w/ respect to the second axis as well as the first ... and so on for higher axes

Several authors (e.g., Pielou, ter Braak) have suggested that DCA is "overzealous" in its removal of the "arch"

A second method for eliminating the "arch" was suggested in 1987 (ter Braak, C.F. Vegetatio 69:69-77)

"Arch" reflects quadratic relationship between first axis and second axis

In addition to the constraint that axes be orthogonal, merely add a second constraint: that axes be uncorrelated w/ the square (cube, etc.) of previous axes

termed "detrending by polynomials", done w/ ter Braak's (1987) canonical correspondence analysis computer program, CANOCO

The second goal of DCA is to "stretch" axis ends

this causes distances in the ordination space to have consistent meaning in terms of compositional differences of samples, or distributional differences of species

DCA is currently popular w/ ecologists, esp. w/ nonlinear data

The most common criticism of DCA is that detrending is artificial

problems ("arch", compression of axes) are "fixed" whether they are real or not

w/ field data, we don't know relationships between species and quadrats

Interpretation and presentation of ordination results (common display options):

1. Quadrat or species lists

   rank order of ordination scores may present a clear gradient (e.g., moisture, successional status)

2. Arranged matrix

   not very useful if 2 gradients (still appears random)

3. Quadrat and species ordination graphs

   if 2 axes, use a series of graphs (e.g., plot 1*2, 1*3)

4. Graph environmental parameters on quadrat ordination

   instead of plotting points for each quadrat, plot value of some environmental variable (e.g., pH); isolines are sometimes drawn

5. Hybrid ordination

   allows various kinds of data to be plotted on one figure

   however, since each "species" (incl. environmental data) and quadrat affects the ordination, it may be undesirable to include environmental data in ordination

6. Trace diagram

   ordination score for one axis (usu. axis 1) and environmental data, plotted by plot location