CHAPTER 20 Detrended Correspondence Analysis From: McCune, B. & J. B. Grace Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon Tables, Figures, and Equations

Figure 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 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.

Figure 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).

Figure 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.

Figure 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.