Detrended Correspondence Analysis DCA

1. Detrended Correspondence Analysis(DCA)

3. CA ordination: axes 1 v 2

4. Detrended Correspondence Analysis (DCA) Hill & Gauch (1980) Modification of CA that attempts to remove �arch effect� and correct compression of gradient extremes Computer program DECORANA (Hill 1979) was widely distributed DCA gained wide acceptance by ecologists in the 1980�s and is still often used, despite known problems.

5. DCA is not really a method, but CA with a couple of tricks Detrending: aims to remove any systematic relationship between scores on ordination axes Rescaling: non-linear adjustment of scaling on each axis in an attempt to achieve a constant rate of species turnover.

6. Detrending in CA, each axis has no linear relationship with previous axes (weighted correlation of zero) it still may have a nonlinear relationship (e.g. arch) in DCA, trial scores on axis 2 are detrended with respect to axis 1 CA Axis 1 is divided into segments and the mean axis 2 score is adjusted to zero within each segment.

7. Detrending Process for Axis 2 SUs are classified into segments along axis 1

8. Detrending Process for Axis 2 mean axis 2 score is adjusted to zero within each segment detrending step is performed during each iteration of the reciprocal averaging process

9. Detrending for later axes SU scores on axis 3 are separately detrended with respect to axis 1 and axis 2 SU scores on axis 4 are separately detrended with respect to axis 1, axis 2 and axis 3 etc� removes systematic relationships between pairs of axes, but does not guarantee a lack of higher order relationships (could still have interactions between axes)

10. DCA (detrending only) axis 2 now represents the variation along simulated gradient 2 (should be a regular grid) compression of extremes of gradient 1 remains.

11. Rescaling nonlinear rescaling process devised by Hill is complex and can�t be completely described here attempts to transform the scores on each axis (including axis 1) monotonically so that the rate of change in species composition is equal at every point on the axis achieved by stretching or shrinking the scaling within segments along the axis.

12. Rescaling individual segments of each axis are expanded or contracted to equalize the within-sample variation of species scores rescaling performed on the species ordination Hill�s scaling within-segment standard deviation is calculated width of each segment adjusted so that a half change in species composition spans ~ 1-1.4 standard deviations according to Hill, rescaling produces SU scores that are scaled in beta diversity units known as �sd� units

13. Rescaling some authors claim that the lengths of DCA axes are good measures of the beta diversity of community data whether the complex adjustments in DCA (with several arbitrary choices such as number of segments) does equalize the rate of species turnover along axes for real data is still controversial does improve ordination performance

14. DCA with both detrending & rescaling excellent recovery of the two gradients on DCA axes 1 v 2

15. Eigenvalues in DCA eigenvalues reported by programs that perform DCA (e.g. CANOCO) are misleading after adjustments by DCA, eigenvalue is �corrupted� no longer represents a fraction of the variance represented by the ordination no equivalent to the trace in DCA, so you can�t compute fractions of total variance

16. Distances in DCA Ordinations detrending and rescaling adjustments mean that distances between SUs and species in DCA ordinations are no longer least-squares approximations to Chi-squared distances unlike PCA and CA, the inter-point distances in DCA have no clear meaning in relation to dissimilarities.

17. The third �trick� in DCA early applications of CA and DCA often found that infrequent species received too much weight and dominated ordination patterns Hill therefore added an option in DECORANA to downweight infrequent species.

18. How does DCA perform on more realistic models and on real data?

19. Evaluation of DCA Performance Minchin (1983, 1987) tested DCA on simulated data sets with various properties: beta diversity shape of species� response curves sampling pattern amount of noise DCA was found to be unreliable, often distorting or obscuring variation related to environmental gradients.

20. Evaluation of DCA Performance DCA often produces �wedge-shaped� ordinations, in which variation on axis 2 is flattened towards one extreme of axis 1 wedge is an artifact of detrending and rescaling, unrelated to any real structure in the data other empirical studies (Kenkel & Orl�ci 1986; Jackson & Sommers 1991) also raise serious doubts about the reliability of DCA.

25. Underlying problems with DCA gradients appear as �arches� in CA spurious logic: therefore any arch-shaped structure in a CA is a curved gradient and should be flattened (NOT!) the wedge distortion in DCA ordinations leads to spurious interpretations SUs at the �squashed� end of axis 1 are incorrectly assumed to be less variable in community composition detrending can remove ecologically interesting variation as well as the �arch�.

26. What about real data? many published DCA ordinations show the characteristic �wedge� pattern.

27. Conclusions DCA seemed like a good idea at the time compared to CA and PCA it does often produce more interpretable and useful ordinations better alternatives are now available and DCA should no longer be used.