Detrended correspondence analysis

Detrended Correspondence Analysis (DCA) is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify ecological community data. For example, Hill and Gauch (1980, p. 55) analyse the data of a vegetation survey of southeast England including 876 species in 3270 relevés. After eliminating outliers DCA is able to identify two main axes: The first axis goes from dry to wet conditions, and the second axis from woodland to weed communities.

History of DCA

It was created in 1979 by Mark Hill of the United Kingdom's Institute for Terrestrial Ecology (now merged into Centre for Ecology and Hydrology) and implemented in an obsolete FORTRAN code package called DECORANA (Detrended Correspondence Analysis), a Correspondence analysis method. DECORANA is sometimes erroneously used for DCA; however, DCA is the underlying algorithm, while DECORANA is a tool for implementing it.

The problem solved by DCA

DCA is used to suppress an artefact inherent in most other multivariate analyses when applied to gradient data. An example is a time-series of plant species colonising a new habitat; early successional species are replaced by mid-successional species, then by late successional ones. When such data are analysed by a standard ordination such as a principal components analysis and presented as a graph the points will be seen to follow a horseshoe shaped curve rather than a straight line (arch effect), even though the process under analysis is a steady and continuous change that human intuition would prefer to see as a linear trend. Outside ecology, the same artefact occurs when gradient data are analysed (eg soil properties along a transect running between 2 different geologies, or behavioural data over the lifespan of an individual) because the curved projection is an accurate representation of the shape of the data in multivariate space.

How DCA solves the problem

DCA is a messy and iterative algorithm, but in practice has shown itself to be a highly reliable and useful tool for data exploration and summary that deserves to be more widely known outside of community ecology (Shaw 2003). It starts by running a standard ordination (CA or reciprocal averaging) on the data, to produce the initial horse-shoe curve in which the 1st ordination axis distorts into the 2nd axis. It then divides the first axis into segnments (default = 26), and rescales each segment to have mean value of zero on the 2nd axis - this effectively squashes the curve flat. It also rescales the axis so that the ends are no longer compressed relative to the middle, so that 1 DCA unit approximates to the same rate of turnover all the way through the data: the rule of thumb is that 4 DCA units mean that there has been a total turnover in the community.

The drawbacks of DCA

No significance tests are available with DCA, although there is a constrained (canonical) version called DCCA in which the axes are forced by Multiple linear regression to correlate optimally with a linear combination of other (usually environmental) variables; this allows testing of a null model by Monte-Carlo permutation analysis.

References

Hill, M.O (1979). DECORANA - A FORTRAN program for Detrended Correspondence Analysis and Reciprocal Averaging. Section of Ecology and Systematics, Cornell University, Ithaca, New York.

Hill, M.O. and Gauch, H.G. (1980). Detrended Correspondence Analysis: An Improved Ordination Technique. Vegetatio 42, 47-58.

Oksanen J & Minchin PR (1997). Instability of ordination results under changes in input data order: explanation and remedies. Journal of vegetation science 8, 447-454

Shaw PJA (2003). Multivariate Statistics for the Environmental Sciences. London: Hodder Arnold

External Link

[1] - PAST (PAlaeontological STatistics) free software including DCA