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.

DCA 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 FORTRAN code package called DECORANA (Detrended Correspondence Analysis), a correspondence analysis method. DCA is sometimes erroneously referred to as DECORANA; however, DCA is the underlying algorithm, while DECORANA is a tool for implementing it.

According to Hill and Gauch (1980), DCA is used to suppress two artifacts 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 (see example below). When such data are analysed by a standard ordination such as a correspondence analysis:

Outside ecology, the same artifacts occur when gradient data are analysed (e.g. 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.

Ter Braak and Prentice (1987, p. 121) cite a simulation study analysing two-dimensional species packing models resulting in a better performance of DCA compared to CA.

...
Wikipedia