PiscesLogoSmallerStill  Reciprocal Averaging - RA

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This method, also called Correspondence Analysis, is a method of showing the relationship between both species and samples (quadrats) in a reduced space. Originally proposed by Hirschfeld (1935) and Fischer (1940) it was first used by ecologists in the 1960s (Roux & Roux, 1967; Benzécri, 1967) - see Kent & Coker (1992) for more details. The method is described by Hill (1973) and a non-mathematical introduction to the technique is given in Kent & Coker (1992). RA uses Chi-squared distance values; this results in low abundance species (variables) having a possibly disproportionately large effect on the ordination produced, and can over-emphasise the difference in samples containing several infrequently-recorded species. RA performs best for analysing samples that were collected along an environmental gradient. If there are no clear environmental gradients in the habitat under study, or the gradients are short, then PCA may give better results. RA can be applied to both presence/absence and quantitative data.


When Reciprocal Averaging is started, the Setup for RA dialog is displayed. There is a single option:


Downweight rare variables. Select this option if the influence of rare species or other variables is to be reduced. If selected, the abundances of variables rarer than the frequency of the commonest divided by 5 are down-weighted in proportion to their frequency. The default is no down-weighting. Click on OK to run the program.


Output for Reciprocal Averaging is presented under a number of tabbed components that can each be viewed by clicking on the tab. These are described in turn below.


Species Scores

Sample Scores

RA plot