Reciprocal Averaging   RA
Reciprocal Averaging   RA
This method, also called Correspondence Analysis, is a method of showing the
relationship between both species and samples (quadrates) in a reduced space.
Originally proposed by Hirschfeld (1935) and Fischer (1940) it was first used by
ecologists in the 1960s (Roux & Roux, 1967; Benzecri, 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 and this results in low abundance species
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 selected from the ordination drop down menu the
setup for RA window is displayed. There is a single option:
Downweight rare species
. Select this option if the influence of rare species is to
be reduced. If selected, the abundance of species rarer than the frequency of the
commonest species divided by 5 are down weighted in proportion to their
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
Computations   Reciprocal Averaging
This text window gives the values of the eigenvalues calculated for each axis.
These are estimated by iteration and this window also gives the residual term for
each iteration. The eigenvalues are calculated to an accuracy of 0.000001. If after
999 iterations, this residual value is not achieved, computation is halted and a
warning message produced. To print this output use File | Print.
Species Scores   Reciprocal Averaging
This window presents in a grid the species scores for the first 4 axes. These
scores are the co ordinates of each species used in the ordination plot (see RA
plot below). To print this output use File | Print.

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