Summary
Three data matrix standardizations, three distance measures, and four ordination equations were tested in a factorial design of 36 variants of polar ordination, including the one originally given by Bray & Curtis (1957), with reciprocal averaging (Hill 1973) serving as a standard of comparison. Their effectiveness was tested on simulated data sets varying in beta diversity and noise, and on two sets of field data.
Of the 36 variants of polar ordinations tested here, the original algorithm of Bray & Curtis was on the whole as good as any. The one modification which improved the Bray & Curtis algorithm for a reasonably large range of data set properties was application of the arcsin transformation to percentage difference values (Loucks 1962). In cases where the beta diversity and noise level of the data set are known, performance of variants can be predicted, and in some cases other variants may offer modest improvement over the Bray-Curtis method. For simulated data with exactly known properties differences in performance are mostly small; for field data several variants may give results essentially equivalent to one another and reciprocal averaging.
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We thank M.O. Hill, R.H. Whittaker and Z. Szöcs for useful discussions and suggestions, and P. Feinsinger and D. May for comments on the manuscript. C.E. French, Jr., T.F. Mason and S.B. Singer provided technical assistance. This work was done under a National Science Foundation grant to R.H. Whittaker.
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Gauch, H.G., Scruggs, W.M. Variants of polar ordination. Vegetatio 40, 147–153 (1980). https://doi.org/10.1007/BF00228478
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DOI: https://doi.org/10.1007/BF00228478