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1 October 2007 Transformation of cover-abundance values for appropriate numerical treatment – Alternatives to the proposals by Podani
Eddy van der Maarel
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Two alternatives are offered to Podani's proposals, based on the claim that Braun-Blanquet cover-abundance estimates cannot be properly analysed by conventional mul-tivariate methods.

1. The ordinal transform scale, based on an extended Braun-Blanquet cover-abundance scale, comes close to a metric cover percentage scale after (1) the abundance values r (very few individuals), (few ind.), 1 (abundant) and 2m (very abundant, cover < 5%) are replaced by cover percentage estimates and (2) the higher Braun-Blanquet values, notably 4 and 5, with cover intervals 50-75% and 75-100%, respectively, are interpreted as estimates of considerably higher cover values than the usual visual projection on the ground (because of the position of stems and leaves in several layers). I propose the equation ln C = (OTV -2)1 a, where C = Cover%, OTV is the 1 to 9 Ordinal Transfer Value and a is a factor weighting the cover values. With this equation cover values in a geometric series are achieved for the nine values in the extended Braun-Blanquet scale from 0.5 % (OTV 1) to 140% (OTV 9) for a = 1.415, and for a = 1.380 from 0.6 % to 160%.

2. This makes use of an earlier developed ‘optimum-transformation’ of cover-abundance values. For each species a frequency distribution of cover-abundance values is determined for a large data set, i.e. of dune slack vegetation. Tiny species have low values (OTVs 1-3) with high frequencies and hardly occur with higher OTV values; here all scores are considered ‘optimal’. In dominant species OTVs 7 to 9 have the highest frequencies and only these values are considered optimal. Species with intermediate OTV ranges have optimum ranges with low-bound OTV = 2,3,4 and 5, respectively. No species were found in the dune slack data set with a frequency distribution justifying an optimum range with low-bound OTV = 6.

For mathematically correct numerical treatments' optimum scores' can be converted to 1 and sub-optimal scores to 0 in order to approach a presence/absence situation.

Both alternatives are suggested to be acceptable approximations to a metric basis for numerical analyses.

Eddy van der Maarel "Transformation of cover-abundance values for appropriate numerical treatment – Alternatives to the proposals by Podani," Journal of Vegetation Science 18(5), 767-770, (1 October 2007).[767:TOCVFA]2.0.CO;2
Received: 15 January 2007; Accepted: 13 May 2007; Published: 1 October 2007

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Geometrical series
Logarithmic scale
Metric scale
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