species (abundances scaled with respect to the species maximum abundance or its
total abundance), or simultaneously to both site and species totals (with the chisquare transformation), depending on the focus of the analysis.
Note that decostand() has a log argument for logarithmic transformation.
But here the transformation is log_b(y) + 1 for y > 0, where b is the base of the
logarithm. Zeros remain untouched. The base of the logarithm is provided by the
argument logbase. This transformation, proposed by Anderson et al. (2006), is
not equivalent to log(y + 1). Increasing the value of the base increases the severity of
the downscaling of large values.
Here are some examples of data standardization illustrated by boxplots (Fig. 2.6).
raw data
sqrt
log
0
1
2
3
4
5
Simple transformations
max
total
0.0
0.2
0.4
0.6
0.8
1.0
Standardizations by species
Hellinger
total
norm
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Standardizations by sites
Chi-square
Wisconsin
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Double standardizations
Fig. 2.6 Boxplots of transformed abundances of a common species, Barbatula barbatula (stone
loach)
22
2 Exploratory Data Analysis