Replacing species with new attributes

Analysis and interpretation is tremendously simplified when the number of attributes (e.g. the species lists) can be reduced. Because the number of species is usually very large the original releves are over-determined: the number of attributes exceeds the number of sampling units. The goal of species reduction is therefore to erase redundancy; that is, where information is carried by two or more species simultaneously. This is most efficiently done by the RANK algorithm (Orloci 1978, see Section 5.6). As explained there, the reduced list of species usually accounts for a surprisingly large amount of explained variance, but it still operates in the same similarity space (the species space), although reduced. Alternatively, we may project our data into a different resemblance space. Several of these spaces are well established in vegetation science:

• The species indicator values, as proposed by Ellenberg (1974), or those of Landolt (1977).

• Growth forms of dominating species, as introduced by Raunkiaer (1937).

• Plant functional types (Box 1996), in which the functioning of the species in its environment is considered.

• Character set types (Orloci & Orloci 1985, Orloci 1991), where anatomical and physiological features of the individual plants represent the new attributes.

• In recent years the term 'trait' (i.e. species described by traits) has increasingly been used (Pillar et al. 2009) to investigate trait patterns of vegetation types.

The formal process projecting releves via species lists into a new variable space is the same as that used in principal component analysis (Section 5.2). It is achieved through matrix multiplication and the new variables are linear combinations of the original; this is shown schematically in Figure 11.5,

Figure 11.5 Projecting a given sample into a new resemblance space. Top: the example of PCA, where species are substituted by axes. Bottom: the species list is replaced by a list of indicator values. See also Pillar et al. (2009).

where the new attributes replacing the species are indicator values (see e.g. Pillar et al. 2009 for a similar illustration). What is needed in addition to the survey data is a matrix of species by indicator values. Here I use the list published by Landolt (1977) calibrated for wetlands, as explained by Feldmeyer-Christe et al. (2007). In the example below the 2265 randomly selected releves from the Swiss wetland data are processed accordingly. In this way the 1413 species are replaced by as few as 8 indicator values. To reveal the new similarity pattern of the releves and its relation to the indicator values I choose correspondence analysis (Section 5.4); the result is shown in Figure 11.6. The resulting point cloud once again has a triangular shape. As

Calthion palustris

Calthion palustris humidity dispersity temperature

nutrients continentality light reaction

Figure 11.6 Ordination of the wetland sample in the indicator space using correspondence analysis. The location of three vegetation types is shown. The usually superimposed plot of indicator values is shown separately in the lower-right ordination.

in Figure 11.1, two of the corners represent the alliances Phragmition aus-tralis and Sphagion medii, but this time the alliance Calthion palustris forms the centre of the ordination. The explanation resides in the characteristics of the method: this alliance is very well represented in the sample (398 releves). Because correspondence analysis operates with deviations from the overall expected state of the sample, frequent types are considered 'normal' and therefore projected close to the centre of the ordination.

The space of indicator values separates the established vegetation types just as well as the species space does. In Figure 11.6 the ordination of the indicator values (lower-right graph) is not superimposed on the ordination of releves, as is commonly practised in correspondance analysis, but is printed separately. The direction of the data points as seen from the centre accords with locations of high values. The length of that same vector expresses the explanatory power of the respective indicator value.

The species space and the indicator space can also be superimposed, as shown in Figure 11.7. The ordination coordinates are the same as in Figure 11.1. The diameter of the bubbles representing the releves is proportional to one indicator value at a time. One could therefore generate eight plots of the kind: one for each indicator value. Figure 11.7 yields an ecological interpretation of the ordination. The corner on the left-hand side, for example, representing the Sphagnion medii, carries high humus values (the peat) and low nutrient values, as is found in peat bogs.

Figure 11.7 Indicator values superimposed on ordinary ordination. The diameter of the bubbles representing the releves is proportional to one indicator value at a time.

Figure 11.7 Indicator values superimposed on ordinary ordination. The diameter of the bubbles representing the releves is proportional to one indicator value at a time.

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