Appendix 4. Details of the multivariate methods used to determine the environmental volume of the species.

In each plot, we recorded 53 variables (Appendix 3) that were ultimately reduced into a three-dimensional, multivariate space. This reduction was done through a two-step, multivariate analysis. The first step consisted of reducing the 53 variables to 12 variables, several of which were multivariate composites.

The first set of three composite variables were derived from 32 binary variables consisting of information on land form (type of morphotectonic unit and type of geomorphological unit), topography, drainage, grassland shape, vegetation physiognomy, and altitude zone. Land form variables were inferred from 1:50000 geological maps, and the rest of variables in this group were inferred from photo-interpretation of 1:20000 panchromatic stereopairs. Composite variables were derived from the first three eigenvectors of a correspondence analysis. These three eigenvectors primarily represented landscape position of the wet grasslands.

The next set of three composite variables consisted of the first three eigenvectors of a PCA based on soil chemical composition: pH, conductivity, sodium, potassium, calcium, magnesium, chloride, sulfate, carbonate and bicarbonate, organic matter, nitrate, nitrogen, and phosphorous. We took five 20-cm depth soil samples regularly distributed within each plot. These five samples were mixed into one composite sample for analyses of soil chemical composition and soil texture. The following soil chemical composition variables were analyzed in a 1:10 soil solution: pH, conductivity, sodium, potassium, calcium, magnesium, chloride, sulfate, carbonate, bicarbonate, and nitrate. Organic matter, nitrogen, and phosphorous were directly analyzed in the soil sample. These three eigenvectors were interpreted as total ion content, proportion of organic matter, and soil acidity.

The seventh composite variable was soil texture, based on the first eigenvector of a PCA of the percentages of sand, silt, and clay. The other five variables were: altitude, actual evapotranspiration, water index, ground slope, and soil wetness. Altitude was estimated with a calibrated altimeter in the field. Actual evapotranspiration and water index were inferred from interpolation of the region climate stations. Ground slope was estimated with a clinometer in the field. Soil wetness was estimated by means of an index based upon qualitative indicators such as gley traits and percentage of saturation. Across all variables, <1% of the data were missing, primarily texture (11%) and nitrate (9%). In these instances, we substituted the mean value for that variable.

These 12 variables defined an environmental space based on the first three eigenvectors from a PCA. This single space was then used to determine the volumes for all species. The distribution of the sites in the space is shown in Fig. 8. All ordination analyses were done with PC-ORD (McCune and Mefford 1995).

The environmental volume of each plant species was measured by determining the maximum and minimum coordinates on all three axes. To do this, for each species on each axis we determined the sites containing that species with the largest and smallest axis scores. The volume was the rectangular solid containing these points. This measure is equivalent to the range volume of Burgman (1989) except that we did not standardize axis length. For species appearing in only one site, the volume was zero. Changing this volume to an arbitrarily chosen small value (e.g., 10% of the smallest two-site volume), would not change the analyses.