Revealing biogeographical patterns by nonlinear ordinations and derived anisotropic spatial filters

Aim Spatial floristic and faunistic data bases promote the investigation of biogeographical gradients in relation to environmental determinants on regional to continental scales. Our aim was to extract major gradients in the distribution of vascular plant species from a grid‐based inventory (the German FLORKART data base) and relate them to long‐term precipitation and temperature records as well as soil conditions. We present an ordination technique capable of coping with this complex data array. The goal was also to sort out the influence of spatial autocorrelation, assuming floristic autocorrelation is anisotropic. Location Germany, at a spatial resolution of 6′ × 10′. Methods Isometric feature mapping (Isomap) was applied as a nonlinear ordination method. Isomap was coupled to ‘eigenvector‐based filters’ for generating spatial reference models representing spatial autocorrelation. What is novel here is that the derived filters are not based on the assumption of equidirectional autocorrelation. Instead, the so‐called ‘principal coordinates of anisotropic neighbour matrices’ build filters to test the influence of geographical vicinity in directions of high similarity among observations. Results The Isomap ordination of floristic data explained more than 95% of the data variance in six dimensions. The leading two dimensions (representing about 80% of the FLORKART data variance) revealed clear spatial gradients that could be related to independent effects of temperature, precipitation and soil observations. By contrast, the third and higher FLORKART dimensions were dominated by an antagonism of anisotropic spatial autocorrelation and soil conditions. A subsequent cluster analysis of the floristic Isomap coordinates educed the spatial organization of the floristic survey, indicating a considerable sampling bias. Conclusions We showed that Isomap provides a consistent methodical framework for both ordination and derived spatial filters. The technique is useful for tracing the often nonlinear features of species occurrence data to environmental drivers, taking into account anisotropic spatial autocorrelation. We also showed that sampling biases are a conspicuous source of variance in a frequently used floristic data base.