Aim: To explore the scale dependence of relationships between novel measures of geodiversity and species richness of both native and alien vascular plants.Location: Great Britain.Time period: Data collected 1995-2015.Major taxa: Vascular plants. Methods:We calculated the species richness of terrestrial native and alien vascular plants (6,932 species in total) across the island of Great Britain at grain sizes of 1 km 2 (n 5 219,964) and 100 km 2 (n 5 2,121) and regional extents of 25-250 km diameter, centred around each 100-km 2 cell. We compiled geodiversity data on landforms, soils, hydrological and geological features using existing national datasets, and used a newly developed geomorphometric method to extract landform coverage data (e.g., hollows, ridges, valleys, peaks). We used these as predictors of species richness alongside climate, commonly used topographic metrics, land-cover variety and human population. We analysed species richness across scales using boosted regression tree (BRT) modelling and compared models with and without geodiversity data.Results: Geodiversity significantly improved models over and above the widely used topographic metrics, particularly at smaller extents and the finer grain size, and slightly more so for native species richness. For each increase in extent, the contribution of climatic variables increased and that of geodiversity decreased. Of the geodiversity variables, automatically extracted landform data added the most explanatory power, but hydrology (rivers, lakes) and materials (soil, superficial deposits, geology) were also important.Main conclusions: Geodiversity improves our understanding of, and our ability to model, the relationship between species richness and abiotic heterogeneity at multiple spatial scales by allowing us to get closer to the real-world physical processes that affect patterns of life. The greatest benefit comes from measuring the constituent parts of geodiversity separately rather than one combined variable (as in most of the few studies to date). Automatically extracted landform data, the use of which is novel in ecology and biogeography, proved particularly valuable in our study.

Biogeographical studies frequently reveal positive correlations between species richness and estimates of environmental water and/or energy. A popular interpretation of this relationship relates the supply of water and energy to productivity, and then, in turn, to richness. Productivity-diversity theories are now legion, yet none has proved sufficiently intuitive to gain broad acceptance. Like productivity, heterogeneity is known to influence diversity at fine spatial scales, yet the possibility that richness might relate to water-energy dynamics at coarse spatial scales via a heterogeneity-generating mechanism has received little attention. In this paper we outline such a conceptual model for plants that is internally consistent and testable. We believe it may help to explain the capacity of environments receiving different inputs of water and energy to support variable numbers of species at a range of spatial scales, the pervasive correlation between productivity and richness, some exceptions to the productivity-diversity relationship, the form of productivity-diversity curves and the link between richness and environmental 'harshness' . The model may also provide an answer to one of the most venerable puzzles in the field of diversity studies: why high inputs of water and energy correspond to more species rather than simply more individuals.

Biogeographical studies frequently reveal positive correlations between species richness and estimates of environmental water and/or energy. A popular interpretation of this relationship relates the supply of water and energy to productivity, and then, in turn, to richness. Productivity-diversity theories are now legion, yet none has proved sufficiently intuitive to gain broad acceptance. Like productivity, heterogeneity is known to influence diversity at fine spatial scales, yet the possibility that richness might relate to water-energy dynamics at coarse spatial scales via a heterogeneity-generating mechanism has received little attention. In this paper we outline such a conceptual model for plants that is internally consistent and testable. We believe it may help to explain the capacity of environments receiving different inputs of water and energy to support variable numbers of species at a range of spatial scales, the pervasive correlation between productivity and richness, some exceptions to the productivity-diversity relationship, the form of productivity-diversity curves and the link between richness and environmental 'harshness' . The model may also provide an answer to one of the most venerable puzzles in the field of diversity studies: why high inputs of water and energy correspond to more species rather than simply more individuals.

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