Appendix A. Supplementary details on the calculation of environmental predictors.
Climatic predictors
Growing degree-days DDEG (°C days) was calculated as the yearly temperature sum above a threshold T0. T0 is the assumed threshold minimum temperature for plant growth. Across larger spatial extents it is often set to 5.56°C (Prentice et al. 1992); however, for alpine grasslands, it is assumed to be lower (Larcher 1995). Here, we used a T0 = 0°C, a value also used in high altitude/latitude modelling (Lenihan 1993). We do not imply an absolute physiological limit with this value (e.g., chilling risk), since it may vary across elevational gradients as a function of species tolerances as well as within-species local adaptations. Instead, we suggest that using the gradients in DDEG is a more meaningful measure of thermal energy (heat sum) available to plants than is elevation.
Average temperature of the coldest month TAV [°C] was calculated as the lowest monthly average temperature per pixel, which is usually January or February in Switzerland. It represents the cold limit constraints on plants.
SFRO (no. days) expresses the sum of frost events after de-hardening during the frost-sensitive time of the year (core 90% of the vegetation period, the days with a mean daily temperature above 3°C). The definition of this period follows the rationale that frost hardening still protects tree tissues in early spring and again in the late fall. Frost was defined as a sudden drop of the daily minimum temperature of < -2.0°C being preceded by a period of at least one day with an average daily temperature of >3°C. Frost was calculated on a daily basis from minimum temperature and maximum temperature measurements.
PREC (mm) is the yearly sum of all monthly precipitation maps. Although it is a rather indirect predictor, it is often used in predictive species habitat modelling. Its advantage is the low degree of aggregation error, since it is interpolated from climate stations.
PDSUM (no. days) is the number of summer precipitation days (June, July, August) with rainfall >1 mm. Significant variation exists in the rate and amount of precipitation across Switzerland. For instance, the Ticino region situated south of the Alps has high annual precipitation sums, but a rather low number of precipitation days, indicating that rainfall events are usually heavy, followed by long drought periods. In contrast, the Northern Alps rarely have drought periods, and have approximately the same annual amount of precipitation.
SRAD (kJ·m-2·day-1) is the potential yearly global radiation. The calculation is based on the methods described in Kumar et al. (1997). Potential global radiation is the sum of potential direct and potential diffuse radiation. The algorithm used accounts for overshadowing by high peaks and ridges. The proportion of diffuse relative to direct solar radiation varies between summer and winter and is a function of solar altitude and terrain reflectance. Potential radiation does not include regional reduction of the atmosphere due to varying daily atmospheric transmittance (moisture, cloudiness, etc.), but is only based on direct potential beam radiation from the sun and the backscatter from the terrain. For details see Kumar et al. (1997).
Topographic AND Soil predictors
SLOPE (°) is the slope angle in degrees, derived directly from the digital elevation model using functions in ArcInfo. While generally considered an indirect variable, it summarizes the intensity of gravitational process. Specifically, it addresses snow creeping and likelihood of avalanches and rock falls. TOPO (range) is the topographic position. Circular moving-windows with increasing radii were applied to a DEM, and the difference between the average elevation of the window and the center cell of the window was calculated. The resulting maps can be interpreted as relative topographic exposure at a given spatial scale (the search radius). The integration of the various exposure maps into one single map was performed through standardized single-window maps. This allowed the combination of small or large topographic exposures at the same time (Zimmermann and Roberts 2001). Positive values express ridges, peaks, exposed sites, while negative values stand for sinks, gullies, valleys or toe slopes. CALC [p/a] is the presence of strictly calcareous bedrock type, reclassified from the Swiss Geotechnical map (1:200,000). Only strict calcareous rocks were mapped as "1" and all other categories were mapped as "0" (incl. quaternary deposits, Flysch, etc.). The following two measures were derived from the digital soil suitability map (Anon. 1980, 1:200'000; spatial accuracy ~200 m) that distinguishes ~140 soil units for which maxima and minima values for a range of soil properties are listed. We derived values of the water holding capacity (WHC) and the nutrient availability (NUTRI), and then used the variation in topographic exposure per soil type across Switzerland to scale the listed ranges of WHC and NUTRI linearly into a spatially explicit map. Therefore, we assumed that minima of WHC and NUTRI are found on ridges, while maxima of WHC and NUTRI per soil type would be located in gullies or slopes. Soil units were mapped at a much smaller spatial scale than whole valleys, and thus the procedure only corrects smaller scale variations. Also, the variation between units was considerably larger than the variation within units. NUTRI (mval/cm2) was used directly in the model, while WHC was further processed to SWB [mm], the site water balance. This is an estimate of the water available to plants during a year (Grier and Running 1977), integrating both climatic and soil parameters (Roberts et al. 1993). Beginning with the first month in autumn when precipitation exceeds potential evapotranspiration (after a possible drought period), the difference between precipitation and potential evapotranspiration was summed over 12 months. The running sum was never allowed to exceed the water holding capacity (WHC), and water in excess of the WHC was presumed to run off. When potential evapotranspiration began to exceed precipitation the difference was subtracted from water in the soil, often achieving significant negative values over the course of a year.
Remotely sensed leaf type predictors
BCC (%) is a continuous measure of the broadleaved tree cover, while CCC (%) represents the cover fraction of needleleaf trees. The values were calculated from the forest-composition map, which was originally derived from multi-temporal Landsat-TM images at a resolution of 25 m (GEOSTAT; BFS 2001). This original map distinguished four classes per leaf type, namely 100%, 66%, 33% and 0%. We then used the aggregate function to average the cover values into the larger pixels of 100 m and 500 m so that final values span the full range from 0 to 100%.
LITERATURE CITED
Anonymous. 1980. Soil suitability map of Switzzerland [German]. In Eidgenussische Drucksachen und Materialzentrale (EDMZ), Bern, Switzerland.
BFS [Bundesamt fuer Statistik]. 2001. Benutzerhandbuch GEOSTAT. Ausgabe 11/2001, Bundesamt fuer Statistik, Bern, Switzerland.
Grier, C. C., and S. W. Running. 1977. Leaf area of mature northwestern coniferous forests: relation to site water balance. Ecology 58:893–899.
Kumar, L., A. K. Skidmore, and E. Knowles. 1997. Modelling topographic variation in solar radiation in a GIS environment. International Journal for Geographical Information Science 11:475–497.
Larcher, W. 1995. Physiological Plant Ecology. Third edition. Springer-Verlag, Berlin, Germany.
Lenihan, J. M. 1993. Ecological responses surfaces for North American tree species and their use in forest classification. Journal of Vegetation Science 4:667–680.
Prentice, C., W. Cramer, and S. P. Harrison, R. Leemans, R. A. Monserud, and A. M. Solomon. 1992. A global biome model based on plant physiology and dominance, soil properties and climate. Journal of Biogeography 19:117–134.
Roberts, D. W., R. F. Fisher, J. M. Long, and S. N. Jack. 1993. The Leaf Area Allocation Model. Final Report. Cooperative Agreement #817539, Environmental Protection Agency (EPA).
Zimmermann, N. E., and D. W. Roberts. 2001. Final report of the MLP climate and biophysical mapping project. Swiss Federal Research Institute WSL, Birmensdorf.