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The relationships between the distribution of alpine species and selected environmental variables are investigated by using two types of generalized linear models (GLMs) in a limited study area in the Valais region (Switzerland). The empirical relationships are used in a predictive sense to mimic the potential abundances of alpine species over a regular grid. Here, we present the results for the alpine sedge Carex curvula ssp. curvula. The modelling approach consists of (1) a binomial GLM, including only the mean annual temperature as explanatory variable, which is adjusted to species presence/absence data in the entire study area; (2) a logistic model restricted to stands occurring within the a priori defined temperature range for the species ‐ which allows ordinal abundance data to be adjusted; (3) the two species‐response functions combined in a GIS to generate a map of the species' potential abundance in …