Plant functional traits can be genetically determined or phenotypically plastic. We assessed the degree of genetic determinism in the functional traits of Andean Polylepis tree species among 14 important traits that enable the species to withstand cold and dry conditions. We conducted a common garden experiment and related the species-specific means of the functional traits to the variables of climatic niche optima of the species (mean annual temperature and annual precipitation), deducing that if the interspecific variation in the functional trait is related to the species climatic niche optima according to the theoretically-expected pattern of climate-trait relationship, the variation of the trait must be genetically determined. In general, the traits were related either to species temperature or precipitation optima. For example, leaf size, maximum photosynthesis rate and root tip abundance were related to temperature, whereas light compensation and light saturation points were related to precipitation. Only leaf size showed a significant phylogenetic signal, indicating that most of the manifested climate–trait relationships are not caused purely by phylogeny, but are mainly a result of species specialisation along an environmental gradient. However, in many cases the relationships were rather weak. This suggests that important functional traits of Polylepis species involve both genetic and phenotypic components aiming to maximise the overall fitness of the species at high elevations.