In "sp_data.csv" file, we gathered 1,167 tree ferns records related to 15 species, from the literature and herbaria (using SpeciesLink - http://splink.cria.org and GBIF Global Biodiversity Information Facility - https://www.gbif.org). We used "SDM" R-script to predict current and future distributions of each tree fern species, based on occurrence records and bioclimatic variables. Our SDMs were formulated using the sdm R-package, through five different algorithms. To avoid biases created by choosing a single statistical algorithm, we built a single final model through an ensemble approach.Using the "beta" script and species maps, we calculated the β-diversity as the total variance of the community (Total β-diversity, or BDTOTAL; sensu Legendre & De Cáceres 2013) and it was subsequently decomposed in Local Contributions to β-Diversity (LCBD). We calculated BDTOTAL based on the Jaccard dissimilarity coefficient (1- similarity). Then, the LCBD was determined based on the partition of BDTOTAL between the cells (Legendre & De Cáceres 2013). The significance of the LCBD values for each cell was obtained through 999 permutations, where the species are distributed randomly and independently along the grid and the LCBD values are calculated for each random distribution. Significant LCBD values were those with p-value < 0.05. We also followed Legendre (2014) by partitioning the BDTOTAL ​​in species replacement and richness difference components. All β-diversity metrics were calculated with the adespatial R-package using the functions beta.div and beta.div.comp.