Identifying areas for multidimensional biodiversity conservation, with a case study in Oaxaca, Mexico

•Taxonomic, functional, and phylogenetic diversity comprise multidimensional diversity.•Multidimensional diversity patterns can be mapped to detect conservation priorities.•Protected areas do not always include sites with high multidimensional biodiversity.•Indigenous communities have a fundamental role in the conservation of biodiversity.•Areas with high multidimensional diversity may have high or low ecological integrity.