Abstract Aim Species richness exhibits striking geographical variation, but the processes that drive this variation are unresolved. We investigated the relative importance of two hypothesized evolutionary causes for the variation in palm species richness across the New World: time for diversification and evolutionary (net diversification) rate. Palms have a long history in the region, with the major clades diversifying during the Tertiary (65–2 Ma). Location Tropical and subtropical America (34° N–34° S; 33–120° W). Methods Using range maps, palm species richness was estimated in a 1° × 1° grid. Mean lineage net diversification was estimated by the mean phylogenetic root distance (MRD), the average number of nodes separating a species from the base of the palm phylogeny for the species in each grid cell. If evolutionary rate limits richness, then richness should increase with MRD. If time limits richness, then old, relict species (with low root distance) should predominantly occur in long-inhabited and therefore species-rich areas. Hence, richness should decrease with MRD. To determine the influence of net diversification across different time frames, MRD was computed for subtribe, genus and species levels within the phylogeny, and supplemented with the purely tip-level measure, mean number of species per genus (MS/G). Correlations and regressions, in combination with eigenvector-based spatial filtering, were used to assess the relationship between species richness, the net diversification measures, and potential environmental and geographical drivers. Results Species richness increased with all net diversification measures. The regression models showed that richness and the net diversification measures increased with decreasing (absolute) latitude and, less strongly, with increasing energy/temperature and water availability. These patterns therefore reflect net diversification at both deep and shallow levels in the phylogeny. Richness also increased with range in elevation, but this was only reflected in the MS/G pattern and therefore reflects recent diversification. Main conclusions The geographical patterns in palm species richness appear to be predominantly the result of elevated net diversification rates towards the equator and in warm, wet climates, sustained throughout most of the Tertiary. Late-Tertiary orogeny has caused localized increases in net diversification rates that have also made a mark on the richness pattern.