An enduring challenge in ecology is to characterise and understand species richness patterns in tropical regions. Species richness maps produced by stacking species distribution model (SDM) range maps could prove useful in this regard, but little attention has been given to this approach. Here we generate a species richness map by stacking the ranges of 86 Mesoamerican fern species modelled by MaxEnt from field data collected by the Sampled Red List Index for Plants project. Predicted species richness showed a hump-backed relationship with elevation, peaking at mid-elevation (1800–2000 m). A remarkably similar pattern was observed in a field survey conducted to validate the approach. Predicted species richness was also low in sites with high water deficits, as previously shown in the fern literature. Beta-diversity in the lowlands was greatest between sites with strongly contrasting water deficits, further emphasising the importance of this environmental variable. The stacked SDM approach was thus able to reproduce broad biogeographical patterns of species richness, despite many of the fern species being represented by fewer than 20 samples.