Aim Despite longstanding investigation, the gradients of species richness remain unknown for most taxa because of shortfalls in knowledge regarding the quantity and distribution of species. Here, we explore the ability of a geostatistical interpolation model, regression-kriging, to recover geographical gradients of species richness. We examined the technique with an in silico gradient of species richness and evaluated the effect of different configurations of knowledge shortfalls. We also took the same approach for empirical data with large knowledge gaps, the infraorder Furnariides of suboscine birds. Innovation Regression-kriging builds upon two cornerstones of geographical gradients of biodiversity, the spatial autocorrelation of species richness and the conspicuous association of species with environmental factors. With this technique, we recovered a simulated gradient of richness using < 0.01% of sampling sites across the region. The accuracy of the regression-kriging is higher when input samples are more evenly distributed throughout the geographical space rather than the environmental space of the target region. Moreover, the accuracy of this method is more sensitive to the sufficiency of sampling effort within cells than to the quantity of sampled localities. For Furnariides birds, regression-kriging provided a geographical gradient of species richness that resembles purported patterns of other groups and illustrated ubiquitous shortfalls of knowledge about bird diversity. Main conclusions Geostatistical interpolation, such as regression-kriging, might be a useful tool to overcome shortfalls in knowledge that plague our understanding of geographical gradients of biodiversity, with many applications in ecology, palaeoecology and conservation.