Disentangling contributions from environmental variables is crucial for explaining global biodiversity patterns. We use wavelet power spectra to separate wavelength-dependent trends across Earth’s surface. Spectra reveal scale- and location-dependent coherence between species richness and topography (E), annual precipitation (Pn), temperature (Tm) and temperature range (ΔT). > 97% of richness of carnivorans, bats, songbirds, hummingbirds and amphibians resides at wavelengths ≳ 103 km. 30–69% is generated at scales ≳ 104 km. At these scales, richness across the Americas is anti-correlated with E and ΔT, and positively correlated with Pn and Tm. Carnivoran richness is incoherent with ΔT, suggesting insensitivity to temperature seasonality. Conversely, amphibian richness is anti-correlated with ΔT at large scales. At scales ≲ 103 km, richness is highest within the tropics. Terrestrial plateaux exhibit coherence between carnivoran richness and E at scales ~ 103 km, reflecting contributions of orogeny/epeirogeny to biodiversity. Similar findings result from transects across other continents. Scale-dependent sensitivities of vertebrate populations to climate are revealed.