Aim: Understanding connections between environment and biodiversity is crucial for conservation, identifying causes of ecosystem stress, and predicting population responses to changing environments. Explaining biodiversity requires an under-standing of how species richness and environment covary across scales. Here, we identify scales and locations at which biodiversity is generated and correlates with environment.Location: Full latitudinal range per continent.Time Period: Present day.Major Taxa Studied: Terrestrial vertebrates: all mammals, carnivorans, bats, song-birds, hummingbirds, amphibians.Methods: We describe the use of wavelet power spectra, cross- power and coherence for identifying scale-dependent trends across Earth's surface. Spectra reveal scale- and location-dependent coherence between species richness and topography (E), mean annual precipitation (Pn), temperature (Tm) and annual temperature range (ΔT).Results: >97% of species richness of taxa studied is generated at large scales, that is, wavelengths ≳103 km, with 30%–69% generated at scales ≳104 km. At these scales, richness tends to be highly coherent and anti-correlated with E and ΔT, and positively correlated with Pn and Tm. Coherence between carnivoran richness and ΔT is low across scales, implying insensitivity to seasonal temperature variations. Conversely, amphibian richness is strongly anti-correlated with ΔT at large scales. At scales ≲103 km, examined taxa, except carnivorans, show highest richness within the trop-ics. Terrestrial plateaux exhibit high coherence between carnivorans and E at scales ∼103 km, consistent with contribution of large-scale tectonic processes to biodiver-sity. Results are similar across different continents and for global latitudinal averages. Spectral admittance permits derivation of rules-of- thumb relating long-wavelength environmental and species richness trends.Main Conclusions: Sensitivities of mammal, bird and amphibian populations to envi-ronment are highly scale dependent. At large scales, carnivoran richness is largely in-dependent of temperature and precipitation, whereas amphibian richness correlates strongly with precipitation and temperature, and anti-correlates with temperature range. These results pave the way for spectral- based calibration of models that pre-dict biodiversity response to climate change scenarios.