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Extreme droughts generally decrease productivity in grassland ecosystems1,2,3 with negative consequences for nature’s contribution to people4,5,6,7. The extent to which this negative effect varies among grassland types and over time in response to multi-year extreme drought remains unclear. Here, using a coordinated distributed experiment that simulated four years of growing-season drought (around 66% rainfall reduction), we compared drought sensitivity within and among six representative grasslands spanning broad precipitation gradients in each of Eurasia and North America—two of the Northern Hemisphere’s largest grass-dominated regions. Aboveground plant production declined substantially with drought in the Eurasian grasslands and the effects accumulated over time, while the declines were less severe and more muted over time in the North American grasslands. Drought effects on species richness shifted from positive to negative in Eurasia, but from negative to positive in North America over time. The differing responses of plant production in these grasslands were accompanied by less common (subordinate) plant species declining in Eurasian grasslands but increasing in North American grasslands. Our findings demonstrate the high production sensitivity of Eurasian compared with North American grasslands to extreme drought (43.6% versus 25.2% reduction), and the key role of subordinate species in determining impacts of extreme drought on grassland productivity. 

An analytical model using three-directional anisotropic (TDA) dispersion and a novel anisotropic relaxation time (RT) relation for modeling the thermal conductivity ( k ) of intercalated layered materials is developed. The TDA dispersion eliminates the restriction of in-plane isotropy and is suitable for TDA materials such as black phosphorous. We compare calculations of k of bulk intercalated layered materials using the isotropic Debye dispersion and BvK dispersion with our TDA dispersion model, paired with both isotropic and anisotropic RTs. We find that calculated k values by the TDA dispersion model agree best with the experimental data. Furthermore, anisotropic RTs largely improve the performance of the Debye and BvK dispersion models whose average relative deviations for the in-plane k are reduced from 17.3% and 23.0% to 4.4% and 8.5%, respectively. Finally, thermal conductivity accumulation functions of intercalated MoS 2 and graphite are numerically calculated based on the TDA dispersion with anisotropic RTs. These models predict that intercalants cause increased contributions from phonons with shorter mean free paths, especially for in-plane thermal conductivity.