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Water availability limits plant growth and production in almost all terrestrial ecosystems(1-5). However, biomes differ substantially in sensitivity of aboveground net primary production ( ANPP) to between-year variation in precipitation(6-8). Average rain-use efficiency ( RUE; ANPP/precipitation) also varies between biomes, supposedly because of differences in vegetation structure and/or biogeochemical constraints(8). Here we show that RUE decreases across biomes as mean annual precipitation increases. However, during the driest years at each site, there is convergence to a common maximum RUE (RUEmax) that is typical of arid ecosystems. RUEmax was also identified by experimentally altering the degree of limitation by water and other resources. Thus, in years when water is most limiting, deserts, grasslands and forests all exhibit the same rate of biomass production per unit rainfall, despite differences in physiognomy and site-level RUE. Global climate models(9,10) predict increased between-year variability in precipitation, more frequent extreme drought events, and changes in temperature. Forecasts of future ecosystem behaviour should take into account this convergent feature of terrestrial biomes.