Technical Abstract: Variability of aboveground net primary production (ANPP) of arid to sub-humid ecosystems displays a closer association with precipitation when considered across space, based on multiyear averages for different locations, than through time, based on year to year change at single locations. Here, we propose a theory of controls of ANPP based on four hypotheses about legacies of wet and dry years that explains space vs. time differences in ANPP-precipitation relationships. We tested the hypotheses using 16 longterm series of ANPP. We found that legacies, revealed by the association of current- vs. previous-year conditions through the temporal series occur across all ecosystem types from deserts to mesic grasslands. Therefore, previous-year precipitation and ANPP control a significant fraction of current-year production. We developed unified models for the controls of ANPP through space and time. The relative importance of current- versus previous-year precipitation changes along a gradient of mean annual precipitation with the importance of current-year PPT decreasing whereas the importance of previous-year PPT remains constant as mean annual precipitation increases. Finally, our results suggest that ANPP will respond to climate-change driven alterations in water availability and, more importantly, that the magnitude of the response will increase with time.