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Most of the Earth System Models ( ESMs ) project increases in net primary productivity ( NPP ) and terrestrial carbon (C) storage during the 21st century. Despite empirical evidence that limited availability of phosphorus (P) may limit the response of  NPP  to increasing atmospheric  CO 2  , none of the  ESMs  used in the previous Intergovernmental Panel on Climate Change assessment accounted for P limitation. We diagnosed from  ESM  simulations the amount of P need to support increases in carbon uptake by natural ecosystems using two approaches: the demand derived from (1) changes in C stocks and (2) changes in  NPP . The C stock‐based additional P demand was estimated to range between −31 and 193 Tg P and between −89 and 262 Tg P for Representative Concentration Pathway ( RCP ) 2.6 and  RCP8.5 , respectively, with negative values indicating a P surplus. The  NPP ‐based demand, which takes ecosystem P recycling into account, results in a significantly higher P demand of 648–1606 Tg P for  RCP2 .6 and 924–2110 Tg P for  RCP8 .5. We found that the P demand is sensitive to the turnover of P in decomposing plant material, explaining the large differences between the  NPP ‐based demand and C stock‐based demand. The discrepancy between diagnosed P demand and actual P availability (potential P deficit) depends mainly on the assumptions about availability of the different soil P forms. Overall, future P limitation strongly depends on both soil P availability and P recycling on ecosystem scale.

Diagnosing phosphorus limitations in natural terrestrial ecosystems in carbon cycle models