International audiencePhosphorus (P) is an essential element for plant growth. Low P availability in soils is likely to limit crop yields in many parts of the world, but this effect has never been quantified at the global scale by process-based models. Here we attempt to estimate P limitation in three major cereals worldwide for the year 2000 by combining information on soil P distribution in croplands and a generic crop model, while accounting for the nature of soil-plant P transport. As a global average, the diffusion-limited soil P supply meets the crop's P demand corresponding to the climatic yield potential, due to the legacy soil P in highly fertilized areas. However, when focusing on the spatial distribution of P supply versus demand...