Models of the global terrestrial biosphere in current Earth system models (climate models with coupled atmosphere, ocean and biosphere) uniformly predict a large current carbon sink caused by CO2 fertilization of terrestrial vegetation that sequesters 1-2 GtC/y. Models with a nitrogen cycle generally predict that a large fraction of the sink will disappear by midcentury because of nitrogen limitation. The models all include some form of Liebig’s Law of the Minimum for nitrogen. All models currently predict that water limited systems will see large and sustained sinks because water use efficiency is increased by elevated CO2. However, FACE experiments and other recent evidence implies that the opposite is true: CO2 fertilization sinks are observed to persist despite N-limitation and the benefits of enhanced water use efficiency have not been observed. We developed a mechanistic version of forest simulation models with competition for light, water and nutrients that can be analyzed mathematically. We used it to compute the most competitive strategies of allocation to foliage, stem wood and fine roots as a function of soils and climate. When fertilized by CO2, these most competitive strategies predict the results of FACE experiments and the opposite of previous global models: sustained CO2 sinks in the face of N-limitation and the absence of sinks in water –limited systems. I explain the cause of these results, the mechanism behind them and how one would test them in the field.