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Vitousek and Farrington (1997) investigated nutrient limitations in soils of different ages. In the abstract of their paper, they say, Walker and Syers (1976) proposed a conceptual model that describes the pattern and regulation of soil nutrient pools and availability during long-term soil and ecosystem development. Their model implies that plant production generally should be limited by N [nitrogen] on young soils and by P [phosphorus] on old soils; N and P supply should be more or less equilibrate on intermediate aged soils. Vitousek and Farrington tested this hypothesis by conducting fertilizer experiments along a gradient of soil age, measuring the average increment in diameter (in mm/yr) of Metrosideros polymorpha trees. Denote by D(N, P, t) the diameter increment (in mm/yr) as a function of the amount of nitrogen (N) added, the amount of phosphorus (P) added, and the age (t) of the soil. Vitousek and Farrington’s experiments showed that $\frac{\partial D}{\partial t}(\mathrm{N}, 0, t)<0$ and $\frac{\partial D}{\partial t}(0, \mathrm{P}, t)>0$ for their choices of N > 0 and P > 0. Explain why their results support theWalker and Syers hypothesis.

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