Discount rates that decline through time prevent derivation of optimal rotations using the standard Faustmann formula. A backwards-recursive simulation has made it possible to derive an optimal of rotations, including with an amenity value that rises both through crop age and through chronological time. Carbon fluxes are complex and difficult to incorporate in this backwards-recursive protocol, especially when carbon prices are predicted to change through time. An alternative forwards-recursive protocol using intelligent trial-and-error has proved capable of solving the optimal sequence of rotations for any combination of declining discount rate and rising amenity and carbon values. The optimal sequence contains rotations that generally – but not invariably – are longer by only a few years than those resulting from imposition of a uniform rotation across all crops. Their net present value is also only a little greater.

中文翻译：

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贴现率下降、非木材效益上升以及最佳轮换顺序

随着时间的推移而下降的贴现率阻碍了使用标准福斯特曼公式推导最佳轮换。向后递归模拟使得获得最佳轮作成为可能，包括随着作物年龄和时间顺序而增加的舒适度值。碳通量很复杂，很难纳入这种向后递归协议中，特别是当碳价格预计会随时间变化时。事实证明，使用智能试错法的另一种前向递归协议能够针对折扣率下降和便利设施和碳价值上升的任意组合解决最佳轮换序列。最佳序列包含的轮作通常（但并非总是）比对所有作物实行统一轮作所产生的轮作时间仅长几年。它们的净现值也只高了一点点。