The representation of carbon allocation (CA) in ecosystem differs tremendously among models, resulting in diverse responses of carbon cycling and storage to global change. Several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems of model structure. We analyzed the mathematical representation of CA in models using concepts from dynamical systems theory; we reviewed a representative sample of models of CA in vegetation and developed a model database within the Python package bgc-md. We asked whether these representations can be generalized as a linear system, or whether a more general framework is needed to accommodate nonlinearities. Some of the vegetation systems simulated with the reviewed models have a fixed partitioning of photosynthetic products, independent of environmental forcing. Vegetation is often represented as a linear system without storage compartments. Yet, other structures with nonlinearities have also been proposed, with important consequences on the temporal trajectories of ecosystem carbon compartments. The proposed mathematical framework unifies the representation of alternative CA schemes, facilitating their classification according to mathematical properties as well as their potential temporal behaviour. It can represent complex processes in a compact form, which can potentially facilitate dialog among empiricists, theoreticians, and modellers.

中文翻译：

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更好地表示植被中碳分配的概念框架和数学工具

不同模型之间生态系统中碳分配（CA）的表示形式差异很大，导致碳循环和存储对全球变化的不同响应。多项研究强调了经验观察与模型预测之间的差异，将这些差异归因于模型结构问题。我们使用动力系统理论的概念分析了模型中CA的数学表示；我们审查了植被中CA模型的代表性示例，并在Python软件包bgc-md中开发了模型数据库。我们询问是否可以将这些表示形式概括为线性系统，或者是否需要一个更通用的框架来适应非线性。使用审查的模型模拟的某些植被系统具有固定的光合产物分区，独立于环境强迫。植被通常表示为没有储藏室的线性系统。然而，还提出了具有非线性的其他结构，这对生态系统碳室的时间轨迹具有重要影响。拟议的数学框架统一了替代CA方案的表示形式，有助于根据数学属性及其潜在的时间行为对其进行分类。它可以以紧凑的形式表示复杂的过程，从而有可能促进经验主义者，理论家和建模者之间的对话。对生态系统碳室的时间轨迹具有重要影响。拟议的数学框架统一了替代CA方案的表示形式，有助于根据数学属性及其潜在的时间行为对其进行分类。它可以以紧凑的形式表示复杂的过程，从而有可能促进经验主义者，理论家和建模者之间的对话。对生态系统碳室的时间轨迹具有重要影响。拟议的数学框架统一了替代CA方案的表示形式，有助于根据数学属性及其潜在的时间行为对其进行分类。它可以以紧凑的形式表示复杂的过程，从而有可能促进经验主义者，理论家和建模者之间的对话。